**Microgrids: Planning, Protection and Control**

Editor

**Hossam A. Gabbar**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editor* Hossam A. Gabbar Ontario Tech University Canada

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

This is a reprint of articles from the Special Issue published online in the open access journal *Energies* (ISSN 1996-1073) (available at: https://www.mdpi.com/journal/energies/special issues/ microgrids planning protection control).

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

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

**ISBN 978-3-0365-3661-3 (Hbk) ISBN 978-3-0365-3662-0 (PDF)**

© 2022 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.

## **Contents**

### *Article* **A DC Microgrid System for Powering Remote Areas †**

**Tri Ardriani 1, Pekik Argo Dahono 1,\*, Arwindra Rizqiawan 1, Erna Garnia 2, Pungky Dwi Sastya 3, Ahmad Husnan Arofat 3 and Muhammad Ridwan 3**

**Abstract:** DC microgrid has been gaining popularity as solution as a more efficient and simpler power system especially for remote areas, where the main grid has yet to be built. This paper proposes a DC microgrid system based on renewable energy sources that employs decentralized control and without communication between one grid point and another. It can be deployed as an individual isolated unit or to form an expandable DC microgrid through DC bus for better reliability and efficiency. The key element of the proposed system is the power conditioner system (PCS) that works as an interface between energy sources, storage system, and load. PCS consists of modular power electronics devices and a power management unit, which controls power delivery to the AC load and the grid as well as the storage system charging and discharging sequence. Prototypes with 3 kWp solar PV and 13.8 kWh energy storage were developed and adopt a pole-mounted structure for ease of transportation and installation that are important in remote areas. This paper presents measurement results under several conditions of the developed prototypes. The evaluation shows promising results and a solid basis for electrification in remote areas.

**Keywords:** DC microgrid; power conditioner system; renewable energy; scalable microgrid

#### **1. Introduction**

As an archipelago with more than 17,000 islands, Indonesia faces a challenge in delivering electricity to all its citizens, particularly to those who live in the remote areas and outer islands. According to the Indonesian Ministry of Energy and Mineral Resources [1], although the total electrification ratio of Indonesia in 2019 has reached almost 99%, there are places that lag behind and around 1 million families still without access to electricity. Additionally, strong grids are only available to the main islands of the country, where the central government and most of the population live. There are also areas where electricity is available only for several hours a day.

Located in the equator, the solar potential in Indonesia is estimated to be around 208 GWp, much higher than other types of RES such as hydro (75 GWp), wind (60 GWp), and geothermal (29.5 GWp) [2]. It is one of the most evenly distributed RES throughout the country. Therefore, a solar-based system is very suitable to accelerate providing electricity to rural villages.

Solar PV has been a popular choice RES because they are getting cheaper by the day and are easy to install. In urban cities, small-scale solar power systems are installed on rooftops, such as described in [3,4], both to provide green energy and to reduce bills. The disadvantage of PV rooftops is that it usually needs the AC grid to run and cannot

**Citation:** Ardriani, T.; Dahono, P.A.; Rizqiawan, A.; Garnia, E.; Sastya, P.D.; Arofat, A.H.; Ridwan, M. A DC Microgrid System for Powering Remote Areas . *Energies* **2021**, *14*, 493. https://doi.org/10.3390/en14020493

Received: 20 December 2020 Accepted: 14 January 2021 Published: 18 January 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/).

operate in stand-alone mode. Extending the main grid to remote areas require a lot of time and effort. One viable solution to this problem is to build independent power systems that do not need to rely on the main grid, i.e., a microgrid. These systems tap into RES near the local load, effectively eliminating the cost needed to draw long cables from the main grid and reducing dependency on fossil fuel-based power generation.

There are two types of microgrids, AC and DC microgrids. In AC microgrids, energy sources that produce DC power, such as PV panels and a fuel cell, will obviously need DC-AC conversion to connect to the lines. Interestingly, sources that produce AC power, such as wind, hydro, and geothermal, may require AC-DC-AC conversion for better synchronized connection to the grid [5–7]. Meanwhile, in DC microgrid, both DC-producing and AC-producing sources may require only one conversion, resulting in fewer converters needed, which in turn gives better efficiency. Nowadays, DC microgrid is gaining popularity due to its simplicity and higher power quality than its AC counterpart [7–9]. In DC system, the control is simpler because there is no problem with synchronization and reactive power [5–17].

Many DC microgrid systems have been proposed in the literature. Refs. [18,19] discuss microgrid systems that are reliant on AC utility. These systems are similar to the ones in [3,4] in that they are more suited for urban areas where the network is strong. In [10], a DC microgrid system for rural areas is designed to be able to operate independently in the absence of power network, but it only has stand-alone mode, meaning it does not have power sharing capability.

For rural areas, building centralized microgrids is a poor choice [11–13]. This is due to the socio-environmental conditions of rural areas. Firstly, the geographical terrain is difficult. This calls for a system that can be easily transported and installed. Secondly, communities are formed in clusters where homes, schools, hospital, and other public facilities are built apart from each other, which means a centralized generation system will have a lot of conductor losses. Thirdly, in rural areas, communication infrastructure is lacking. Therefore, the system needs to be able to operate in stand-alone mode. To accommodate future expansion, the equipment that go into the system have to be modular and can be installed in a plug-and-play manner [5].

Distributed DC microgrid systems are proposed in [11–17]. Refs. [11–15] take into account the fact that a lot of home appliances can run on low-voltage DC power. These devices also do not require a lot of power. Because of that, the system can be designed with low specification that costs considerably less than other systems. Unfortunately, its strength can also be its weakness, because at present, AC-powered home appliances are still very common.

The systems described in [16,17] are made of a DC bus and power converters that interface it with the energy source, ESS, and other microgrid elements. Loads will tap into the DC bus directly. This system can be built for large scale; however, loads may be located far away from the source and the distribution losses may be quite high.

In addition to the topology, discussion on power electronics technology and control methods is indispensable. There are a lot of different power converter topologies to choose from, all ranging from basic, uni-directional DC-DC converter, to multilevel and modified converters [14,16,20–23] with unique features that can be harnessed for a plethora of different purposes. Although, a system with many different kinds of power converters, such as in [10,16,24], may be expensive due to the higher design and production cost. Furthermore, replacement units may be limited to the same manufacturer, making it an inflexible system. Ref. [25] proposes a uniform design of multi-purpose converters for microgrids, but presently the technology has only been applied to DC-to-DC conversion.

In the realm of control techniques, one of the central issues is the power sharing method between microgrid elements. Ref. [26] proposes forecasting algorithm for an isolated DC microgrid system to regulate power flow. This algorithm has succeeded in reducing generation costs, but the predictive aspect of the control is prone to uncertainties and complex to implement. Ref. [27] propose droop control method based on state of charge (SoC). These methods are easier to implement, especially because in rural areas, maintenance and operation have to be kept simple. Ref. [28] proposes using peer-to-peer control between microgrids, while [29] opts using switching frequency modulation-based communication, which is a good choice for systems in urban area where communication link can be established fairly easily, but not as feasible in the country and remote islands. Generally, individual microgrid control is preferred because failure in one system may not affect the others [30,31].

This paper proposes a DC microgrid system that has all the requirements mentioned above, as well as the main building block of the system. The key features of this system are as follow: (1) Modular; (2) expandable; (3) independent/without communication; (4) easily transported; and (5) each system covers a small ground area. The last point is crucial for places with land-ownership problems. Figure 1 shows a multi-point DC microgrid of the proposed system, with the primary equipment denoted as PCS. Each system consists of the following four elements: (1) A locally available energy source; (2) ESS; (3) AC loads; and (4) DC bus interconnection. If more points are to be integrated, they can be connected via the DC grid. Each point is capable of both taking and giving energy from and to the grid.

**Figure 1.** The proposed DC microgrid system.

This paper is structured as follows: PCS as the main element of the proposed system will be explained in Section 2. Comparison with other DC microgrid systems that have been proposed and implemented for rural areas will also be covered in this section. Section 3 discusses the evaluation of PCS to show the feasibility of implementing this system. Section 4 touches on the business and investment side of the proposed DC microgrid installation for a remote area in Indonesia. Finally, Section 5 contains the conclusion to this paper.

#### **2. A Modular, Independent, and Expandable DC Microgrid System**

#### *2.1. Power Conditioner System*

PCS is the primary element in the DC microgrid system proposed in this paper. It interfaces an energy source such as solar PV, wind, and hydro, an ESS, AC loads, and the DC grid. PCS consists of power converters to harvest energy from the source, charge and discharge the ESS, and regulate power to loads and grid. Figure 2a shows the inner configuration of a PCS. It may be deployed to form an isolated, independent system, but it can also connect to other PCS and share power between each other. Each PCS has its own management unit that keeps track the energy stored in its ESS, and export or import power to and from its neighboring points according to this data [32].

**Figure 2.** (**a**) Block diagram of a power conditioner system (PCS). (**b**) Converters topology employed in PCS.

Figure 2b shows the converter topology that is being used for this system. It can be seen that the hardware has the same bridge topology that can be used either as DC-DC, DC-AC, or AC-DC converter. However, at present the system is designed primarily for solar PV. By using this approach, the technology is made simple, which is important for application in remote islands. Modular plug and play feature may be expected of this system.

The power converters inside PCS are connected by an internal DC link bus (Figure 2b), whose voltage is being maintained at 500 V. At the beginning of operation, precharging action takes place as soon as the ESS is plugged into the storage chopper terminal. Once the DC link voltage is established, the management unit then activates the source chopper, inverter, and DC grid chopper depending on the specified SoC limits. Each PCS has the total capacity of 3 kW.

Table 1 lists the specification of the converters in every PCS, whereas Table 2 shows the state of each converter based on SoC. The flowchart in Figure 3 shows the decision-making process of the management unit according to guidelines set in Table 2.

**Table 1.** Specifications of each converter in a PCS unit.

**Table 2.** PCS converter states based on state of charge (SoC).

\* Source chopper operates based on the availability of power generated by PV panels.

**Figure 3.** Flowchart of the PCS management unit.

The proposed DC microgrid system has the capability of working both as a singlepoint and multi-point system to serve single or multiple clusters of loads. Figure 4 shows the multi-point configuration with different kinds of loads. A single-point system converts power from the source and stores it in the battery and/or transfer it to the AC loads. In the multi-point mode, the proposed DC microgrid system works similar to a single point, but power sharing capability is through the DC bus. Each point controls its charge and discharge states with its own management unit the way it does in a single-point system and independent of what the other point does.

**Figure 4.** Multi-point DC microgrid configuration.

Figure 5 shows the power flow in the system based on the storage SoC level. The system that has higher energy level, or state of charge (SoC), exports power, whereas the system that lacks energy imports it. Consider the leftmost system. Its SoC is above 70%, so the DC grid chopper works in discharge mode regardless of what state the source chopper and storage chopper are in. Similarly, if the SoC is under 30%, then the management unit will automatically set the DC grid chopper to charging (not shown in the figure).

**Figure 5.** Power flow in multi-point DC microgrid system.

In the middle-level SoC, DC grid chopper operation is based on the status of the source and storage choppers. If the storage chopper is running, then power is supplied from the source and the PCS has the ability to send power out via the DC grid terminal. On the contrary, if the source chopper is not running, then the power of the unit is wholly supplied by battery. This causes the management unit to set the DC grid chopper to charging. Consider the middle and rightmost system in Figure 5. The system in the middle charges its storage system because the source is unavailable, while the system on the right-hand side exports power even though its storage is not in full condition because the source is available. The operational settings that are shown in Table 2 are configurable prior to field installation.

#### *2.2. Implementation of the Proposed DC Microgrid System in Isolated Remote Areas*

In rural areas, oftentimes the land to install public facilities is difficult to obtain because of unclear ownership or the land is forbidden to be used as per the local or cultural belief. To minimize the installation area, the proposed DC microgrid system can be configured as pole-mounted along with the other equipment such as PV panels and batteries. Figure 6 shows a solar tower with a set of PV panels, a PCS, batteries, and a control panel. Multi-point implementation of this configuration is shown in Figure 1.

**Figure 6.** Solar tower: An implementation of PCS.

Houses in remote islands are assumed to use electricity for very basic needs, such as lighting, cooking, and, in places with access to communication facilities, to power up phones. Therefore, in this context, each house may be limited to use around 0.5 kWh each day. An individual system of the proposed DC microgrid has capacity of 3 kWp and 13.8 kWh of ESS per cluster, which is reasonable to serve 0.5 kWh per day for 10 houses. The system such as the one in Figure 6 uses 12 PV panels of 260 Wp each to achieve 3 kWp. The panels are positioned as a canopy shading around 18 m2 of ground to minimize land utilization.

In the proposed system, every point is designed with higher power rating, where loads can connect directly to the load converter side of PCS. Table 3 compares the key characteristics of proposed method and several DC microgrid systems in the literature. All of these systems have modular components that make scaling up the size of the network easy, and each independent unit is designed for small-power use of rural homes. The main advantage of the proposed DC microgrid system over the others are the AC output into which the loads plug. Even though a lot of home appliances operate on DC power, ACpowered devices are still in abundance and easily obtained. By using a power system that outputs AC power, users are not required to change all of their electronic appliances. It will also be easier to switch to the AC utility grid when it reaches the remote areas.

