Multi-Energy Systems

Edited by Zbigniew Leonowicz, Arsalan Najafi and Michał Jasinski

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**Multi-Energy Systems**

## **Multi-Energy Systems**

Editors

**Zbigniew Leonowicz Arsalan Najafi Michał Jasi ´nski**

Basel • Beijing • Wuhan • Barcelona • Belgrade • Novi Sad • Cluj • Manchester

*Editors*

Zbigniew Leonowicz Wroclaw University of Science and Technology Wroclaw Poland

Arsalan Najafi Wroclaw University of Science and Technology Wroclaw Poland

Michał Jasinski ´ Wroclaw University of Science and Technology Wroclaw Poland

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Topic published online in the open access journals *Energies* (ISSN 1996-1073), *Mathematics* (ISSN 2227-7390), *Smart Cities* (ISSN 2624-6511 ), *Designs* (ISSN 2411-9660), and *Clean Technologies* (ISSN 2571-8797) (available at: https://www.mdpi.com/topics/ multi energy).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

Lastname, A.A.; Lastname, B.B. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-9426-2 (Hbk) ISBN 978-3-0365-9427-9 (PDF) doi.org/10.3390/books978-3-0365-9427-9**

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## **Contents**

Reprinted from: *Energies* **2022**, *15*, 690, doi:10.3390/en15030690 .................... **215**

#### **Xuyang Zhong, Zhiang Zhang, Ruijun Zhang and Chenlu Zhang**

AC-DC Systems Reprinted from: *Mathematics* **2022**, *10*, 2337, doi:10.3390/math10132337 ............... **495**

### **About the Editors**

#### **Zbigniew Leonowicz**

Zbigniew Leonowicz (Senior Member, IEEE) received his M.Sc. and Ph.D. degrees in electrical engineering from Wroclaw University of Science and Technology, Wroclaw, Poland, in 1997 and 2001, respectively, as well as a habilitation degree from Bialystok University of Technology, Bialystok, Poland, in 2012. Since 1997, he has worked for the Electrical Engineering Faculty, Wroclaw University of Technology. He was also awarded the title of full professor by the President of Poland and the President of the Czech Republic in 2019. Since 2019, he has worked as a Professor at the Department of Electrical Engineering, where he is currently the Chair of Electrical Engineering Fundamentals.

#### **Arsalan Najafi**

Arsalan Najafi received his B.Sc. degree in electrical engineering from the University of Kurdistan, Sanandaj, Iran, in 2009, as well as his M.Sc. and Ph.D. degrees in electrical engineering from the University of Birjand, Birjand, Iran, in 2011 and 2016, respectively. He won a grant from the Polish National Agency for Academic Exchange (NAWA) under the Ulam Program hosted by Wroclaw University of Science and Technology, Wroclaw, Poland. He is currently an associate professor with the Wroclaw University of Science and Technology. His research interests include the operation and planning of multi-energy systems, electric vehicles, electricity markets, and optimization theory and its application in power systems.

#### **Michał Jasi ´nski**

Michał Jasinski received his Ph.D. and D.Sc. degrees in electrical engineering from Wrocław ´ University of Science and Technology in 2019 and 2022, respectively. Since 2018, he has worked for the Electrical Engineering Faculty, Wroclaw University of Science and Technology, where he is currently an assistant professor. He is the author and coauthor of more than 100 scientific publications. Currently, he is an Editorial Board Member at *Clean Energy* (Oxford University Press) and the Associate Editor of *Network: Computation in Neural Systems* (Taylor and Francis).

### *Article* **Multi-Objective Optimization of Autonomous Microgrids with Reliability Consideration**

**Maël Riou 1,\*, Florian Dupriez-Robin 2, Dominique Grondin 3, Christophe Le Loup 1, Michel Benne 3 and Quoc T. Tran 4**

**Abstract:** Microgrids operating on renewable energy resources have potential for powering rural areas located far from existing grid infrastructures. These small power systems typically host a hybrid energy system of diverse architecture and size. An effective integration of renewable energies resources requires careful design. Sizing methodologies often lack the consideration for reliability and this aspect is limited to power adequacy. There exists an inherent trade-off between renewable integration, cost, and reliability. To bridge this gap, a sizing methodology has been developed to perform multi-objective optimization, considering the three design objectives mentioned above. This method is based on the non-dominated sorting genetic algorithm (NSGA-II) that returns the set of optimal solutions under all objectives. This method aims to identify the trade-offs between renewable integration, reliability, and cost allowing to choose the adequate architecture and sizing accordingly. As a case study, we consider an autonomous microgrid, currently being installed in a rural area in Mali. The results show that increasing system reliability can be done at the least cost if carried out in the initial design stage.

**Keywords:** microgrid; off-grid; reliability; sizing; genetic algorithm

#### **1. Introduction**

Electricity is at the heart of modern economies, and its share in the global energy demand continues to increase [1]. Global electricity demand is expected to grow by 30% by 2040, this growth is largely dominated by developing countries. Most modern economies have robust electricity grids, which guarantee a high degree of reliability to end-users. There is a direct link between access to reliable electricity and economic and social development. However, in many places in the world, electricity access is still lacking. Around 759 million people had no access to electricity worldwide in 2019 [2]. Most of the concerned population lives in Sub-Saharan Africa and Asia. For the regions where the electricity grid is not present, different solutions are available. Grid extension appears to be the logical option, however, this solution becomes less viable as the distance from existing grid infrastructure increases, and as the density, load demand, and revenues of the concerned population decrease [3]. One promising alternative is to build small electricity grids known as microgrids which mutualize production assets to consumers as opposed to standalone systems [4]. It is estimated that at least 34 million people had access to electricity from standalone systems (71%) and microgrids (29%) between 2010 and 2017 [3]. Microgrids integrate more and more renewable resources as the prices of these technologies get more competitive. In terms of the type of renewable resources used, we can cite solar photovoltaics, wind, biomass, micro-hydro, and tidal energy [5]. Autonomous microgrids, which have no connection to the national electricity grid, are the topic of interest in this

**Citation:** Riou, M.; Dupriez-Robin, F.; Grondin, D.; Le Loup, C.; Benne, M.; Tran, Q.T. Multi-Objective Optimization of Autonomous Microgrids with Reliability Consideration. *Energies* **2021**, *14*, 4466. https://doi.org/10.3390/en14154466

Academic Editor: Zbigniew Leonowicz

Received: 29 June 2021 Accepted: 13 July 2021 Published: 23 July 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

paper. In Section 2, a review is given including important aspects related to reliability and existing methods for designing these types of power systems. In Section 3, the method developed to size autonomous microgrids taking into consideration reliability aspects is introduced. In Section 4, a microgrid project used as a case study for this article is described. In Section 5, the results obtained after applying the proposed method to the case study are presented.

#### **2. Literature Review on Autonomous Microgrid Design**

This paper focuses on microgrids that have no ability to connect to the grid and are therefore referred to as autonomous microgrids, also known as mini-grids in the context of rural energy access [6–8]. These systems have been used for a long time as a solution to bring access to electricity to remote locations where grid extension is unaffordable. The cut in renewable energy prices has introduced new types of autonomous microgrids, based on renewable energy resources and energy storage. The power ratings of these systems can range from as little as 50 kVA to a few MVA. Only PV systems and diesel generators (*Gensets*) are considered as the potential sources of generation. PV arrays can be either DC coupled (*PVdc*), AC coupled (*PVac*), or integrated into a hybrid architecture where one part of the solar system is connected to a DC bus and another part is connected to an AC bus. Figure 1 shows the microgrid architecture that is considered for the paper. Energy storage systems (*ESSs*) are used to store excess renewable energy, allowing for a further decrease in the use of fossil-based generation and can be in the form of electrochemical, kinetic, compressed air, or gravitational; however, only battery storage is considered in this paper. A power conversion system (*PCS*) is required to interface the DC sources (*ESS* and *PVdc*) to the AC bus.

**Figure 1.** Architecture of the considered microgrids.

Several articles have reviewed the methodologies proposed for the sizing and optimization of autonomous hybrid systems [9–14]. Al-falahi et al. [10] listed various indicators used as design objectives. Most of them are economic, reliability, and environmental indicators. Social indicators can also be found in some papers. The authors have observed that single-objective articles were focusing on the optimization of a cost indicator, whereas multi-objective articles were often focusing on the objectives of cost and reliability. The cost thus represents the first optimization objective and includes investment, operation, maintenance, and replacement costs. A recent review on the sizing methodologies of hybrid renewable energy systems from Lian et al. [15] shows that a large proportion of the reviewed sizing methodologies were focusing on off-grid/autonomous applications

(79%). To classify the different methods available, Tezer et al. [11] distinguish classical optimization approaches to meta-heuristic approaches. Classical methods require limiting mathematical properties linked to the objective function and include for example the iterative optimization method and linear programming. Meta-heuristic methods include higher-level algorithms to control the whole process of search to explore the solution space efficiently and avoid local optima. These methods can be applied to a wide range of optimization problems. We can distinguish "neighborhood" meta-heuristics developing a single solution at a time to "distributed" or "population-based" meta-heuristics that process a whole population at a time, such as particle swarm optimization (PSO) and genetic algorithms (GA). Various articles have used genetic algorithms to size hybrid energy systems. Katsigiannis et al. [16] use the NSGA-II to design a small autonomous hybrid power system comprising of both renewable and conventional power sources with the objectives of minimizing the energy cost of the system and total greenhouse gas emission during the system lifetime. Reliability was however not considered. Kamjoo et al. [17] have used the NSGA-II algorithm to obtain the trade-offs between cost and reliability in order to size a wind/solar/battery system. Roy et al. [18] used the NSGA-II algorithm to size a multi-energy system solely on renewable energy under the objectives of cost (*LCOE*) and reliability. Refs. [19–23] have considered long-term sizing with multi-step investments using optimization techniques.

Some reviews also focus on available tools for the design and planning of hybrid renewable energy systems [24–26]. Various articles use the software Homer to size hybrid energy systems [27]. Homer is an optimization software that is used to design hybrid systems for microgrid/stand-alone applications. It performs simulations of all possible configurations, calculates energy flows, and lists results according to their relative cost of energy (*COE*). iHOGA is another hybrid system optimization tool that can be used similarly to model and simulate various components [28]. The authors in [29] make a comparative assessment of Homer and iHoga using a case study, with the motivation that the latter has not been explored as much in the literature. An interesting feature of iHOGA is its ability to perform multi-objective optimization, using up to three objectives (Net Present Cost, CO2 emissions, and Unmet Load), it offers also more flexibility in the control strategies used in the simulations.

Reliability can have different meanings and can account for different aspects depending on the application and field. It can be summarized as the ability of a system to perform as intended without any failure and within the desired performance limits for a specified time, in its lifetime conditions [30]. In power systems, reliability deals with power interruptions, whereas power quality concerns the quality of the sine wave when power is available. Therefore, phenomena of interest in power quality studies, such as swells, swags, impulses, and harmonics are not explored in reliability studies. The reliability of power systems can be separated into adequacy and security [31]. Adequacy relates to the ability of power systems to supply the demand with adequate generation and transmission facilities with a desired level of reserve and can be evaluated in long-term planning studies [30]. Security relates to the ability of the power system to withstand sudden contingencies and outages and is more often integrated into short-term reliability assessment.

Reviews have investigated the use of reliability objectives in designing hybrid systems. Several studies involve reliability assessment in the design of microgrids [32–36]. Most of the reliability indicators used relate to adequacy assessment and account for the risk that generation is lower than consumption [11]. The main adequacy indicators used in the literature for sizing hybrid systems are loss of power supply probability (*LPSP*), loss of load probability (*LOLP*), expected energy not supplied (*EENS*), deficiency of power supply probability (*DPSP*), loss of load expected (*LOLE*), and loss of energy expected (*LOEE*) [15]. The software tools for hybrid system optimization mentioned above also account solely for system adequacy. In the Homer software, reliability can be used as a constraint, specifying a maximum capacity shortage fraction allowed. This capacity shortage accounts for the shortage of generation to power the load, as well as insufficient reserves from the reserve

requirement set up by the user. iHOGA also includes a reliability constraint using the indicator of unmet load; however, this indicator does not account for operating reserves.

Some papers in the literature have investigated the security assessment of microgrids. In [37], Paliwal et al. use a Particle Swarm Optimization method to determine optimal autonomous microgrid component sizing with the incorporation of reliability constraints. The reliability analysis of the microgrid is carried out using a multi-state availability model (MSAM) of different generators to calculate the percentage of risk state probability (generation is inadequate to supply load) and the percentage of healthy state probability (system has adequate reserves). Xu et al. [38–40] have integrated the consideration of protection and operation into the reliability evaluation of microgrids. However, the reliability analysis developed is not focusing on purely autonomous microgrids with centralized generation and is not integrated into a design method. Escalera et al. [41] suggest that security aspects could be incorporated into reliability analysis in the design phases of microgrids, as the size of the considered systems is small enough to limit the computation time. Security assessment, which in conventional power systems is performed with a short-term horizon, could thus be implemented in long-term planning. Peyghami et al. [30] introduce a new framework for the reliability evaluation of modern power systems. According to the author, security assessment would focus on static phenomena, dynamic and transient, and cybersecurity. In rural autonomous microgrids, security issues are mainly concerned with the stability and thermal limitations of the power electronic interfaces. These limitations impact considerably the protection scheme of the microgrids, as those are typically based on conventional overcurrent devices.

There is thus a research gap in the literature related to the consideration of reliability in the design of isolated microgrid systems, often focusing solely on adequacy. There is a need to model how the design can influence reliability, considering other aspects, such as component failure and protection. There is also a need to explore further the trade-off between design objectives such as cost, reliability, and renewable integration. Therefore, this paper proposes a novel method to size individual components as well as redundancy by exploring the trade-offs between the objectives mentioned above and considering the impact of component failure and protection malfunction on reliability. It aims not to return the optimal sizing of the system, but rather to give the designer the means to carefully select the preferred option according to the observed trade-offs. The method is described in Section 3. A case study is presented in Section 4, and the results obtained from applying the method to this case study are discussed in Section 5 before a conclusion is drawn.