#### **Table 3.** Comparison of several DC microgrid systems.

>K^

ddZz

**No. Source Description Topology** 5 Proposed System • Distributed generation. • DC grid voltage: 370 V. • Load voltage: 230 VAC 1-phase • Power rating per unit: 3 kW. • Each unit supplies a cluster of houses and manages its own energy consumption individually. • Outputs 230 VAC to accommodate common home appliances that run on AC power. h^ ϯϳϬs ddZz ϭW^hE/dϯ<t § >K^ ϱϬϬs ddZz ϭW^hE/dϯ<t § >K^ ϱϬϬs

#### **Table 3.** *Cont.*

### **3. Functional and Performance Evaluation of the Proposed DC Microgrid System**

#### *3.1. Evaluation Methodology*

There are two evaluation sections: Lab testing and field testing. In lab testing, the proposed DC microgrid system are tested as a single-point system and a multi-point system. Dummy SoC data are used to avoid having to charge or discharge the batteries to the desired level as doing so is too time-consuming. Single-point system evaluation mainly focuses on each point's functional specifications. Precharging sequence is done manually using 192-ohm resistor and 40-amps DC circuit breaker. The multi-point system evaluation tests the PCS operation sequence. Their DC grid terminals are being connected and the parameters observed. The units automatically precharge as they get connected to power source and then follow the same procedure as in single system initialization.

The parameters and equipment used for lab testing are as follow: Two sets of batteries: OPZV batteries 240-V 1,000-Ah and LiFePo batteries 256-V 70-Ah; two sets of PV modules: each consists of 40 50-Wp 12-V PV panels in series and parallel to achieve a total 340 V and 2 kWp; and two sets of 3-kW heater as resistive loads.

The field testing is conducted to gather data regarding conductor losses. Conductor losses need to be evaluated because in the target location for implementing this system, the residential area is thinly distributed. Figure 7 shows the field-testing setup. PCS are loaded with LED lights located 100 m away from it, assuming that the houses in rural villages could be this far apart from the energy source. Measurements are done at the AC output terminal of the PCS and at the load connection point. The charging and discharging process are also monitored with changing load currents.

**Figure 7.** PCS field evaluation with distant loads.

#### *3.2. Evaluation Results*

#### 3.2.1. Lab Testing

The storage chopper activates after the management unit (operated manually by using a laptop PC) gives the signal. Current drawn from battery indicates that the battery chopper is working. The measured voltage at DC link is 500 V. The battery chopper charges battery after the PV is connected to the source input terminal and the SoC in the management unit is set to 4%. The battery charging operation indicates that the PV chopper is working. When the inverter is activated and loaded, the current flows from both the PV and battery via their respective choppers.

Performance of the inverter is summarized in Figure 8. During this test, PV is deactivated, and the supply goes solely from the battery. The inverter voltage output is stable at 228 V AC, loaded at maximum 2.4 kW. The amount of DC power that is converted into AC is generally measured by the efficiency that can be calculated by using Equation (1).

$$\text{Efficiency} = \frac{\text{AC Output}}{\text{Battery Input}} \tag{1}$$

**Figure 8.** Inverter evaluation: (**a**) Efficiency vs. load, (**b**) voltage and current THD vs. load, and (**c**) battery and inverter voltage vs. load.

The efficiency data are shown in Figure 8a. The efficiency rises together with the load increase, reaching over 90% with load above 1100 W. It can be expected that at full load the efficiency will be higher than 92.75%. The power quality measurement results in Figure 8b shows that the harmonic level is well below standardized limits according to the IEEE Std 519-2014. The distortion levels increase along with the load in an almost linear manner. According to the trend, at full load they are predicted not to exceed the standard limit. The inverter also feeds stable voltage throughout the test, delivering up to 80% of rated output power without any significant drop in voltage, as shown in Figure 8c.

The DC grid chopper is being activated last. During this test, because the SoC is set to 4%, the DC grid chopper runs in charging mode (refer to Figure 4). When it is not connected to the other PCS to draw current from, the measured voltage at the DC grid chopper terminal is 390 V.

During this test, the power consumption of PCS units is also measured. In idle state when no switching occurs, the power consumed is 16–20 W. When switching occurs, the power consumption rises to 100 W.

For the multi-point evaluation, the precharging sequence is done automatically using precharging module within PCS. The precharging is done in 1.5 s and the discharging in 2 s. To make the PCS share power between each other, SoC of one PCS is set to 30% with the PV disconnected, while SoC of the other PCS is set to 70%. The management unit of the first PCS will detect that its battery needs to be charged. Therefore, management unit of the first PCS sets its DC grid chopper to charging mode. Meanwhile, management unit of the second PCS sets its DC grid chopper to discharging mode. Because the first PCS is set to absorb power from the DC bus and the second PCS to inject power, power will naturally flow from the second PCS to the first one.

#### 3.2.2. Field Testing

Figure 9a shows that the inverter output voltage drops at the load point of connection. The proposed DC microgrid system does not use closed-loop control to keep constant voltage in the consumer to keep the simplicity. In addition, the household devices in remote area are not sensitive to constant voltage. At 9 A of load current (70% of rated current), the voltage drop does not exceed 10% of its nominal value, which is still acceptable for common AC-powered household devices. The voltage drops more when the load current is bigger due to the losses at the cable. Figure 9b shows the measured power at both end of the cable. During this experiment, the cable type NYYHY 3 × 2.5 mm2 that is readily available in general stores was used. If a better quality is required, a different type of cable with less resistance may solve the problem.

Figure 10 shows the charging and discharging of battery bank with varying load current. This experiment is done by increasing and then decreasing the load demand. When the PV produces power more than the load demand (the charging process at the lefthand side), PCS will charge the battery, signified by the negative battery power. When the load demands power higher from the PV capacity (the discharging process in the middle), the battery enters discharging mode, hence the positive battery power. Battery gives out the necessary power to meet the load demand, and the power it exerts rises along with the increase in load current. PCS then goes back to charging mode when the load demand decreases to under the PV production. This experiment shows that the charging and discharging of the battery bank has worked well to meet the needs of the varying loads.

**Figure 9.** Field testing results: (**a**) Voltage drop on cable, and (**b**) losses on cable.

**Figure 10.** Battery charging and discharging process with varying load current.

#### **4. LCOE and Investment Analysis**

Levelized cost of energy (LCOE) is defined as the average total cost to build and operate a power plant per output energy in a certain period of time. LCOE can be calculated Equation (2).

$$LCOE = \frac{NPVCost}{NPVProducts} = \frac{\sum \frac{I(t) + M(t) + F}{(1+r)^t}}{\sum \frac{E(t)}{(1+r)^t}} \tag{2}$$

where:

*I* = initial investment cost, *M* = O&M cost, *F* = fuel cost,

*E* = energy produced by the plant,

*r* = discount rate,

*t* = time,

*NPVCost* = net present value from the total cost spent in the plant's lifetime, and *NPVProduce* = net present value of the total energy generated by the plant during its lifetime.

The *LCOE* is computed using the following assumptions: Three systems such as described in Figure 1 will be installed, which amount to total capacity of 9 kWp, each system can be used to serve 10 homes running common home electronic appliances; investment cost of each system is US\$23,375; system efficiency is 95%; sun light is accessible for an average 4.5 h/day all year; PV panel output degradation is 0.5%/year; O&M cost is 0.5% from investment cost/year; O&M growth rate is 2%; interest rate is 9%/year, and because 70% of the investment comes from bank loan, the discount rate is 10.8%; and the project lifespan is 20 years.

For 20 years, the total *NPV* for investment and O&M is US\$72,975 and the total generated energy is 107.4 kW. Therefore, the *LCOE* = *NPVCost NPVProduce* = US\$72,975 107.4 = US\$0.68/kWh. If the tariff is the same as *LCOE*, the internal rate of return (IRR) is 10.82% and pay out in 8.26 years. This implies that in order for this project to be economically feasible, the *LCOE* specifies the minimum tariff for this system. US\$ 0.68/kWh is inexpensive compared to diesel generator that is generally the main electricity source in remote areas. Adding up the costs of transporting fuels, the total production cost may be well above US\$ 1/kWh. Moreover, by using the proposed DC microgrid, we will reduce dependency on the already dwindling fossil fuel reserves.

#### **5. Conclusions**

This paper proposes a new DC microgrid system concept that is suitable for accelerating electricity delivery to rural and remote areas that has no access to the main utility grid. Its modularity makes it easily transported and provides flexibility to the overall system. The DC interface between points is also advantageous when they need to combine with other points due to the absence of the need to synchronize as in AC-interfaced systems.

PCS is the key equipment for the proposed microgrid system. It interfaces the microgrid elements such as energy sources, ESS, and load, by using the same converter topologies for those different purposes. It can be deployed as an individual isolated unit and also form a grid through the DC bus for better reliability and efficiency. PCS manages the available power and the load requirements, while able to exchange power between connected points.

Prototypes have been developed to demonstrate the proposed DC microgrid system, with capacity of 3 kWp of solar PV and 13.8 kWh of battery each. One such system can be used to supply a cluster of 10 households. They are implemented in a pole-mounted structure to save space, while the PV panels form a canopy shading 18 m2 of ground. The system can be expanded to create a DC microgrid network by connecting several single isolated systems through 370 VDC bus.

The proposed DC microgrid system has been tested in laboratory and in the field, both as a single-point and a multi-point system. Each of them runs well both in either modes, reaching 92.75% of efficiency, and confirmed low THD levels, where the voltage THD is 2.078% and current THD is 2.124%. The prototype field testing successfully demonstrated the battery charge and discharge sequences following several load conditions. Voltage drops is also tested to confirm the acceptable level of voltage in the consumer's household devices. Financial analysis based on LCOE concludes that the proposed system is feasible for implementation with the minimum tariff US\$0.68/kWh.

**Author Contributions:** Conceptual development P.A.D., A.R., and T.A.; economic analysis E.G.; implementation and field testing A.H.A., P.D.S., and M.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is funded by the LPDP, Indonesia. This research is also partially funded by the Indonesian Ministry of Research and Technology/National Agency for Research and Innovation, and Indonesian Ministry of Education and Culture, under World Class University Program managed by Institut Teknologi Bandung.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would also like to thank Sanken Electric Co., Ltd. and PT Len Industri (Persero), for cooperation during this research.

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

#### **Abbreviations**

#### **References**

*Article*

## **Performance Comparison between Two Established Microgrid Planning MILP Methodologies Tested On 13 Microgrid Projects**

#### **Michael Stadler 1,2,3,4,\*, Zack Pecenak 1, Patrick Mathiesen 1, Kelsey Fahy 1 and Jan Kleissl 4**

Received: 10 August 2020; Accepted: 28 August 2020; Published: 28 August 2020

**Abstract:** Mixed Integer Linear Programming (MILP) optimization algorithms provide accurate and clear solutions for Microgrid and Distributed Energy Resources projects. Full-scale optimization approaches optimize all time-steps of data sets (e.g., 8760 time-step and higher resolutions), incurring extreme and unpredictable run-times, often prohibiting such approaches for effective Microgrid designs. To reduce run-times down-sampling approaches exist. Given that the literature evaluates the full-scale and down-sampling approaches only for limited numbers of case studies, there is a lack of a more comprehensive study involving multiple Microgrids. This paper closes this gap by comparing results and run-times of a full-scale 8760 h time-series MILP to a peak preserving day-type MILP for 13 real Microgrid projects. The day-type approach reduces the computational time between 85% and almost 100% (from 2 h computational time to less than 1 min). At the same time the day-type approach keeps the objective function (OF) differences below 1.5% for 77% of the Microgrids. The other cases show OF differences between 6% and 13%, which can be reduced to 1.5% or less by applying a two-stage hybrid approach that designs the Microgrid based on down-sampled data and then performs a full-scale dispatch algorithm. This two stage approach results in 20–99% run-time savings.

**Keywords:** Microgrid; DER; planning; MILP; optimization; run-time; full time-series optimization; data reduction; DER-CAM; XENDEE

#### **1. Introduction**

Microgrid deployment is accelerating rapidly and roughly 2300 Microgrids were operational or planned worldwide in 2018 [1]. In the last 6 months of 2018, 240 additional Microgrid projects were added to the Navigant database, demonstrating a steady increase in Microgrid projects. More impressive is the increase in 2019. As of June 2019, Navigant identifies 4475 Microgrid projects worldwide [2]. Microgrid Knowledge [3] estimates that the Microgrid market will reach US\$31 billion by the year 2027, underscoring the need for effective, fast Microgrid design and planning tools to keep up with the increasing number of projects.

The research community provides several different methodologies to plan a Microgrid from an economic perspective. All methodologies need to match energy supply with Microgrid demand to determine the annual energy costs, Net Present Value (NPV), or emissions from Microgrid adoption. Investment costs, operation and maintenance costs, subsidies, tax incentives or carbon costs among

others are considered in this calculation [4]. The goal of these approaches is to determine the optimal combination of Distributed Energy Resources (DER) and their sizes to meet the demand, subject to constraints and inputs.

In simulation or trial and error approaches, the user changes input data (e.g., investment costs for DER) to analyze the impact on the results (e.g., adopted technologies in a Microgrid) [5]. While simulation approaches are helpful to understand a complex system by running multiple iterations in a manual fashion, simulation approaches do not have built-in mechanisms (i.e., mathematical solvers) to find the best or optimal solution (e.g., optimal DER capacity). Since there are often millions of combinations for technology choices and operational levels, simulation approaches can require enormous numbers of iterations to find the optimal technology combinations. Optimal operational dispatches (e.g., unit commitment for multiple DERs) are also elusive for simulation approaches, and will significantly increase runtimes. Fescioglu-Unver et al. [6] conclude that rule-based, i.e., assumption-based simulation approaches are not viable to guarantee optimal dispatch results; instead optimization techniques should be used to increase the profitability of Microgrids.

Mixed Integer Linear Programming (MILP) optimization algorithms and associated mathematical solvers can overcome the limitations of simulation approaches and deliver optimal economic and/or green house gas solutions in a single run, creating a viable path to identify the best DER portfolio and dispatch.

As indicated in [7] the process of designing a Microgrid, which comprises conceptual design, technical design, electrical analysis, power flow analysis, and implementation, can be very time consuming. Thus, any economic optimization algorithm attempting to deliver the optimal DER portfolio, lowest costs, and optimal dispatch must be fast while maintaining accuracy. Examples for such optimization tools are REopt [8] and DER-CAM [9]. These tools are already actively used in the Microgrid industry for real Microgrid design. Reopt uses a full-scale MILP approach optimizing each hour of the year explicitly while DER-CAM relies on a peak-preserving day-type approach to reduce run-times.

Other examples for economic Microgrid optimization algorithms can be found in [10–12]. A common challenge for these optimization algorithms is run-time, which ranges between 0.1 and 280 h, depending on the considered technologies in a Microgrid and optimization approach (see Figure 1). Each optimization approach using a full annual dataset of 8760 hourly data points exhibits run-times above 2.8 h, rendering such approaches impractical for real-world Microgrid design projects since dozen or even hundreds of sensitivity runs might be needed. [10,11] demonstrate that down-sampling the data to representative days can reduce the run-time below 1 h. However, down-sampling impacts on the objective function and technology adoption need to be analyzed for multiple Microgrid and DER projects. Schütz et al. in [11] perform a comparison for two test cases between an 8760 optimization and different k-means down-sampling approaches. Gabrielli et al. in [10] test different optimization methods to address the issue of discontinuity between representative periods when modeling seasonal storage in energy systems, but for only two test cases.

**Figure 1.** Run-time comparisons for different optimization approaches and use-cases. The different model setups tested in [10–12] result in considerable different run-times. The legend is ordered from small to large computational time. Please note the logarithmic scale.

Fahy et al. [13] demonstrate a peak load preserving down-sampling method and compare the technology selection as well as the Objective Function (OF) to a full-scale time-series optimization approach (FSO). For a single example, the results show OF differences below 1% and no technology adoption difference, but run-time savings of 90%. The authors of [13] also show that clustering with k-means always delivers worse OF results than the peak-preserving day-type approach selected for this study.

The literature review and our research indicate that traditional FSO approaches might be prohibitive for wide-spread Microgrid design, unless special hybrid optimization (HO) approaches are used. Typically, such HO approaches use two stages, in which the first stage optimizes the Microgrid technology adoption based on down-sampled representative day optimization (RO) [14]. Technology adoption results from the first stage are used to inform the second stage for dispatch optimization. Pecenak et al. [15] introduce a new HO approach that applies a minimum DER constraint, derived from the first HO stage, to the second stage. This approach also guarantees robust Microgrid outage modeling solutions by combining the peak preserving day-type approach with a FSO approach.

Down-sampling methodologies and HO approaches show great potential for industry applications, but an extensive performance comparison involving more than two test sites is lacking. Thus, this research compares the peak load preserving down-sampling RO approach from [13] and the FSO approach for 13 real Microgrid projects in the US. We address how the Microgrid setup and input data drive OF differences between the RO and FSO, as well as the impact of DER sizing deviations in the two models. Additionally, we research how the embedded MILP dispatch modeling of the second (dispatch) stage in an HO reduces the OF differences between RO and FSO.

#### **2. Model Description and Used Data Down-Sampling**

The mathematical optimization model has been documented in the literature numerous times and is based on the Distributed Energy Resources Customer Adoption Model (DER-CAM) [9]. Several studies have expanded on DER-CAM. Mashayekh et al. [16] added power flow and multi-node capabilities, allowing for optimal placement of DER technologies in a distribution network. To keep run-times low for such a power flow version the RO is needed. Cardoso et al. [17] describe an Ancillary Service market MILP extension for DER-CAM and show how such markets impact the Microgrid design. Milan et al. [18] introduce nonlinear efficiency modeling for CHP systems and describe the MILP in detail. Especially the modelling of nonlinear behavior increases the run-times considerably and call for RO approaches. A DER-CAM version with considerations of passive building measures is established in [19], which allows DER and building technology optimization to create zero carbon solutions. Another version considers electric vehicle (EV) modeling under uncertainty [20] and has been applied to assess the impact of EV interconnections on optimal DER solutions. The authors of [21] consider outage modeling in DER-CAM by adding a particle swarm optimization to determine the optimal investment and operation of DER equipment. Solar variability has been incorporated by [22] and the impact on Microgrid design has been studied. The most recent version of DER-CAM implements also an efficient multi-year optimization [23] based on a RO. In this paper we use DER-CAM, implemented in XENDEE [24], as basis for the peak load preserving down-sampling RO runs for the 13 Microgrid projects.

The process of solving the MILP based on Figure 2 can be very time consuming since the amount (represented as arrow width) of each energy flow is not static over the modeled time horizon, but can change considerably with each time-step, because of, e.g., available solar radiation or changes in electric rates. Solving such a MILP with full time-series data sets, each containing 8760 data points for hourly resolution or 35,040 for 15 min resolution (or even more data points in a multi-year setting), can take hundreds of hours. Thus, down-sampling methodologies are used to reduce the run-time. We refer to this down-sampling representative day optimization as RO.

**Figure 2.** Sankey diagram for the Microgrid DER-CAM/XENDEE MILP. The five energy end-uses on the right hand side need to be supplied with energy at minimized annual energy costs or CO2 emissions. The MILP analyzes the energy flows (different arrows) in each time-step and decides on the optimal investment capacities and technologies as well as energy flows in each time-step, constituting an optimal dispatch profile.

#### *2.1. Peak Preserving Day-Types Representative Optimization (RO)*

The peak preserving RO is a special data reduction method that preserves both total annual energy demand and demand peaks. The peak preserving approach reduces annual hourly demand data into typical weekday and weekend profiles as well as peak demand day profiles. For each month m, one 24 h profile of each day-type is constructed with an hourly resolution. The total annual energy consumption is calculated using multipliers to scale up typical weekday, weekend, and peak demand day-type profiles, with the multipliers ND representing the number of times each day-type d occurs in a given month m (NDm,d).

The peak demand day profile for each month is constructed by selecting at each hour the maximum demand across any given day in the month. The resulting peak day profile represents both peak daily consumption and peak monthly demand. An example of the peak demand profile is shown in Figure 3.

**Figure 3.** Daily demand for each day in an example March month and peak demand day profile constructed from selecting maximum hourly demand across all days.

The representative weekday and weekend demand profiles must both represent the average weekday and weekend demand behavior, while also maintaining the monthly total energy consumption. Therefore, the average weekday and weekend profiles are adjusted to account for the energy contained in the peak demand profiles. The monthly demand data are separated into sets of weekday and weekend data. The sets are summed to calculate the total weekday demand and weekend demand for each hour in the day. The total weekday demand data for month m is modified by subtracting the peak demand, multiplied by the number of peak days expected to occur in the month, from the weekday consumption at each hour the peak occurred on a weekday. As indicated by [13] the number of peak days is not crucial and just using one peak day profile in the optimization is sufficient. The same approach is used to modify the weekend consumption data, based on peaks occurring on weekends. The modified total weekday and weekend demand data sets are averaged into 24-h representative weekday and weekend demand profiles.

#### RO MILP

The energy end-uses (u) are grouped into three characteristic groups d: weekdays, weekend days, and peak days for each month. The MILP approach is solved for the entire year, resulting in 36 daily profiles and 864 hourly data points. A brief overview of the MILP is given in what follows and additional selected constraints are given in Figure 4.

$$\begin{aligned} \text{The objective function minimizes the total costs } \mathbf{C} \\ = & \sum\_{\mathbf{m}} \text{MFix}\_{\mathbf{m}} + \sum\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} u \sim\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \mathbf{C}\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \cdot \text{N} \mathbf{D}\_{\mathbf{m}, \mathbf{d}} \\ & + \sum\_{\mathbf{u}, \mathbf{m}, \mathbf{p}} \max\iota \sim\_{\mathbf{u}, \mathbf{p}, \mathbf{m}} \text{D}\_{\mathbf{u}, \mathbf{p}, \mathbf{m}} \\ + \sum\_{\mathbf{f}} \max\iota\_{\mathbf{f}} \text{Fix}\_{\mathbf{\xi}^{\mathbf{f}}} \text{ANN}\_{\mathbf{\xi}} + \sum\_{\mathbf{c} \in \mathbf{s}} \left( \mu r\_{\mathbf{c}\mathbb{L}\lambda^{\mathbf{s}}} \text{Fix}\_{\mathbb{L}\mathbf{\xi}\lambda} + c \mu\_{\mathbf{c}\mathbb{L}\lambda^{\mathbf{s}}} \text{Var}\_{\mathbb{L}\mathbf{\xi}\lambda} \right) \cdot \text{ANN}\_{\mathbf{\xi}\lambda} \\ & + \sum\_{\mathbf{j}, \mathbf{m}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \frac{\text{gcn}\_{\mathbf{\xi}\mathbf{m}, \mathbf{d}, \mathbf{h}}}{\eta} \text{GEN}\_{\mathbf{\xi}\mu, \mathbf{m}, \mathbf{d}, \mathbf{h}} \cdot \text{ND}\_{\mathbf{m}, \mathbf{d}} + \sum\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} d r\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \cdot \text{DR} \mathbf{C}\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \cdot \text{ND}$$

$$\begin{aligned} \text{Major constraint Energy balance}:\\ \sum\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \text{LOAD}\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} + \sum\_{\mathbf{i}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \text{self}\_{\mathbf{i}, \mathbf{m}, \mathbf{d}, \mathbf{h}} + \sum\_{\mathbf{s}, \mathbf{m}, \mathbf{d}, \mathbf{h}} dr\_{\mathbf{s}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \\ = \sum\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \text{\textit{u}} \sim\_{\mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} + \sum\_{\mathbf{i}, \mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \text{gen}\_{\mathbf{i}, \mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} + \sum\_{\mathbf{s}, \mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \text{sout}\_{\mathbf{s}, \mathbf{u}, \mathbf{m}, \mathbf{d}, \mathbf{h}} \end{aligned} \tag{2}$$

**Figure 4.** Selected constraints of the MILP.

*Indices*

#### *2.2. Full-Scale Time-Series Optimization (FSO)*

Since DER-CAM was programmed as a RO model, the FSO requires some adjustment of the day-type framework to emulate an FSO. The FSO MILP model is derived from the RO model by modifying NDm,d to represent the real number of days in a month instead of the number of representative day-types. Thus, instead of e.g., using 22 representative weekdays, eight weekend days, and one peak profile for the RO, we convert NDm,d into a binary matrix containing ones to identify the real days observed in each month. In the case of January 2020, the matrix consists of ones from 1 to 31. For February 2020 it consists of ones from 1 to 29 and zeros for 30 and 31, etc. Days must be linked in time to allow energy to shift between consecutive days, creating a real seasonal model. The authors of [15] describe the changes needed to create an FSO model in detail.

Additionally, we link the RO and FSO to create a Hybrid Optimization (HO) approach. In such an HO approach the sizing (e.g., DER capacity) solution from the down-sampled RO will be used as fixed input for the FSO. In other words, the FSO just optimizes the dispatch of the RO-designed Microgrid using the full time-series data which preserves short run-times. To differentiate between a real FSO, which also sizes DERs, and the full time-series dispatch optimization within the HO, we call the latter TSO. The second part of this paper will compare the OF and run-time results of a simple RO with those of an HO, utilizing a TSO as a second stage.

#### **3. Microgrid Projects**

#### *3.1. General Description of Microgrid Projects*

Table 1 presents an overview of the Microgrid projects. Cases were selected to represent a diverse variety of host types, geographic locations, tariff characteristics, and total load consumption. These Microgrid projects have been modeled by the authors in detail. All the projects are optimized using the RO, FSO, and HO models, and results are assessed from an economic perspective.

All Microgrids are grid connected without grid outages considered, except for Mil2, for which we modeled a 24-h outage on the day with the highest electric peak demand, which in this case constitutes also the highest daily energy consumption. None of the Microgrids are allowed to sell electricity to the utility, except for Un1, which is on a net-metering tariff and can export surplus electricity to the utility. To analyze effects of electricity sales we will show hypothetical sensitivity runs for selected sites in Section 4.2.

The tariffs and technology data are summarized in the Appendices A and B.