#### **3. Method for Sizing Autonomous Microgrids**

This section describes the methodology developed for the sizing and design of autonomous microgrids. The methodology aims to give the user the means to select the optimal component sizing, architecture, as well as control strategy, regarding the objectives of cost, renewable integration, and reliability. There are two general approaches to solve multi-objective optimization problems. The first approach consists of collecting all objectives into a single objective function, using a weighted sum, or treating some objectives as constraints [11]. The second approach is Pareto-based optimization, which uses the Pareto-dominance concept. The Pareto-front is the set of all solutions for which the corresponding objective vectors cannot be improved in any dimension without degradation in another [20]. When considering three objectives, the Pareto-front becomes a three-dimensional surface. The Pareto-based approach was preferred because it does not require fixing a priority or a limit on one of the objectives and it gives the ability to observe trade-offs between optimization objectives.

#### *3.1. Global Multi-Objective Optimisation Method*

A genetic algorithm was selected for its ability to implement various control algorithms and component models without the need to adapt the optimization formulation. A schematic of the global method developed is presented in Figure 2. This method is

presented in [42]. In the evaluation of each microgrid configuration, the simulation gives indicators for the objectives of cost and renewable energy integration and the reliability analysis gives the indicator of unavailability. Both evaluations are performed in a python environment [43]. The planning horizon is 15 years.

**Figure 2.** Global multi-objective optimization method developed using the NSGA-II algorithm.

The genetic algorithm NSGA-II, developed by K. Deb et al. [44], is used to obtain the non-dominant pareto frontier of the objectives. The advantage of this type of algorithm is that it can efficiently explore the search space. It starts with creating an initial population of a predefined size. Each individual from the population is then evaluated with the simulation and reliability analysis. The population is then ranked based on three indicators (cost, renewable integration, reliability). The algorithm applies a selection, crossover, and mutation to create a new child population. The parent population and children are then combined and ranked to select individuals for the new generation. This process is replicated until the stop criteria are reached. The selection is based on elitism, ensuring the non-dominated individuals from the combined parent and child populations are passed to the next generation.

The variables to optimize are shown in Table 1. Redundancy of diesel generators and PCS inverters is also considered. Different dispatch strategies are considered including "load following" and "cycle charging" as defined in [45]. The NSGA-II algorithm is implemented with the package Pymoo [46], whose settings are given in Table 2. The computation requirement for a population size of 65 is around 11 min per generation.

**Table 1.** Sizing variables of the genetic algorithm.

**Table 2.** Tuning of the genetic algorithm.

The first optimization objective is the net present cost (*NPC*) expressed in k€, and is calculated through Equation (1), where *NPCi* is the net present cost of component *i* and includes investment cost *Cinv*,*i*, yearly operation cost *CO*&*M*,*i*,*t*, and replacement cost *Crep*,*i*,*t*, as calculated in Equation (2). *r* is the discount rate.

$$NPC = NPV\_{PV\_{oc}} + NPV\_{PV\_{dc}} + NPV\_{ESS} + NPV\_{Genset} + NPV\_{AFE} \tag{1}$$

$$NPC\_i = C\_{inv,i} + \sum\_{y=1}^{Y} \frac{C\_{O\&M,i,t} + C\_{rep,i,t}}{\left(1 + r\right)^t} \tag{2}$$

The second optimization objective is the renewable integration as is calculated with Equation (3). The objective is calculated through Equation (3), with *PGenset*(*t*) being the power produced by all gensets at time *t*, *PLoad*(*t*) being the load consumption at time *t*, Δ*t* being the simulation time step, and *T* the total number of time steps in the project duration considered.

$$Share\_{R.E.} = 1 - \frac{\sum\_{t=1}^{T} P\_{\text{Gensert}}(t) \times \Delta t}{\sum\_{t=1}^{T} P\_{\text{Load}}(t) \times \Delta t} \tag{3}$$

The third optimization objective concerns reliability. The unavailability *UμGrid* is to be minimized and is given as the ratio of the expected energy not served (*EENS*) to the yearly load demand. The *EENS* indicator is a sum of three components which are detailed in Section 3.3.

$$\mathrm{U}\_{\mu\mathrm{Grid}} = 100 \cdot \frac{EENS\_{\mu\mathrm{Grid}}}{E\_{Load}} = 100 \cdot \frac{EENS\_{\mathrm{Adequ.}} + EENS\_{\mathrm{Cont.}} + EENS\_{\mathrm{Prot.}}}{E\_{Load}} \tag{4}$$

#### *3.2. Simulation Platform Developed*

The simulation is made in Python 3.6 (Python Software Foundation, https://www. python.org/ (accessed on 22 July 2021)) and is based on various models describing the behavior of the different microgrid components [43]. The simulation time step is taken as 10 min to account for variability in the load and renewable energy production as well as to model the control of microgrid components with sufficient time resolution. The input data is available as 1-year irradiation and temperature data as well as 15-years load consumption data. Only active power flows are considered in the simulation. The same model is used to calculate the power at the Maximum Power Point for the PV array connected to the AC bus (*PPVac*,*mppt*) and the one connected to the DC bus (*PPVdc*,*mppt*). Equation (5) describes the model where *PPV*,*nom* is the nominal power of the installed PV array (kWp), *Gtot*, *β*(*t*) is the global horizontal irradiance in the plane of array (W/m2), and *ηPV*, *glob*(*t*) is the efficiency of the global PV array.

$$P\_{PV,mppt}(t) = P\_{PV,nom} \times \frac{G\_{tot, \, \beta}(t)}{1000} \times \eta\_{PV, \, \, \S^{lab}}(t) \tag{5}$$

*ηPV*, *glob*(*t*) (p.u.) includes temperature losses, inverter losses, and other miscellaneous losses as calculated in Equation (6), where *ηinv*(*t*) is the inverter efficiency at time t (p.u.), *Lossesconst* are constant losses and account for cable losses, mismatch, and dirt (p.u.), *αtemp* is the temperature derating coefficient according to the datasheet of the PV module (%/◦C), *Tc*(*t*) is the module cell temperature (◦C), and *Tc*, *ref* is the reference cell temperature at Standard Test Conditions (◦C).

$$\eta\_{PV,\\_glob}(t) = \eta\_{inv}(t) \times (1 - \text{Losses}\_{const} \times \left[1 - \frac{a\_{temp}}{100} \times \left(T\_c(t) - T\_{c,\\_ref}\right)\right] \tag{6}$$

The module cell temperature *Tc*(*t*) is calculated as per Equation (7), where *Ta*(*t*) is the ambient temperature at time t (◦C), *Tc NOCT* is the nominal operating cell temperature [ ◦C], *Ta NOCT* is the nominal operating ambient temperature (◦C), *GNOCT* is the nominal operating irradiance (W/m2).

$$T\_{\mathfrak{c}}(t) = T\_{\mathfrak{a}}(t) + \left(T\_{\mathfrak{c}\ \mathrm{NOCT}} - T\_{\mathfrak{a}\ \mathrm{NOCT}}\right) \times \frac{\mathrm{G}\_{\mathrm{tot},\mathfrak{f}}(t)}{\mathrm{G}\_{\mathrm{NOCT}}} \tag{7}$$

The EMS model calculates active power setpoints for each microgrid component. Only the battery system does not receive a setpoint as its power output is the difference between the power from the bi-directional inverter and the power produced by the PV array connected to the DC bus, both controlled by the energy management system (*EMS*).

The genset controller model decides to start/stop individual gensets and dispatches the global genset power setpoint to each available unit. The PV converter model applies a saturation of the active power setpoint to the nominal power rating of the converter as well as an efficiency based on an efficiency versus operating power curve. The *PCS* also applies a saturation and an efficiency to the setpoint but allows for bi-directional power flow.

#### *3.3. Reliability Analysis Method*

As discussed in Section 2, reliability can address both adequacy and security aspects. In the sizing method developed, security aspects of component failure and protection failure are considered in addition to generation adequacy. These two aspects considered are described in this section. The system size is sufficiently small to be able to integrate these aspects in a genetic algorithm with acceptable computation time. The methodology is described in this section.

#### 3.3.1. Adequacy Assessment

Adequacy relates to the ability of power systems to supply the demand with adequate generation and transmission facilities with a desired level of reserve and can be evaluated in long-term planning studies [30]. The indicator used in this paper for assessing adequacy is the expected energy not supplied (*EENS*), which can be calculated from the simulation results. At each time-step, the load power not supplied due to insufficient generation capability *PN*.*S*.(*t*) is obtained from Equation (8), *Pprod*, *total*(*t*) being the sum of active powers from all generating sources. The *EENS* indicator is then calculated from Equation (9).

$$P\_{N.S.}(t) = \begin{cases} \begin{array}{l} P\_{\text{Load}}(t) \\ 0 \end{array} & \text{if } P\_{\text{prod, total}}(t) < P\_{\text{Load}}(t) \\ \text{otherwise} & \end{cases} \tag{8}$$

$$EENS\_{Adequ.} = \sum\_{t}^{T} P\_{\text{N.S.}}(t) \times \Delta t \tag{9}$$

#### 3.3.2. Contingency Enumeration Method

The first security aspect considered is the static response to component failure. Different methods exist to obtain reliability indices in this regard. An enumerative contingency analysis, often used for reliability analysis on conventional power systems, can be easily applied for this application as a small number of components are present in the type of microgrids considered. The following component failures are considered:

Each component is modeled with a short-term failure rate *λn*,*t* corresponding to the failure probability of component n at time step t. Failure rates are assumed constant throughout the component life. A blackout state is obtained when there is not enough reserve power to counteract the contingency or when no backup master unit is available to take over the role of grid-forming. For each of the considered failures, the steps illustrated in Figure 3 are followed.

**Figure 3.** Schematic of the contingency enumeration method.

First, the available up and down reserves before contingency are calculated for each time step from the simulation results. The reserve of the storage system and the reserve of the diesel generators are assumed to be effective in counterbalancing generator failures and to be independent of the grid-forming configuration. The storage system reserve (up and down) is the minimum between the power reserve available on the inverters and the power reserve available in the batteries that could be released during the time required to turn on/off an additional generator (if available). The reserve on the diesel generators is calculated based on their nominal power rating for the up-regulating reserve and based on their minimum acceptable operating power for the down-regulating reserve. The number of master units (operated in grid-forming) depends on the selected gridforming configuration. In this paper, we consider a single-master configuration, where the grid-forming unit(s) is switched between a diesel generator(s) and the *PCS* inverter(s).

For each considered contingency, the available up and down reserves after the failure of element n, *PresCn*,*t*, are calculated by subtracting the reserve provided by the failed unit from the available reserve before contingency. The net power after contingency is then calculated by subtracting the power produced by the failed unit from the available reserve after failure. It is used to estimate whether the available reserve at time t is sufficient to counterbalance the loss of element n. If at t, component n is generating power, then the up-regulating reserve is used. However, if it is absorbing power, the down-regulating reserve is used. The loss of element n at time t induces a blackout of the microgrid if one of the following conditions are met:

If a blackout state is predicted, then the blackout rate *λblackoutCn*,*t* due to contingency *n* is equal to the short-term failure rate of element *n λn*,*t* and a repair time *μblackoutCn*,*t* is allocated. This repair time depends on the remaining nominal power available in the microgrid after contingency. If sufficient nominal power is available to power the load, the repair time is only the time taken to restart the microgrid. Otherwise, the repair time is calculated according to the time the microgrid can be maintained online with the remaining nominal power. The short-term reliability index at each time step *t* is calculated by summing each product of failure rate and repair time corresponding to all considered contingencies:

$$r\_t = \begin{bmatrix} \lambda\_{blackout\gets1,t} \\ \lambda\_{blackout\gets1,t} \\ \cdots \\ \lambda\_{blackout\getsn,t} \end{bmatrix} \cdot \begin{bmatrix} \mu\_{blackout\gets1,t} \\ \mu\_{blackout\gets2,t} \\ \cdots \\ \mu\_{blackout\getsn,t} \end{bmatrix} \tag{10}$$

The chosen index to evaluate the reliability related to component failures is the expected energy not supplied (*EENS*) and is calculated with Equation (11).

$$EENS\_{\text{cont.}} = \Delta t \cdot \sum\_{t=1}^{T} d\_{t}.r\_{t} \tag{11}$$

#### 3.3.3. Protection Reliability Assessment

Protection selectivity is another important issue to address in autonomous microgrids, especially as the microgrids of interest can operate in various modes with different shortcircuit levels available. There is a need to design a protection scheme that is operating well in all configurations of the microgrid. The protection scheme that is used in our case is based on conventional overcurrent relays and fuses. These devices require a sufficient level of short-circuit current to operate in case of a fault.