#### *3.2. Electric Load Data*

For each case except Un4, hourly metered load data for one year was used in this analysis (8760 data points per case for FSO and HO). In the absence of metered load data, for Un4, data from the Commercial and Residential Hourly Load Profile database for a hospital was used since the modeled site is a medical University [25]. Segments of the time-series electric load data for Un3 and Un4 are provided in Figure 5.

**Figure 5.** Example time-series electric load data for Un3 (solid line, left *y*-axis) and Un4 (dashed line, right *y*-axis). Hours 120–168 are weekend days.

 Flat energy rate just for

Non-coincident

 demand charge,

**Table 1.** winter months, TOUER:

Overview of considered

 Microgrid projects for this research. FER: Flat energy rate, FSER: Flat seasonal energy rate, FER-winter:

Time-Of-Use

 energy rate,

TOUER-summer:

Time-Of-Use

 energy rate just for summer months, NCDC:

Figure 6 summarizes the electric load data statistics. Total annual electric load is the sum of the hourly electric load profile over the entire year. Annual load variability is the sum of the absolute value of hourly energy ramp rates (*ERRn*) normalized by the total annual electric load to ensure that load volatilities can be compared between sites (Equation (3)).

$$Annual\text{ Load }Variable\text{ }Variability = \frac{\Sigma\left(abs\left(ERR\_{\text{H}}\right)\right)}{\Sigma\_{\text{m,d,h}}load\_{\text{m,d,h}}} = \sum\_{m,d,h} \frac{load\_{m,d,h} - load\_{m,d,h-1}}{\Sigma\_{\text{m,d,h}}load\_{m,d,h}}\tag{3}$$

**Figure 6.** Summary of electric load data for all cases as a function of annual electric load (GWh) and load variability (-) expressed as the sum of the absolute values of all 1 h power changes normalized by the total annual load.

For example, the Un3 metered data is more volatile, with severe late afternoon ramps and a total variability equal to 12.4% of its annual load. Un4, on the other hand, is relatively smooth, and therefore, shows low variability numbers of 4.2% in Figure 6, which also can be attributed to the load modeling. Overall, the two industrial sites (Ind and Man) have the lowest variability. The military sites Mil1 and Mil3 have significantly larger annual loads than the other cases.

#### *3.3. Solar Radiation Data*

Several sources of solar radiation data were used for the different Microgrid projects as input for the RO, FSO, and TSO MILP: real measurements of solar radiation (two projects), Helioscope [26] data (six projects), and PVWatts data based on the NREL National Solar Radiation Database from satellite data (NSRDB, five projects) [27]. While the FSO and TSO use the 8760 PV Watts output directly, the RO uses an average daily profile for each month constructed from the 8760 time-series.

Similar to Figure 6, Figure 7 compares the solar production data across all sites via the capacity factors and total variability. Similar to the demand, total solar variability is calculated by summing

over the absolute values of solar production ramp rates (*SRRn*) and normalizing them by the total energy production (Equation (4)).

$$\text{Annual Solar Variable} = \frac{\Sigma(abs(SRR\_n))}{\sum\_{\mathbf{m},\mathbf{d},\mathbf{h}} PV\_{m,\mathbf{d},\mathbf{h}}} = \sum\_{\mathbf{m},\mathbf{d},\mathbf{h}} \frac{PV\_{m,\mathbf{d},\mathbf{h}} - PV\_{m,\mathbf{d},\mathbf{h}-1}}{\Sigma\_{\mathbf{m},\mathbf{d},\mathbf{h}} PV\_{m,\mathbf{d},\mathbf{h}}} \tag{4}$$

**Figure 7.** Solar production summary for all cases expressed through the annual capacity factor and the normalized annual solar variability.

Figure 7 is useful to infer case-by-case differences in the solar resource. For example, Mil1, Mil2, and Mil4 are located in sunny locations with little variability due to clouds. As such, variability is low and total solar production and capacity factors are high. Conversely, Com is in a region with low total solar production and high variability, indicating frequent cloud cover and ramp events.

#### **4. Results**

#### *4.1. Representative Optimization (RO) versus Full-Scale Time-Series Optimization (FSO)*

Table 2, Figures 8 and 9 present the high level results for all 13 Microgrid cases, comparing the objective functions of RO and FSO, technology adoptions, and run-times. The run-time savings for the analyzed cases can range between almost 100% and 85%.

In total, 10 cases out of the 13 show OF differences below 1.5%. Un4, with a very high solar variability (see Figure 7) and small load variability shows the highest OF difference. This could explain the 97.4% difference in PV adoption between the RO and FSO. Some cases show very similar OFs for the RO and FSO models despite significant changes in the technology adoption, which is expected for MILP approaches. Examples are the Ind case with a −32% difference in EES adoption, but only a −0.5% OF difference or the Res case with a 56.9% difference in EES adoption, but only a −0.3% difference in the OF (see also Figure 9).

**Figure 8.** OF differences (bars) and run-time savings (line) for the RO approach compared to the FSO. Negative run-time numbers represent savings.

**Figure 9.** Variations in RO technology adoption compared to the FSO. The OF difference compared to FSO is shown as a dashed line.

It is worth noting that the Ind and Res cases experience opposite solar and load volatilities: Ind has a relative high solar variability compared to the Res case (see Figure 7) and a small load variability compared to the Res case (see Figure 6). Note that in the Ind and Res case the available PV space is fully utilized, explaining the exact same PV sizes in both optimization models.

Un3 with the highest load variability experiences one of the highest run-time savings between the two MILP models (99.8%), a very low OF difference of −0.8%, moderate PV difference (16%), very small EES differences (2%), and no difference in fuel fired DG adoption.

The Mil2 includes a 24 h outage and the possibility to install DG units. Since the RO model preserves the peak loads from the full time-series load data and the DG units contribute to the worst case outage modeling (highest power demand and electric energy consumption in a day in this case), the installed fuel fired DG units in the FSO and RO model match. The differences in the PV (24.3%) and EES (−21.4%) adoptions are influenced by the different granularity of the solar radiation modeling in the RO and FSO—the RO uses an average monthly solar production profile, while the FSO uses the full-scale time-series. However, the OF (e.g., project cost) differs by only 0.4%.

Com and Un4 show significant OF differences with higher costs in the RO model (i.e., ΔOF >0), which creates a budget cushion for these projects when modeled with RO, but could also render these projects economically unattractive. Their technology selection in the RO is higher except for the smaller EES numbers in the RO model for Un4 (Figure 9). Un2, on the other hand, shows significant lower costs in the RO model, indicating that there is no clear trend on whether the RO is over- or underestimating OFs.

Figure 9 also shows that if sizing of several technologies differ for a Microgrid (seven cases), then RO oversizing of one technology is usually balanced by undersizing of another. In four of those seven cases RO oversizes PV and undersizes storage compared to the FSO, indicating that the technologies could be to some extent interchangeable.

Among these 13 Microgrid designs, there is no clear relationship between the solar variability and the deviation in the OF solution (Figure 10). Com, Un4, and Un2 tend to have higher solar variability and are the three cases which exhibit OF deviations greater than 1.5%. However, sites Man, Ind, and Mil5 also have high solar variability and small OF differences. However, for Mil5 no DER investments are optimal and installed. On the other hand, the load variability seems to have no significant impact on the OF differences, indicating that the peak-preserving down-sampling is an effective method to capture load spikes.

**Figure 10.** Scatter plot comparing the absolute value of OF deviation of each case as a function of solar variability (*y*-axis) and load variability (*x*-axis). The size of the circle represents the OF deviation of each case.

#### *4.2. Sensitivity to Electricity Sales*

A limitation of the Microgrid projects is that only site Un1 is explicitly considering energy sales to the utility, which inherently limits the economic viability and sizing for DERs, especially for solar PV. Thus, sensitivity scenarios are performed to assess the impact of electricity sales on OF differences as well as DER technology selections. For these sensitivities, two cases were selected, one with a minor OF difference of −1.2% (Mil4) and one with a considerable difference of −6.8% (Un2). These sites are representative as universities and military sites are prime Microgrid candidates considering their abundance in the set of real Microgrid projects in Table 1.

The sales prices are assumed to be the same as the energy purchase prices from the utility during the same time period. Capacity bidding or Ancillary Service market participation is not considered.

For the Un2 case, including energy sales the OF difference is reduced to −2.0% (see column 1 in Table 3 for the Un2 cases). In this particular case, the OF deviation reduction may be explained by identical PV capacity investments. When sales are considered, PV is attractive enough that both algorithms invest in PV to its spatial limit. However, the Un2 sales with FSO case shows less EES, which causes the Microgrid to import and export more energy on an annual basis compared to the RO approach (see Table 4 cells Un2 sales/A/B/D/E).

 In the Un2 case with sales the PV adoption is reaching the maximum available space at the site.

use (RO data-FSO data)/RO data.

The Mil4 sales case does not show significant changes compared to the case without sales. The OF differences change from −1.2% to −1.1% and the PV/EES adoptions show slightly smaller differences compared to the Mil4 no sales case (see Table 4).

However, as indicated by Mil4 sales in Table 4, reduced differences in the technology adoption do not necessarily lead to a reduced difference in the imported energy. For Mil4, Δ PV changes from −12.5% to −12.4% and Δ EES from −7.1% to −6.3%, but Δ import decreases from −5.2% to −7.2% (Table 4).

These results underscore the complexity of such modelling problems and that similar technology adoption capacities can result in similar OFs, but different parts of the result can change in different directions.

**Table 4.** Import and export balance for the energy sale sensitivity runs as well as the original runs without sales.

#### *4.3. The Influence of Optimal Dispatch Modeling—The Hybrid Optimization (HO)*

The large OF differences for Com and Un4 and the connection to extreme relative capacity deviations will be analyzed.

In both Com and Un4, RO modeling delivers higher optimal capacities of PV and DG/CHP. In particular, the RO almost doubles the PV capacity for Un4 and invests in 182 kW of PV for Com, while FSO does not select any PV in Com. Only the optimal EES in the Un4 FSO is slightly higher than for the RO. We hypothesize that the OF differences resulting from large capacity deviations in the RO can be mitigated by dispatch optimization. To test this, optimal dispatch modeling in the FSO, based on optimal capacities from the RO, is performed. This approach constitutes a two stage Hybrid Optimization (HO) approach, in which we refer to the FSO as TSO to indicate that the full-scale time-series optimization of the second state will optimize the operational planning (i.e., dispatch), but not the capacities. The HO approach allows assessing the impact of dispatch on the OF differences. Additionally, the HO allows assessing the feasibility of a Microgrid designed by an RO when modeled using raw time-series data.

Taking the optimal investment capacity results from the RO and fixing them in the TSO model while allowing for dispatch optimization, yields OFs that are very similar to the FSO, but with better run-times as indicated in Table 5. The Com RO case shows a 5.7% OF deviation compared to the FSO OF. Using the 2-stage HO process with TSO reduces the deviation to 1.4%. Similarly, the Un4 RO deviation of 13.2% is reduced to a 0.6% difference with HO. Every other case also shows a reduction in the OF difference compared to the FSO with better run-times than the FSO.

These results are important for Microgrid planning and operation since they indicate that even though there occasionally are higher deviations between RO and FSO capacity results, the fast HO is very viable and will result in a similar OF as the slower FSO. The unit dispatch optimization absorbs OF deviations that arise from differences in the capacities between the models. Note that the TSO dispatch optimization in the HO is similar to dispatch modeling in real Microgrids through Model Predictive Controllers (MPC). Thus, actual Microgrid dispatch is economically robust (i.e., will achieve similar revenues and costs) to capacity differences introduced by sub-optimal RO modeling during Microgrid planning.

**Table 5.** Objective function as well as run-time differences between the HO and FSO. OF: Objective Function; R-time: Run-time; RO: Representative Optimization; HO: Hybrid Optimization; FSO: Full-Scale Time-Series Optimization.

#### **5. Conclusions**

This paper advances the field of Microgrid planning and operation through a comprehensive analysis of objective function and technology adoption results of peak preserving day-types Representative Optimization (RO). Not only does the analysis include a large number of Microgrids (13) with different load and renewable resource time-series, but also a great diversity of tariffs and technology assumptions. The uniqueness of the paper also stems from industry relevance in that the Microgrids are actually being considered for construction or are already being built and were analyzed in commercial applications.

The results support the widespread application of RO in Microgrid planning. The special peak-preserving day types approach represents a full time-series of 8760 h with 3 days in each month or 864 time-steps. For all but three Microgrids the objective function differences are less than 1.5%, yet run-time savings are from 85% to almost 100% compared to full-scale time-series optimization (FSO). Such run-time savings enable more detailed analysis through sensitivity studies, probabilistic parameter inputs (Monte Carlo Simulation) and decision-making, and multi-year horizon analysis.

Three analyzed Microgrids have larger OF differences at 5.7%, −6.8%, and 13.2% in the RO. All these outliers experience higher solar variability than others. However, three other Microgrids with similar or even higher solar variability experience very small OF differences of 0.0%, −0.2%, and −0.5%, indicating that there is no clear trend on how solar variability impacts the results of both models. The impact of load variability seems to be minimal, indicating that the peak-preserving day-type RO is very effective. While such larger OF differences may still be tolerable given other uncertainties in Microgrid planning, they can be mitigated through hybrid optimizations (HO) that optimize technology dispatch in a second stage, using capacity results from the first stage RO and the full time-series data in the second stage. HO still supports run-time savings of 20–99%, but reduces OF differences to less than 1.5% across the board.