Reliability analysis of the protection scheme aims at assessing how well the protection will perform for a particular architecture and sizing, regarding coordination and selectivity, considering two possible causes of protection malfunction:

The different steps toward the protection reliability assessment method are described in Figure 4. The microgrid is modeled with the package Pandapower [47] in the Python environment, which is used for static network analysis. All buses, lines, converters, and loads are modeled. The first step consists of calculating short-circuit currents on each microgrid configuration observed from the simulation. These configurations correspond to all possible on/off combinations of the different short-circuit current contributors, including gensets, *PCS* inverters, and *PVac* inverters. Next, load flow simulations are made for each simulation time-step to calculate the current flowing through each protection. Reliability indicators are then calculated to assess the protection scheme. Three probability distributions must be obtained to calculate these reliability indicators:

The probability of insensitivity of protection *i* is the probability that the pick-up current is higher than the short-circuit current available at the protection. This probability is calculated by Equation (12) using a convolution of the probability distributions of *Ir* and *Isc*:

$$P\_{\text{insensitivity},i} = p(Ir\_i > Isc\_i) \tag{12}$$

The probability of the over-tripping of protection *i* is the probability that the load flow current *In* is higher than the pick-up current *Ir*. This is illustrated in Equation (13) and also calculated by convolution:

$$P\_{\text{overtrip};p\text{ing},i} = p(In\_i > Ir\_i) \tag{13}$$

These indicators are then combined into a single indicator for reliability assessment of the protection scheme, which is the expected energy not supplied (*EENS*), calculated with Equations (14)–(17), *λi* being the short-circuit rate, |*Pi*| the mean power flowing through protection *i* (obtained from simulation results), *rsc* the short-term repair time of faults, and *rblc* the repair time following a blackout.

$$EENS\_{\text{protein}} = \sum\_{i}^{I} EENS\_{\text{insensitivity},i} + EENS\_{\text{overlap},i} + EENS\_{\text{normal},i} \tag{14}$$

$$EENS\_{insensitivity,i} = \lambda\_i \cdot P\_{insensitivity,i} \cdot \left| P\_i \right| \cdot (r\_{sc} + r\_{blc}) \tag{15}$$

$$EENS\_{overtrip,i} = (1 - \lambda\_i) \cdot P\_{overtripping,i} \cdot \left| P\_i \right| \cdot (r\_{blc}) \tag{16}$$

$$EENS\_{normal,i} = \lambda\_i \cdot \left(1 - P\_{insensitivity,i}\right) . \ \left|P\_i\right| \cdot \left(r\_{sc}\right) \tag{17}$$

**Figure 4.** Overview of the method developed to assess protection reliability.

#### **4. Case Study Description**

The methodology introduced in the previous section was applied to a case study of an autonomous microgrid currently in installation in the rural localities of Sanando and Tissala in Mali, shown on a map in Figure 5. This microgrid project was enabled by the Energizing Development Program (EnDev) and coordinated by GIZ together with AMADER and the municipality of Sanando. This project aims to build a hybrid power station including a solar PV array, a diesel generator (*Genset*), and a battery storage system (*ESS* + *PCS*) connecting both villages. The operation and maintenance of the microgrid will then be carried out by a consortium including Entech Smart Energies and Sinergie SA. There was initially no electricity grid available to inhabitants, some of them relying on individual solutions (gensets or small solar systems).

**Figure 5.** Localization of the microgrid case study.

The objectives of the operation of the hybrid system to be installed in the villages of Sanando-Tissala are to minimize fuel consumption on-site, to limit the aging of the equipment, and minimize the risk of blackout. To optimize the performance of the system, the following functions will be implemented in the Energy Management System:

Figure 6 shows the layout of the case study with the variables to optimize using the method. A wide range of values were considered for the optimization variables as shown in Table 3.

**Figure 6.** Schematic of the case study.

**Table 3.** Variable range of the genetic algorithm.

The simulation of the system operation requires various technical parameters whose values are shown in Table A1 in Appendix A. To calculate the net present cost of each sizing configuration, cost parameters regarding investment, operation, and replacement are also required for each component and are shown in Table A2. Investment costs are modeled with two coefficients, as proposed in [48]. Coefficient b accounts for the decreasing unit cost of the equipment with increasing size. The resulting investment cost is given by Equation (18).

$$C\_{inv,i} = P\_i \cdot \left( a \cdot P\_i^{-b} \right) \tag{18}$$

The reliability parameters are given in Appendix A in Table A3 for the contingency enumeration method and in Table A4 for the protection reliability assessment.

#### **5. Results and Discussion**

The multi-objectives optimization method presented in Section 3 was applied to the case study. The NSGA-II has led to the 3D Pareto surface shown in Figure 7. There is a strong relationship between all three objectives. To increase the renewable energy integration, an increase in net present cost is required. Configurations without gensets (in blue) lead to an increased unavailability and increased net present cost compared to configurations with gensets (in orange). Configurations with renewable energy integration less than 93% are not included in the Pareto frontier. They are thus not leading to an improvement in either net present cost or reliability. Considering the control strategy, only load following dispatch was found in the Pareto surface, which proves this type of control more interesting for this level of renewable integration.

Figure 8 shows the same Pareto points in a 2D graph with the third objective of reliability shown in a color scale. It can be observed that reliability can be improved with a small increase in net present cost for a similar renewable energy integration. In this figure, six configurations of interest have been selected for more detailed analysis:

The least-cost configuration (config 1) can be obtained at a net present cost of 1.050 M€ over the 15-year period considered. An improvement in reliability (config 2) can be obtained for a net present cost of 1.074 M€. A solution with 0% unavailability (config 3) can be obtained at a cost of 1.089 M€. A compromise between all three objectives (config 4) can be found for a net present cost of 1.091 M€, having a renewable energy integration above 95% and an unavailability under 0.1%. A 100% renewable energy solution can be obtained for a net present cost of 1.130 M€ but with high unavailability of 1.2% (config 5). Reaching

a high level of reliability with 100% renewable energy integration (config 6) would require oversizing considerably the components and, therefore, adds significant costs to the design (1.76 M€).

**Figure 7.** 3D Pareto surface of non-dominated solutions (in orange: solutions with gensets, in blue: solutions with no gensets).

**Figure 8.** 2D Pareto front with the third objective of reliability shown in color and six selected configurations of interest.

These six configurations are further explored in the following figures. In Figure 9, the reliability indicator is decomposed into the different aspects considered. The leastcost configuration has a significant lack of generation capacity (*UAdequacy* of 0.4%). The most renewable configuration also has a significant unavailability related to adequacy and to contingencies. For other configurations, unavailability is essentially related to contingencies. The aspect of protection is well managed in these six configurations with a sufficient short-circuit capacity and the configurations of the Pareto surface have an unavailability related to protection malfunction that is null.

**Figure 9.** Sources of unavailability for the six selected configurations.

Figure 10 shows the installed PV power, battery capacity, *PCS* power, and the genset nominal power. In terms of architecture, AC-coupled PV power was preferred, except for the reliability/RE trade-off which is a hybrid AC/DC configuration. The least-cost configuration has a small renewable energy capacity in terms of PV power and battery capacity installed (180 kWp/400 kWh). To increase the reliability (cost/reliability trade-off), an increase in the genset capacity is required (60 kW). The most reliable configuration is similar to the "cost/reliability trade-off" with an increase in PV power (200 kWp) and an additional genset unit (2 × 40 kW). The fourth configuration, being a compromise on the three objectives, requires a small increase in PV power and battery capacity as compared to the least cost option as well as three genset units installed (3 × 20 kW). The most renewable configuration has a significant amount of PV power installed (260 kWp) and *ESS* (620 kWh). The configuration with the most renewable integration and constrained unavailability (reliability/RE trade-off) leads to a further increase in PV and battery capacity, without reaching 100% renewable integration. This configuration has also three 13 kW gensets installed, as well as three *PCS* units of 27 kVA each. Apart from this configuration, an optimum size of one unit of 80 kVA for the *PCS* inverter is found.

**Figure 10.** Component sizes for the six selected solutions with unavailability contribution.

Figure 11 shows the energy flows in the 15-year period for each of the six selected configurations. A small part of the energy production in all configurations is from the

gensets. When looking at how this energy is consumed, an important share of the PV production is curtailed, from 31% for the least cost configuration up to 68% for the reliability/RE trade-off.

**Figure 11.** Energy flows for the six selected solutions.

Figure 12 shows the cash flows involved in these six configurations. The investment costs are dominated by the *ESS* and PV systems. BOS corresponds to the balance of system costs to integrate the storage system. Regarding O&M costs, fuel and genset maintenance costs are a significant part of the two first configurations but are less dominant as renewable integration is increased. The replacement costs are dominated by battery costs. Although, the "most renewable" and "reliability/RE trade-off" configurations have a larger battery capacity installed, the cycling is expected to be less and, therefore, the battery replacement cost over the 15 years is less important.

**Figure 12.** Cashflows for the six selected solutions.

#### **6. Conclusions**

This paper presents a method to optimize an autonomous microgrid considering the three design objectives of cost, renewable integration, and reliability. The multi-objective optimization is implemented with a genetic algorithm and involves a simulation of the system operation as well as a reliability analysis for each configuration evaluated. By accounting for reliability related to component failure and protection, the method gives an additional investigation on the impact of microgrid design on power availability. Additionally, rather than finding a single optimal configuration, it helps to understand the trade-offs between all objectives and estimating the cost of improving either renewable integration, reliability, or both. This method was applied to a case study of a rural microgrid in Mali to size the different microgrid components. The Pareto surface obtained shows all non-dominated solutions over the three design objectives. It was first observed that high renewable integration could be obtained without impacting the long-term cost and reliability. The cost of having high reliability was found to be low in this typical case study. Six different solutions were illustrated, each representing a trade-off between the three design objectives. With the proposed method, the user can decide to select a sizing according to the chosen trade-off. Reaching a high level of reliability with 100% renewable energy integration would require oversizing considerably the components and, therefore, add significant costs to the design. Moreover, it leads to an important curtailment of surplus renewable energy. This energy could however be used for other applications such as long-term energy storage, water heating, or water pumping.

**Author Contributions:** Writing and editing, M.R.; supervision, F.D.-R., D.G., C.L.L., Q.T.T. and M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by ANRT.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank the GIZ for its contribution to this paper and for giving us the opportunity to apply our method to a real case study.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Parameters of the Optimization Method**

**Table A1.** Technical parameters of the optimization method.

**Table A1.** *Cont.*

**Table A2.** Economical parameters of the optimization method.

**Table A3.** Parameters for the contingency enumeration method [49].

**Table A4.** Parameters for the protection reliability assessment.

#### **References**

### *Article* **Thermodynamic Analysis and Systematic Comparison of Solar-Heated Trigeneration Systems Based on ORC and Absorption Heat Pump**

**Jesús García-Domínguez \* and J. Daniel Marcos**

Department of Energy Engineering, National Distance Education University, UNED, 28040 Madrid, Spain<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Modular and scalable distributed generation solutions as combined cooling, heating and power (CCHP) systems are currently a promising solution for the simultaneous generation of electricity and useful heating and cooling for large buildings or industries. In the present work, a solar-heated trigeneration approach based on different organic Rankine cycle (ORC) layouts and a single-effect H2O/LiBr absorption heat pump integrated as a bottoming cycle is analysed from the thermodynamic viewpoint. The main objective of the study is to provide a comprehensive guide for selecting the most suitable CCHP configuration for a solar-heated CCHP system, following a systematic investigation approach. Six alternative CCHP configurations based on single-pressure and dual-pressure ORC layouts, such as simple, recuperated and superheated cycles, and their combinations, and seven organic fluids as working medium are proposed and compared systematically. A field of solar parabolic trough collectors (SPTCs) used as a heat source of the ORC layouts and the absorption heat pump are kept invariant. A comprehensive parametric analysis of the different proposed configurations is carried out for different design operating conditions. Several output parameters, such as energy and exergy efficiency, net electrical power and electrical to heating and cooling ratios are examined. The study reveals that the most efficient CCHP configuration is the single-pressure ORC regenerative recuperated superheated cycle with toluene as a working fluid, which is on average 25% and 8% more efficient than the variants with single-pressure simple cycle and the dual-pressure recuperated superheated cycle, respectively. At nominal design conditions, the best performing CCHP variant presents 163.7% energy efficiency and 12.3% exergy efficiency, while the electricity, cooling and heating productions are 56.2 kW, 223.0 kW and 530.1 kW, respectively.

**Keywords:** trigeneration (CCHP); organic rankine cycle (ORC); solar thermal energy; parametric optimisation; performance comparison

#### **1. Introduction**

One of the potential applications that combine the use of low or medium temperature solar energy and organic Rankine cycle (ORC) is a trigeneration thermal system, which can be defined as combined cooling, heating and power (CCHP) production simultaneously from the same energy source [1]. In this regard, the thermodynamic analysis to optimise the performance of this system is an important area of research to improve energy efficiency.

In particular for ORC technology, in the last few years, different investigations have been carried out aimed at evaluating its technical, economic and market penetration differentiating its wide range of application according to the driven energy source [2–7]. In order to compare different configurations of the ORC system and different working fluids, Branchini et al. [8] carried out a parametric analysis through different performance indexes, concluding that both the evaporation pressure and the maximum temperature of the heat source are determining parameters in the performance of the power cycle. Delgado-Torres et al. [9] carried out an analysis and optimisation of a low temperature

**Citation:** García-Domínguez, J.; Marcos, J.D. Thermodynamic Analysis and Systematic Comparison of Solar-Heated Trigeneration Systems Based on ORC and Absorption Heat Pump. *Energies* **2021**, *14*, 4770. https://doi.org/10.3390/ en14164770

Academic Editor: Zbigniew Leonowicz

Received: 15 July 2021 Accepted: 1 August 2021 Published: 5 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

solar driven ORC system considering different solar collector technologies as well as different cycle configurations and organic working fluids. The results obtained indicate that a recovery stage downstream of the turbine implies higher average temperatures in the cycle, and therefore, higher cycle efficiency.

Likewise, for CCHP systems based on ORC power cycle, several studies were done in recent years to determine the thermal and economic performance for different system configurations [10–15]. Al-Sulaiman et al. [16] analysed and compared three CCHP systems with different prime mover approaches: a solid oxide fuel cell (SOFC), a biomass boiler and SPTCs. The results indicated that the maximum electrical efficiency is achieved for the SOFC system with a value of 19%, being 15% for the biomass system, and 15% for the solar energy system. Al-Sulaiman et al. [17] designed and assessed a trigeneration system driven by solar parabolic trough collectors (SPTCs) to produce 500 kW of electricity through an ORC system. The results show that the maximum electrical efficiency is 15%, while the overall efficiency of the CCHP is 94%. Suleman et al. [18] proposed a new system combining solar and geothermal energy as prime movers for multigeneration applications. The overall energy and exergy efficiencies of the system are found to be 54.7% and 76.4%, respectively. Bellos and Tzivanidis [19] analysed a solar-driven CCHP system through a parametric optimisation for different working fluids and design parameters. In the optimum case, the electric exergy and energy efficiency found are 27.9% and 22.5%, respectively, while the energetic performance varied from 130% to 180%.

The use of SPTCs in combination with different ORC layouts and absorption heat pumps for trigeneration systems have been already examined to date. However, there are no known studies aimed at optimising solar-powered trigeneration systems by means of systematic comparison of multiple ORC configuration and the correspondent parametric analysis. Therefore, the current investigation has a significant contribution by analysing and optimising the use of concentrated solar energy and ORC technology as a prime mover for a trigeneration plant. In this paper, the performance of six alternative CCHP configurations based on single-pressure and dual-pressure ORC layouts, such as simple, recuperated, and superheated cycles, and their combinations, is analysed and compared, considering seven working fluids. All the analysed CCHP configurations are fed with thermal input from SPTCs through a close loop that constrains the minimum temperature of the heat source at the evaporator outlet. A single-effect H2O/LiBr absorption heat pump is integrated as a bottoming cycle to meet heating and cooling demands simultaneously.

The objective of this work is twofold: on one hand, to provide a comprehensive guide for selecting the most suitable solar-heated CCHP configuration in terms of system energy and exergy efficiency by means of a fair systematic comparison between the six layouts and the seven working fluids; on the other, to evaluate parametrically all the CCHP alternatives for a wide range of solar field outlet temperature and ORC condensation temperature aiming for the design of the most efficient system that may be coupled with buildings or industries for combined generation, or as a back-up, of electricity, cooling and heating.

#### **2. Thermodynamic Analysis of CCHP Solutions**

The CCHP system assessed in this study is mainly composed of an ORC as a power generator, which is driven by a field of SPTCs. Six alternative ORC layouts are compared under steady-state conditions and seven organic fluids are considered as working medium. A single-effect H2O/LiBr absorption heat pump is integrated as a bottoming cycle to meet heating and cooling demands simultaneously.

#### *2.1. Investigated Thermodynamic CCHP Configurations*

In order to determine the most suitable solar-heated CCHP configuration, a thermodynamic analysis is conducted for the six configurations represented in Figures 1–6. The six ORC layouts are: (i) single-pressure simple cycle (1P SC), (ii) single-pressure superheated cycle (1P SH), (iii) single-pressure recuperated cycle (1P REC), (iv) single-pressure recuperated superheated cycle (1P REC + SH), (v) single-pressure regenerative recuperated

superheated cycle (1P REG + REC + SH) and (vi) dual-pressure recuperated superheated cycle (2P REC + SH).

**Figure 1.** Case 1: CCHP with single-pressure ORC simple cycle (1P SC).

**Figure 2.** Case 2: CCHP with single-pressure ORC superheated cycle (1P SH).

**Figure 3.** Case 3: CCHP with single-pressure ORC recuperated cycle (1P REC).

**Figure 4.** Case 4: CCHP with single-pressure ORC recuperated superheated cycle (1P REC + SH).

The selection of the appropriate working fluid plays a highly important role in the system design as the ORC energy and exergy efficiency must be as high as possible, and the fluid must be chemically stable in the selected working temperature range. Environmental and safety issues must also be considered. For the present work, seven organic working fluids have been selected in order to deal with solar field outlet temperature values between 180 ◦C and 260 ◦C, typical values for a field of SPTCs used in existing ORC systems.

**Figure 5.** Case 5: CCHP with single-pressure ORC regenerative recuperated superheated cycle (1P REG + REC + SH).

**Figure 6.** Case 6: CCHP with dual-pressure ORC recuperated superheated cycle (2P REC + SH).

#### *2.2. CCHP Performance Indexes*

The overall performance assessment equations of the CCHP considered are presented in this section. The energy and exergy efficiency of the ORC are calculated, taking into account the efficiency of SPTC. The Petela model [20] is used for the exergy flow of the solar irradiation presented in Equation (7).

$$\eta\_{\rm cr,ORC} = \frac{W\_{\rm turb} - W\_{\rm ORC,pump}}{Q\_{\rm sol} \cdot \left(1 - \frac{4}{3} \cdot \frac{T\_0}{T\_{\rm sun}} + \frac{1}{3} \cdot \left(\frac{T\_0}{T\_{\rm sun}}\right)^4\right)};\tag{14.18}$$

$$\begin{aligned} \eta\_{\text{cr},\text{ORC}} &= \frac{W\_{\text{t}uv} - W\_{\text{ORC},\text{pump1}} - W\_{\text{ORC},\text{pump2}}}{Q\_{\text{air}} \left(1 - \frac{4}{3} \cdot \frac{T\_0}{T\_{\text{air}}} + \frac{1}{3} \cdot \left(\frac{T\_0}{T\_{\text{air}}}\right)^4\right)}; & \text{for Case 5} \\\eta\_{\text{cr},\text{ORC}} &= \frac{W\_{\text{t}uv} - W\_{\text{ORC},\text{pump}} - W\_{\text{Eray},\text{pump}}}{Q\_{\text{air}} \left(1 - \frac{T\_0}{T\_{\text{air}}} + \frac{1}{3} \cdot \left(\frac{T\_0}{T\_{\text{air}}}\right)^4\right)}; & \text{for Case 6} \end{aligned}$$

where:

*Wturb* = . *mORC*·(*h*4 − *h*5); *f or Case 1 Wturb* = . *mORC*·(*h*6 − *h*7); *f or Cases 2*, *4 Wturb* = . *mORC*·(*h*5 − *h*6); *f or Case 3 Wturb* = . (*mORC*,*A* + . *mORC*,*B*)·*h*8 − . *mORC*,*A*·*h*9 − . *mORC*,*B*·*h*10; *f or Case 5 Wturb* = . *mORC*,*A*·(*h*11 − *h*12) + . (*mORC*,*A* + . *mORC*,*B*)·(*h*13 − *h*14); *f or Case 6* (3) *WORC*,*pump* = . *mORC*·(*h*2 − *h*1); *f or Cases 1*–*4 WORC*,*pump*1 = . *mORC*·(*h*2 − *h*1); *f or Case 5 WORC*,*pump*2 = . *mORC*·(*h*5 − *h*4); *f or Case 5 WEvap*,*pump* = . *mORC*·(*h*8 − *h*7); *f or Case 6* (4)

### *Qsol* = *DNI*·*wap*·*LSPTC*·*NSPTC* (5)

The energy and exergy efficiency of the trigeneration system are defined as

(2)

$$\begin{aligned} \eta\_{\text{cft},\text{fri}} &= \left( \frac{W\_{\text{turb}} - W\_{\text{OC},\text{pump}} + Q\_{\text{f}} + Q\_{\text{d}} + Q\_{\text{f}}}{Q\_{\text{sol}}} \right); & \quad & \quad \text{for Cases 1-4} \\ \eta\_{\text{cft},\text{fri}} &= \left( \frac{W\_{\text{turb}} - W\_{\text{OC},\text{pump}} - W\_{\text{OC},\text{pump}} + Q\_{\text{f}} + Q\_{\text{d}} + Q\_{\text{d}}}{Q\_{\text{sol}}} \right); & \quad \text{for Case 5} \end{aligned} \tag{6}$$

$$\eta\_{\text{ent,tri}} = \left(\frac{\eta\_{\text{ent,v}} - \eta\_{\text{ent,v},\text{quadp}}}{Q\_{\text{sol}}}\right); \tag{6}$$

$$\eta\_{\text{ent,tri}} = \left(\frac{W\_{\text{t}\text{hr}} - W\_{\text{O\%C,p},\text{quadp}} - W\_{\text{Etop,p},\text{quadp}} + Q\_{\text{f}} + Q\_{\text{d}} + Q\_{\text{c}}}{Q\_{\text{sol}}}\right); \tag{7}$$

$$\eta\_{cc, \text{tri}} = \begin{pmatrix} \frac{W\_{\text{turb}} - W\_{\text{ORC, pump}} + Q\_{c'} \left(t\_0/t\_{17} - 1\right) + \left(Q\_d + Q\_{c'}\right) \cdot \left(1 - t\_0/t\_{13} ""\right)}{Q\_{\text{sol}} \cdot \left(1 - \frac{4}{3} \cdot \frac{T\_0}{1 \text{var}} + \frac{1}{3} \cdot \left(\frac{T\_0}{1 \text{var}}\right)^4\right)} \\\\ \frac{T\_0}{\eta\_{\text{sol}}} \cdot \frac{T\_0}{1 \text{var}} + \frac{1}{3} \cdot \left(\frac{T\_0}{1 \text{var}}\right)^4 \cdot \left(\frac{T\_0}{1 \text{var}}\right)^3 \\\\ \frac{T\_0}{\eta\_{\text{sol}}} \cdot \left(\frac{T\_0}{1 \text{var}}\right)^4 \cdot \left(\frac{T\_0}{1 \text{var}}\right)^5 \end{pmatrix}$$

$$\eta\_{cx,dir} = \begin{pmatrix} \frac{W\_{\text{lur}} - W\_{\text{OH}, pump1} - W\_{\text{OH}, pump2} + Q\_{r'} \cdot (t\_0/t\_{12} \, ^{\mu} - 1) + (Q\_3 + Q\_2) \cdot (1 - t\_0/t\_{13} \, ^{\mu})}{Q\_{\text{olv}} \left(1 - \frac{4}{3} \cdot \frac{T\_0}{t\_{\text{max}}} + \frac{1}{3} \cdot \left(\frac{T\_0}{t\_{\text{max}}}\right)^4\right)}\\\\ \frac{W\_{\text{lur}} - W\_{\text{OH}, pump} - W\_{\text{Ellup}, pump} + Q\_{r'} \cdot (t\_0/t\_{1} \, ^{\mu} - 1) + (Q\_3 + Q\_2) \cdot (1 - t\_0/t\_{13} \, ^{\mu})}{Q\_{\text{olv}} \left(1 - \frac{T\_0}{T} \cdot \frac{T\_0}{t\_{\text{max}}} + \frac{1}{3} \cdot \left(\frac{T\_0}{T\_{\text{min}}}\right)^4\right)} \end{pmatrix}; \qquad \text{for Case 5} \tag{7}$$

The coefficient of performance (COP) of the heat pump for cooling and heating mode is defined as

$$\text{COP}\_{\text{cool}} = \frac{Q\_{\text{f}}}{Q\_{d} + W\_{\text{S.pump}}} \tag{8}$$

$$\text{COP}\_{hcat} = \frac{Q\_c + Q\_a}{Q\_d + W\_{S,pump}} \tag{9}$$

#### *2.3. CCHP Thermodynamic Calculation Procedure and Numerical Assumptions*

The mathematical modelling of the proposed trigeneration system with all its variants is based on mass and energy balances applied to each component of the system under steady-state conditions. For a given configuration and a given working fluid, the inlet and outlet thermodynamic states of each component are calculated on the basis of the same given input data and assumptions using Engineering Equations Solver (EES) software.

The energy formulations of the SPTC model (Equations (10)–(14)) are based on the equations presented in [21] for an absorber pipe with a glass envelope, as shown in Figure 7. The energy balance in a section of the absorber pipe depends mainly on: (i) radiation losses

from the glass envelope to the open sky . (*q* 57*rad*); (ii) convection losses from the glass envelope to the environment ( . *q* 56*conv*); (iii) radiation losses from the selective coating of the metal tube to the glass envelope ( . *q* 34*rad*); (iv) conduction losses through metal pipe supports ( . *q cond*,*bracket*).

**Figure 7.** One-dimensional steady-state energy balance of SPTC [21].

All heat losses described in this section are evaluated in an analytical manner using the thermodynamic and fluid-mechanical equations and correlations governing heat transfers by conduction, convection and radiation. A stationary energy balance for the cross-section of the absorber pipe is then proposed, applying the principle of energy conservation to each of the surfaces of the section. Due to the complexity involved in this type of development, numerous simplifying hypotheses have been made. Most of these assumptions are made considering that temperatures, heat fluxes and thermodynamic properties are uniform around the perimeter of the absorber pipe.

Absorber inner surface. The useful heat that the solar thermal oil receives is the result of transfer by conduction through the absorber tube.

$$
\dot{q}'\_{12conv} = \dot{q}'\_{23cond} \tag{10}
$$

Absorber outer surface. The heat that the surface of the absorber receives from the sun, after taking into account both the optical and geometric effects of the collector, is the result of the sum of the heat fluxes due to the absorber–glass radiation, internal convection, heat loss through the absorber pipe support brackets and the fraction of energy that is finally conducted through the thickness of the absorber pipe into the fluid.

$$\dot{q}'\_{\;3\text{Sol}\,\text{Abs}} = \dot{q}'\_{\;2\text{3cond}} + \dot{q}'\_{\;34\text{rad}} + \dot{q}'\_{\;34\text{conv}} + \dot{q}'\_{\;\text{cond},\text{bracket}} \tag{11}$$

Glass envelope inner surface. The heat that is evacuated from the absorber outer surface through the space between the absorber and the glass envelope (regardless of whether there is a vacuum or not) is the same as that is transferred by conduction through the thickness of the glass. . . .

$$q'\_{\text{~{34}}nd} + q'\_{\text{~{34}}conv} = q'\_{\text{~{45}}cond} \tag{12}$$

Glass envelope outer surface. The heat that falls upon the external surface is in balance with the heat that the system releases to the outside from the external surface of the glass envelope. .

$$
\dot{q'}\_{5SolAbs} + \dot{q'}\_{45cond} = \dot{q'}\_{56conv} + \dot{q'}\_{57rad} \tag{13}
$$

Considering that the region between the absorber pipe and the glass envelope has been vacuumed, the convective heat transfer between the two surfaces ( . *q* 34*conv*) can be considered negligible. Hence, under these assumptions, the useful thermal power ( . *q* 12*conv*) can be reformulated as follows:

$$\dot{q}'\_{\text{util}} = \dot{q}'\_{\text{3SolAbts}} + \dot{q}'\_{\text{5SolAbts}} - (\dot{q}'\_{\text{56conv}} + \dot{q}'\_{\text{57rad}} + \dot{q}'\_{\text{cond,bracket}}) \tag{14}$$

The overall efficiency of the SPTC considers all types of losses [21,22]: optical, geometric and thermal, and it can be defined as the ratio between the useful thermal power delivered to the solar thermal oil, and the solar resource available based on the direct normal irradiance (DNI). . .

$$\eta\_{SPTC} = \frac{q\_{\
u}^{\prime}}{\dot{q}\_{\
u}^{\prime}} = \frac{q\_{\
u}^{\prime}}{DNI \cdot w\_{ap}} \tag{15}$$

where . *q u* is defined as .

$$\dot{q}'\_{\
u} = \frac{\dot{m}\_{\rm sol} \mathbb{C} p\_{\rm sol} \left( T\_{\rm sol\,out} - T\_{\rm sol\,in} \right)}{L\_{\rm SPT}} \tag{16}$$

The solar field includes SPTCs (PTMx-24 from the company Soltigua) with a total collecting area of 617.4 m2, consisting of five rows with two collectors per row. The specifications of the collector and the parameters of the solar system that have been selected in this analysis are defined in Table 1. The selected values are reasonable, and they were taken from Refs [9,17,19,21].