The choice of RO versus HO depends on individual preferences of prioritizing run-time or OF accuracy and optimized dispatch might be one of the most important features in a Microgrid Design tool since it provides the possibility to mitigate design problems and sub-optimal capacity selections. This hypothesis will be tested in follow-on research, comparing different dispatch strategies for different DER capacities in built Microgrids.

We would also like to acknowledge a limitation of this paper: the day-type approach cannot simulate energy transfer between days and months and should not be used if seasonal storage is anticipated to be part of the solution. In such cases the presented day-type MILP needs to be modified, which will be discussed in future work.

**Author Contributions:** M.S. contributed to the data collection process, optimization runs, analyses, interpretations, and writing. Z.P. contributed to the data collection process, optimization runs, analyses, interpretations, and writing. P.M. contributed to the optimization runs, analyses, interpretations, and writing. K.F. contributed to the data collection process, optimization runs, and writing. J.K. contributed to analyses, interpretations, and writing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors want to thank the Microgrid team at WorleyParsons and Advisian for the numerous opportunities to experience Microgrid planning and design challenges firsthand and being able to work on exciting real Microgrid projects. We also extend our gratitude to our colleagues Adib Naslé and Scott Mitchell for their outstanding support on implementing the optimization algorithms in our optimization platform and enabling us to perform the optimization runs in such an effective manner.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A Tari**ff **Data**

For each site, the proper utility tariff was collected or provided by the client and used in the optimization. Table A1 summarizes this information.

**Table A1.** Summary of electric tariffs and supporting documents.

#### **Appendix B Technology Data**

PV technology costs are presented in Table A2. Costs are based on client input or literature data. The PV costs include soft costs (e.g., labor costs) and inverter costs. The PV costs as well as Operation and Maintenance (O&M) costs are generally within the ranges reported by [35]. Per client request the O&M costs for Res and the PV costs for Un2 are outside of the range reported by [35].

**Table A2.** PV technology assumptions used in the Microgrid projects. "Max. space for PV" represents the maximum available onsite space for PV generation.

Effective Electric Energy Storage (EES) costs and assumptions are shown in Table A3. Effective EES costs consider incentives and are, therefore, low compared to [36]. Lifetime numbers can also vary significantly depending on allowed operational conditions, meaning allowed max charging or discharging rates or minimum levels of the state of charge.

Table A4 summarizes the natural gas and diesel fired DG and CHP assets. For most cases, multiple options have been provided, mostly distinguished by different unit sizes, unit costs, electric efficiencies or the heat to power ratios. The heat to power ratio specifies the amount of heat generated from 1 kWh electricity. The data is based on vendor data and inputs from the project partners. DG and CHP capacity costs, electric efficiencies, and heat to power ratios broadly agree with the assumptions for the commercial demand model from the Annual Energy Outlook 2020 report [37]. The lifetime numbers seem to be more conservative (smaller) compared to EIA, with the exception of the microturbine lifetimes, which are higher than reported by EIA. The diesel genset costs are in line with [38].

The maximum annual operating hours are based on project constraints such as air regulation or technical constraints.

*Energies* **2020**

, *13*, 4460

#### **References**

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Design of a Methodology to Evaluate the Impact of Demand-Side Management in the Planning of Isolated/Islanded Microgrids**

**Juan Carlos Oviedo Cepeda 1,***∗***, German Osma-Pinto 1, Robin Roche 2, Cesar Duarte 1, Javier Solano 1, Daniel Hissel 2**

Received: 28 April 2020; Accepted: 28 June 2020; Published: 4 July 2020

**Abstract:** The integration of Demand-Side Management (DSM) in the planning of Isolated/Islanded Microgrids (IMGs) can potentially reduce total costs and customer payments or increase renewable energy utilization. Despite these benefits, there is a paucity in literature exploring how DSM affects the planning and operation of IMGs. The present work compares the effects of five different strategies of DSM in the planning of IMGs to fulfill the gaps found in the literature. The present work embodies a Disciplined Convex Stochastic Programming formulation that integrates the planning and operation of IMGs using three optimization levels. The first level finds the capacities of the energy sources of the IMG. The second and third levels use a rolling horizon for setting the day-ahead prices or the stimulus of the DSM and the day-ahead optimal dispatch strategy of the IMG, respectively. A case study shows that the Day-Ahead Dynamic Pricing DSM and the Incentive-Based Pricing DSM reduce the total costs and the Levelized Cost of Energy of the project more than the other DSMs. In contrast, the Time of Use DSM reduces the payments of the customers and increases the delivered energy more than the other DSMs.

**Keywords:** Isolated/Islanded Microgrids; planning; operation; Demand-Side Management

#### **1. Introduction**

Despite the efforts of governments around the world, access to electric energy in isolated regions remains a challenge [1,2]. Isolated/Islanded Microgrids (IMGs) could play a significant role in providing power to these areas where extending the utility grid is not economically feasible [3]. The implementation of Demand-Side Management (DSM) in the planning of Microgrids (MGs) reduces total costs, Levelized Cost of Energy (LCOE), and customer payments, or increases renewable energy utilization [4–9]. In this regard, it seems interesting to investigate if the application of DSMs in the planning of IMGs can bring similar benefits. Despite this, there is a paucity of literature exploring how DSMs can affect IMGs' planning and operation.

The implementation of DSM aims to affect the patterns of consumer consumption using direct or indirect strategies [10,11]. Direct strategies are composed of Direct Load Control and Interruptible/Curtailable Programs. In Direct Load Control strategies, there is a remote controller sending signals to customers' appliances, like air conditioners, heating systems, water heaters, or public lighting, on short notice. The signals can turn the appliances on/off, switch tariffs, or inform about current electricity prices. Interruptible/Curtailable Programs offer alternatives as biding programs, Emergency Demand Response (DR) programs, Capacity Market programs, and ancillary services, such as frequency support [12,13]. Indirect DSMs are composed of pricing programs, rebates/subsidies, and education programs. Pricing programs charge dynamic tariffs for energy, which can be power-based, energy-based, or a combination of both [14,15]. Energy-based tariffs incentivize energy conservation, and, therefore, are desired in IMG applications, where the energy generation is limited [16]. Instead of having a fixed flat rate, dynamic fares vary in time to reveal the actual costs of producing energy. These rates include the Time of Use (ToU) rate, Critical Peak Pricing (CPP), Extreme Day Pricing (EDP), Extreme Day Critical Peak Pricing (ED-CPP), Day-Ahead Dynamic Pricing (DADP), and Real-Time Pricing (RTP). Properly designed tariffs motivate the customers to shift their demand to off-peak periods, when the electricity price is lower and it is more convenient to produce electricity [17].

Some works in the literature explore how DSM affects the planning of MGs. Kahrobaee et al. propose a sizing approach to determine the capacity of a Wind Turbine and a Battery Energy Storage System (BESS) for a smart household considering price variations in the tariffs [18]. The authors designed a three-step process combining a rule-based controller, a Monte Carlo approach, and a Particle Swarm Optimization to perform the sizing of the components. However, the uncoordinated combination of multiple stages and the lack of an optimization formulation for energy management can lead to sub-optimal results. Erdinc et al. [19] aimed to address these drawbacks by providing a Mixed Integer Linear Programming (MILP) formulation to design an optimal energy management strategy. The work considers the seasonal and weekly variations in the load profiles in the presence of a Real-Time Pricing tariff scheme. However, it does not consider how to design the DSM itself and how different DSMs will impact the sizing of the energy sources. Kerdphol et al. propose a sizing approach for BESS using Particle Swarm Optimization to improve the frequency stability of an MG [20]. The work integrates a dynamic DSM considering load shedding of non-critical loads to rapidly restore the system frequency and reduce the BESS capacity. A rule-based controller used for the load shedding and a Particle Swarm Optimization formulation used for the sizing of the BESS prove to be adequate to regulate the frequency of the MG. However, the rule-based controller and the lack of forecast models to anticipate the critical events can lead to sub-optimal results.

Nojavan et al. [21] propose a bi-objective Mixed-Integer Non-Linear Programming (MINLP) formulation to optimally site and size a BESS in an MG considering DSM. The authors designed two optimization objectives to reduce total costs and Loss of Load Expectation. The work uses an *-*-constraint method to draw the Pareto optimal curve and a fuzzy satisfying technique to find the best solution. Nevertheless, the authors assume that 20% of the load reacts to a Time of Use (ToU) tariff, ignoring the effects of the demand's self-elasticity. Majidi et al. use a Monte Carlo Scenario reduction technique to determine the size of a BESS in an MG [22]. The work considers the effects of uncertainties in the forecasted renewable generated power and forecasted consumption. However, similarly to [21], the authors do not consider how the customers react to the DSM; they assume that 20% of the load will react to a ToU tariff. Amir et al. [23] propose a combined algorithm to find the size and energy management strategy of a Multi-Carrier Microgrid. The work proposes a mathematical model with high sophistication that uses an MINLP formulation to obtain the optimum dispatch strategy and Genetic Algorithms to obtain the capacities of the energy sources. The work measures the changes in the patterns of consumption of the customers considering varying prices for the different forms of energy. The planning of the Multi-Carrier Microgrid considers demand and price growth over a five-year optimization horizon. Nevertheless, this work does not design the DSM. It only considers the effects of the prices of the energy providers on the Multi-Carrier Microgrid.

Planning of IMGs refers to the set of decisions that the planner must make to design an IMG project. Such decisions include: Setting the energy mix, computing the sizing of the energy sources, and defining the energy dispatch strategy, the economic incentives, and the energy tariffs, amongst others [24–26]. This set of decisions has significant consequences on the performance of IMG projects, where high penetration of renewable energy sources can reduce system inertia, thus challenging

system frequency regulation, control schemes, and transient stability [13]. DSMs can partially solve some of the inherent challenges of planning IMGs.

Chauhan et al. propose to compute the sizing of the energy sources of an IMG considering a DSM that reschedules shiftable loads depending on if it is the winter or summer season [27]. The work uses an Integer Linear Programming (ILP) formulation to find the optimal rescheduling of shiftable loads and a Discrete Harmony Search algorithm to compute the sizing. A considerable drawback of the work is that the DSM only focuses on reducing the peak demand while ignoring maximizing exploitation of renewable energy. Amrollahi et al. combine an MILP formulation and the capabilities of HOMER software to compute the sizing of an IMG composed only of renewable energy sources [28]. Due to the lack of dispatchable energy sources, the authors propose the use of a DSM to reschedule shiftable loads. Rescheduling helps to balance mismatch between electric energy generation and consumption. Mehra et al. propose a work to measure the economic value of applying DSM in the sizing of a nanogrid [29,30]. The work considers the dis-aggregation of electrical demand in critical and non-critical appliances. In addition, the work takes advantage of low-cost computation intelligent devices, such as the "utility-in-a-box" solution, to implement active DSM [31]. The authors use an exhaustive search algorithm to determine the capacities of the Photo-Voltaic (PV) system and the BESS. Nevertheless, the work considers the effects of only one kind of DSM over a small-sized grid.

Prathapaneni et al. propose a multi-objective stochastic sizing algorithm that aims to minimize lifetime costs and degradation of the energy sources [32]. The work considers the effects of a DSM that uses shiftable loads, like electric vehicles or pumped hydro storage in an IMG. The work uses an Accelerated Particle Swarm Optimization (APSO) to compute the sizing of energy sources. Despite considering lifetime costs of the IMG and degradation of energy sources, the work considers a basic DSM over reduced amounts of loads that are not always present in IMG applications. Luo et al. propose a sizing methodology for an IMG using a bi-level optimization algorithm [33]. The first level computes the energy sources' capacities, considering the effects of different combinations of public subsidies for the installation of energy sources. The second level performs the dispatch strategy for the energy sources of the IMG using an MINLP formulation. In the second level of optimization, the authors implement a rescheduling mechanism of shiftable loads. A study case shows that DSM reduces installed capacities of the energy sources for the IMG.

Kiptoo et al., similarly to [28], aimed to implement a DSM to balance generation and electricity demand in an IMG only composed of renewable energy sources [34]. The DSMs consider rescheduling shiftable loads. However, the authors aim to improve the work of [28] by adding an electrical demand forecasting module using a Random Forest (RF) regression forecasting approach. The work shows that the proposed methodology reduces the total costs of the IMG project by 12.41%. Rehman et al. used HOMER software to find capacities of energy sources in an IMG [35]. The work considers a DSM capable of rescheduling shiftable loads and uses Simulink to evaluate the operation of the IMG. The use of Simulink allows the authors to design and test a model predictive control. The model predictive control controls the power during grid-connected operation and regulates load voltage in the islanding operation of the MG. Table 1 summarizes the works found in the literature that deal with the integration of DSM in the planning of IMGs, and that highlight knowledge gaps and the characteristics of the present work. It is vital to notice that Table 1 presents only the articles that consider IMGs because they are strictly related to the present work.

**Table 1.** Summary of the literature review.

Despite that some of the works found in the literature evaluate the effects of DSM in the planning phase of MGs and IMGs, none of them compare the effects of different DSMs using the same test-bench. The works found by authors do not focus on design and impact evaluation of DSM over total costs and operational aspects of IMG projects. Moreover, few of the works consider the financial aspects of the cooperation between private and public capital to fund IMG projects. Additionally, none of them allow defining tariffs that guarantee the sustainability of the IMG project over time. In this regard, the present article aims to fulfill gaps found in the literature review by providing a methodology capable of:

The formulation uses flat, ToU, CPP, DADP, and Incentive-Based Pricing (IBP) tariffs as DSM strategies. It also proposes a Direct Load Curtailment (DLC) strategy that curtails customers' electrical demand if required.

The formulation assumes that the DSMs modify the patterns of consumption of the customers, which will lead to a change in the capacities of energy sources [36–39]. The results of the application of the methodology provide the optimal size of the energy sources, the optimal energy dispatch, the optimal tariffs, the economic incentives, and the load curtailment. The rest of the article proceeds as follows: Section 2 presents the definition of the problem and the proposed solution. Section 3 presents a case study as an example of the application of the methodology, and Section 4 includes its results and analysis. Finally, Section 5 presents the conclusions of the work and future directions.

#### **2. Definition of the Problem and Proposed Solution**

The present work aims to illustrate for planners and policymakers the benefits of applying DSM for IMG planning. For that purpose, the methodology integrates sizing and IMG operation using three different optimization levels, as shown by Figure 1. The first level obtains the sizes of energy sources using a Monte Carlo analysis. The second level uses a day-ahead rolling horizon over the same optimization horizon of the first level to define incentives, tariffs, and load curtailment of each of the strategies of DSM. Finally, the third level simulates the microgrid operation by iterating in the same rolling horizon that the second level uses. The third level performs the simulation to compute the optimal dispatch strategy after weather and demand profiles are known.

The rolling horizon computes one day in advance at each time and rolls over one year. Each day, the second level computes the proper day-ahead DSM stimulus that the third level uses to compute the day-ahead response of the customers. The second level computes these stimuli using day-ahead forecasts of electrical demand. The third level applies the stimulus found in the second level to compute the customers' response. While the first and second level assess the uncertainties in day-ahead forecasts of the demand and in weather variables, the third level assumes perfect knowledge of these variables. This assumption allows the methodology to compute the impacts of errors in forecasts over the DSM performance. The formulation computes the total costs of operation on the third level. Sections 2.1–2.3 present a detailed explanation of each of the levels. Appendix A, present in Table A1 a description of all the variables used in the following sections with their respective names and units.

**Figure 1.** Graphical description of the proposed methodology.

#### *2.1. First Level: Sizing*

The formulation of the first optimization level *a*1 can be stated as:

$$\begin{aligned} J(\mathbf{x}^\*) &= \underset{\mathbf{x}}{\text{minimize}} \quad a\_1(\mathbf{x}, \mathbf{j})\\ \text{subject to} \quad b\_i(\mathbf{x}, \mathbf{j}) &= 0 \; i = 1, \dots, B, \\ c\_i(\mathbf{x}, \mathbf{j}) &\ge 0 \; i = 1, \dots, C \end{aligned} \tag{1}$$

where *x* represents the decision variables, *ξ* represents the uncertainties of the electrical demand, *bi*, *i* = 1, ... , *B* are convex functions in *x* for each value of the random variable *ξ*, and *ci*, *i* = 1, ... , *C* are deterministic affine functions. Since *a*1 ,*bi*, *i* = 1, ... , *B* and *ci*, *i* = 1, ... , *C* are convex on *x*, the definition of Formulation (1) is a convex optimization problem [40] ([41], Chapter 7).

IMG projects can receive funding from public or private capital. To compute the effects of the funding sources over the total costs, profits, and customer payments, the formulation of *a*1 introduces factors *ϕcg*, *ϕci*, *ϕog*, and *ϕoi*, where *ϕci* + *ϕcg* = 1 and *ϕoi* + *ϕog* = 1. The formulation of *a*1 is designed to minimize the Capital Expenditures (CAPEX) and the Operational Expenditures (OPEX) of the IMG. Equations (2)–(10) describe the formulation of *a*1.

$$X\_1 = \underset{C\_{\text{ul}}, E\_{\text{ul}}}{\text{arg min}} \ q\_{\text{cg}} \sum\_{u=1}^{\text{LI}} \mathbb{C}\_{\text{ul}} I\_{\text{ul}} + q\_{\text{og}} \sum\_{t=1}^{T} \sum\_{u=1}^{\text{LI}} (\lambda\_{u,t} + \Lambda\_{u,t}) E\_{u,t} \tag{2}$$

where the CAPEX (*ζ*) and OPEX (*ϑ*) refer to:

$$\mathcal{L} = \sum\_{\nu=1}^{\mathcal{U}} \mathbb{C}\_{\nu} I\_{\nu} \tag{3}$$

$$\theta = \sum\_{t=1}^{T} \sum\_{u=1}^{\mathcal{U}} (\lambda\_{u,t} + \Lambda\_{u,t}) E\_{u,t} \tag{4}$$

and *Cu*, *Iu*, *λu*,*t*, Λ*u*,*t*, and *Eu*,*t* represent the installed capacity, unitary investment cost, unitary dispatch costs, unitary maintenance costs, and dispatched energy by the *u* energy source, respectively.

It is worth noting that the formulation of Equation (2) replaces *minimize* with *argmin*, and assigns the results to the variable *X*1. This replacement occurs because the second and third methodology levels require the values of the decision variables , but not the value of the achieved minimum. The rest of the optimization formulations in the document maintain the replacement.

The proposed formulation considers the energy prices as the only revenue stream for the investors. Equation (5) introduces a constraint to guarantee that the private investors recover their investments and the expected Internal Rate of Return *R*.

$$-\left(\varphi\_{ci}\sharp + \varphi\_{oi}\theta\right)(1+R) + \sum\_{t=1}^{T} \pi\_{\mathfrak{n},t} D\_{f,t} \ge 0\tag{5}$$

where *ϕci* and *ϕoi* represent the percentage of payments of the private investor for the CAPEX and OPEX costs, and *πn*,*t* represents the prices of the *n* tariff. Equation (6) considers the elasticity (*et*) of the customers at a time *t*, the initial price of the energy (*πflat*), and the initial demand (*Do*,*t*) to compute the final demand (*Df* ,*t*). Equation (7) introduces an energy conservation factor Ψ*c* to define how the total energy consumption over the optimization horizon changes after the introduction of DSM. Values of Ψ*c* ≤ 1 decrease the total energy consumption, while values of Ψ*c* ≥ 1 increase the total energy consumption over the optimization horizon. A value of Ψ*c* = 1 indicates that the total energy consumption over the optimization horizon remains constant after the introduction of DSMs.

$$\sigma\_t = \frac{\pi\_{flat}(D\_{f,t} - D\_{o,t})}{D\_{o,t}(\pi\_{n,t} - \pi\_{flat})} \tag{6}$$

$$\sum\_{t=1}^{T} D\_{f,t} - \Psi\_c \sum\_{t=1}^{T} D\_{o,t} = 0 \tag{7}$$

The formulation of *a*1 also includes the energy balance Equation (8), a constraint that limits energy excess (*EEt*), and a constraint that limits the lack of energy (*LEt*), (9) and (10), respectively. Equations (9) and (10) introduce the parameter *z* to control the desired level of reliability in the IMG.

$$\sum\_{t=1}^{T} \sum\_{u=1}^{II} E\_{u,t} - EE\_t + LE\_t - D\_{f,t} = 0 \tag{8}$$

$$\sum\_{t=1}^{T} EE\_t \le (1 - z) \sum\_{t=1}^{T} D\_{f,t} \tag{9}$$

$$\sum\_{t=1}^{T} LE\_t \le (1 - z) \sum\_{t=1}^{T} D\_{f,t} \tag{10}$$

Additionally, the *a*1 formulation includes Equations (14) till (26) in order to evaluate the impact of DSM strategies on the sizing of the IMG (changing the horizon from 24 to 8760 h, respectively).

#### *2.2. Second Level: Setting of Day-Ahead DSM Values*

The formulation of the second optimization level *a*2 solves the following problem:

$$X\_2 = \underset{E\_{\
u, \mathcal{h}}^F, E\_{\mathcal{h}}^F, L E\_{\mathcal{h}}^F}{\text{arg min}} \ \varphi\_{\mathcal{log}} \sum\_{h=1}^{24} \sum\_{u=1}^{1l} \ (\lambda\_{u,h} + \Lambda\_{u,h}) E\_{u,h}^F + \omega E E\_h^F + \omega L E\_h^F \tag{11}$$

$$\text{s.t. } \sum\_{h=1}^{24} \sum\_{u=1}^{lI} E\_{u,h}^F - E E\_h^F + L E\_h^F - d\_{f,h}^F = 0,\tag{12}$$

where *EEF h* and *LEF h* are the 24 day-ahead forecasted energy excess (a non-positive variable) and the forecasted lack of energy (a non-negative unrestricted variable), respectively, and *ω* is a penalization factor. *EF u*,*h* and *dF f* ,*h* represent the 24 day-ahead forecasted dispatch of the *u* energy sources and the 24 day-ahead forecasted electrical demand, respectively.

The formulation of the second optimization level *a*2 uses the capacities *Cu*, the day-ahead forecasts of energy resources *GF h* , and forecasts of electric demand *dF o*,*h* as inputs in order to compute the day-ahead stimulus for the five Γ*n*,*h* DSM strategies. Four of the DSM strategies use *πn* in Equation (5) as an indirect stimulus to modify the customer consumption patterns. Those four DSM strategies are: Time of Use pricing (ToU), Critical Peak Pricing (CPP), Day-Ahead Dynamic Pricing (DADP), and Incentive-Based Pricing (IBP). The last DSM uses a Direct Load Curtailment strategy that sheds a percentage of load when required. The baseline case for comparisons uses a flat tariff and no DSM. The description of the baseline case and each of the DSMs proceeds in the following subsections [42].

#### 2.2.1. Flat Tariff (Baseline Case)

In general terms, the unitary value of a flat tariff is the sum of all the costs of producing the energy divided by the total amount of energy produced [43]. Equation (13) describes the yearly payments using a regular flat tariff.

$$\Theta\_{flat} = \frac{\zeta + \sum\_{t=1}^{T} \theta\_t}{\sum\_{t=1}^{T} D\_{f,t}} (1+R) \sum\_{t=1}^{T} D\_{f,t} \tag{13}$$

However, this traditional approach does not set an optimal tariff to recover investments while minimizing energy costs. Here, we propose the introduction of a decision variable *πflat* into the formulation to find the optimum price for the tariff.

$$\Theta\_{flat} = \pi\_{flat} \sum\_{t=1}^{T} D\_{f,t} \tag{14}$$

#### 2.2.2. Time of Use Tariff

ToU tariffs vary daily or seasonally on a fixed schedule, using two or more constant prices [44]. One of the main benefits of this type of tariff is its stability over long periods, which gives the customer a better ability to adapt to it [45,46]. To create a ToU tariff, the planner must define the number of *Y* blocks and the starting and ending hours of each *y* block [45]. The optimization problem considers the prices *πy* of the *Y* number of blocks as decision variables to be computed. Equation (15) presents the yearly payments using *Y* different block hours of prices.

$$\Theta\_{tou} = \sum\_{t=1}^{T} \sum\_{y=1}^{Y} \pi\_{y} D\_{f,t} \tag{15}$$

The methodology computes the ToU and flat tariffs in the first optimization level *a*1 and the demand response of the customers in the third level *a*3. The second level is not used for the flat tariff and the ToU tariff because they do not have daily variations. The algorithm computes the flat and ToU tariffs following the same process used to find the capacities of the energy sources *Cu*, using adapted versions of Equations (30) and (31).