**Table 1.** Input data for SPTC model.

The ORC modelling is performed for the six CCHP configuration variants represented in Figures 1–6. Apart from the inputs coming from the solar field model, which are the solar field outlet temperature and mass flow rate, the key input thermodynamic variables required for the calculations are:

### • The condensation temperature.

For the ORC layouts corresponding to Case 5 and Case 6, the extraction pressure is selected strategically between condensation and evaporation pressures with the aim to obtain the maximum thermodynamic efficiency of each cycle.

The evaporator, or so-called heat recovery system, is the element that serves as the link between the heat source, provided by the SPTCs, and the steam cycle. In the evaporator, the fluid passes through different stages depending on the ORC layout considered. Initially, in the economiser the fluid is heated to the fluid evaporation temperature minus a Delta T, called the approach point (AP); in the evaporator, heat is added to the saturated liquid to produce saturated vapor at constant temperature and pressure. In case a superheater is considered, the saturated vapor is heated above the evaporation temperature until design conditions are reached. The evaporator design parameters used in the study are the pinch point (PP)—difference between the solar field mass flow and the organic fluid the approach point (AP)—difference between the organic fluid temperature leaving the evaporator and the saturation temperature—and the live steam outlet temperature *TLS*. All these values are given in Table 2.

**Table 2.** Input data for ORC model.

\* For recuperated cycles (Cases 3–6). \*\* For superheated cycles (Cases 2, 4–6). \*\*\* For non-superheated cycles (Cases 1, 3)

Figure 8 represents the correspondent heat transfer–temperature diagrams for a singlepressure evaporator with superheater (a) that applies to Cases 2, 4–5, and for a dualpressure evaporator with low-pressure and high-pressure superheaters, (b) that applies to Case 6.

With regard to the absorption heat pump, several modelling studies with experimental validation for specific and generic absorption machines can be found in the literature reviewed [23–26]. In the proposed absorption heat pump model, there is a total of 18 states, each of which is determined by its temperature, pressure, enthalpy, flow, H2O/LiBr concentration, etc. The assumptions used in the single-effect absorption chiller are:

The input data used in the absorption heat pump model is given in Table 3. The selected values are reasonable and conservative to avoid the formation of crystals from the H2O/LiBr solution.

**Figure 8.** Scheme and heat transfer-temperature diagram for two variants of evaporators: (**a**) Single-pressure with superheater; (**b**) Dual-pressure with low-pressure and high-pressure superheaters.

#### **3. Results and Discussion**

In the framework of the above constraints and assumptions, the methodology pursued to analyse the CCHP configuration variants from the thermodynamic viewpoint is organised as follow. First of all, for a given configuration and a given working fluid, an analysis of each pair is performed according to the nominal conditions indicated in Tables 1–3. Then, a systematic comparison of each combination is carried out by means of the evaluation of the performance indexes indicated in Section 2.1. Thereafter, a parametric approach is conducted for the best pair (configuration variant and working fluid) to evaluate the effect of different system operating parameters on the energy and exergy efficiency of the ORC and on the overall CCHP system performance. Finally, for each of the identified best pair, a muti-objective optimisation study is performed based on the same operating parameters following the criteria of system energy and exergy.

With such methodology, it is possible to determine the best performing CCHP variant in terms of system energy and exergy efficiency within the six analysed alternatives and for the seven organic working fluids, and on the other hand, to assess how the variation of some design operating parameters can affect the performance of the system and what the optimum values for such parameters are for each variant in terms of system performance.

#### *3.1. Analysis of CCHP Variants*

Tables 4–6 represent the energy and exergy efficiency of the ORC and the overall CCHP system performance for each of the proposed CCHP configurations and organic working fluids at nominal conditions, indicated in Tables 1–3.

**Table 4.** Results for Case 1: CCHP with single-pressure ORC Simple cycle (1P SC).

**Table 5.** Results for Case 2: CCHP with single-pressure ORC superheated cycle (1P SH).

**Table 6.** Results for Case 3: CCHP with single-pressure ORC recuperated cycle (1P REC).

The performance indexes indicated in Tables 4–9 show that for the six CCHP configurations and the seven organic working fluids analysed, the best performing variant is the CCHP with single-pressure ORC regenerative recuperated superheated cycle (Case 5) with toluene as a working fluid. The achieved energy and exergy efficiency are: 11.24% and 12.04%, respectively, for the ORC, and 163.7% and 12.3%, respectively, for the CCHP. The electricity, cooling and heating productions are 56.2 kW, 222.3 kW and 530.1 kW, respectively. On average for the seven working fluids considered, in terms of ORC energy efficiency Case 5 is 25% more efficient than Case 1 (1P SC). In terms of which organic working fluid is best suited depending on the configuration, benzene performs best for Cases 1 and 2, and toluene for Cases 3–6.

A CCHP with a single-pressure ORC superheated cycle (Case 2) only results in an increase in efficiency if a recovery stage is available downstream of the turbine. The performance indexes show that on average for the seven working fluids considered, in terms of ORC energy efficiency, Case 2 is 1.6% less efficient than Case 1 (1P SC).

**Table 7.** Results for Case 4: CCHP with single-pressure ORC recuperated superheated cycle (1P REC + SH).

**Table 8.** Results for Case 5: CCHP with single-pressure ORC regenerative recuperated superheated cycle (1P REG + REC + SH).

**Table 9.** Results for Case 6: CCHP with dual-pressure ORC recuperated superheated cycle (2P REC + SH).

The main objective in evaporator design is to minimise losses and maximise heat transfer from the solar heat source. This is achieved by introducing multiple pressure levels; as the temperature curves of the heat source and the organic fluid are better adapted to each other (see Figure 8b) the efficiency of the evaporator increases, but also its complexity and cost, as more heat exchangers are introduced. The results obtained for Case 6 (2P REC + SH) show that the fact to include two pressure levels in the evaporator does not imply a performance improvement of the CCHP system in comparison with Case 3 (1P REC), Case 4 (1P REC + SH) and Case 5 (1P REG + REC + SH); in fact, on average, for the seven working fluids considered, in terms of ORC energy efficiency Case 6 is about 8% less efficient than Case 5. This is explained because the temperature of the heat source at the evaporator outlet is constrained by the close loop of SPTCs, which impacts on the capacity of the dual-pressure evaporator to maximise the heat recovery from the solar heat source.

#### *3.2. Parametric Analysis*

In this subsection, a parametric approach is conducted for the best pair analysed previously (configuration variant and working fluid) to evaluate the effect of different system parameters on the energy and exergy efficiency of the ORC and on the overall CCHP system performance.

#### 3.2.1. Effect of the Solar Field Outlet Temperature

The selection of an optimal evaporation temperature for the ORC is determined by the heat delivered by the solar field; a weakness of solar parabolic trough technology is the limited outlet temperature of the solar field [27]. This study aims to illustrate the influence of the solar field outlet temperature, varying in the range of 180–260 ◦C, on the efficiency of the ORC and on the overall trigeneration system. Table 10 and Figure 9 represent the system performance and electrical and thermal generation for each analysed pair.

**Table 10.** Results of the parametric simulation with the solar field outlet temperature (*T*1).

As can be observed in Table 9 and Figure 10, higher values of the solar field outlet temperature mean an increase in ORC energy and exergy efficiency, and in CCHP exergy efficiency. This is due to a higher temperature of the heat source causing a higher organic fluid evaporation pressure in the ORC, leading to higher heat recovery efficiency in the evaporator. For Case 5, which is the best performing variant, with the increase in the heat source inlet temperature, the efficiency of the ORC increases from 9.0% to 16.3%. In terms of relative increase for the electricity produced by the turbine, the increase of the heat source inlet temperature of 180–260 ◦C represents an increase of 83% (from 45.0 kW to 82.5 kW).

**Figure 9.** Effect of the solar field outlet temperature on: (**a**) ORC energy efficiency; (**b**) CCHP exergy efficiency.

**Figure 10.** Effect of ORC condensation temperature on: (**a**) ORC energy efficiency; (**b**) CCHP exergy efficiency.

For the CCHP with dual-pressure ORC (Case 6), the relative increase either for the ORC energy efficiency and electricity produced by the turbine with respect to the increase in the heat source inlet temperature of 180–260 ◦C is significantly greater: 90% for the ORC efficiency (from 8.2% to 15.5%) and 92% for electricity produced by the turbine (from 40.6 kW to 78.1 kW).

#### 3.2.2. Effect of ORC Condensation Temperature

The single-effect absorption heat pump requires a certain heat input in the desorber within a specific temperature range for its operation. This inlet temperature is determined by the condensation temperature of the ORC, so it is important to identify which is the optimal operating temperature based on the production that needs to be prioritised.

In this study, the effect of the ORC condensation temperature is examined from 85 to 105 ◦C, and system performance and electrical and thermal generation for each analysed pair are presented in Table 11 and Figure 10.

**Table 11.** Results of the parametric simulation with ORC condensation temperature (*T*1).

ORC condensation temperature can be a good parameter for controlling the cooling and heating power to be produced by the absorption heat pump. It is observed that as the ORC condensation temperature increases, both the ORC energy efficiency and CCHP exergy efficiency decrease; the lower the condensing pressure, the higher the capacity to extract work from the turbine. For Case 5, with the increase of the ORC condensation temperature, the efficiency of the ORC decreases from 9.1% to 11.9%; in relative terms for the electricity produced by the turbine, the increase in the ORC condensation temperature of 85–105 ◦C represents a decrease of 23% (from 59.6 kW to 45.7 kW).

Regarding the energy efficiency of the trigeneration system, the effect is the opposite, as the condensation temperature increases the overall efficiency of the system also increases because the heat input to the absorption heat pump desorber is greater, and therefore the heat of the evaporator, absorber and condenser are also greater.

#### *3.3. Optimisation Analysis*

The optimisation procedure proposed is based on the optimisation of the analysed operating parameters (see Table 12), and not of the system devices, following strict energy and exergy efficiency criteria. Therefore, a multi-objective optimisation approach is considered for each of the identified best pairs requiring the simultaneous satisfaction of certain objectives, that is the ORC energy efficiency (Equation (1)) and CCHP exergy efficiency (Equation (7)).

**Table 12.** Optimisation variables.

The Pareto front is probably one of the most common approaches used for multiobjective optimisation problems in thermodynamics [28,29]. However, the most straightforward approach to solve these problems is the weighted sum method [30,31], that combines all the multi-objective functions into one scalar by summing the corresponding objectives with some appropriate weights. For the trigeneration system analysis considered in this paper, the bi-objective optimisation is constructed by summing the two beforementioned objectives with some appropriate weights, as follows:

$$\begin{array}{l}\text{MAX} \left(\text{MOF} = w\_1 \cdot \eta\_{\text{en,CRF}} + w\_2 \cdot \eta\_{\text{ex,tri}}\right) \\ 0 \le w\_1, w\_2 \le 1 \\ w\_1 + w\_2 = 1 \end{array} \tag{17}$$

where *w*1 and *w*2 are the weighting coefficients for the ORC energy efficiency and CCHP exergy efficiency, respectively. Though any set of optimal solutions can be chosen by selecting the desired values of weighting coefficients, the two objectives are assumed to be of the same importance. The "Conjugate Directions Method" which is supported by EES is used in the bi-objective optimal design (Equation (17)). The results obtained for each of the identified best pair are shown in Table 13.

**Table 13.** Results of the multi-objective optimisation.

The obtained results remark that the optimum design for all the analysed cases is produced for the maximum solar field outlet temperature (260 ◦C) and the minimum ORC condensation temperature (85 ◦C). The best performing pair is Case 5 with toluene, presenting values of ORC energy efficiency and CCHP exergy efficiency of 16.82% and 18.23%, respectively. In comparison with nominal design conditions, the optimum design for Case 5 is, in terms of ORC energy efficiency, 50% more efficient.

#### **4. Conclusions**

A comprehensive and systematic comparative thermodynamic analysis of six different solar-heated CCHP systems based on ORC and absorption heat pump is conducted. Any configuration can produce electricity, heating and cooling in temperature levels ideal for building or small-medium industry applications. The most suitable CCHP configuration has been identified in terms of system energy and exergy efficiency, as well as the best working fluid for each configuration variant. Through parametric and muti-objective optimisation analysis, it has been possible to determine how the solar field outlet temperature and the ORC condensation temperature affect the performance of the CCHP system for each best pair (configuration variant and working fluid). The main findings of the study are summarised below:

**Author Contributions:** Conceptualisation, J.G.-D. and J.D.M.; methodology, J.G.-D. and J.D.M.; software, J.G.-D.; validation, J.D.M.; formal analysis, J.G.-D. and J.D.M.; investigation, J.G.-D.; resources, J.G.-D. and J.D.M.; data curation, J.G.-D. and J.D.M.; writing—original draft preparation, J.G.-D.; writing—review and editing, J.G.-D. and J.D.M.; visualisation, J.G.-D.; supervision, J.D.M.; project administration, J.D.M.; funding acquisition, J.D.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to acknowledge the financial support of the Regional Research and Development in Technology Programme 2018 (ref. P2018/EMT-4319) in the frame of the ACES2030- CM project.