#### 2.2.3. Critical Peak Pricing

The CPP tariff can be 3 to 5 times higher than the usual tariff, but is allowed only a few days per year [46]. In Equation (16), *πbase* is a scalar variable that is chosen to be equal to the flat tariff *πflat*. *πpeak* is a decision variable of dimension 24 and is computed one day in advance. Equation (16) defines the day-ahead forecasted payments using a CPP tariff, and Equation (17) defines the day-ahead hourly critical peak price.

$$\boldsymbol{\Theta}\_{\rm cpp}^{\rm F} = \boldsymbol{\pi}\_{\rm base} \sum\_{h=1}^{\tau\_{\rm base}} \boldsymbol{d}\_{f,h}^{\rm F,has} + \sum\_{h=1}^{\tau\_{\rm peak}} \boldsymbol{\pi}\_{\rm peak,h}^{\rm F} \boldsymbol{d}\_{f,h}^{\rm F,peak} \tag{16}$$

$$
\pi^{\rm F}\_{\rm cpp,h} = \pi\_{\rm bras} + \pi^{\rm F}\_{\rm peak,h} \tag{17}
$$

A critical forecasted event, such as high demand or low generation capacity, triggers the critical peak price in a CPP tariff. In this regard, the CPP tariff must include a predictor of the critical event and a decision mechanism to set the value of the critical price. The first optimization level formulation *a*1 uses historical data, which implies that the formulation has full knowledge over the optimization horizon (T = 8760 h). The perfect knowledge allows the formulation to state constraint (18), which limits the apparition of the critical price only to a few hours in a year. Equation (18) uses variable *ϕpeak* to control the number of hours with critical price allowed and *δpeak* to define how many times the base price *πbase* is scaled up. The planner defines *ϕpeak δpeak*, and *πbase*, *πpeak*, *τbase*, and *τpeak* are decision variables that the optimization formulation computes.

$$\sum\_{t=1}^{T} \pi\_{peak, t} \le \, \! \! \! \sigma\_{peak} T \delta\_{peak} \, \! \! \pi\_{base} \tag{18}$$

However, in order to simulate the operation of the IMG, the rolling horizon will only know the forecasts one day in advance. The formulation must define a mechanism to determine the conditions that allow the critical peak price to take place. Thus, it defines the critical event as low daily forecasted primary energy resources (lower than a predefined threshold ). The decision mechanism sets the day-ahead value of the critical price using the variable *πF peak*,*h*. Equation (19) describes the mechanism to set the CPPs in the operational phase of the IMG.

$$\pi\_{\text{cpp},\text{lv}}^{\text{F}} = \begin{cases} \pi\_{\text{base}} + \pi\_{\text{peak},\text{lv}}^{\text{F}} & \text{if } \sum\_{h=1}^{24} \mathcal{G}\_{h}^{\text{F}} \le \varrho \\ \pi\_{\text{base}} & \text{otherwise} \end{cases} \tag{19}$$

#### 2.2.4. Day-Ahead Dynamic Pricing

DADP refers to a tariff that is announced one day in advance to customers and has hourly variations. This scheme offers less uncertainty to customers than "hour- ahead pricing" or "real-time pricing," thus allowing them to plan their activities [47,48]. Equation (20) introduces the day-ahead payments under a DADP tariff, using *πF h* as a decision variable vector of dimension 24.

$$\mathfrak{G}\_{dadp}^{\mathrm{F}} = \sum\_{h=1}^{24} \pi\_h^{\mathrm{F}} d\_{f,h}^{\mathrm{F}} \tag{20}$$

#### 2.2.5. Incentive-Based Pricing

The IBP tariff provides discounts in the tariff to the customers to increase the electric energy consumption or an extra fare to penalize it. The planner can decide the IBP base price to be equal to the flat tariff *πflat* to guarantee a constant value each day. Variable *πF inc*,*h* computes the day-ahead hourly incentives and can take positive or negative values. Equation (21) defines the day-ahead payments using the IBP tariff.

$$\Theta\_{\rm inc}^{\rm F} = \sum\_{\rm h=1}^{24} d\_{f,\rm h}^{\rm F} (\pi\_{\rm busc} + \pi\_{\rm inc,h}^{\rm F}) \tag{21}$$

All of the *N* tariffs must have restrictions to avoid null or excessive pricing. Governments, policymakers, or IMG owners can guarantee fair tariffs to the customers with constraint (22).

$$
\pi\_n^{\text{min}} \le \pi\_n \le \pi\_n^{\text{max}} \tag{22}
$$

#### 2.2.6. Direct Load Curtailment Strategy

The DLC strategy curtails a portion *-F h* out of forecasted demand if required. The planner of the IMG decides the percentage of curtailed demand *κ*. The final demand and day-ahead payments are defined as follows:

$$d\_{f,h}^F = d\_{o,h}^F - \epsilon\_h^F \tag{23}$$

$$\boldsymbol{\Theta}\_{\rm dlc}^{\rm F} = \sum\_{h=1}^{24} d\_{f,h}^{\rm F} \pi\_{f\rm lat} \tag{24}$$

The general restrictions for the DLC strategy are defined as follows:

$$
\boldsymbol{\epsilon}\_h^F \le \boldsymbol{\kappa} d\_{f,h}^F \tag{25}
$$

$$\sum\_{h=1}^{24} \epsilon\_h^F \le \kappa \sum\_{h=1}^{24} d\_{f,h}^F \tag{26}$$

#### *2.3. Third Level: Real Operation of the IMG*

The formulation of the third optimization level *a*3 solves the following problem:

*Energies* **2020**, *13*, 3459

$$X\_3 = \underset{E\_{u,h}^R, EE\_h^R, LE\_h^R}{\text{arg min}} \ q\_{\mathcal{O}\mathbb{S}} \sum\_{h=1}^{24} \sum\_{u=1}^{1l} (\lambda\_{u,h} + \Lambda\_{u,h}) E\_{u,h}^R + \omega E E\_h^R + \omega L E\_h^R \tag{27}$$

$$\text{s.t.} \sum\_{h=1}^{24} \sum\_{u=1}^{lI} E\_{u,h}^R - E E\_h^R + L E\_h^R - d\_{f,h}^R = 0,\tag{28}$$

where the formulation computes the real dispatch of energy sources using capacities *Cu*, real energy resources *GR h* , real final electric demand *dR f* ,*h*, and the energy prices *πn* of each DSM in order to compute the real dispatch of the *U* energy sources of the IMG.

In addition to Equations (27) and (28), the formulation of *a*3 must include physical restrictions for all the *U* energy sources used to design the IMG (maximum battery charge and discharge rates, maximum power generator output, amongst others). It is essential to highlight that *EER h* and *LER h* in the third level refer to energy that generators produce in excess and energy that the generators can not provide, respectively. The first level constrains the allowed quantity of excess (Equation (9)) and lack (10) of energy. The second level uses a penalization factor for these variables (Equation (11)). However, the third level is just an accumulator, a counter of these quantities.

#### **3. Case Study**

The case study aims to illustrate the capabilities and performance of the proposed methodology and considers the design of an IMG composed of a PV, a BESS, and a Diesel Generator (DG) System, as Figure 2 shows. The case study assumes that the microgrid can have two different types of load. The case study uses the load type one when the planner chooses a DSM based on price. The load type one has Smart Meters. The case study uses the second type of load when the planner decides to use the DSM based on DLC. The second type of load has a device as "GridShare" to perform the curtailment of the electrical demand [31]. The case study considers six IMG designs: Baseline case (flat tariff and no DSM) and one design for each of the proposed DSM (ToU, CPP, DADP, IBP, DLC). The results of the designs using DSM are compared with the baseline case design. All of the optimization formulation was written in Python 3.7 using the CVXPY 1.0 package [49,50]. The selected solver is MOSEK, due to its flexibility, speed, and accuracy [51,52].

The case study includes a Monte Carlo Sampling (MCS) approach to deal with the uncertainties of the stochastic formulation. The MCS approach builds different scenarios by sampling the Probability Distribution Functions (PDFs) of electrical demand. In order to build scenarios, a pre-processing step fits the historic electrical demand into monthly/hourly PDFs. For simplicity and for the sake of reduction in computational burden, the case study assumes the demand follows a Gaussian process without a covariance matrix. Afterwards, a random sampling process of the monthly/hourly PDFs builds the demand for each sample *s* of the MCS approach. Equation (29) describes the sampling process. Figure 3 shows monthly/hourly fitted distributions using a continuous line to represent the mean and a shaded area to represent the standard deviation.

$$D\_t|m\_\prime h \sim f(\psi\_{m\_\prime h})\tag{29}$$

In Equations (2), (11) and (27), *X*1, *X*2, and *X*3 represent the *S* solutions of minimizing *a*1, *a*2, and *a*3, respectively. The *Cu* capacities of the energy sources selected for the IMG in the first level must supply 95% of the *S* electrical demands with *z* level of reliability (as defined by Equation (10)). A post-processing step fits the *Cu* results to a PDF *φu*, and obtains the Cumulative Distribution Function (CDF) Φ*u*. The evaluation of the inverse of the CDF Φ*u* at 0.95 provides the values of energy source capacities *Cu*. These values will supply electrical demand with the desired reliability level 95% of the time (95% of all the scenarios).

$$
\Phi\_{\rm u} = \int\_{-\infty}^{\infty} \phi\_{\rm u} d\mathcal{C}\_{\rm u} \tag{30}
$$

$$\mathbb{C}\_{\mu} = \Phi\_{\mu}^{-1}(0.95) \tag{31}$$

**Figure 2.** Architecture of the islanded/isolated microgrid of the case study.

**Figure 3.** Fitting of the electrical demand.

#### *Geographic and Weather Conditions of the Case Study*

The case study is located at longitude 77 16 8 West and latitude 5 41 36 North (Nuquí, Colombia). The study case uses the Meteonorm database of the PvSyst software to obtain the Global Horizontal Radiation (GHI) and temperature conditions of the geographical region. Additionally, the study case uses Homer Pro software to obtain a standard community electrical demand. The standard community electrical demand that Homer Pro provides has hourly steps over a one-year horizon. Figure 4 shows the historic yearly standard profile of the electrical demand that Homer Pro provides. Figure 5 shows the yearly GHI. Figure 6 shows the yearly temperature.

**Figure 4.** Yearly electrical demand.

**Figure 6.** Yearly temperature.

The Monte Carlo Sampling analysis shown in Equation (29) builds the scenarios for the stochastic analysis using the standard community electrical demand obtained from Homer Pro (shown in Figure 4) and a scale factor of 20. The cost of diesel used for the optimization is 0.75 USD/liter. The case study takes the Diesel Generator model from [53], the PV system model from [54–56], and the BESS model from [57]. Table 2 summarizes the unitary installation and maintenance costs of the equipment obtained from regional providers. The values assigned to *πn*,*min* and *πn*,*max* in constraint (22) are 0 USD/kWh, and two times the price of the current flat tariff of urban areas in Colombia, 0.34 USD/kWh, respectively [58].

**Table 2.** Unitary system costs for simulations.

Additionally, the methodology takes as inputs the values of Ψ*c*, *e*, *ϕcg*, *ϕci*, *ϕog*, *ϕoi*, *ω*, *κ*, *GH h* , *Iu*, *λu*, Λ*u*, and *S*. Planners or policymakers can decide these values or perform sensitivity analyses over each of them. Table 3 shows the values used for simulations in this work. The following section uses the MCS approach and the inputs of Table 3 to compute the results and for the case study.

**Table 3.** Values of the input parameters for the simulations.

#### **4. Results and Analysis**

The case study aims to evaluate the effects of five different DSMs over the optimization results of the proposed formulation. The five considered DSMs are ToU, CPP, DADP, IBP, and DLC. The study case evaluates different aspects of the effects of the DSMs. Section 4.1 shows the average of each of the tariffs and the curtailment of the DLC strategy. Section 4.2 shows the effects of the DSMs over the sizing of the energy sources of the IMG. Section 4.3 aims to analyze the impacts of the DSMs over the economic aspects of the microgrid. This section analyzes the impacts of DSMs over total costs, profits of private investors, customer payments, and LCOE. Additionally, the section considers the delivered energy and fuel consumption. Section 4.4 presents the effects of the forecast errors over the operation of the IMG. Section 4.5 presents percentage variations in crucial indicators as total cost of the project and LCOE between the first and the third optimization levels. Finally, Section 4.6 shows a comparison of the performance of all the DSMs.

#### *4.1. Demand Side Management Analysis*

Each of the Γ*n* DSM strategies uses a different stimulus to modify customer consumption patterns. Γ*ToU*, Γ*CPP*, Γ*DADP*, and Γ*IBP* use tariffs as an indirect stimulus to modify those patterns. Figure 7 shows the average daily stimulus and the Standard Deviation (STD) of the DSMs. The lines represent daily averages of the DSM strategies, and shaded area represents STDs.

**Figure 7.** Daily average price of the selected tariffs.

Figure 7 presents energy prices. It is interesting to notice that IBP and DADP tariffs reduce the energy price in the middle of the day. The reduction occurs due to the presence of photovoltaic generation in the IMG. IBP and DADP DSMs incentivize customers to increase energy consumption when it is cheaper to generate electric energy.

The Γ*DLC* DSM curtails a percentage of the demand. Figure 8 shows the daily average of the curtailed values in a continuous line and the STD of the curtailed energy in a shaded area.

**Figure 8.** Daily average load curtailment for the Γ*DLC* DSM.

The stimulus introduced by DSM strategies modifies customers' consumption patterns. Using Equation (6) and the stimulus computed using Equations (15)–(26), it is possible to compute the demand response. Figure 9 shows the demands after the application of DSM. The lines represent daily averages of the electrical demand, and shaded area represents the STDs.

**Figure 9.** Daily average load for each of the DSMs and the base case.

It is interesting to note in Figure 7 that the IBP rate tends to be similar to the DADP rate. Therefore, it produces similar effects over electrical demand (see Figure 9). The lack of hourly restrictions on the appearance of the incentive of the IBP tariff causes this to occur. However, the design of hourly restrictions will rely on the experience of the IMG planner, which may ultimately lead to sub-optimal results.

#### *4.2. Sizing Analysis*

The variations in the customers' consumption patterns modify the IMG sizing. Figure 10 presents the variations in the sizing of the Diesel Generator, the photovoltaic system, and the BESS for the five DSMs.

**Figure 10.** Comparison of the sizing of the energy sources for the DSM against the base case. Diesel Generator and photovoltaic capacities are in kW, and the Battery Energy Storage System (BESS) capacity is in kWh.