**Data Availability Statement:** Data are contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**

#### **References**

### *Article* **An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids**

**Ahmed Ginidi 1, Abdallah Elsayed 2, Abdullah Shaheen 1, Ehab Elattar 3 and Ragab El-Sehiemy 4,\***

**Abstract:** This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two recent algorithms: heap-based algorithm (HBA) and jellyfish search algorithm (JSA). The proposed hybrid HBJSA seeks to make use of the explorative features of HBA and the exploitative features of the JSA to overcome some of the problems found in their standard forms. The proposed hybrid HBJSA, HBA, and JSA are validated and statistically compared by attempting to solve a real-world optimization issue of the CHP economic dispatch. It aims to satisfy the power and heat demands and minimize the whole fuel cost (WFC) of the power and heat generation units. Additionally, a series of operational and electrical constraints such as non-convex feasible operating regions of CHP and valve-point effects of power-only plants, respectively, are considered in solving such a problem. The proposed hybrid HBJSA, HBA, and JSA are employed on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84- and 96-unit systems. The experimental results demonstrate that the proposed hybrid HBJSA outperforms the standard HBA and JSA and other reported techniques when handling the CHP economic dispatch. Otherwise, comparative analyses are carried out to demonstrate the suggested HBJSA's strong stability and robustness in determining the lowest minimum, average, and maximum WFC values compared to the HBA and JSA.

**Keywords:** heap-based algorithm; jellyfish search algorithm; economic dispatch; combined heat and power plants

#### **1. Introduction**

The energy supply in the globe is shifting toward high efficiency, sustainability, and low carbon content [1]. In conventional power units, a large amount of energy is wasted during the conversion of fossil fuels into electricity because of the low efficiency of these conventional plants. However, by utilizing the CHP economic dispatch, the whole fuel cost (WFC) may be reduced by 10–40%, energy efficiency can be increased to 90%, and greenhouse gases (GHG) can be reduced by roughly 13–18% [2]. The heat and electrical energy in the CHP system can be generated from a single source at the same time. The vital optimization challenge for the CHP economic dispatch is to find the minimum WFC of heat and power supply. There are several constraints that should be considered in the CHP economic dispatch, involving a load balance of the system, capacity limitations

**Citation:** Ginidi, A.; Elsayed, A.; Shaheen, A.; Elattar, E.; El-Sehiemy, R. An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids. *Mathematics* **2021**, *9*, 2053. https:// doi.org/10.3390/math9172053

Academic Editor: Zbigniew Leonowicz

Received: 3 August 2021 Accepted: 20 August 2021 Published: 26 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of generation plants, the valve-point effect of thermal plants, and the heat and power mutual dependency provided by CHP. Two main categories of optimization approaches are explained to solve the CHP economic dispatch problem in recent research, comprising mathematical and heuristic optimization techniques [3,4].

One such task is the economic dispatch of the power system, which entails coordination, planning, and scheduling generators in an efficient manner. Due to the imposed equality and inequality restrictions, the economic dispatch issue exhibits nonlinear behavior. The economic dispatch problem has been highlighted as a multimodal optimization problem that will be difficult to tackle. Because actual issues are multimodal in nature, gradient methods are inapplicable [5]. In [6], an enhanced multi-objective particle swarm optimizer (MOPSO) model was used to manage a bi-objective dispatch framework in order to enhance the power quality and economic costs. In this study, a deep learning approach has been used to improve wind forecast accuracy where uncertainty analysis is a critical component of any assessment of a wind farm's long-term electricity output [7]. In [8], an improved antlion optimizer was presented to search for potential solutions for the economic dispatch issue in power systems with thermal units in order to minimize the generating fuel costs and guarantee that all restrictions are within functioning ranges. In [9], a modified crow search optimization was applied for solving the economic dispatch considering the environmental impacts and high-voltage direct current systems.

Added to that, the CHP economic dispatch has been solved throughout lots of conventional and mathematical approaches. In [10], a decentralized solution based on bender decomposition (BD) was performed for the optimal schedule of the CHP economic dispatch. The Lagrange relaxation (LR) and LR with surrogate sub-gradient (LRSS) have been employed in [11,12] with two levels to find out the optimal solution for studying the CHP economic dispatch. In [13], sequential quadratic programming (SQP) was combined with the LR method, where the LR technique was applied to the optimal CHP scheduling, and SQP was applied on a portion of the CHP problem to check the validity of the acquired operating point inside the trust region. In [14], the envelope-based branch and bound (EBB) approach was utilized for optimal planning of the CHP.

However, to deal with the non-convex objective function of the CHP economic dispatch and to overcome computational time efforts, heuristic approaches have been applied on the mentioned problem, such as the genetic algorithm (GA) [15], opposition teaching learning-based optimization (OTLBO) [16], differential evolution (DE) [17], multi-player harmony search (MPHS) algorithm [18], cuckoo search (CS) [19], and whale optimization algorithm (WOA) [20]. In [21], a greedy randomized adaptive search procedure (GRASP) method was hybridized with DE optimization and applied for the CHP economic dispatch to increase global search capacity while avoiding converging to local minima. In [22], an advanced mutation mechanism was involved in real coded GA and applied to the CHP economic dispatch for minimizing the operation cost, in order to enhance the convergence characteristics. In [23], an improved GA based on a new crossover and mutation was utilized to solve the CHP economic dispatch problem for handling constraints and applied to four cases for assessing the performance of the approach. In [24], a biogeography-based learning PSO (BLPSO) was carried out to improve the solution accuracy and overcome premature convergence where each particle utilized a migration operator to update itself depending on the best position of the whole particles. In addition, a multi-objective PSO has emerged with non-dominated sorting GA [25], and a modified version of shuffle frog leaping (MVSFL) algorithm [26] has been successfully employed on the CHP economic dispatch with limited small-scale applications, which are 5-unit and 7-unit systems.

The authors of [27] presented a combined optimization approach for power systems, which managed energy with power market and active microgrids in electric vehicle parking lots, diverse CHP economic dispatches, power and heat storage units, and distributed production. In [28], a Manta ray foraging optimizer (MRFO) was incorporated with adaptive constraint handling for solving the CHP economic dispatch, whereas the impact of the inclusion of wind power based on the MRFO was investigated in [29]. Moreover, a two-stage

mathematical programming has been proposed in [30] to deal with the nondifferentiable portion of valve-point loading influence and attain a convex operating zone in the CHP economic dispatch problem. In [31], the authors investigated the heat in power equipment and the availability of power flexibility in CHP technology from district heating networks.

Recently, two novel algorithms, heap-based algorithm (HBA) and jellyfish search algorithm (JSA), have been introduced to solve global optimization problems. Firstly, the HBA is a powerful metaheuristic optimization that is inspired from organization hierarchy created by Qamar Askari et al. [32]. Its simplicity and effectiveness enforce the research direction into its promising implementations in solving engineering problems. In [33], the HBA was efficiently utilized for parameter estimation of fuel cells, while it was applied for the CHP economic dispatch in [34] and optimal reactive power dispatch in [35]. Secondly, the standard JSA, inspired from jellyfish movements, was created by J.-S. Chou and D.-N. Truong in January 2021 [36]. In [37], the JSA was employed for a spectrum defragmentation algorithm in an elastic optical network. In [38], the JSA was utilized for efficient power system operation based on optimal power flow, whereas it was effectively applied in distribution networks to integrate distributed generators and the static volt-ampere reactive compensator [39]. In this paper, a novel hybrid heap-based and jellyfish search algorithm (HBJSA) is proposed, which combines the benefits of the standard HBA and standard JSA. Compared with the standard HBA and standard JSA, the proposed HBJSA uses an adjustment mechanism to support explorative and exploitative characteristics. The adjustment mechanism is constructed to boost the explorative features at the start of iterations by enhancing the generated solutions via HBA. Furthermore, towards the conclusion of iterations, it augments and enhances the exploitative features by growing the generated solutions via JSA. The efficiency of the HBA, JSA, and the proposed HBJSA is evaluated for solving the CHP economic dispatch by considering various constraints of heat production and power output balance.

The rest of this paper is structured as follows: the CHP economic dispatch problem is characterized in Section 2, whereas Section 3 includes a description of the standard HBA, the standard JSA, and the proposed hybrid HBJSA. Furthermore, Section 4 presents the outcomes of these algorithms and discussion for simulation, while a conclusion is presented in Section 5 of this work.

#### **2. Problem Formulation**

The general form of the CHP economic dispatch problem is described in Figure 1. This figure shows the single line diagram of the 24-unit test system for the CHP economic dispatch problem. As shown, different sources of the CHP, heat only, and power-only units supply power and heat are combined together to satisfy the power and heat demands.

The objective function of the CHP economic dispatch problem can be illustrated as depicted in the following equation [2]:

$$\text{Min}\{\text{WFC}\} = \text{Min}\left\{\sum\_{i=1}^{Npp} \mathbb{C}\_{i} \left(P\_{i}^{pp}\right) + \sum\_{h=1}^{Nhp} \mathbb{C}\_{h} \left(H\_{h}^{hp}\right) + \sum\_{k=1}^{N\mathbb{C}p} \mathbb{C}\_{k} \left(P\_{k}^{\mathbb{C}p}, H\_{k}^{\mathbb{C}p}\right)\right\} \text{(USD/h)} \quad \text{(1)}$$

The three terms of costs manifested in Equation (1) are explained in Equations (2)–(4) as in [20]. The cost function of a power-only plant involves quadratic and sinusoidal terms, where the sinusoidal term displays the valve-point impacts as signified in Equation (2). Furthermore, the heat-only cost is formulated in Equation (3), while the CHP cost function is represented in Equation (4).

**Figure 1.** A single line diagram of the CHP economic dispatch problem considering the 24-unit test system.

$$\left| \mathbb{C}\_{i}(P\_{i}^{pp}) = a\_{i}(P\_{i}^{pp})^{2} + b\_{i}P\_{i}^{pp} + c\_{i} + \left| \lambda\_{i} \sin(\rho\_{i}(P\_{i}^{pp\_{\min}} - P\_{i}^{pp})) \right| \text{ (USD/h)}\tag{2}$$

$$\mathcal{C}\_{\dot{\jmath}}(H\_{\dot{\jmath}}^{hp}) = a\_{\dot{\jmath}}(H\_{\dot{\jmath}}^{hp})^2 + b\_{\dot{\jmath}}P\_{\dot{\jmath}}^{pp} + c\_{\dot{\jmath}}\text{ (USD/h)}\tag{3}$$

$$\mathbb{C}\_{k}(P\_{k}^{cp},H\_{k}^{cp}) = a\_{k}(P\_{k}^{cp})^2 + b\_{k}P\_{k}^{pp} + c\_{k} + d\_{k}(H\_{k}^{cp})^2 + e\_{k}H\_{k}^{cp} + f\_{k}H\_{k}^{cp}P\_{k}^{cp} \text{(USD/h)} \tag{4}$$

Diverse constraints for feasible solutions are illustrated for the CHP economic dispatch problem as follows:

$$\sum\_{i=1}^{N\_{pp}} P\_i^{pp} + \sum\_{j=1}^{N\_{cp}} P\_j^{cp} = P\_d \tag{5}$$

$$\sum\_{j=1}^{N\_{cp}} H\_j^{cp} + \sum\_{k=1}^{N\_{hp}} H\_k^{hp} = H\_{d\prime} \tag{6}$$

Furthermore, power-only and heat-only capacity limits are exposed in Equation (7) and Equation (8), respectively. In addition to that, capacity limits of CHP are designated in Equations (9) and (10).

$$P\_i^{pp\text{min}} \le P\_i^{pp} \le P\_i^{pp\text{max}} \quad i = 1, \dots, N\_{pp\text{\prime}} \tag{7}$$

$$\left|H\_j^{lp\text{min}} \le H\_j^{lp} \le H\_j^{lp\text{max}} \quad i = 1, \dots, N\_{lp\text{\textquotedbl{}}} \tag{8}$$

$$P\_k^{cp\text{min}}(H\_k^{cp}) \le P\_k^{cp} \le P\_k^{cp\text{max}}(H\_k^{cp}) \quad k = 1, \dots, N\_{cp} \tag{9}$$

$$H\_k^{cp\_{\min}}(P\_k^{cp}) \le H\_k^{cp} \le H\_k^{cp\_{\max}}(P\_k^{cp}) \quad k = 1, \dots, N\_{\text{cp}} \tag{10}$$

In the above constraints, Equations (5) and (6) demonstrate the power generated and the power demand balance and the heat generated and the demand balance, respectively.

#### **3. Hybrid HBJSA for CHP Economic Dispatch Problem**

#### *3.1. Standard HBA*

The standard HBA concept is based on the corporate rank hierarchy (CRH), which states that a team can arrange itself in a hierarchy to fulfill organizational goals [32]. The HBA is classified into three levels: interaction among subordinates, self-contribution of employees and their immediate supervisor, and interaction among colleagues.

In the CRH model, the population is manifested by the full CRH, whereas the heap node is manifested by the search agent. The search agent's fitness is the master of the heap node, and the population index of the search agent is the value of the heap node. The agent position of each search can be updated as:

$$\mathbf{x}\_i^k(t+1) = B^k + \gamma(2r - 1) \left| B^k - \mathbf{x}\_i^k(t) \right| \tag{11}$$

The *k*th component of λ vector → *λ* is represented by:

$$
\lambda^k = 2r - 1 \tag{12}
$$

γ is computed as follow:

$$\gamma = \left| 2 - \frac{\left( t \bmod \frac{t}{C} \right)}{\frac{t}{4C}} \right| \tag{13}$$

The parameter (*C*) in Equation (14) controls the variation. However, this parameter will complete in *T* iterations as follows:

$$\mathbf{C} = T^{\text{max}} / 25 \tag{14}$$

Added to that, the interaction between colleagues is modeled. As manifested in Equation (15), the position of each agent (→ *xi*) is updated by its arbitrarily selected colleague → *Sr*:

$$\mathbf{x}\_{l}^{k}(t+1) = \begin{cases} \begin{array}{c} S\_{r}^{k} + \gamma \lambda^{k} \Big| S\_{r}^{k} - \mathbf{x}\_{i}^{k}(t) \Big| , \quad f(\stackrel{\rightarrow}{S}\_{r}) < f(\stackrel{\rightarrow}{\mathbf{x}\_{i}^{\cdot}}(t)) \\\ \mathbf{x}\_{l}^{k} + \gamma \lambda^{k} \Big| S\_{r}^{k} - \mathbf{x}\_{i}^{k}(t) \Big| , \quad f(\stackrel{\rightarrow}{S}\_{l}) \ge f(\stackrel{\rightarrow}{\mathbf{x}\_{i}^{\cdot}}(t)) \end{array} \end{cases} \tag{15}$$

where the fitness of the search agent can be represented by *f*.

Additionally modeled is the self-contribution of each employee, where the position of each agent is updated in this level according to the following equation:

$$
\mathfrak{x}\_i^k(t+1) = \mathfrak{x}\_i^k(t) \tag{16}
$$

Finally, the position updating equations have been emerged. The roulette wheel probabilities, *p*1, *p*2, and *p*3, are selected to balance the exploration and exploitation processes. The search agent updates its position using Equation (16). Selecting the proportion *p*1 is carried out by using Equation (17) as:

$$p\_1 = 1 - \frac{t}{T^{max}}\tag{17}$$

The search agent updates its position using Equation (11). Selecting the proportion *p*2 is carried by using Equation (18) as:

$$p\_2 = p\_1 + \frac{1 - p\_1}{2} \tag{18}$$

The search agent updates its position using Equation (17). Selecting the proportion *p*3 is carried out by using Equation (19) as:

$$p\_3 = p\_2 + \frac{1 - p\_1}{2} = 1\tag{19}$$

Hence, the general positions' updating mechanism of the HBA is formulated as in Equation (20):

$$\mathbf{x}\_{i}^{k}(t+1) = \begin{cases} \mathbf{x}\_{i}^{k}(t), & p \le p\_{1} \\ \mathbf{B}^{k} + \gamma \lambda^{k} \left| \mathbf{B}^{k} - \mathbf{x}\_{i}^{k}(t) \right|, p\_{1} < p < p\_{2} \\ \mathbf{S}\_{r}^{k} + \gamma \lambda^{k} \left| \mathbf{S}\_{r}^{k} - \mathbf{x}\_{i}^{k}(t) \right|, p\_{2} < p \le p\_{3} \text{ and } f(\mathbf{S}\_{r}) < f(\mathbf{x}\_{i}^{\rightarrow}(t)) \\ \mathbf{x}\_{r}^{k} + \gamma \lambda^{k} \left| \mathbf{S}\_{r}^{k} - \mathbf{x}\_{i}^{k}(t) \right|, p\_{2} < p \le p\_{3} \text{ and } f(\mathbf{S}\_{r}) \ge f(\mathbf{x}\_{i}^{\rightarrow}(t)) \end{cases} \tag{20}$$

The main steps of the proposed HBA are depicted in Figure 2.

**Figure 2.** Flowchart of the HBA.

#### *3.2. Standard JSA*

The JSA is inspired by the jellyfish movements whether they move in the ocean current or within their swarm [36]. The jellyfish population can be mathematically modeled as:

**Figure 3.** Flowchart of the JSA.

The time control function *CF*(*t*) value is assessed as described in Equation (22), and it is varied from 0 to 1 over time:

$$CF(t) = \left| \left( 1 - \frac{t}{T^{\text{max}}} \right) \times \left( 2 \times rand(0, 1) - 1 \right) \right| \tag{22}$$

If the *CF* is greater than the constant *COo* (to be 0.5), the new location of each jellyfish can be formulated as demonstrated in Equation (23)

$$X\_i(t+1) = R \times (X^\* - \mathfrak{Z} \times R \times \mu) + X\_i(t) \tag{23}$$

If *CF* value is more than *COo*, each jellyfish location is updated depending on the movement within the swarm, as clarified in Equations (24) and (25).

$$X\_i(t+1) = 0.1 \times R \times (\mathbb{U}\_b - L\_b) + X\_i(t) \tag{24}$$

$$X\_{i}(t+1) = \begin{cases} X\_{i}(t) + \mathbb{R} \times (X\_{j}(t) - X\_{i}(t)) & \text{if } f(X\_{i}) \ge f(X\_{j}) \\\ X\_{i}(t) + \mathbb{R} \times (X\_{i}(t) - X\_{j}(t)) & \text{if } f(X\_{i}) < f(X\_{j}) \end{cases} \tag{25}$$

As soon as a jellyfish moves at the back of the search zone boundaries, it will go back, as is demonstrated in Equation (26), to the reverse boundary.

$$\begin{cases} \begin{array}{cc} X'\_{i,d} = (X\_{i,d} - \mathcal{U}\_{b,d}) + L\_b(d) & \text{if} \quad X\_{i,d} > \mathcal{U}\_{b,d} \\\ X'\_{i,d} = (X\_{i,d} - L\_{b,d}) + \mathcal{U}\_b(d) & \text{if} \quad X\_{i,d} < \mathcal{L}\_{b,d} \end{array} \end{cases} \tag{26}$$

where *Xi,d* expresses the *i*th jellyfish location in *d*th dimension. The main steps of the JSA are depicted in Figure 3.

#### *3.3. Proposed Hybrid HBJSA*

In this sub-section, a hybrid HBJSA is proposed to combine the benefits of the standard HBA and standard JSA. Compared with standard HBA and standard JSA, the proposed HBJSA employs an adjustment mechanism to support the explorative and exploitative characteristics. This mechanism is constructed to boost the explorative feature at the start of iterations by enhancing the generated solutions via HBA. Furthermore, toward the conclusion of iterations, it augments and enhances the exploitative feature by growing the generated solutions via JSA. The adjustment mechanism is executed by employing an adaptive coefficient (*ϕ*) designed as follows:

$$\varphi = \frac{t}{2 \times T^{\text{max}}} \tag{27}$$

From this equation, the coefficient (*ϕ*) is correlated positively with the number of iterations increases until it reaches 0.5 at the highest quantity of iterations. The more the value of the coefficient (*ϕ*) increases, increasing of the generated solutions via JSA will be updated by Equation (28) as follows:

$$\mathbf{x}\_i^k(t+1) = \mathbb{R} \times (Leader^k - \mathbb{S} \times \mathbb{R} \times \boldsymbol{\mu}) + \mathbf{x}\_i^k(t) \tag{28}$$

where *Leader* is the leader position of the search agents, which achieves the minimum fitness value.

Another point of view for handling the CHP economic dispatch problem, the objective function in Equation (1) is updated to incorporate penalized terms of the power and heat units constraints as follows:

$$OF = WFC + Pen\_v \sum\_{j=1}^{N\_c} B\_v \left( P\_j^C \left( H\_j^C \right) - P\_j^{CLinit} \left( H\_j^C \right) \right) \tag{29}$$

where the term (*PCLimit j* (*HC j* )) is the power limit to the CHP j heating output; *ψv* is a penalized coefficient for CHP operating violating; *Bv* equals 1 when there is violation or 0 when there is not. Accordingly, the farthest violated operating point will have a greater penalty.

Figure 4 illustrates the main steps of the proposed hybrid HBJSA for handling the CHP economic dispatch problem. For more information about the proposed HBJSA, the main steps can be summarized as follows:

**Figure 4.** Flowchart of the proposed HBJSA.

Figure 3 shows the second type of mutually dependent CHP unit. They are dealt with as the penalty function that is added in the considered fitness function (OF) in Equation (29). As shown in Figure 3, when an operational point is inside the limits, it has a *Bv* value of zero, while the infeasible locations have a *Bv* value of one. On the other side, the greater the penalty amount, the farther the infeasible point is from the nearest border.

As a result, the proposed hybrid HBJSA has a greater capacity for looking for suitable locations. Furthermore, a stopping condition is used in which the ideal result is attained if the maximum number of iterations is reached. HBA penalizes infeasible solutions to varying degrees based on their distance from the next feasible point.

#### **4. Simulation Results**

The proposed HBJSA, the standard HBA, and JSA are employed on four test systems. The first two test systems are medium-scale 24-unit and 48-unit systems, whereas the second two test systems are large-scale 84-unit and 96-unit test systems. The number of iterations (T) and population size (npop), which are the main two parameters of the standard HBA, the standard JSA, and the proposed HBJSA account for 3000 and 100, respectively, for all systems. MatlabR2017b is utilized to carry out the simulations using CPU (2.5 GHz) Intel(R)-Core (TM) i7-7200U and 8 GB of RAM.

#### *4.1. Simulation Results of the 24-Unit Test System*

The data for the obtained system are mentioned in [40], which illustrates that 2350 MW and 1250 MWth are the load demand and heat demand, respectively, and it has five heat units, 13 thermal units, and six CHP units. The HBA, JSA, and proposed HBJSA are applied on this test system, and the corresponding MW, MWth for each unit, and WFC are demonstrated in Table 1. It can be manifested that the proposed HBJSA provides the optimal solution for WFC minimization, which accounts for USD 57,968.5399, while the standard HBA and the standard JSA account for USD 57,994.51 and USD 58,739.5241, respectively.

Moreover, convergence characteristics of the proposed HBJSA versus the standard HBA and the standard JSA for the 24-unit test system of the CHP economic dispatch problem are depicted in Figure 5. It is seen from that figure that the proposed hybrid HBJSA is capable of improving the solution quality compared to the standard HBA and the standard JSA. At the last 400 iterations, the proposed hybrid HBJSA provides a higher exploitative feature and, finally, reaches the lowest WFC of USD 57,968.5399. Additionally, the standard HBA, the standard JSA, and the proposed HBJSA effectively achieve all constraints with 100% accuracy, as illustrated in Table 1.

In addition, a comparison between the HBA, JSA, and the proposed HBJSA is conducted in Table 2 for the 24-unit system of CHP economic dispatch with respect to reported techniques such as PSO [40], time-varying acceleration coefficients-PSO (TVAC-PSO) [40], group search optimization (GSO) [41], and improved GSO (IGSO) [42], MRFO [28], and supply demand algorithm (SDA) [34]. In this table, ranking order is evaluated in ascending order based on the minimum WFC. From this table, the proposed hybrid HBJSA achieves the first rank with the lowest WFC. On the other side, the standard HBA occupies the second rank, while the standard JSA occupies the last rank. This table demonstrates that the proposed HBJSA overwhelmed the standard HBA, the standard JSA, and the reported recent techniques for achieving minimum WFC.

**Table 1.** Comparison between HBA, JSA, and the proposed HBJSA for the 24-unit test system of CHP economic dispatch problem.

**Figure 5.** Convergence characteristics of the proposed HBJSA versus the HBA and JSA for the 24-unit system of CHP economic dispatch.

**Table 2.** Comparison between HBA, JSA, and HBJSA with respect to reported techniques for the 24-unit system of CHP economic dispatch.

#### *4.2. Simulation Results of the 48-Unit Test System*

**Table 3.** Comparison between HBA, JSA, and the proposed HBJSA for the 48-unit test system of CHP economic dispatch problem.

The data for the obtained system are mentioned in [40], which illustrates that 4700 MW and 2500 MWth are the load demand and heat demand, respectively, and it has 10 heat units, 26 thermal units, and 12 CHP. The HBA, JSA, and proposed HBJSA are applied to this test system, and the corresponding MW, MWth for each unit, and WFC are demonstrated in Table 3. It can be manifested that the proposed HBJSA provides the optimal solution for WFC minimization, which accounts for USD 116,140.34, while the standard HBA and the standard JSA account for USD 116,439.96 and USD 117,365.09, respectively.

Moreover, convergence characteristics of the proposed HBJSA versus the standard HBA and the standard JSA for the 48-unit test system of the CHP economic dispatch problem are depicted in Figure 6. It is seen from that figure that the proposed hybrid HBJSA is capable of improving the solution quality compared to the standard HBA and the standard JSA. After 900 iterations, the suggested hybrid HBJSA delivers more exploitative features and ultimately achieves the lowest WFC of USD 116,140.34. Additionally, the standard HBA, the standard JSA, and the proposed HBJSA effectively achieve the power and heat balance constraints with 100% accuracy, as illustrated in Table 3.

**Figure 6.** Convergence characteristics of the proposed HBJSA versus the HBA and JSA for the 48-unit system of CHP economic dispatch.

In addition to this, a comparison between the HBA, JSA, and proposed HBJSA is conducted in Table 4 for the 48-unit system of CHP economic dispatch with respect to other reported techniques such as MRFO [28], SDA [34] TVAC-PSO [40], CPSO [40], GSO [43], modified PSO [44], OTLBO [16], and MGSO [43] and gravitational search algorithm (GSA) [45]. Additionally, crow search algorithm (CSA) [46], grey wolf algorithm (GWA) [47], salp swarm algorithm (SSA) [48], multi-verse algorithm (MVA) [49], DE [50], MPA [51–53], civilized swarm optimization CSO [54] and Powell's pattern search PPS [54] are applied to the CHP economic dispatch for this system.

**Table 4.** Comparison between HBA, JSA, and HBJSA with respect to reported techniques for the 48-unit system of CHP economic dispatch.

In this table, ranking order is evaluated in ascending order based on the minimum WFC. From this table, the proposed hybrid HBJSA achieves the first rank with the lowest WFC. On the other side, the standard HBA occupies the second rank, while the standard JSA occupies the tenth rank. This table demonstrates that the proposed HBJSA overwhelmed the standard HBA, the standard JSA, and reported recent techniques for achieving minimum WFC.

#### *4.3. Simulation Results of the 84-Unit Test System*

The data for the tested system are mentioned in [20]. The power and heat demands equal 12,700 MW and 5000 MWth, respectively, and it has 20 heat units, 40 thermal units, and 24 CHP. The HBA, JSA, and proposed HBJSA are investigated to this test system, and the corresponding MW, MWth for each unit, and WFC are demonstrated in Table 5. It can be manifested that the proposed HBJSA provides the optimal solution for WFC minimization, which accounts for USD 288,820.7, while the standard HBA and the standard JSA account for USD 289,822.4 and USD 290,323.8, respectively.

Moreover, convergence characteristics of the proposed HBJSA are depicted in Figure 7 versus the standard HBA and the standard JSA for the 84-unit test system of the CHP economic dispatch problem. It is seen from that figure that the proposed hybrid HBJSA is capable of improving the solution quality compared with HBA and JSA. At the last 950 iterations, the proposed hybrid HBJSA provides a higher exploitative feature and, finally, reaches the lowest WFC of USD 288,820.7. Additionally, the standard HBA, the standard JSA, and the proposed HBJSA effectively achieve all constraints with 100% accuracy, as illustrated in Table 5.