On the one side, Figure 10 shows that ToU- and IBP-based DSMs require less installed capacity than the other alternatives. On the other side, Figure 10 shows that DLC and CPP DSMs do not considerably reduce the energy sources' installed capacities. However, reductions in installed capacities do not necessarily mean that one DSM is better than others. The following sections contribute with different analyses to determine which of the DSMs can be more suitable for IMG applications.

#### *4.3. Economic Analysis*

The DSM introduction in the IMG planning modifies total costs, investors' profits, customers' payments, total delivered energy, and LCOE, among others. Equations (32)–(36) present how to compute these values, and Figure 11 shows the results for the five DSM strategies and the base case.

$$\text{Total costs} = \zeta + \vartheta \tag{32}$$

$$\text{Profits} = \sum\_{t=1}^{T} \pi\_{n,t} D\_{f,t} - \left(\varphi\_{ci}\zeta + \varphi\_{oi}\vartheta\right) \tag{33}$$

$$\text{Payments} = \sum\_{t=1}^{T} \pi\_{n,t} D\_{f,t} \tag{34}$$

$$\text{Energy} = \sum\_{t=1}^{T} D\_{f,t} - |EE\_{f,t}| - |LE\_{f,t}| \tag{35}$$

$$\text{LCOE} = \frac{\text{Energy}}{\text{Total costs}} \tag{36}$$

**Figure 11.** Comparison of the costs and the Levelized Cost of Energy (LCOE) of the five DSMs against the base case.

#### *4.4. Assessment of the Impact of Forecast Errors*

In the operational stage of the IMG, the proposed formulation computes the DSM stimulus using day-ahead load forecasts. Instead of using a particular method to perform the forecasts, the approach adds Gaussian noise to the real demand to build the forecasted demand, as is stated by Equations (37) and (38). This approach allows measurement of the impact of forecast errors over the final results in the third stage (after knowing the real values of the load).

$$
\Delta \nu \sim \mathcal{N}(\mu, \sigma^2) \tag{37}
$$

$$d\_h^F = d\_h^R \nu$$

Thus, this section presents a sensitivity analysis of the impact of forecast errors. By computing the simulations again, considering forecast errors of 0%, 5%, 10%, and 15%, this approach computes forecast errors using the Mean Absolute Percentage Error. Table 4 relates the percentage of error with the STD used in Equation (37).

**Table 4.** input parameters for simulations.

It is significant to notice that the reported errors correspond to the average error for all the forecasts of all the simulated scenarios. In the 0% error case, the forecasted demand values are equal to the real values *dF h* = *dR h* . The case study found that the methodology is unable to compute the day-ahead stimulus of the DSMs when the forecast errors are near to 20% (*σ*2 = 0.2512).

Figure 12 shows that the impact of the forecast errors in the total costs, the delivered energy, the investors' profits, the customers' payments, and the LCOE is not significant. The variation between the case with perfect forecasts and 15% error in the forecasts is less than 1%. The DADP tariff presents the highest variation in profits and payments of the customers, which drop 1% as compared to the case where the forecast errors are zero.

**Figure 12.** Effects of the forecast errors over the main results. (**a**) Forecast errors effects for a Critical Peak Pricing (CPP) DSM. (**b**) Forecast errors effects for a Day-Ahead Dynamic Pricing (DADP) DSM. (**c**) Forecast errors effects for an Incentive-Based Pricing (IBP) DSM. (**d**) Forecast error effects for a Direct Load Curtailment (DLC) DSM.

#### *4.5. Assessment of the Relation between the First and Third Optimization Levels*

This article presents the design of a methodology to compute the effects of five different DSMs over the sizing of IMGs. However, in order to calculate the energy sources' capacities, only the first optimization level of the proposed methodology is required. The second and the third optimization level formulations evaluate the performance of the IMG once it is in operation. Figure 13 reveals the percentage variations between the results from the first and third optimization levels for the five DSMs and the base case.

The first level of the proposed methodology uses a scenario approach built upon historical data and considers an optimization horizon of one year. The second and third levels use a scenario approach built upon forecasts to predict DSMs and consider a rolling horizon with an optimization horizon of one day over a year. Figure 13 presents the comparison between the average results from the first and third levels when the error in the forecasts is 10%. The extra costs, payments, and LCOE, as well as the reductions in profits and payments, are the result of the change of the optimization horizons and the use of historical instead of forecast data. Planners can also compute percentage variations between the first and third levels for different forecast errors and can utilize trends in percentage variations of each of the values to avoid executing the second and third levels of the methodology. Just by executing the first level and considering the percentages' variations in their calculations will be enough to estimate the total costs of the IMG project.

**Figure 13.** Percentage differences between the results of the first level and the third level for the five DSMs and the base case.

#### *4.6. Performance Comparison of the Five DSMs*

The five DSMs have different performance in different aspects. Equation (39) is adopted to measure the performance of each of the DSMs.

$$\text{Performance} = \frac{\text{worst} - \text{current}}{\text{worst} - \text{best}} \tag{39}$$

Figure 14 shows that DADP and IBP tariffs perform better than the other DSMs. However, these rates require announcing energy prices one day in advance, so customers reorganize their consumption daily. In the context of IMG, hourly variations of the tariffs might not be the best option in some scenarios. In those scenarios, a ToU tariff or CPP tariff can give a satisfying solution as well.

**Figure 14.** Performance comparison of the base case and the five DSMs

#### **5. Conclusions**

The present work proposes a methodology to design and evaluate five DSMs in the planning and operation of IMGs. The methodology allows determination of the optimal size, optimal energy dispatch strategy, and optimal stimulus for the DSMs using a Disciplined Convex Stochastic Programming approach. The work designs and evaluates the effects of the five DSMs using one case study as a test-bench, which makes this work the first attempt to do so in the literature known by the authors.

The proposed methodology can help policymakers design proper regulations for IMG projects that consider the social conditions of customers and private investors. Additionally, the methodology can be useful for IMG planners or entrepreneurs that want to build profitable business models providing energy to isolated communities. In this regard, the methodology allows policymakers to:

Additionally, the methodology allows IMG planners or entrepreneurs to:

The methodology can provide the benefits mentioned above to its users if the assumptions that it was built upon are fulfilled. In this regard, by sharpening the assumptions, the methodology will adapt better to the conditions of IMG projects. Considering more energy sources, sophisticated models of customer elasticities, and demand response models adapted to local conditions, among others, will improve the methodology as well.

Finally, it is essential to highlight the technical characteristic of the present study, which aims to inform planners and policymakers about the benefits of applying DSMs in the planning of IMGs. However, policymakers should perform comprehensive social and behavioral studies to evaluate the potential of acceptance of price-based or direct load curtailment DSMs in the context of IMGs.

**Author Contributions:** Conceptualization, J.C.O.C.; Formal analysis, J.C.O.C.; Funding acquisition, G.O.-P.; Investigation, J.C.O.C.; Methodology, J.C.O.C., R.R., C.D., J.S., and D.H.; Project administration, G.O.-P.; Software, J.C.O.C.; Supervision, C.D.-G. and J.S.; Validation, J.C.O.C., R.R., J.S., and D.H.; Writing—original draft, J.C.O.C.; Writing—review and editing, J.C.O.C., R.R., Cesar Duarte, J.S., and Daniel Hissel. All authors have read and agreed to the published version of the manuscript.

**Funding:** Administrative Department of Science, Technology, and Innovation (Departamento Administrativo de Ciencia, Tecnología e Innovación)-COLCIENCIAS, Contracts No. 80740-191-2019 and FP44842-450-2017 (ECOS-NORD).

**Acknowledgments:** The authors wish to thank the Department of Electrical, Electronics, and Telecommunications Engineering (Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones) of the Vice-Rectorate for Research and Extension (Vicerrectoría de Investigación y Extensión) from the Universidad Industrial de Santander (Project 8593).

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **Appendix A**

**Table A1.** Variable declaration.

**Table A1.** *Cont*.

#### **References**

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

### *Article* **A Virtual Tool for Load Flow Analysis in a Micro-Grid**

**Giovanni Artale 1, Giuseppe Caravello 1, Antonio Cataliotti 1, Valentina Cosentino 1, Dario Di Cara 2,\*, Salvatore Guaiana 1, Ninh Nguyen Quang 3, Marco Palmeri 1, Nicola Panzavecchia 2 and Giovanni Tinè 2**

Received: 29 May 2020; Accepted: 16 June 2020; Published: 18 June 2020

**Abstract:** This paper proposes a virtual tool for load flow analysis in energy distribution systems of micro-grids. The solution is based on a low-cost measurement architecture, which entails low-voltage power measurements in each secondary substation and a voltage measurement at the beginning of the medium voltage (MV) feeder. The proposed virtual tool periodically queries these instruments to acquire the measurements. Then, it implements a backward–forward load flow algorithm, to evaluate the power flow in each branch and the voltage at each node. The virtual tool performances are validated using power measurements acquired at the beginning of each MV feeder. The uncertainties on each calculated quantity are also evaluated starting from the uncertainties due to the used measurement instruments. Moreover, the influence of the line parameter uncertainties on the evaluated quantities is also considered. The validated tool is useful for the online analysis of power flows and also for planning purposes, as it allows verifying the influence of future distributed generator power injection. In fact, the tool is able to off-line perform the load flow calculation in differently distributed generation scenarios. The micro-grid of Favignana Island was used as a case study to test the developed virtual tool.

 Introduction**

The growing demand to increase the percentage of renewable energy and reduce diesel consumption led the distributor system operator (DSO) of micro-grids, as those of small islands, to carry out an analysis in order to verify the safety management of the power grid and to redesign it in case it does not satisfy the grid constraints. In such islands, several issues arise in terms of power system safe operation and planning [1–7], considering the specific characteristics of these kinds of distribution networks, which are relatively small, with a high variability between the winter and summer loads and not always sufficiently covered by public communication infrastructures. Apart from actual energy policies and regulatory frameworks, or technical capabilities enabled by advanced modeling and analysis tools, an important issue for effectively increasing the distributed generation and storage systems presence in distribution networks is the possibility for DSOs to achieve new simple and versatile tools for power system monitoring and management purposes. These tools have to be based on proper communication and measurement infrastructures, which should be feasible for DSOs themselves, in terms of low cost, flexibility and expandability features, in order to allow

their development starting from the existing instrumentation and equipment typically employed in such networks.

Several papers can be found in the literature concerning the measurement and communication technologies in distribution systems. For example, in [8–12], a wide overview is given of measurement technologies and architectures for the smart distribution grids, including metering and communication infrastructures. For distribution networks, especially those of isolated islands, supervisory control and data acquisition (SCADA) systems are typically employed for monitoring, protection and control purposes. As regards measurement instrumentation, several kinds of equipment are considered, such as smart meters and sensors, power quality analyzers, phasor measurement units (PMUs) and micro-PMUs (μPMUs), and so on, which can be more or less suitable, depending on the considered distribution system management applications and the particular characteristics of the considered network. In particular, many recent researches have been focused on PMUs and μPMUs for distribution network monitoring, control and diagnostic applications [13–19]. However, such solutions can be unsuitable for small island micro-grids, because power lines are short and/or the intrinsic costs of such instrumentation are high. To reduce the installation costs, some authors propose to use a few measurement points and to integrate them with load estimations [20–27]; however, when dealing with load estimations (or pseudo-measurements), higher uncertainty levels are generally expected and more sophisticated algorithms can be needed for the distribution system state's estimation, which also may entail higher computational costs. The integration of differently distributed measurement solutions have also been investigated, for example, considering the possibility of smart meter and power quality meter exploitation or SCADA- and PMU-enhanced integration, for a number of applications (load forecasting, optimization, demand side management, fault detection and so on) [28–40]. If the application of such solutions is envisaged for small distribution networks, such as those addressed in this paper, the main problems are related to the processing of algorithms' accuracy and complexity, considering the reasonable computational capabilities of the DSOs control centers. Another fundamental element to enable network observability is the communication between these measurement devices and the control room of the micro-grid. Different solutions can be used for this purpose: optic fiber, power line communications, GSM, wireless and so on. The different communication solutions must be compared in terms of cost, reliability, security, environmental impact and power quality effects [41–47], considering also their availability and suitability in islanded micro-grids.

In summary, the main issues to apply these technologies in the case of small islanded grids are:

In this paper, these aspects are considered, for proposing solutions especially tailored for the case of an island's distribution network. The basic aim of this work was the development of a feasible tool for load flow analysis and power system planning, based on a low-cost distributed measurement system. The proposed solution has been implemented on-field, on the real distribution network of the Island of Favignana (Italy, Mediterranean Sea). To fully investigate the suitability of the proposed solution, it has to be characterized by the means of an uncertainty analysis, considering both the real measurement data and the network parameters uncertainty propagation on the power flow estimations. Experimental results are presented to validate the algorithm and verify its capability to evaluate in real time the power flows with good accuracy. Furthermore, off-line simulations based on real measurement data have been carried out, showing how the proposed virtual tool is also useful to study the impact of distributed generation in an isolated network. The proposed solution allows addressing

all the aforementioned issues in terms of reduced costs, thanks to the use of low-cost instrumentation communication infrastructures, without affecting the capability for the real-time evaluation of the power flows and to plan the network improvement, avoiding critical situations due to the distributed generation and loads variability.