In addition, a comparison study between the HBA, JSA, and proposed HBJSA is conducted in Table 6 for the 84-unit system of CHP economic dispatch with respect to reported techniques such as WOA [20], MRFO [28], marine predators algorithm (MPA) [42], improved MPA (IMPA) [42], and SDA [34]. In this table, ranking order is evaluated in ascending order based on the minimum WFC. From this table, the proposed hybrid HBJSA achieves the first rank with the lowest WFC. On the other side, the standard HBA occupies the second rank while the standard JSA occupies the fifth rank. This table demonstrates that the proposed HBJSA overwhelmed the standard HBA, the standard JSA, and reported recent techniques for achieving minimum WFC.

**Table 5.** Comparison between HBA, JSA, and the proposed HBJSA for the 84-unit test system of CHP economic dispatch problem. (a) Power outputs from power only and CHP units. (b) Heat outputs from CHP and heat-only units.

**Figure 7.** Convergence rates of the proposed HBJSA versus the HBA and JSA for the 84-unit system of CHP economic dispatch.

**Table 6.** Comparison between HBA, JSA, and HBJSA with respect to reported techniques for the 84-unit system of CHP economic dispatch.

#### *4.4. Simulation Results of the 96-Unit Test System*

The data for the obtained system are mentioned in [20], which illustrates that 12700 MW and 5000 MWth are the load demand and heat demand, respectively, and it has 20 heat units, 52 thermal units, and 24 CHP units. The standard HBA, standard JSA, and proposed HBJSA are applied to this test system, and the corresponding MW, MWth for each unit, and WFC are demonstrated in Table 7. It can be manifested that the proposed HBJSA provides the optimal solution for WFC minimization, which accounts for USD 234,836.04, while the standard HBA and the standard JSA account for USD 235,102.65 and USD 235,277.05, respectively.

**Table 7.** Comparison between HBA, JSA, and the proposed HBJSA for the 96-unit test system of CHP economic dispatch problem. (a) Power outputs from power only and CHP units. (b) Heat outputs from CHP and heat-only units.

Hg66 77.96514 105.49604 85.12105 Hg90 119.99947 119.9983 120 Hg67 112.78318 115.78643 108.31842 Hg91 118.32769 119.99419 119.89929 Hg68 98.469051 76.943631 85.900861 Hg92 451.81766 398.46975 449.27757

**Table 7.** *Cont*.

Moreover, convergence characteristics of the proposed HBJSA versus the standard HBA and the standard JSA for the 96-unit test system of the CHP economic dispatch problem are depicted in Figure 8. From this figure, the proposed hybrid HBJSA is capable of improving the solution quality compared to the standard HBA and the standard JSA. At the last 1000 iterations, the proposed hybrid HBJSA provides a higher exploitative feature and, finally, reaches the lowest WFC of USD 234,836.04. Additionally, the standard HBA, the standard JSA, and the proposed HBJSA effectively achieve all constraints with 100% accuracy, as illustrated in Table 7.

**Figure 8.** Convergence characteristics of the proposed HBJSA versus the HBA and JSA for the 96-unit system of CHP economic dispatch.

In addition, a comparison study between the standard HBA, JSA, and the proposed HBJSA is conducted in Table 8 for the 96-unit system of CHP economic dispatch with respect to reported techniques such as WVO-PSO [55], WOA [20], MPA [42], IMPA [42], MRFO [29], and SDA [34]. In this table, the ranking order is evaluated in ascending order based on the minimum WFC. From this table, the proposed hybrid HBJSA achieves the first rank with the lowest WFC. On the other side, the standard HBA occupies the second rank, while the standard JSA occupies the fourth rank. Additionally, this table demonstrates that the proposed HBJSA overwhelmed the standard HBA and the standard JSA and reported recent techniques for achieving minimum WFC.

**Table 8.** Comparison between HBA, JSA, and HBJSA with respect to reported techniques for the 96-unit test system of CHP economic dispatch problem.

#### *4.5. Statistical Assessment of HBA, JSA, and Proposed Hybrid HBJSA for CHP Economic Dispatch*

For all test systems, the proposed hybrid HBJSA, HBA, and JSA are run several times, and the corresponding whiskers box plots are drawn in Figure 9. For the 24-unit system, as shown in Figure 9a, the proposed hybrid HBJSA outperforms HBA and JSA in finding the lower minimum, average, and maximum WFC values. The proposed hybrid HBJSA achieves minimum, average, and maximum WFC values of USD 57,968.539, USD 58,103.95, and USD 58,293.6, respectively. On the other side, the HBA achieves minimum, average, and maximum WFC values of USD 57,994.51, USD 58,111.3, and USD 58,309.416, respectively, whereas the JSA obtains counterparts of USD 58,739.524, USD 58,968.565, and USD 59,125.33, respectively.

For the 48-unit system, as shown in Figure 9b, the proposed hybrid HBJSA outperforms HBA and JSA in finding the lowest minimum WFC value of USD 116,140.335. Compared to the HBA, the proposed hybrid HBJSA obtains lower maximum WFC values of USD 117,848.43 where the HBA obtains USD 117,980.55, while both acquire comparable WFC values of USD 116,952.6 and USD 116,946.22 for the proposed hybrid HBJSA and HBA, respectively. Compared to the JSA, the proposed hybrid HBJSA presents great superiority, since the JSA obtains minimum, average, and maximum WFC values of USD 117,365.09, USD 117,911.105, and USD 118,456.98, respectively.

For the 84-unit system, as shown in Figure 9c, the proposed hybrid HBJSA outperforms HBA and JSA in finding the lower minimum, average, and maximum WFC values. The proposed hybrid HBJSA achieves minimum, average, and maximum WFC values of USD 288,820.68, USD 289,813.827, and USD 291,251.73, respectively. On the other side, the HBA achieves minimum, average, and maximum WFC values of USD 289,822.392, USD 290,891.01, and USD 292,342.51, respectively, whereas the JSA obtains counterparts of USD 290,323.82, USD 292,366.86, and USD 293,747.44, respectively.

For the 96-unit system, as shown in Figure 9d, the proposed hybrid HBJSA outperforms HBA and JSA in finding the lower minimum, average, and maximum WFC values. The proposed hybrid HBJSA achieves minimum, average, and maximum WFC values of USD 234,836.0389, USD 235,646.129, and USD 235,967.06, respectively. On the other side, the HBA achieves minimum, average, and maximum WFC values of USD 235,102.65, USD 2,356,921.613, and USD 239,119.46, respectively, whereas the JSA obtains counterparts of USD 235,277.05, USD 236,688.76, and USD 237,940.189, respectively.

All these comparative assessments illustrate the high stability and robustness of the proposed HBJSA in finding the lowest minimum, average, and maximum WFC value compared with the HBA and JSA.

(**a**) 24-unit test system.

(**b**) 48-unit test system.

**Figure 9.** *Cont*.

(**c**) 84-unit test system.

**Figure 9.** Whiskers box plot for the proposed HBJSA versus HBA and JSA for solving the CHP economic dispatch problem.

From these implementations, the practical use of the HJBSA for a larger scale as 84-unit and 96-unit test systems do not require cloud solutions. It requires the input data of the system as follows:

#### **5. Conclusions**

In this paper, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is presented for solving the CHP economic dispatch problem. The proposed hybrid heap-based and jellyfish search algorithm (HBJSA) combines the benefits of the standard HBA and standard JSA. Compared with standard HBA and standard JSA, the proposed HBJSA uses an adjustment mechanism in order to support the explorative and exploitative characteristics. In the proposed HBJSA, an adjustment mechanism has been constructed to boost the explorative feature at the start of iterations by enhancing the generated solutions via HBA. Furthermore, towards the conclusion of iterations, it augments and enhances the exploitative feature by growing the generated solutions via JSA. Besides, the HBA, JSA, and the proposed HBJSA have been utilized to solve the complex CHP economic dispatch problems with hard constraints, which are the feasible operating area of CHP units and valve-point effects. They are applied on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84-unit and 96-unit systems.

The major contributions of this paper are:

**Author Contributions:** A.G.: conceptualization, methodology, writing—original draft preparation; A.E.: validation, writing—original draft; A.S.: software, data curation, writing—original draft preparation, visualization, investigation. R.E.-S.: supervision, validation, revision; corresponding author E.E.: writing—reviewing and editing, funding. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Taif University, grant number TURSP-2020/86.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This work was supported by Taif University Researchers Supporting Project number (TURSP-2020/86), Taif University, Taif, Saudi Arabia.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**

#### **References**

### *Article* **Hydro–Connected Floating PV Renewable Energy System and Onshore Wind Potential in Zambia**

**Kumbuso Joshua Nyoni 1,\*, Anesu Maronga 1, Paul Gerard Tuohy 2 and Agabu Shane 3,\***

**Abstract:** The adoption of a diversification strategy of the energy mix to include low-water consumption technologies, such as floating photovoltaics (FPV) and onshore wind turbines, would improve the resilience of the Zambian hydro-dependent power system, thereby addressing the consequences of climate change and variability. Four major droughts that were experienced in the past fifteen years in the country exacerbated the problems in load management strategies in the recent past. Against this background, a site appraisal methodology was devised for the potential of linking future and existing hydropower sites with wind and FPV. This appraisal was then applied in Zambia to all the thirteen existing hydropower sites, of which three were screened off, and the remaining ten were scored and ranked according to attribute suitability. A design-scoping methodology was then created that aimed to assess the technical parameters of the national electricity grid, hourly generation profiles of existing scenarios, and the potential of variable renewable energy generation. The results at the case study site revealed that the wind and FPV integration reduced the network's real power losses by 5% and improved the magnitude profile of the voltage at nearby network buses. The onshore wind, along with FPV, also added 341 GWh/year to the national energy generation capacity to meet the 4.93 TWh annual energy demand, in the presence of 4.59 TWh of hydro with a virtual battery storage potential of approximately 7.4% of annual hydropower generation. This was achieved at a competitive levelized cost of electricity of GBP 0.055/kWh. Moreover, floating PV is not being presented as a competitor to ground-mounted systems, but rather as a complementary technology in specific applications (i.e., retrofitting on hydro reservoirs). This study should be extended to all viable water bodies, and grid technical studies should be conducted to provide guidelines for large-scale variable renewable energy source (VRES) integration, ultimately contributing to shaping a resilient and sustainable energy transition.

**Keywords:** energy transition; site appraisal and ranking; time complementarity; onshore wind; levelized cost of electricity; hydro generation; grid integration; floating photovoltaics; energy mix; electrical load; dispatch

#### **1. Introduction**

#### *1.1. Overview*

Man-made reservoirs currently have a global footprint of not less than 400,000 km2, theoretically translating into a floating photovoltaic (FPV) potential in the terawatt scale, excluding anchoring and mooring considerations. Mooring involves securing a system of devices on water that are connected with fasteners or wires and anchored to the floor of the water body. The 2017 installed global cumulative PV capacity of 400 GWp is presently exceeded by the FPV global conservative estimate on man-made reservoirs [1]. Floating photovoltaics, otherwise known as "floatovoltaics", originally gained acceptance in Japan

**Citation:** Nyoni, K.J.; Maronga, A.; Tuohy, P.G.; Shane, A. Hydro–Connected Floating PV Renewable Energy System and Onshore Wind Potential in Zambia. *Energies* **2021**, *14*, 5330. https:// doi.org/10.3390/en14175330

Academic Editor: Zbigniew Leonowicz

Received: 4 July 2021 Accepted: 17 August 2021 Published: 27 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

owing to limitations in land acquisition and utilization for new power generation projects and thus took advantage of unused water surfaces [2]. Moreover, the new market of FPV swiftly came into fruition as the price of solar photovoltaic modules dropped by 75 percent, between 2010 and 2017, and PV panel efficiency increased from 14 to 21 percent. [3–5]. From the global viewpoint, between 2015 and 2018, more than 100 FPV plants had been installed and commissioned, with a total cumulative equivalent capacity of 1.3 GWp [1,6,7]. With approximately 73 percent of the total global installed capacity in 2018 translating to an equivalent of 950 MW, China had become the FPV systems market leader. The remainder of the installed capacity was distributed among South Korea (6%), the United Kingdom (1%), Japan (16%), and Taiwan (2%), while the rest of the world was represented by 2% at the beginning of 2019. However, no fewer than thirty countries had FPV projects under development [1]. Albeit on a large scale, FPV technology deployment having been initially pioneered by Asian countries (i.e., Thailand, China, Japan, and South Korea), interest had also spread to South America, North America and Europe [8,9]. Consequently, this technology could be embraced by Sub-Saharan African (SSA) countries to complement ground-mounted-based photovoltaics.

According to a recent World Bank and Joint Research Centre (JRC) under the European Commission study, installing floating photovoltaics on 1% of the area of the African hydropower reservoirs corresponds to 101 GWp of FPV potential. This could double the current installed hydropower capacity and increase the electricity output by 58%. Moreover, a 5% and 10% retrofitting of FPV on the reservoirs could translate into 506 GWp and 1011 GWp, respectively, in the African context [1]. Combining solar PV with hydropower installations and hybridizing their output is of keen interest in many countries, in particular for smaller and weaker grids in Sub-Saharan Africa and in places with significant differences in water availability between the dry and wet seasons. The hybrid "hydro + solar PV" plant could behave as a PV + battery plant but can be more affordable and safer while retaining the benefits of hydropower [1,2]. Additionally, FPV presents the added benefit of saving water by decreasing the evaporation in reservoirs. Adding solar capacity (land-based or floating) to existing hydropower plants utilizes the existing transmission infrastructure. Hydropower can smooth the variable output by serving as a storage asset. The FPV brings out resilience by helping manage periods of low water availability [3–5].

#### *1.2. Objectives and Research Contributions*

The specific aims of this study are: (1) to document and categorize the potential of FPV and wind near hydropower sites; (2) to develop a selection process based on the documented capabilities of the sites; (3) to develop a systematic scoping design process that can be applied anywhere in the country, region or globe. This will be achieved through: