Tuglie and Torelli [21] developed a new load following dispatch algorithm that correlates system imbalances with unbalanced transaction in a bilateral transaction‐based market. The developed algorithm is implemented on the IEEE 30‐bus test system under a variety of operating conditions. In Bizon [22], a hybrid power source comprising wind energy con‐ version system, solar Photovoltaic system, and fuel cell system with energy storage system is designed and optimized for load‐following dispatch strategy. The battery/supercapaci‐ tor hybrid energy storage system operates as an auxiliary source for supplying the power deficit based on dynamic balance strategy. An optimal energy management system for a stand‐alone wind turbine/photovoltaic/hydrogen/battery hybrid system with supervisory control based on fuzzy logic is presented in Pablo et al [23]. The energy management sys‐ tem in Ref. [23] uses a fuzzy logic control to satisfy the energy demanded by the load and maintain the state‐of‐charge of the battery and the hydrogen tank level between desired tar‐ get margins, while trying to optimize the utilization cost and lifetime of the energy storage system. A new method to model and control the aggregated power demand from a popula‐ tion of thermostatically controlled load, with the goal of delivering ancillary services such

**2. Cycle‐charging and load‐following dispatch strategy**

utilized in this study [19, 20].

excess is used to charge the battery [7].

respectively.

An autonomous electric power system is one that is not connected to the utility for one or all of the reasons given in the last paragraph. Wind and solar resources are local energy resources that can be efficiently and economically harnessed to provide electric power to remote site electricity consumers. While the cost of such renewable resources are cost‐free, but the system required for harnessing and processing the energy plus the balance of sys‐ tem (BOS) is expensive. However, the system cost of wind and solar energy systems have been continuously decreasing because of the increase in the acceptance and deployment of the energy systems based on renewable resources. For the many Africa people who do not have access to modern energy system, it has been proven that high‐quality electric power can be delivered to remote areas using local energy resources such as wind, solar, biomass, and so on [4–6].

Many of the historical technological advantages that resulted in AC power system to domi‐ nate over DC power systems are not valid any longer. For example, in the electric power gen‐ eration sector, many distributed energy resources, such as electrochemical storage systems, fuel cells system, and photovoltaic systems, produce efficient and economical DC power. Many of the modern electrical and electronic loads, as well as energy storage systems, are either internally DC power operated or worked equally well with DC power sources and connect to the AC systems through power electronic converters [7]. Overall improved sys‐ tem efficiency, reduced system cost, increased reliability, and reduced system footprint are attained when multiple conversion stages are eliminated in externally operated AC power system for internally operated DC power devices. Also, many power quality issues, such as harmonics and unbalances, are not present in DC power systems [8, 9]. Advancements in power electronic technology continue unabated, leading to more applications in modern systems such as VSC‐HVDC, electric vehicles, wireless power transfer, fuel cells vehicles, and so on [10, 11].

The design of hybrid renewable energy systems has been extensively studied, and numer‐ ous optimization techniques, such as genetic algorithm (GA), linear programming, etc., have been implemented for optimum economic and technical feasibility [12–16]. Many software packages, such as HOMER Pro [9], RETScreen [17], and Hybrid2 [18], have been devel‐ oped for the proper selection of appropriate generation technologies and capacity sizing. This software makes a multi‐objective optimization process easy to carry out to arrive at a robust and reliable decision. HOMER Pro is user‐friendly software produced by the national renewable energy laboratory by the department of energy in the USA. It uses hourly data for the assessment of hybrid renewable energy systems and performs optimization based on net present cost (NPC). HOMER Pro is used in this study because of its proven ability to design, model, simulate, and perform sensitivity analysis of complex mix of different energy technologies, thermal and electrical load, and storage devices. Both cycle‐charging and load‐following dispatch strategies are available to choose from or use simultaneously as utilized in this study [19, 20].

The rest of the chapter is organized as follows. A brief discussion of two different dispatch strategies used in hybrid energy systems is provided in Section 2 of this chapter. All the energy system components of the studied autonomous hybrid AC/DC microgrid system are briefly discussed in Section 3. Section 4 explains the capability and functionalities of Hybrid Optimization Model of Electric Renewable (HOMER) as powerful software that is designed and optimized for modeling, simulating, optimizing, and performing sensitivity analysis of micropower systems. The system model and simulation process of the studied hybrid sys‐ tem is comprehensively detailed in Section 5 of this chapter. The system simulation results and discussion and conclusion are given in the penultimate and Section 7 of this chapter, respectively.

## **2. Cycle‐charging and load‐following dispatch strategy**

economic viability of such action infeasible. Distributed generation technology based on diesel generators has often been considered as a viable solution but the sky‐rocketing of diesel fuel price and the increasing cost of delivery to remote sites have called for providing a sustainable solution that is environmentally friendly, economical, affordable, and easily accessible. To this end, the use of locally available energy resource has been accepted as a sustainable solution in providing electricity for rural and remote settlements. Matching the consumer demand profile and renewable energy production always has been perceived as enormous problem but can be mitigated by incorporating adequate sized energy storage

An autonomous electric power system is one that is not connected to the utility for one or all of the reasons given in the last paragraph. Wind and solar resources are local energy resources that can be efficiently and economically harnessed to provide electric power to remote site electricity consumers. While the cost of such renewable resources are cost‐free, but the system required for harnessing and processing the energy plus the balance of sys‐ tem (BOS) is expensive. However, the system cost of wind and solar energy systems have been continuously decreasing because of the increase in the acceptance and deployment of the energy systems based on renewable resources. For the many Africa people who do not have access to modern energy system, it has been proven that high‐quality electric power can be delivered to remote areas using local energy resources such as wind, solar, biomass,

Many of the historical technological advantages that resulted in AC power system to domi‐ nate over DC power systems are not valid any longer. For example, in the electric power gen‐ eration sector, many distributed energy resources, such as electrochemical storage systems, fuel cells system, and photovoltaic systems, produce efficient and economical DC power. Many of the modern electrical and electronic loads, as well as energy storage systems, are either internally DC power operated or worked equally well with DC power sources and connect to the AC systems through power electronic converters [7]. Overall improved sys‐ tem efficiency, reduced system cost, increased reliability, and reduced system footprint are attained when multiple conversion stages are eliminated in externally operated AC power system for internally operated DC power devices. Also, many power quality issues, such as harmonics and unbalances, are not present in DC power systems [8, 9]. Advancements in power electronic technology continue unabated, leading to more applications in modern systems such as VSC‐HVDC, electric vehicles, wireless power transfer, fuel cells vehicles, and

The design of hybrid renewable energy systems has been extensively studied, and numer‐ ous optimization techniques, such as genetic algorithm (GA), linear programming, etc., have been implemented for optimum economic and technical feasibility [12–16]. Many software packages, such as HOMER Pro [9], RETScreen [17], and Hybrid2 [18], have been devel‐ oped for the proper selection of appropriate generation technologies and capacity sizing. This software makes a multi‐objective optimization process easy to carry out to arrive at a robust and reliable decision. HOMER Pro is user‐friendly software produced by the national

systems [2, 3].

300 System Reliability

and so on [4–6].

so on [10, 11].

Two system dispatch strategies are employed in HOMER Pro namely: cycle‐charging and load‐following dispatch strategy. Under the load‐following dispatch strategy, a power gen‐ erator produces only enough to serve the load and does not charge the battery bank. For the cycle‐charging dispatch strategy, the generator run at full power to serve the load and any excess is used to charge the battery [7].

Tuglie and Torelli [21] developed a new load following dispatch algorithm that correlates system imbalances with unbalanced transaction in a bilateral transaction‐based market. The developed algorithm is implemented on the IEEE 30‐bus test system under a variety of operating conditions. In Bizon [22], a hybrid power source comprising wind energy con‐ version system, solar Photovoltaic system, and fuel cell system with energy storage system is designed and optimized for load‐following dispatch strategy. The battery/supercapaci‐ tor hybrid energy storage system operates as an auxiliary source for supplying the power deficit based on dynamic balance strategy. An optimal energy management system for a stand‐alone wind turbine/photovoltaic/hydrogen/battery hybrid system with supervisory control based on fuzzy logic is presented in Pablo et al [23]. The energy management sys‐ tem in Ref. [23] uses a fuzzy logic control to satisfy the energy demanded by the load and maintain the state‐of‐charge of the battery and the hydrogen tank level between desired tar‐ get margins, while trying to optimize the utilization cost and lifetime of the energy storage system. A new method to model and control the aggregated power demand from a popula‐ tion of thermostatically controlled load, with the goal of delivering ancillary services such as frequency regulation and load following, is developed by Callaway [24]. It is shown in the paper that identified models perform only marginally better than the theoretical model. Subho and Sharma [25] developed a hybrid system with cycle charging dispatch strategy using swarm optimization algorithm for a remote area in India. A comparative study of par‐ ticle swarm optimization (PSO), genetic algorithm, and HOMER is performed in Ref. [25]. PSO is judged to be better than GA and HOMER in terms of the minimum cost of electricity generation. In another paper by Subho and Sharma [26], different optimization algorithms and software packages are used to evaluate the economics of a hybrid renewable energy sys‐ tem. It is concluded that cycle charging strategy is most cost‐effective compared to the load following and peak shaving dispatch strategies.

The insolation intensity is strongly related to the solar cell current, and the cell operating temperature is inversely proportional to the output voltage across the solar cell. These factors

Techno-Economic Feasibility Study of Autonomous Hybrid AC/DC Microgrid System

*PV YPV I* \_\_*T I S*

Where fPV is the PV derating factor, YPV is the rated capacity of the PV array (kW), IT is the global

A generic flat plate PV system is selected for the modeled hybrid microgrid from the HOMER Pro components library with a rated capacity of 40 kW. The capital cost of the PV is \$3000/kWp,

A blowing wind consists of kinetic energy carried by the atmospheric air. The moving air is converted to rotational kinetic energy by the rotor blade of the wind turbine system. The rotating rotor is coupled via a solid shaft to an electrical generator to generate AC electric power. The extraction of the power contained in the moving is limited by the aerodynamic

The theoretically generated turbine power limit of which is 59% is known as the Betz limit. Most of the modern wind turbines are practically in the 30–40% range. Equation 1 below gives the relationship between the extracted power and other parameters and variable of a wind

the standard amount of radiation used to rate the capacity of the PV array given as 1 kW/m2

solar radiation (beam plus diffuse) incident on the surface of the PV array (kW/m2

replacement cost of \$2000, and operation and maintenance cost of \$10.00/year.

(1)

http://dx.doi.org/10.5772/intechopen.69582

), and IS is

.

303

basically limit the maximum power that can be generated by the solar cell [30]. Homer Pro calculates the power output of the PV array using equation 1 below.

*PPV* = *f*

**3.2. Wind energy conversion system**

efficiency of the rotor blade as illustrated in **Figure 2**.

**Figure 2.** Wind energy conversion system (WECS) adopted from Ref. [31].

Both dispatch strategies are employed in this study to determine which is economically viable and technically feasible.

## **3. Energy system components**

For the considered autonomous electric power system model in this study, all the components and energy resources involved are briefly discussed. The components related to this work are Solar PV, wind energy conversion system (WECS), electrochemical battery storage device, and bidirectional power electronics converter.

## **3.1. Solar PV energy system**

Solar PV technology uses semiconductor material, such as silicon, to convert solar radia‐ tion energy to direct current (DC) electrical power. The generated DC power is regulated by charge regulator to charge electrochemical battery storage device. The electrochemical stor‐ age device supplies power directly to the electrical load if it is a DC load. If not, an inverter is used to convert the DC power supplied by the electrochemical storage device into an AC power for the AC load.

PV cell is usually modeled using a single diode or double diodes, but a single‐diode model is shown in **Figure 1**. Series and shunt resistances represented in the figure are used to rep‐ resent the leakage current and the inherent loss due to internal electrical connection, respec‐ tively [27–29].

**Figure 1.** Single‐diode model of solar cell.

The insolation intensity is strongly related to the solar cell current, and the cell operating temperature is inversely proportional to the output voltage across the solar cell. These factors basically limit the maximum power that can be generated by the solar cell [30].

Homer Pro calculates the power output of the PV array using equation 1 below.

$$P\_{pv} = f\_{pv} Y\_{pv} \frac{I\_r}{I\_s} \tag{1}$$

Where fPV is the PV derating factor, YPV is the rated capacity of the PV array (kW), IT is the global solar radiation (beam plus diffuse) incident on the surface of the PV array (kW/m2 ), and IS is the standard amount of radiation used to rate the capacity of the PV array given as 1 kW/m2 .

A generic flat plate PV system is selected for the modeled hybrid microgrid from the HOMER Pro components library with a rated capacity of 40 kW. The capital cost of the PV is \$3000/kWp, replacement cost of \$2000, and operation and maintenance cost of \$10.00/year.

#### **3.2. Wind energy conversion system**

as frequency regulation and load following, is developed by Callaway [24]. It is shown in the paper that identified models perform only marginally better than the theoretical model. Subho and Sharma [25] developed a hybrid system with cycle charging dispatch strategy using swarm optimization algorithm for a remote area in India. A comparative study of par‐ ticle swarm optimization (PSO), genetic algorithm, and HOMER is performed in Ref. [25]. PSO is judged to be better than GA and HOMER in terms of the minimum cost of electricity generation. In another paper by Subho and Sharma [26], different optimization algorithms and software packages are used to evaluate the economics of a hybrid renewable energy sys‐ tem. It is concluded that cycle charging strategy is most cost‐effective compared to the load

Both dispatch strategies are employed in this study to determine which is economically viable

For the considered autonomous electric power system model in this study, all the components and energy resources involved are briefly discussed. The components related to this work are Solar PV, wind energy conversion system (WECS), electrochemical battery storage device,

Solar PV technology uses semiconductor material, such as silicon, to convert solar radia‐ tion energy to direct current (DC) electrical power. The generated DC power is regulated by charge regulator to charge electrochemical battery storage device. The electrochemical stor‐ age device supplies power directly to the electrical load if it is a DC load. If not, an inverter is used to convert the DC power supplied by the electrochemical storage device into an AC

PV cell is usually modeled using a single diode or double diodes, but a single‐diode model is shown in **Figure 1**. Series and shunt resistances represented in the figure are used to rep‐ resent the leakage current and the inherent loss due to internal electrical connection, respec‐

following and peak shaving dispatch strategies.

and technically feasible.

302 System Reliability

**3.1. Solar PV energy system**

power for the AC load.

**Figure 1.** Single‐diode model of solar cell.

tively [27–29].

**3. Energy system components**

and bidirectional power electronics converter.

A blowing wind consists of kinetic energy carried by the atmospheric air. The moving air is converted to rotational kinetic energy by the rotor blade of the wind turbine system. The rotating rotor is coupled via a solid shaft to an electrical generator to generate AC electric power. The extraction of the power contained in the moving is limited by the aerodynamic efficiency of the rotor blade as illustrated in **Figure 2**.

The theoretically generated turbine power limit of which is 59% is known as the Betz limit. Most of the modern wind turbines are practically in the 30–40% range. Equation 1 below gives the relationship between the extracted power and other parameters and variable of a wind

**Figure 2.** Wind energy conversion system (WECS) adopted from Ref. [31].

energy conversion system. The wind speed is strongly coupled to the available power, whereas the power coefficient depends on the tip speed ration (TSR) and the blade pitch angle [10, 16].

$$P = \frac{1}{2} A \rho \mathbb{C}\_p V^3 \tag{2}$$

for various applications. Among the operational parameters of Lead‐Acid battery, maximum state of discharge (DOD), minimum state of charge (SOC), cycle times, round trip efficiency, maximum charge rate, maximum discharge rate are the most important. This battery technol‐ ogy also needs regular maintenance and should be well ventilated especially if it is not the

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305

A generic 1 kWh lead‐acid battery is selected from the Homer Pro library for the hybrid microgrid presented in this study. The nominal voltage of the battery is 12 V configured in a string of 20 batteries (240 Vdc) to conform to the bidirectional rectifier rated input voltage. The maximum capacity and round trip efficiency of the battery are 83.4 Ah and 80% respectively. The capital cost is \$300/kWh, replacement cost of \$200/kWh, operation and maintenance cost

Power electronics converters are needed for various power conversions and conditioning to optimally match electrical power source with electrical and electronic loads. Four main types of such converters are available: AC‐AC, AC‐DC, DC‐DC, and DC‐AC power converter [7]. A bidirectional power electronic converter is considered in this study because the wind energy conversion system is modeled as an AC power source, whereas the energy storage and solar PV are modeled as DC power source. Such power electronic converter allows power to flow bidirectionally between the AC and DC bus. Such functionality is possible by adequately

sealed type [7].

of \$20/unit/year.

**3.4. Static power converters**

**Figure 4.** Three‐phase pulse‐width modulation (PWM) rectifier.

*A* is the rotor swept area, *ρ* is the air density, *Cp* is the power coefficient that is dependent on the rotor blade pitch angle and tip speed ratio, and *V* is the average wind speed.

HOMER Pro determines the output power of the wind turbine in a four‐step process. In the first step, it determines the average wind speed for the hour at the anemometer height by referring to the wind resource data. In the second step of the process, it determines the cor‐ responding wind speed at the turbine's height using either the logarithmic law or the power law (the logarithmic law is used in this study). Thirdly, it refers to the turbine's power curve to calculate its output power value at that hourly wind speed assuming standard air density. Finally, it multiplies that output power value by the air density ratio, which is the ratio of the actual air density to the standard air density. HOMER Pro also assumes that air density ratio is constant throughout the year.

A generic wind turbine model of 10 kW rated power is selected in HOMER Pro for the study. The capital cost is \$5000/kW, replacement cost of \$5000/kW, operation, and maintenance cost of \$500/year, operational lifetime of 20 years. The hub height of the generic wind turbine model is 24 m above sea level. The power curve of the selected turbine is shown in **Figure 3**.

#### **3.3. Electrochemical battery energy storage system**

A common electrochemical energy storage used in autonomous and emergency standby is Lead‐Acid battery that has proven to be robust, cost‐efficient, and cost‐effective. However, many new battery technologies are being developed and utilized for practical applica‐ tions with improved operational characteristics but are currently more expensive than the traditionally used battery technology [7]. With the interest in electric vehicle, lithium‐ion battery technology is in the pole position to be the mainstream electrochemical technology

**Figure 3.** 10 kW generic wind turbine power curve (HOMER Pro).

for various applications. Among the operational parameters of Lead‐Acid battery, maximum state of discharge (DOD), minimum state of charge (SOC), cycle times, round trip efficiency, maximum charge rate, maximum discharge rate are the most important. This battery technol‐ ogy also needs regular maintenance and should be well ventilated especially if it is not the sealed type [7].

A generic 1 kWh lead‐acid battery is selected from the Homer Pro library for the hybrid microgrid presented in this study. The nominal voltage of the battery is 12 V configured in a string of 20 batteries (240 Vdc) to conform to the bidirectional rectifier rated input voltage. The maximum capacity and round trip efficiency of the battery are 83.4 Ah and 80% respectively. The capital cost is \$300/kWh, replacement cost of \$200/kWh, operation and maintenance cost of \$20/unit/year.

#### **3.4. Static power converters**

energy conversion system. The wind speed is strongly coupled to the available power, whereas the power coefficient depends on the tip speed ration (TSR) and the blade pitch angle [10, 16].

*AρCp V*3 (2)

is the power coefficient that is dependent on

2

HOMER Pro determines the output power of the wind turbine in a four‐step process. In the first step, it determines the average wind speed for the hour at the anemometer height by referring to the wind resource data. In the second step of the process, it determines the cor‐ responding wind speed at the turbine's height using either the logarithmic law or the power law (the logarithmic law is used in this study). Thirdly, it refers to the turbine's power curve to calculate its output power value at that hourly wind speed assuming standard air density. Finally, it multiplies that output power value by the air density ratio, which is the ratio of the actual air density to the standard air density. HOMER Pro also assumes that air density ratio

A generic wind turbine model of 10 kW rated power is selected in HOMER Pro for the study. The capital cost is \$5000/kW, replacement cost of \$5000/kW, operation, and maintenance cost of \$500/year, operational lifetime of 20 years. The hub height of the generic wind turbine model

A common electrochemical energy storage used in autonomous and emergency standby is Lead‐Acid battery that has proven to be robust, cost‐efficient, and cost‐effective. However, many new battery technologies are being developed and utilized for practical applica‐ tions with improved operational characteristics but are currently more expensive than the traditionally used battery technology [7]. With the interest in electric vehicle, lithium‐ion battery technology is in the pole position to be the mainstream electrochemical technology

is 24 m above sea level. The power curve of the selected turbine is shown in **Figure 3**.

the rotor blade pitch angle and tip speed ratio, and *V* is the average wind speed.

*P* = \_\_1

304 System Reliability

*A* is the rotor swept area, *ρ* is the air density, *Cp*

**3.3. Electrochemical battery energy storage system**

**Figure 3.** 10 kW generic wind turbine power curve (HOMER Pro).

is constant throughout the year.

Power electronics converters are needed for various power conversions and conditioning to optimally match electrical power source with electrical and electronic loads. Four main types of such converters are available: AC‐AC, AC‐DC, DC‐DC, and DC‐AC power converter [7]. A bidirectional power electronic converter is considered in this study because the wind energy conversion system is modeled as an AC power source, whereas the energy storage and solar PV are modeled as DC power source. Such power electronic converter allows power to flow bidirectionally between the AC and DC bus. Such functionality is possible by adequately

**Figure 4.** Three‐phase pulse‐width modulation (PWM) rectifier.

modulating the semiconductor switches that are embedded in the power converter topology [7, 32]. Such configuration that operates as an active end rectifier is shown in **Figure 4**.

is performed to give an indication of the system robustness which is reported in Section 4

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307

The investigated hybrid AC/DC microgrid system model architecture is shown in **Figure 5**. The system consists of two electrical buses: AC and DC bus. To ensure improved overall sys‐ tem efficiency, 25% of total electrical load is the DC load that is connected to the DC bus. The wind turbine and solar energy system are connected to the AC and DC bus, respectively. In modeling the battery, HOMER Pro includes in the battery model, a charge regulator to ensure that the specified operating condition is not violated via the SOC and DOD characteristic curves. The interlinking power converter connects the two buses together by acting as a recti‐ fier or inverter depending on the power state of the hybrid system. In the rectifier mode, it transfers power from the AC bus to the DC bus whenever there is excess power in the AC bus and there is instant demand of power from the DC bus. Alternatively, in the inverter mode of operation, power is transferred from the DC bus to the AC bus whenever there is excess power on the DC and there is instant demand of power from the AC bus. In both modes of operation, the SOC of the energy storage system is to be taken into consideration. The dis‐ patch strategy can be set in HOMER Pro. Load‐following and cycle‐charging dispatch strate‐ gies are available for selection in HOMER Pro. Under the load‐following strategy, generators produce only enough power to serve the load, and do not charge the energy storage device. For the cycle‐charging, the excess energy available after serving the load is used to charge the

that follows.

battery [2, 7, 34].

**5. System modeling and simulation**

**Figure 5.** Autonomous AC/DC hybrid microgrid system.

HOMER Pro assumes that the inverter and rectifier capacities are not surge capacities that the device can tolerate for only short periods of time, but rather, constant capacities that the device can withstand for as long as needed [7].

A Leonics MTP41FP 25 kW 240V DC bidirectional power converter is selected for the studied hybrid AC/DC microgrid to interconnect the DC and AC bus. The capital cost of the bidirectional converter is \$600/kW, replacement cost of \$600, operation and main‐ tenance cost of \$0/year. The lifetime of the selected converter is 10 years and its inverter efficiency is 96% while the rectifier relative capacity is chosen to be 80% and its efficiency is 94%.

**Table 1** shows the associated costs of all the system model components. These costs are used in Section 4 to perform the system simulation in HOMER Pro software.

**Table 1.** Costs of system model components [33].

## **4. HOMER pro simulation environment**

HOMER Pro software is able to evaluate off‐grid or grid connected power system design, choose the best system based on cost, technical requirements, or environmental consider‐ ations. It can also simulate many design configurations under market uncertainty and evalu‐ ate risk plus the ability of the modeler to choose the best addition or retrofit for an existing system [7].

HOMER Pro software is used in this research investigation. Wind energy conversion sys‐ tem, solar PV system, bidirectional converter, electrochemical batteries, AC primary load, and renewable resources are modeled and analyzed. Energy resources data, system com‐ ponents data, typical community load profile, and system components costs are some of the important parameters that are used as inputs in the HOMER Pro model. AC and DC bus are created in the HOMER Pro model to facilitate the connection of different types of locally available resources. HOMER Pro is able to optimize feasible electric power system configurations that are technically possible [7]. Sensitivity analysis of feasible configurations is performed to give an indication of the system robustness which is reported in Section 4 that follows.

## **5. System modeling and simulation**

modulating the semiconductor switches that are embedded in the power converter topology

HOMER Pro assumes that the inverter and rectifier capacities are not surge capacities that the device can tolerate for only short periods of time, but rather, constant capacities that the

A Leonics MTP41FP 25 kW 240V DC bidirectional power converter is selected for the studied hybrid AC/DC microgrid to interconnect the DC and AC bus. The capital cost of the bidirectional converter is \$600/kW, replacement cost of \$600, operation and main‐ tenance cost of \$0/year. The lifetime of the selected converter is 10 years and its inverter efficiency is 96% while the rectifier relative capacity is chosen to be 80% and its efficiency

**Table 1** shows the associated costs of all the system model components. These costs are used

**Replacement cost per unit**

**Operating and maintenance cost per unit per year**

HOMER Pro software is able to evaluate off‐grid or grid connected power system design, choose the best system based on cost, technical requirements, or environmental consider‐ ations. It can also simulate many design configurations under market uncertainty and evalu‐ ate risk plus the ability of the modeler to choose the best addition or retrofit for an existing

\$300 \$200 \$20

HOMER Pro software is used in this research investigation. Wind energy conversion sys‐ tem, solar PV system, bidirectional converter, electrochemical batteries, AC primary load, and renewable resources are modeled and analyzed. Energy resources data, system com‐ ponents data, typical community load profile, and system components costs are some of the important parameters that are used as inputs in the HOMER Pro model. AC and DC bus are created in the HOMER Pro model to facilitate the connection of different types of locally available resources. HOMER Pro is able to optimize feasible electric power system configurations that are technically possible [7]. Sensitivity analysis of feasible configurations

in Section 4 to perform the system simulation in HOMER Pro software.

**unit of rated value**

PV panels \$3000 \$2000 \$10 Wind turbine \$5000 \$5000 \$500 Bidirectional power converter \$600 \$600 \$0

[7, 32]. Such configuration that operates as an active end rectifier is shown in **Figure 4**.

device can withstand for as long as needed [7].

**System component Capital cost per**

**Table 1.** Costs of system model components [33].

Electrochemical battery storage

**4. HOMER pro simulation environment**

is 94%.

306 System Reliability

system

system [7].

The investigated hybrid AC/DC microgrid system model architecture is shown in **Figure 5**. The system consists of two electrical buses: AC and DC bus. To ensure improved overall sys‐ tem efficiency, 25% of total electrical load is the DC load that is connected to the DC bus. The wind turbine and solar energy system are connected to the AC and DC bus, respectively. In modeling the battery, HOMER Pro includes in the battery model, a charge regulator to ensure that the specified operating condition is not violated via the SOC and DOD characteristic curves. The interlinking power converter connects the two buses together by acting as a recti‐ fier or inverter depending on the power state of the hybrid system. In the rectifier mode, it transfers power from the AC bus to the DC bus whenever there is excess power in the AC bus and there is instant demand of power from the DC bus. Alternatively, in the inverter mode of operation, power is transferred from the DC bus to the AC bus whenever there is excess power on the DC and there is instant demand of power from the AC bus. In both modes of operation, the SOC of the energy storage system is to be taken into consideration. The dis‐ patch strategy can be set in HOMER Pro. Load‐following and cycle‐charging dispatch strate‐ gies are available for selection in HOMER Pro. Under the load‐following strategy, generators produce only enough power to serve the load, and do not charge the energy storage device. For the cycle‐charging, the excess energy available after serving the load is used to charge the battery [2, 7, 34].

**Figure 5.** Autonomous AC/DC hybrid microgrid system.

The simulation process models the micropower system under investigation, and the opti‐ mization process determines the optimal system configuration that satisfies the modeler‐ specific constraints at the lowest total net present cost. The sensitivity analysis functionality of HOMER Pro allows energy planner, which energy technology combinations are optimal under different conditions [7, 9].

**Figure 6.** Community daily AC load profile.

The AC load daily and DC load profiles are shown in **Figures 6** and **7**, respectively. The data used for this plot are shown in **Table 2**. The community load profile used in this study is the

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309

The wind and solar resource data are obtained from the NASA Surface Metrological and Solar Energy database website. **Figure 8** depicts the monthly average solar global horizontal irradiance data. These monthly average data are averaged over 22‐year period (July 1983–June 2005) [35]. The solar irradiance of Cape Town is low during the winter months of April, May, June, and July as shown in **Figure 8**. The wind speed data are also obtained from NASA Surface Metrological and Solar Energy database website. Wind speed at 50 m above the surface of the earth for terrain similar to airport, and monthly averaged values over 10 years period (July 1983–June 1993) are used in this work. These data are displayed in **Figure 9** (NASA Surface

The Cape Town average wind speed as reported by the NASA database is nearly constant

reference load date available in the HOMER Pro library [9].

**Figure 9.** Average wind speed of Cape Town South Africa.

**Figure 8.** Monthly average solar global horizontal irradiance of Cape Town South Africa.

throughout the year, with average speed hovering around 6 m/s.

Meteorology and Solar Energy).

**Figure 7.** Community daily DC load profile.

**Table 2.** Community load profile data.

**Figure 8.** Monthly average solar global horizontal irradiance of Cape Town South Africa.

**Figure 9.** Average wind speed of Cape Town South Africa.

The simulation process models the micropower system under investigation, and the opti‐ mization process determines the optimal system configuration that satisfies the modeler‐ specific constraints at the lowest total net present cost. The sensitivity analysis functionality of HOMER Pro allows energy planner, which energy technology combinations are optimal

**AC load DC load**

Average consumed energy 165.56 14.39 Average power (kW) 6.9 0.6 Peak power (kW) 23.17 2.67 Load factor 0.3 0.22

under different conditions [7, 9].

308 System Reliability

**Figure 7.** Community daily DC load profile.

**Figure 6.** Community daily AC load profile.

**Table 2.** Community load profile data.

**Electrical loads**

The AC load daily and DC load profiles are shown in **Figures 6** and **7**, respectively. The data used for this plot are shown in **Table 2**. The community load profile used in this study is the reference load date available in the HOMER Pro library [9].

The wind and solar resource data are obtained from the NASA Surface Metrological and Solar Energy database website. **Figure 8** depicts the monthly average solar global horizontal irradiance data. These monthly average data are averaged over 22‐year period (July 1983–June 2005) [35]. The solar irradiance of Cape Town is low during the winter months of April, May, June, and July as shown in **Figure 8**. The wind speed data are also obtained from NASA Surface Metrological and Solar Energy database website. Wind speed at 50 m above the surface of the earth for terrain similar to airport, and monthly averaged values over 10 years period (July 1983–June 1993) are used in this work. These data are displayed in **Figure 9** (NASA Surface Meteorology and Solar Energy).

The Cape Town average wind speed as reported by the NASA database is nearly constant throughout the year, with average speed hovering around 6 m/s.

## **6. Results and discussions**

The hybrid microgrid system consisting of PV system, wind turbine, bidirectional converter, lead‐acid battery, and DC and AC load shown in **Figure 4** is simulated in HOMER Pro software environment. Both cycle‐charging and load‐following dispatched strategies are investigated. Plausible selected system component ratings are chosen for the simulation to ensure that there is enough search space for HOMER Pro to obtain an optimal system configuration. Net present cost is used as an economic metric to assess the optimal feasible configuration.

The optimal system configuration with load‐following dispatch strategy consists of a 50‐kW generic flat plate PV system, 20 kW wind turbine, 15 kW bidirectional power electronic con‐ verter, and 160 kWh lead‐acid battery consisting of eight string. The initial capital cost of this optimal configuration is \$307 000. The total present cost is \$558,717, with levelized cost of energy (COE) being \$0.3652, and the operational cost is of \$11 363 throughout the project lifetime. The number of autonomy is 11 days. For more simulation results, see **Figure 10**.

The optimal system configuration with cycle‐charging dispatch strategy consists of a 30‐kW generic flat plate PV system, 20 kW wind turbine, 15 kW bidirectional power electronic con‐ verter and 140 kWh lead‐acid battery consisting of seven strings. The initial capital cost of this optimal configuration is \$241,000. The total present cost is \$453,517, with levelized cost of energy (COE) being \$0.2973, and the operation cost is of \$9 593 throughout the project life‐ time. The number of autonomy is 10 days. For more simulation results, see **Figure 11**.

> For the same technically feasible configuration, the total net present cost and the initial capi‐ tal cost of the load‐following dispatch strategy are more expensive than the cycle‐charging dispatch strategy. The levelized cost of energy of optimal configuration with load‐following strategy is higher compared to the one with cycle‐charging dispatch strategy. In the periods of extended cloudy season and low solar insolation, the configuration with load‐following

Techno-Economic Feasibility Study of Autonomous Hybrid AC/DC Microgrid System

http://dx.doi.org/10.5772/intechopen.69582

311

The use of renewable energy as local energy resources enhances the accessibility and affordabil‐ ity of energy to unconnected areas around the world. Renewable energies, such as wind, solar, and biomass, have the potential to reduce the energy poverty of rural areas and sites very far from the grid. Being local resources, they also provide higher energy security to the populace. The technical and economic analysis of the designed hybrid AC/DC micropower system stud‐ ied in this work reveals the optimal electric power system configuration that is technically and economically viable using the net present cost as the econometric index. It is concluded that it is marginally better to dispatch load‐following strategy for higher net present cost and autonomy compared to cycle‐charging strategy dispatch. For lower levelized cost of energy (COE) and initial capital cost, it is marginally better to consider a cycle‐charging dispatch

dispatch strategy offers a marginally extended period of autonomy.

**Figure 11.** Simulation results of the optimal architecture with cycle‐charging dispatch strategy.

strategy compared to a load‐following dispatch strategy.

**7. Conclusion**

**Figure 10.** Simulation results of the optimal architecture with load‐following dispatch strategy.

Techno-Economic Feasibility Study of Autonomous Hybrid AC/DC Microgrid System http://dx.doi.org/10.5772/intechopen.69582 311

**Figure 11.** Simulation results of the optimal architecture with cycle‐charging dispatch strategy.

For the same technically feasible configuration, the total net present cost and the initial capi‐ tal cost of the load‐following dispatch strategy are more expensive than the cycle‐charging dispatch strategy. The levelized cost of energy of optimal configuration with load‐following strategy is higher compared to the one with cycle‐charging dispatch strategy. In the periods of extended cloudy season and low solar insolation, the configuration with load‐following dispatch strategy offers a marginally extended period of autonomy.

## **7. Conclusion**

**6. Results and discussions**

310 System Reliability

The hybrid microgrid system consisting of PV system, wind turbine, bidirectional converter, lead‐acid battery, and DC and AC load shown in **Figure 4** is simulated in HOMER Pro software environment. Both cycle‐charging and load‐following dispatched strategies are investigated. Plausible selected system component ratings are chosen for the simulation to ensure that there is enough search space for HOMER Pro to obtain an optimal system configuration. Net present cost is used as an economic metric to assess the optimal feasible configuration.

The optimal system configuration with load‐following dispatch strategy consists of a 50‐kW generic flat plate PV system, 20 kW wind turbine, 15 kW bidirectional power electronic con‐ verter, and 160 kWh lead‐acid battery consisting of eight string. The initial capital cost of this optimal configuration is \$307 000. The total present cost is \$558,717, with levelized cost of energy (COE) being \$0.3652, and the operational cost is of \$11 363 throughout the project lifetime. The number of autonomy is 11 days. For more simulation results, see **Figure 10**.

The optimal system configuration with cycle‐charging dispatch strategy consists of a 30‐kW generic flat plate PV system, 20 kW wind turbine, 15 kW bidirectional power electronic con‐ verter and 140 kWh lead‐acid battery consisting of seven strings. The initial capital cost of this optimal configuration is \$241,000. The total present cost is \$453,517, with levelized cost of energy (COE) being \$0.2973, and the operation cost is of \$9 593 throughout the project life‐

time. The number of autonomy is 10 days. For more simulation results, see **Figure 11**.

**Figure 10.** Simulation results of the optimal architecture with load‐following dispatch strategy.

The use of renewable energy as local energy resources enhances the accessibility and affordabil‐ ity of energy to unconnected areas around the world. Renewable energies, such as wind, solar, and biomass, have the potential to reduce the energy poverty of rural areas and sites very far from the grid. Being local resources, they also provide higher energy security to the populace.

The technical and economic analysis of the designed hybrid AC/DC micropower system stud‐ ied in this work reveals the optimal electric power system configuration that is technically and economically viable using the net present cost as the econometric index. It is concluded that it is marginally better to dispatch load‐following strategy for higher net present cost and autonomy compared to cycle‐charging strategy dispatch. For lower levelized cost of energy (COE) and initial capital cost, it is marginally better to consider a cycle‐charging dispatch strategy compared to a load‐following dispatch strategy.

## **Author details**

Atanda K. Raji

Address all correspondence to<EMAIL_ADDRESS>
Centre for Distributed Power and Electronic Systems, Cape Peninsula University of Technology, Bellville Campus, Cape Town, South Africa

[12] Kusakana K, Vermaak HJ, Numbi BP. Optimal sizing of a hybrid renewable energy plant using linear programming. In: Proceedings of IEEE PES Power Africa 2012 Conference and Exposition; 09‐13 July 2012; Johannesburg, South Africa. http:// ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6498608 (Accessed 23‐04‐2016) [13] Connoly D, Lund H, Mathiesen BV, Leahy M. A review of computer tools for analys‐ ing the integration of renewable energy into various energy systems. Applied Energy.

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[15] Yang HX, Lu L, Zhou W. A novel optimization sizing model for hybrid solar– wind power

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**Maintenance**

**Section 4**

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**Chapter 17**

Provisional chapter

**Resource Planning to Service Restoration in Power**

DOI: 10.5772/intechopen.69573

Resource Planning to Service Restoration in Power

Whenever there are extreme weather events, electric power distribution systems are generally affected largely because they are highly subject by their constructive nature: overhead networks. In this context, the management of maintenance actions is generally referred to as emergency service order, usually associated with a lack of supply and requiring human intervention. The key issue for the resource planning refers to an estimation of service time that allows for more assertive planning possible. This chapter proposes a predictive modelling of emergency services for resource planning when considering the geographic dispersion of such services and also the time windows that comprise the amount of service time demanded. After presenting the methodological procedures, a case study depicts the application of the proposed method in order to

Keywords: power distribution systems, decision-making, predictive modelling,

Certain regions are subject to frequent adverse weather events of sufficient intensity to cause damage to the electrical networks, requiring human intervention to verify and eliminate the causes of such disruption and thus leading to the creation of emergency service orders. These orders, with a high degree of uncertainty and urgency, along with commercial orders, with a

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Distribution Systems**

Distribution Systems

Maria Clara Ferreira Almeida da Silva,

Magdiel Schmitz, Maria Clara Ferreira Almeida da Silva, Vinícius Jacques Garcia, Daniel Bernardon, Lynceo Favigna Braghirolli

http://dx.doi.org/10.5772/intechopen.69573

support proactive service routing.

emergency services, service restoration

Vinícius Jacques Garcia, Daniel Bernardon, Lynceo Favigna Braghirolli and Júlio Fonini

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Magdiel Schmitz,

and Júlio Fonini

Abstract

1. Introduction

Provisional chapter

## **Resource Planning to Service Restoration in Power Distribution Systems** Resource Planning to Service Restoration in Power

DOI: 10.5772/intechopen.69573

Distribution Systems

Magdiel Schmitz, Maria Clara Ferreira Almeida da Silva, Vinícius Jacques Garcia, Daniel Bernardon, Lynceo Favigna Braghirolli and Júlio Fonini Magdiel Schmitz, Maria Clara Ferreira Almeida da Silva, Vinícius Jacques Garcia, Daniel Bernardon, Lynceo Favigna Braghirolli

Additional information is available at the end of the chapter and Júlio Fonini

http://dx.doi.org/10.5772/intechopen.69573 Additional information is available at the end of the chapter

#### Abstract

Whenever there are extreme weather events, electric power distribution systems are generally affected largely because they are highly subject by their constructive nature: overhead networks. In this context, the management of maintenance actions is generally referred to as emergency service order, usually associated with a lack of supply and requiring human intervention. The key issue for the resource planning refers to an estimation of service time that allows for more assertive planning possible. This chapter proposes a predictive modelling of emergency services for resource planning when considering the geographic dispersion of such services and also the time windows that comprise the amount of service time demanded. After presenting the methodological procedures, a case study depicts the application of the proposed method in order to support proactive service routing.

Keywords: power distribution systems, decision-making, predictive modelling, emergency services, service restoration

## 1. Introduction

Certain regions are subject to frequent adverse weather events of sufficient intensity to cause damage to the electrical networks, requiring human intervention to verify and eliminate the causes of such disruption and thus leading to the creation of emergency service orders. These orders, with a high degree of uncertainty and urgency, along with commercial orders, with a

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

previously defined route, become a task of great relevance for the network operation center of the electric distribution systems and qualifying even more the highly dynamic environment involved. The key issue for the resource planning, with regard to the service crews, refers to an estimation of service time that allows for more assertive planning possible, improving the crew throughput.

The use of repair crews becomes imperative precisely to overcome the limitations that interfere with the remote control equipment, since the insulation of the defect can even be performed

Resource Planning to Service Restoration in Power Distribution Systems

http://dx.doi.org/10.5772/intechopen.69573

319

From this crew management comes the well-known emergency dispatching problem to repair crews already scheduled with pre-programmed services, which leads to a change of course and describes the problem of dynamic routing of vehicles [3]. Exactly in the context of service operations in electric power distribution utilities, the problem of this work is defined in [4].

The nature of the optimization problem has its roots on minimizing the waiting time between the detection of the defect and the arrival of crews at the service location, because the less this time the less the time without supply, thus contributing to the reliability of the electric power

Another aspect worth mentioning is the random nature of events: the occurrence of emergency orders. In case of a reactive system, each new pending emergency order, or a set of them, gives rise to the problem of dynamic routing [5]. In addition, the routing problem associated with the context of this work also presents an important particularity: the service time in each service location, which is exactly the estimated service time for resolution. It follows that the

From the conclusions of [7], it can be observed that a decision that is completely reactive, responding to the disturbances generated by the creation of emergency orders, can lead to a sequence of mistaken decisions due to the loss of the 'global vision' related to the whole

This chapter aims to anticipate the occurrence of emergency services in order to provide a proactive approach to dispatch, in which emergency occurrences can be assumed to be prob-

The routing problem is usually addressed by assuming that attributes (customer demands, travel and service times, orders criticality) are previously known. However, most of the real cases present some level of uncertainty [8]. Anticipating these uncertainties already in planning phase is important because it allows a more precisely routing plan and favouring the crew management, operational cost reduction and also avoiding penalties from regulatory agencies through improvement of reliability indicators and the revenue from the energy sale,

According to [9], the data of vehicle-routing problems can be 'Static and deterministic', 'Static and stochastic', 'Dynamic and deterministic' and 'Dynamic and stochastic'. Exactly, this last class is that related to this work, referred many times as partially dynamic, this approach assumes that some of the unknown data are in stochastic format. A proactive planning can be realized by transforming the stochastic knowledge in dummy consumers with expected ser-

able and therefore likely to be included in routing solutions of programmed orders.

automatically but its correction requires human interference.

dispatch problem is closed to the problem of minimum latency [6].

problem depicted after analysing all the past events over the day.

distribution system.

3. Demand forecasting

by reducing supply disruptions.

vice time and temporal and spatial position.

Considering the need to define a typical behaviour to those orders, this chapter proposes a predictive modelling of emergency services for resource planning when considering the geographic dispersion of such services and also the time windows that comprise the amount of service time demanded. The methodology to resource planning presented in this chapter is based on the predictive modelling of emergency service by defining random variables to denote how much service time is demanded in each portion of the whole geographic area considered and also how important such demands may be in the sense of reliability indexes, as number of customers and the amount of power not supplied.

Following this definition of random variables, one may obtain the service time to attend emergency services stratified by each region and also restricted to a certain time window, that is, 1-h interval. With this information, a decision-making process may be conducted to define the number of hours demanded by maintenance crews that will be needed to attend all the services in the 1-h interval. The whole picture when assuming 1 day demand will be possible by collecting all these 1-h intervals, furnishing the geographic location and the on-site service time to a possible proactive-routing approach.

In order to show how the methodology may be applied, a case study is developed considering a horizon of emergency service occurrences, from a given Brazilian Power Utility. The purpose of this case study is not only about the past but also about how to update the case study of actual occurrences in such a way that they may be considered for future estimations.

The process of conducting statistical analyses to construct the time series for each given 1-h interval is depicted in a graphic user interface also allowing the timeline description of the estimation of service time dispersed over the geographic area assumed, followed by the decision-making process of selecting the most relevant random variables to denote the service time demanded.

## 2. Service restoration by repair crews

Although the advent of smart grids has conducted to increasing the level of automation [1], the need for human intervention is particularly necessary in cases of extreme weather events or even in the occurrence of collisions in overhead networks, which become exposed by itself and may cause the lack of power supply.

This interruption refers to the switching from normal to the emergency operating condition [2], in all of the networks or even in a restricted part of it, conducting customers to the lack of power supply and affecting continuity indexes. In addition, companies still have the billing process affected by not addressing the load demand for a certain period.

The use of repair crews becomes imperative precisely to overcome the limitations that interfere with the remote control equipment, since the insulation of the defect can even be performed automatically but its correction requires human interference.

From this crew management comes the well-known emergency dispatching problem to repair crews already scheduled with pre-programmed services, which leads to a change of course and describes the problem of dynamic routing of vehicles [3]. Exactly in the context of service operations in electric power distribution utilities, the problem of this work is defined in [4].

The nature of the optimization problem has its roots on minimizing the waiting time between the detection of the defect and the arrival of crews at the service location, because the less this time the less the time without supply, thus contributing to the reliability of the electric power distribution system.

Another aspect worth mentioning is the random nature of events: the occurrence of emergency orders. In case of a reactive system, each new pending emergency order, or a set of them, gives rise to the problem of dynamic routing [5]. In addition, the routing problem associated with the context of this work also presents an important particularity: the service time in each service location, which is exactly the estimated service time for resolution. It follows that the dispatch problem is closed to the problem of minimum latency [6].

From the conclusions of [7], it can be observed that a decision that is completely reactive, responding to the disturbances generated by the creation of emergency orders, can lead to a sequence of mistaken decisions due to the loss of the 'global vision' related to the whole problem depicted after analysing all the past events over the day.

This chapter aims to anticipate the occurrence of emergency services in order to provide a proactive approach to dispatch, in which emergency occurrences can be assumed to be probable and therefore likely to be included in routing solutions of programmed orders.

## 3. Demand forecasting

previously defined route, become a task of great relevance for the network operation center of the electric distribution systems and qualifying even more the highly dynamic environment involved. The key issue for the resource planning, with regard to the service crews, refers to an estimation of service time that allows for more assertive planning possible, improving the crew

Considering the need to define a typical behaviour to those orders, this chapter proposes a predictive modelling of emergency services for resource planning when considering the geographic dispersion of such services and also the time windows that comprise the amount of service time demanded. The methodology to resource planning presented in this chapter is based on the predictive modelling of emergency service by defining random variables to denote how much service time is demanded in each portion of the whole geographic area considered and also how important such demands may be in the sense of reliability indexes, as

Following this definition of random variables, one may obtain the service time to attend emergency services stratified by each region and also restricted to a certain time window, that is, 1-h interval. With this information, a decision-making process may be conducted to define the number of hours demanded by maintenance crews that will be needed to attend all the services in the 1-h interval. The whole picture when assuming 1 day demand will be possible by collecting all these 1-h intervals, furnishing the geographic location and the on-site service

In order to show how the methodology may be applied, a case study is developed considering a horizon of emergency service occurrences, from a given Brazilian Power Utility. The purpose of this case study is not only about the past but also about how to update the case study of

The process of conducting statistical analyses to construct the time series for each given 1-h interval is depicted in a graphic user interface also allowing the timeline description of the estimation of service time dispersed over the geographic area assumed, followed by the decision-making process of selecting the most relevant random variables to denote the service

Although the advent of smart grids has conducted to increasing the level of automation [1], the need for human intervention is particularly necessary in cases of extreme weather events or even in the occurrence of collisions in overhead networks, which become exposed by itself and

This interruption refers to the switching from normal to the emergency operating condition [2], in all of the networks or even in a restricted part of it, conducting customers to the lack of power supply and affecting continuity indexes. In addition, companies still have the billing

process affected by not addressing the load demand for a certain period.

actual occurrences in such a way that they may be considered for future estimations.

number of customers and the amount of power not supplied.

time to a possible proactive-routing approach.

2. Service restoration by repair crews

may cause the lack of power supply.

throughput.

318 System Reliability

time demanded.

The routing problem is usually addressed by assuming that attributes (customer demands, travel and service times, orders criticality) are previously known. However, most of the real cases present some level of uncertainty [8]. Anticipating these uncertainties already in planning phase is important because it allows a more precisely routing plan and favouring the crew management, operational cost reduction and also avoiding penalties from regulatory agencies through improvement of reliability indicators and the revenue from the energy sale, by reducing supply disruptions.

According to [9], the data of vehicle-routing problems can be 'Static and deterministic', 'Static and stochastic', 'Dynamic and deterministic' and 'Dynamic and stochastic'. Exactly, this last class is that related to this work, referred many times as partially dynamic, this approach assumes that some of the unknown data are in stochastic format. A proactive planning can be realized by transforming the stochastic knowledge in dummy consumers with expected service time and temporal and spatial position.

With such definitions, the next section describes how to address the uncertainty by performing demand-forecasting techniques.

Ftþ1 ¼ αxt þ ðαÞFt (1)

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321

where t = actual period; Ft+1 = future forecasting; xt = demand in the period t; Ft = forecasting to

With these definitions, what one has is the theoretical basis to realize the forecasts of time of

However, it is necessary to consider that only the service time forecasting is not enough to answer the questions pointed out by this work, which are the service time related to a certain part of the geographic area considered and also related to a time interval defined [13, 14]. Exactly these challenges will be illustrated in the next section, which describes the methodo-

Following the contribution by Ferrucci et al. [7], inspired by the paper of Ichoua et al. [15], the approach proposed in this work also considers the classification of orders information that has already occurred, based at service time of each request, as pointed out in Figures 2 and 3.

Figure 2. Variation analysis from the historical information. Day of the week and time of the day.

t; α (0 < α < 1) is a smoothing constant.

service from the available time series.

logical procedures that are employed.

4. Proposed methodology

## 3.1. Demand forecasting

Considering the external service orders of electric power utilities, we treat two different types of situations, the commercial and the emergency orders. The commercial ones have a typical input behaviour, known deadline and, as a consequence of these characteristics, can be planned in advance, without technical or legal problems involving power failures. By contrast, the emergency orders are randomly generated, with the corresponding dynamic character [10].

As to the attendance capacity, all the available crews have commercial and emergency demand during the workday, overlapping one each other and respecting the attendance priority. This behaviour can be seen in Figure 1, where there is a considerable difference between the planned route and the route performed mainly due to the occurrence of emergency orders: they have higher priority with respect to commercial orders and cause modification on the route every time they are considered.

These constant changings on planned route by knowing customers and their attributes progressively classify the problem addressed as dynamic and stochastic [7]. One possible alternative that is adopted in this work is associated with an attempt to predict the emergency occurrences and answering when and where they may occur [11].

Indispensable in the planning and in the strategies for decision-making, demand forecasting oriented towards a future period should rely on precise techniques [11]. Of the commonly used techniques to perform the forecasting, the exponential-smoothing approach can be applied to predict continuous and discrete variables.

The exponential smoothing provides the service time to the analysis horizon, using Eq. (1), according to [12]

Figure 1. Routing of crews with emergency-order fulfilment.

$$F\_{t+1} = a\mathbf{x}\_t + (a)F\_t \tag{1}$$

where t = actual period; Ft+1 = future forecasting; xt = demand in the period t; Ft = forecasting to t; α (0 < α < 1) is a smoothing constant.

With these definitions, what one has is the theoretical basis to realize the forecasts of time of service from the available time series.

However, it is necessary to consider that only the service time forecasting is not enough to answer the questions pointed out by this work, which are the service time related to a certain part of the geographic area considered and also related to a time interval defined [13, 14]. Exactly these challenges will be illustrated in the next section, which describes the methodological procedures that are employed.

## 4. Proposed methodology

With such definitions, the next section describes how to address the uncertainty by performing

Considering the external service orders of electric power utilities, we treat two different types of situations, the commercial and the emergency orders. The commercial ones have a typical input behaviour, known deadline and, as a consequence of these characteristics, can be planned in advance, without technical or legal problems involving power failures. By contrast, the emergency orders are randomly generated, with the corresponding dynamic character [10]. As to the attendance capacity, all the available crews have commercial and emergency demand during the workday, overlapping one each other and respecting the attendance priority. This behaviour can be seen in Figure 1, where there is a considerable difference between the planned route and the route performed mainly due to the occurrence of emergency orders: they have higher priority with respect to commercial orders and cause modification on the

These constant changings on planned route by knowing customers and their attributes progressively classify the problem addressed as dynamic and stochastic [7]. One possible alternative that is adopted in this work is associated with an attempt to predict the emergency

Indispensable in the planning and in the strategies for decision-making, demand forecasting oriented towards a future period should rely on precise techniques [11]. Of the commonly used techniques to perform the forecasting, the exponential-smoothing approach can be applied to

The exponential smoothing provides the service time to the analysis horizon, using Eq. (1),

occurrences and answering when and where they may occur [11].

demand-forecasting techniques.

route every time they are considered.

predict continuous and discrete variables.

Figure 1. Routing of crews with emergency-order fulfilment.

according to [12]

3.1. Demand forecasting

320 System Reliability

Following the contribution by Ferrucci et al. [7], inspired by the paper of Ichoua et al. [15], the approach proposed in this work also considers the classification of orders information that has already occurred, based at service time of each request, as pointed out in Figures 2 and 3.

Figure 2. Variation analysis from the historical information. Day of the week and time of the day.

corresponding to the maximum value of variation allowed. This artifice prevents exceptional

The relationship between the scale of the geographical area considered and the coefficient of variation is performed both temporally and spatially. In order to increase the forecasting accuracy, historical data are stratified to each quadrant of the area considered for each day of the week and for each hour of the day. The methodology to proceed with this stratification is

Beta (β) corresponds to the maximum value of variation allowed, normally 0.5, without considering those regions without emergency-order occurrences. Therefore, the referred coef-

Instead of manually testing multiple values for the coefficient of variation, the algorithm minimizes a nonlinear function obtained from an interpolation in order to determine the best value for that coefficient. This procedure aims to minimize the size of the quadrants obtained

The main contribution of this work is the stratification of the data in order to have a more accurate forecast, since the coefficient of variation is calculated for each defined quadrant.

This section describes the computational study, performed to evaluate the proposed model. The model presented in algorithm of Table 1 was implemented in the computational tool GNU Octave, chosen for its efficiency features in numerical processing and matrix computation, as

The model was tested using an actual historical data set, provided by a power distribution utility from southern Brazil. Constituted of 9408 emergency orders in a period of 12 months, the sample is endowed with several attributes, as latitude, longitude, year, month, day, week-

Size: Vector representing the values referring to the side of the area analysed in the calculation. This measure is in kilometres. The higher the number of analysed values, the greater is the

Another point to be considered is that the lower the value reported on size vector: the minimum value for the area side size may vary, depending on the study region, that is, urban or

0 < coefficient of variation ≤ β (2)

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disturbances from leading to distortions in the statistic analysis process.

taking into account the constraint related to the coefficient of variation.

day, hour of day and service time, used for the analysis performed.

accuracy of the function obtained by the interpolation.

detailed in the algorithm of Table 1.

5. Case study

5.1. Instance

5.2. Parameters setting

well as being open-source software.

ficient of variation has the following limits:

Figure 3. Variation analysis from the historical information. Geographical and time interval.

There is a well-defined pattern from the requested service time for each day of the week, very similar to business days unlike non-business days. In addition, Figure 2 also shows that request demand is higher from 8 am to 8 pm. The last feature with regard to the influence on future requests is related to the geographical location: Figure 3 depicts several layers, each one referring to one time interval, with their corresponding surface composed by cuboids; each cuboid's height refers to a level of service time required in the respective area.

The division of the geographical area and the identification of time windows to define the required service time are performed by stratifying and separating the historical data in order to identify a particular time series for each part of the geographical area and also particular for each interval of 1 day of the week.

### 4.1. Demand-forecasting methodology

A natural treatment to deal with emergency-order uncertainties would be to optimize the expected values. However, the proposed methodology approaches a restrictive model of chances [16], where each viable solution must be at an acceptable and predetermined level of failure. In the presented model (see Algorithm 1), this constraint is represented by a coefficient, corresponding to the maximum value of variation allowed. This artifice prevents exceptional disturbances from leading to distortions in the statistic analysis process.

The relationship between the scale of the geographical area considered and the coefficient of variation is performed both temporally and spatially. In order to increase the forecasting accuracy, historical data are stratified to each quadrant of the area considered for each day of the week and for each hour of the day. The methodology to proceed with this stratification is detailed in the algorithm of Table 1.

Beta (β) corresponds to the maximum value of variation allowed, normally 0.5, without considering those regions without emergency-order occurrences. Therefore, the referred coefficient of variation has the following limits:

$$0 < \text{coefficient of variation} \le \beta \tag{2}$$

Instead of manually testing multiple values for the coefficient of variation, the algorithm minimizes a nonlinear function obtained from an interpolation in order to determine the best value for that coefficient. This procedure aims to minimize the size of the quadrants obtained taking into account the constraint related to the coefficient of variation.

The main contribution of this work is the stratification of the data in order to have a more accurate forecast, since the coefficient of variation is calculated for each defined quadrant.

## 5. Case study

This section describes the computational study, performed to evaluate the proposed model. The model presented in algorithm of Table 1 was implemented in the computational tool GNU Octave, chosen for its efficiency features in numerical processing and matrix computation, as well as being open-source software.

## 5.1. Instance

There is a well-defined pattern from the requested service time for each day of the week, very similar to business days unlike non-business days. In addition, Figure 2 also shows that request demand is higher from 8 am to 8 pm. The last feature with regard to the influence on future requests is related to the geographical location: Figure 3 depicts several layers, each one referring to one time interval, with their corresponding surface composed by cuboids; each

The division of the geographical area and the identification of time windows to define the required service time are performed by stratifying and separating the historical data in order to identify a particular time series for each part of the geographical area and also particular for

A natural treatment to deal with emergency-order uncertainties would be to optimize the expected values. However, the proposed methodology approaches a restrictive model of chances [16], where each viable solution must be at an acceptable and predetermined level of failure. In the presented model (see Algorithm 1), this constraint is represented by a coefficient,

cuboid's height refers to a level of service time required in the respective area.

Figure 3. Variation analysis from the historical information. Geographical and time interval.

each interval of 1 day of the week.

322 System Reliability

4.1. Demand-forecasting methodology

The model was tested using an actual historical data set, provided by a power distribution utility from southern Brazil. Constituted of 9408 emergency orders in a period of 12 months, the sample is endowed with several attributes, as latitude, longitude, year, month, day, weekday, hour of day and service time, used for the analysis performed.

## 5.2. Parameters setting

Size: Vector representing the values referring to the side of the area analysed in the calculation. This measure is in kilometres. The higher the number of analysed values, the greater is the accuracy of the function obtained by the interpolation.

Another point to be considered is that the lower the value reported on size vector: the minimum value for the area side size may vary, depending on the study region, that is, urban or

Interpolation: In order to obtain a polynomial function that best represents the analysed data set, the Lagrange interpolation is used. It is important to highlight that the interpolation can be made with any other function which best describes the data set. The Lagrange interpolation method can construct a polynomial of n degree, which coincides with a given function in n + 1 points, according to the description of the method next

Lagrange interpolation theorem: Given n+1 distinct points, z0, z1, …, zn and n+1 values, w0, w1,

lnðzÞ ¼ ðz � z0Þðz � z1Þ…ðz � zk�1Þðz � zkþ1Þ…ðz � znÞ

lkðzÞ ¼ GnðzÞ ðz � zkÞG0

k¼0 wk

Eq. (8) is known as the Lagrange Interpolation Formula, and the polynomials lk(z) are called the interpolating or sampling of the Lagrange interpolation. In this problem, the zn points are the size

Table 2 presents the optimization result, with the cell values corresponding to the coefficient of

pnðzÞ ¼ Xn

sample, and the wn values the coefficients of variation.

pnðziÞ ¼ wi, i ¼ 0, 1, …n (3)

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ðzk � z0Þðzk � z1Þ…ðzk � zk�1Þðzk � zkþ1Þ…ðzk � znÞ (4)

Gn ¼ ðz � z0Þðz � z1Þ…ðz � znÞ (5)

nðzkÞ (7)

nðzkÞ (8)

k ¼ ðzk � z0Þðzk � z1Þ…ðzk � zk�1Þðzk � zkþ1Þ…ðzk � znÞ (6)

GnðzÞ ðz � ZkÞG0

…, wn, there exists a unique polynomial pn(z) ∈ Pn for which

Let us introduce the following polynomials of degree n:

presented by [17].

where k = 0,1,2,…,n.

G0

and hence it follows from Eq. (4) that

Now let

Then

Eq. (7) becomes

5.3. Results

variation and the area side size.

Table 1. Geographic area optimization algorithm.

rural area. Therefore, the following vector sizes were chosen, measured in kilometres: sizeVector = [0.4 0.6 0.8 1].

Beta (β): As previously informed, it corresponds to the maximum value to the coefficient of variation allowed to ensure the lowest acceptable variance. This value was set to 0.5.

Interpolation: In order to obtain a polynomial function that best represents the analysed data set, the Lagrange interpolation is used. It is important to highlight that the interpolation can be made with any other function which best describes the data set. The Lagrange interpolation method can construct a polynomial of n degree, which coincides with a given function in n + 1 points, according to the description of the method next presented by [17].

Lagrange interpolation theorem: Given n+1 distinct points, z0, z1, …, zn and n+1 values, w0, w1, …, wn, there exists a unique polynomial pn(z) ∈ Pn for which

$$p\_n(z\_i) = w\_{i\prime} i = 0, 1, \ldots n \tag{3}$$

Let us introduce the following polynomials of degree n:

$$l\_n(z) = \frac{(z-z\_0)(z-z\_1)...(z-z\_{k-1})(z-z\_{k+1})...(z-z\_n)}{(z\_k-z\_0)(z\_k-z\_1)...(z\_k-z\_{k-1})(z\_k-z\_{k+1})...(z\_k-z\_n)}\tag{4}$$

where k = 0,1,2,…,n.

Now let

$$G\_n = (z - z\_0)(z - z\_1)...(z - z\_n) \tag{5}$$

Then

$$\mathbf{G}'\_{k} = (\mathbf{z}\_{k} - \mathbf{z}\_{0})(\mathbf{z}\_{k} - \mathbf{z}\_{1})...(\mathbf{z}\_{k} - \mathbf{z}\_{k-1})(\mathbf{z}\_{k} - \mathbf{z}\_{k+1})...(\mathbf{z}\_{k} - \mathbf{z}\_{n})\tag{6}$$

and hence it follows from Eq. (4) that

$$l\_k(z) = \frac{G\_n(z)}{(z - z\_k)G\_n'(z\_k)}\tag{7}$$

Eq. (7) becomes

$$p\_n(z) = \sum\_{k=0}^n w\_k \frac{G\_n(z)}{(z - Z\_k)G\_n'(zk)}\tag{8}$$

Eq. (8) is known as the Lagrange Interpolation Formula, and the polynomials lk(z) are called the interpolating or sampling of the Lagrange interpolation. In this problem, the zn points are the size sample, and the wn values the coefficients of variation.

#### 5.3. Results

rural area. Therefore, the following vector sizes were chosen, measured in kilometres: sizeVector

23 Find the minimum of the function size (mean Coefficient Of Variation) in the range: 0 <= mean Coefficient Of

Input: Database reading containing the following data for each order: latitude, longitude, year, month, day, day of

13 #Thus, we have a matrix with the coefficients of variation associated with the respective area side size, for each area of

2 Construction of the grid with the definition of the geographical positions for the size considered.

Beta (β): As previously informed, it corresponds to the maximum value to the coefficient of

variation allowed to ensure the lowest acceptable variance. This value was set to 0.5.

= [0.4 0.6 0.8 1].

24 end-for 25 end-for

Algorithm 1—Geographic area optimization

4 for area = 1 to n do #Where n is the total of areas

the grid, day of the week and time of day. 14 #Elimination of data with high randomness

18 for 0 < coefficient Of Variation <= beta do

Table 1. Geographic area optimization algorithm.

19 Calculation of the mean Coefficient Of Variation for all areas

22 Determine the characteristic function by the Lagrange interpolation procedure.

15 for day of the week = 1 até 7 do 16 for hour = 1 to 24 do 17 for size = 0.4 to 1 do

Variation<=beta

20 end-for 21 end-for

5 Select a specific area of the grid. 6 for day of the week = 1 to 7 do 7 for hour = 1 to 24 do

Function: Temporal clustering of orders per hour and day of the week. Input: size vector = [0.4:0.2:1]; #Vector with area side size values

3 Order assignment to the respective areas based on the geographical position.

8 Calculation of the coefficient Of Variation for the selected area.

week, time and service time.

1 for size = 0.4 to 1 do

324 System Reliability

9 end-for 10 end-for 11 end-for 12 end-for

> Table 2 presents the optimization result, with the cell values corresponding to the coefficient of variation and the area side size.

Figure 4 presents one solution, with the service time required for emergency-order attendance in the corresponding geographical area and restrict to a given hour of the day, in this case, it is a Tuesday evening, 19 h. From Table 2, one notes that the side area size of each quadrant is 0.4 km, with a coefficient of variation equal to 0.33325. It is worth noting that the dispersion depicted in Figure 4 is for only those quadrants that respect the coefficient of variation

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From the results of service times of Figures 4–8, one may note that the more precise the stratification, and the consequent reduction in the size of the side of the area (0.4 km), the greater the dispersion of the areas with the greatest demand. Such behaviour makes it more

Figures 9–12 depict the number of selected areas to forecast service time, considering a Tuesday and varying the area side size from 0.4 to 1 km. An important relationship between area side size and the number of selected areas: as area side size increases, the number of areas decreases and also the accuracy to define the dummy nodes to be further used in a routing

constraint.

solution approach.

precise to define the area with the highest demand.

Figure 4. Service time history at Tuesday/19 h.

Note that the NaN indicates that there was no coefficient of variation within the established limits.

Table 2. Optimization result (coefficient of variation, area side size).

The results presented in Table 2 show that not all hours of the day respect the coefficient of variation constraint: one can note that periods with more incidences of emergency orders (e.g. from 19 to 23 h) presented more precise data, analytically we can see that in the period with less emergency-orders occurrence (e.g. from 1 to 6 h), the data did not present the necessary reliability.

Figure 4. Service time history at Tuesday/19 h.

The results presented in Table 2 show that not all hours of the day respect the coefficient of variation constraint: one can note that periods with more incidences of emergency orders (e.g. from 19 to 23 h) presented more precise data, analytically we can see that in the period with less emergency-orders occurrence (e.g. from 1 to 6 h), the data did not present the necessary

Note that the NaN indicates that there was no coefficient of variation within the established limits.

Table 2.

Hour of the day

326 System Reliability

Day of the week

Figure 4 presents one solution, with the service time required for emergency-order attendance in the corresponding geographical area and restrict to a given hour of the day, in this case, it is a Tuesday evening, 19 h. From Table 2, one notes that the side area size of each quadrant is 0.4 km, with a coefficient of variation equal to 0.33325. It is worth noting that the dispersion depicted in Figure 4 is for only those quadrants that respect the coefficient of variation constraint.

From the results of service times of Figures 4–8, one may note that the more precise the stratification, and the consequent reduction in the size of the side of the area (0.4 km), the greater the dispersion of the areas with the greatest demand. Such behaviour makes it more precise to define the area with the highest demand.

Figures 9–12 depict the number of selected areas to forecast service time, considering a Tuesday and varying the area side size from 0.4 to 1 km. An important relationship between area side size and the number of selected areas: as area side size increases, the number of areas decreases and also the accuracy to define the dummy nodes to be further used in a routing solution approach.

Figure 5. Service time history at Tuesday/20 h.

Figure 7. Service time history at Tuesday/22 h.

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Figure 8. Service time history at Tuesday/23 h.

Figure 6. Service time history at Tuesday/21 h.

Figure 7. Service time history at Tuesday/22 h.

Figure 8. Service time history at Tuesday/23 h.

Figure 6. Service time history at Tuesday/21 h.

Figure 5. Service time history at Tuesday/20 h.

328 System Reliability

Figure 9. Number of selected areas at Tuesday for area side size of 0.4 km.

Figure 11. Number of selected areas at Tuesday for area side size of 0.8 km.

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Figure 12. Number of selected areas at Tuesday for area side size of 1 km.

Figure 10. Number of selected areas at Tuesday for area side size of 0.6 km.

Figure 11. Number of selected areas at Tuesday for area side size of 0.8 km.

Figure 9. Number of selected areas at Tuesday for area side size of 0.4 km.

330 System Reliability

Figure 10. Number of selected areas at Tuesday for area side size of 0.6 km.

Figure 12. Number of selected areas at Tuesday for area side size of 1 km.

## 6. Conclusion

An inherent issue of the vehicle-routing problem is due to uncertainty of real-time planning attached to the emergency orders, where the latency of an order is minimized generally conflicting with the goal of minimizing travel time, since the pre-established route is changed.

[3] Psaraftis HN. In: Golden BL and Assad AA. (Eds). Vehicle routing: Methods and studies. Dynamic Vehicle Routing Problems. North Holland, Amsterdam, The Netherlands:

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[4] Garcia VJ, Bernardon DP, Abaide AR, Bassi OA, Dhein G. Reliability assessment by coordinating maintenance vehicles in electric power distribution systems. Procedia-Social

[5] Psaraftis HN. Dynamic vehicle routing: Status and prospects. Annals of Operations

[6] Angel-Bello F, Alvarez A, García I. Two improved formulations for the minimum latency

[7] Ferrucci F, Bock S, Gendreau M. A pro-active real-time control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods. European Journal of

[8] Gounaris C, et al. An adaptive memory programming framework for the robust capaci-

[9] Toth P, Vigo D. Vehicle Routing Problems, Methods, and Applications. DEI, University of

[10] Taha HA. Operations Research: An Introduction. Pearson/Prentice Hall; New Jersey.

[11] Makridakis S. METAFORECASTING: Ways of improving forecasting accuracy and use-

[12] Hillier FS, Lieberman GJ. Introduction to Operations Research: Cases Developed. New

[13] Guimarães I, Garcia VJ, Bernardon DP, Foninni J. Emergency prediction in electric utilities: A case study from South Brazil. In: European Conference on Modelling and Simula-

[14] Garcia VJ, et al. Emergency work orders in electric distribution utilities: From business process definition to quantitative improvements. In: 47th International Universities'

[15] Ichoua S, Gendreau M, Potvin J. Exploiting knowledge about future demands for real-

[16] Braaten S, et al. Heuristics for the robust vehicle routing problem with time windows.

[17] Zayed AI, Butzer PL. Chapter 3—Lagrange interpolation and sampling theorems. In: Marvasti FA, editor. Nonuniform Sampling: Theory and Practice. Springer Science + Business Media, LCC; Kluwer Academic/Plenum Publishers, New York. 2001. pp. 123–127

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Power Engineering Conference; 2012

This work has presented an approach to support proactive real-time vehicle routing, by using an algorithm to estimate service time demand related to emergency orders and considering geographical attributes and time windows. From the results obtained by this approach, one may successfully use dummy nodes obtained by the forecast method proposed to be included in a further real-time routing solution. The main purpose is to support this solution in order to minimize the waiting time and the latency, by decreasing the displacements over the route directions over the day.

Computational results indicate that the forecast of service demand can be performed with great precision when optimizing the geographical area considered, showing that the integration of derived stochastic knowledge results in a more accurate dimensioning of the service teams, and significant reductions in the discrepancy between the planned and executed routes may be obtained.

## Acknowledgements

The authors of this chapter would like to thank the Power Distribution Company RGE Sul by the technical and financial support on the Research and Development project called 'Dynamic operations planning', linked to the National Electric Energy Agency(ANEEL).

## Author details

Magdiel Schmitz1 , Maria Clara Ferreira Almeida da Silva1 , Vinícius Jacques Garcia1 \*, Daniel Bernardon1 , Lynceo Favigna Braghirolli1 and Júlio Fonini2

\*Address all correspondence to<EMAIL_ADDRESS>

## References

[3] Psaraftis HN. In: Golden BL and Assad AA. (Eds). Vehicle routing: Methods and studies. Dynamic Vehicle Routing Problems. North Holland, Amsterdam, The Netherlands: Dalctraf. 1988. pp. 223–248

6. Conclusion

332 System Reliability

may be obtained.

Author details

Magdiel Schmitz1

Daniel Bernardon1

References

editor. IEEE; 2017. p. 1

Acknowledgements

An inherent issue of the vehicle-routing problem is due to uncertainty of real-time planning attached to the emergency orders, where the latency of an order is minimized generally conflicting with the goal of minimizing travel time, since the pre-established route is changed. This work has presented an approach to support proactive real-time vehicle routing, by using an algorithm to estimate service time demand related to emergency orders and considering geographical attributes and time windows. From the results obtained by this approach, one may successfully use dummy nodes obtained by the forecast method proposed to be included in a further real-time routing solution. The main purpose is to support this solution in order to minimize the waiting time and the latency, by decreasing the displacements over the route directions over the day.

Computational results indicate that the forecast of service demand can be performed with great precision when optimizing the geographical area considered, showing that the integration of derived stochastic knowledge results in a more accurate dimensioning of the service teams, and significant reductions in the discrepancy between the planned and executed routes

The authors of this chapter would like to thank the Power Distribution Company RGE Sul by the technical and financial support on the Research and Development project called 'Dynamic

[1] Arif A, Wang Z, Wang J, Chen C. Power distribution system outage management with cooptimization of repairs, reconfiguration, and DG dispatch. In: Transaction on Smart Grid,

[2] Murphy L, Wu F. Comprehensive analysis of distribution automation systems. Technical

, Vinícius Jacques Garcia1

\*,

operations planning', linked to the National Electric Energy Agency(ANEEL).

, Maria Clara Ferreira Almeida da Silva1

\*Address all correspondence to<EMAIL_ADDRESS>
2 RGE Sul Power Utility, Rio Grande do Sul, Brazil

1 Federal University of Santa Maria, Rio Grande do Sul, Brazil

Report M90/72. Berkeley: University of California; 1990

, Lynceo Favigna Braghirolli1 and Júlio Fonini2

**Chapter 18**

**Provisional chapter**

**Imperfect Maintenance Models, from Theory to**

**Imperfect Maintenance Models, from Theory to**

DOI: 10.5772/intechopen.69286

The role of maintenance in the industrial environment changed a lot in recent years, and today, it is a key function for long-term profitability in an organization. Many contributions were recently written by researchers on this topic. A lot of models were proposed to optimize maintenance activities while ensuring availability and high-quality requirements. In addition to the well-known classification of maintenance activities—preventive and corrective—in the last decades, a new classification emerged in the literature regarding the degree of system restoration after maintenance actions. Among them, the imperfect maintenance is one of the most studied maintenance types: it is defined as an action after which the system lies in a state somewhere between an "as good as new" state and its pre-maintenance condition "as bad as old." Most of the industrial companies usually operate with imperfect maintenance actions, even if the awareness in actual industrial context is limited. On the practical definition side, in particular, there are some real situations of imperfect maintenance: three main specific cases were identified, both from literature analysis and from experience. Considering these three implementations of imperfect maintenance actions and the main models proposed in the literature, we

illustrate how to identify the most suitable model for each real case.

**Keywords:** imperfect maintenance, optimization model, reliability

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Maintenance is defined as "the combination of all technical, administrative and managerial actions during the lifecycle of an item intended to retain it in or restore it to, a state in which it can perform the required function" [1]. Maintenance is everywhere, when there are systems, machines, elements that we use every day, requiring specific actions for functioning correctly, since degradations and failures reduce the effectiveness in their use. The industrial

Filippo De Carlo and Maria Antonietta Arleo

Additional information is available at the end of the chapter

Filippo De Carlo and Maria Antonietta Arleo

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69286

**Abstract**

**1. Introduction**

**Practice**

**Practice**

**Provisional chapter**

## **Imperfect Maintenance Models, from Theory to Practice Practice**

**Imperfect Maintenance Models, from Theory to**

DOI: 10.5772/intechopen.69286

Filippo De Carlo and Maria Antonietta Arleo

Filippo De Carlo and Maria Antonietta Arleo Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69286

#### **Abstract**

The role of maintenance in the industrial environment changed a lot in recent years, and today, it is a key function for long-term profitability in an organization. Many contributions were recently written by researchers on this topic. A lot of models were proposed to optimize maintenance activities while ensuring availability and high-quality requirements. In addition to the well-known classification of maintenance activities—preventive and corrective—in the last decades, a new classification emerged in the literature regarding the degree of system restoration after maintenance actions. Among them, the imperfect maintenance is one of the most studied maintenance types: it is defined as an action after which the system lies in a state somewhere between an "as good as new" state and its pre-maintenance condition "as bad as old." Most of the industrial companies usually operate with imperfect maintenance actions, even if the awareness in actual industrial context is limited. On the practical definition side, in particular, there are some real situations of imperfect maintenance: three main specific cases were identified, both from literature analysis and from experience. Considering these three implementations of imperfect maintenance actions and the main models proposed in the literature, we illustrate how to identify the most suitable model for each real case.

**Keywords:** imperfect maintenance, optimization model, reliability

## **1. Introduction**

Maintenance is defined as "the combination of all technical, administrative and managerial actions during the lifecycle of an item intended to retain it in or restore it to, a state in which it can perform the required function" [1]. Maintenance is everywhere, when there are systems, machines, elements that we use every day, requiring specific actions for functioning correctly, since degradations and failures reduce the effectiveness in their use. The industrial

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

sector is perhaps one of the most interested in maintenance actions since companies need to guarantee their required productivity targets. Despite this, maintenance has not always had the attention it deserved and for many years it was a "Cinderella function" [2], but recently its role was revalued, and since the 1960s, it was considered as a specific organizational unit [3]. According to Sherwin [2], the reasons why maintenance was a "Cinderella function" for so many years are mostly historical and can be overcome by new information technology (IT). IT, in fact, simplifies data acquisition and analysis of systems requiring maintenance activities, whereas integrated IT allows mathematical optimization of many aspects related to maintenance, such as costs and availability [2].

One of the strategies to adopt in order to increase awareness of maintenance importance in industrial and productive contexts is to prove its effectiveness [4]. It is essential to measure maintenance performance, for the justification of investments in this function [5] and for strategic thinking for asset managers. However, in the existing literature, only the internal efficiency is measured even if the maintenance contribution toward a total business goal should be measured (both external effectiveness and internal efficiency). Life-cycle profit (LCP) could be a fair measure of overall effectiveness for highlighting both value and cost of maintenance [2]. Maintenance, in fact, consists of so many activities that it is difficult to quantify its benefits at an individual activity level, whereas at a macro level, it is difficult to find the best trade-off between costs and benefits for the company profit [6].

Despite all that, today it is accepted that maintenance is a key function for long-term profitability in an organization [7], and for this reason, organizations are treating maintenance as an important part of their business [8], in the same way as other functions like production, marketing, sales and so on. Effective maintenance management, in fact, requires a multidisciplinary approach where maintenance is viewed strategically from the overall business perspective [9]. Companies invest in early reliability estimation also in order to setup their on-field service [10].

Maintenance engineering is one of the three main maintenance organizational processes, as

**Engineering**

Proacve maintenance Maintenance prevenon

Imperfect Maintenance Models, from Theory to Practice http://dx.doi.org/10.5772/intechopen.69286 337

Condion Based Maintenance/ Predicve maintenance

Maintenance has a unique role also in the latest 4th Generation Industrial Revolution (Industry 4.0), which focuses on intelligent products and production processes [14]. The new digital industrial technology defines a transformation where sensors, machines, workpieces and Information Systems are connected along the value chain: internet allows communication between humans and machines in cyber-physical systems (CPS). The interaction with surrounding systems is able to create self-aware and self-learning machines condition, with consequent improvement of overall performance and maintenance management [15]. It is clear that maintenance processes must be integrated in an effective way in the Industry 4.0 framework. Digitalization and networking, in particular, shall provide an increasing amount of actor and sensor data which can support the continuous monitoring of the process and of the machines conditions. Data, in fact, can be recorded and transmitted in real time to the cloud for predictive maintenance analysis.

Maintenance engineering is strictly connected to maintenance management and maintenance implementation. In fact, the maintenance implementation process gets orders from maintenance management, to which refer on their progress. Maintenance management sends information to maintenance engineering function for reliability and maintenance analysis. Then, maintenance engineering, through tools and specific software, defines maintenance plans to be transferred to

It is well recognized, however, that in many asset-intensive industries, maintenance costs are an important part of the operational cost [5], both for preventive and for corrective maintenance activities. Even if corrective and preventive maintenance is the most known maintenance

maintenance management function and, finally, to maintenance implementation [16].

shown in **Figure 2**, adapted from Furlanetto et al. [16].

Correcve maintenance

**Prevenon**

**Figure 1.** From failure to prevention [11].

The maintenance role evolution in industrial context could be summarized through **Figure 1**, proposed by Furlanetto and Mastriforti [11].

Corrective maintenance (CM) is certainly the approach with the lowest prevention and engineering contributions since it simply reacts to an occurred failure. Moving from CM to prevention maintenance, it goes from a defeatist and passive approach to a more "aggressive" one, where engineering principles and the aim of preventing future failures are the most important aspects in maintenance management.

Therefore, maintenance engineering is nowadays a very important function in industrial context. It is usually defined as "a staff function whose prime responsibility is to ensure that maintenance techniques are effective, equipment is designed and modified to improve maintainability, on-going maintenance technical problems are investigated, and appropriate corrective and improvement actions are taken" [12]. It is a very strategic resource essential for ensuring production capacity, product quality and best lifecycle cost. It is related to Business Continuity and to High-Reliability Organization (HRO) too: the choice of a specific maintenance policy, in fact, defines a more or less compliant maintenance approach to the HRO paradigm [13].

**Figure 1.** From failure to prevention [11].

sector is perhaps one of the most interested in maintenance actions since companies need to guarantee their required productivity targets. Despite this, maintenance has not always had the attention it deserved and for many years it was a "Cinderella function" [2], but recently its role was revalued, and since the 1960s, it was considered as a specific organizational unit [3]. According to Sherwin [2], the reasons why maintenance was a "Cinderella function" for so many years are mostly historical and can be overcome by new information technology (IT). IT, in fact, simplifies data acquisition and analysis of systems requiring maintenance activities, whereas integrated IT allows mathematical optimization of many aspects related to mainte-

One of the strategies to adopt in order to increase awareness of maintenance importance in industrial and productive contexts is to prove its effectiveness [4]. It is essential to measure maintenance performance, for the justification of investments in this function [5] and for strategic thinking for asset managers. However, in the existing literature, only the internal efficiency is measured even if the maintenance contribution toward a total business goal should be measured (both external effectiveness and internal efficiency). Life-cycle profit (LCP) could be a fair measure of overall effectiveness for highlighting both value and cost of maintenance [2]. Maintenance, in fact, consists of so many activities that it is difficult to quantify its benefits at an individual activity level, whereas at a macro level, it is difficult to find the best trade-off

Despite all that, today it is accepted that maintenance is a key function for long-term profitability in an organization [7], and for this reason, organizations are treating maintenance as an important part of their business [8], in the same way as other functions like production, marketing, sales and so on. Effective maintenance management, in fact, requires a multidisciplinary approach where maintenance is viewed strategically from the overall business perspective [9]. Companies invest in early reliability estimation also in order to setup their

The maintenance role evolution in industrial context could be summarized through **Figure 1**,

Corrective maintenance (CM) is certainly the approach with the lowest prevention and engineering contributions since it simply reacts to an occurred failure. Moving from CM to prevention maintenance, it goes from a defeatist and passive approach to a more "aggressive" one, where engineering principles and the aim of preventing future failures are the most

Therefore, maintenance engineering is nowadays a very important function in industrial context. It is usually defined as "a staff function whose prime responsibility is to ensure that maintenance techniques are effective, equipment is designed and modified to improve maintainability, on-going maintenance technical problems are investigated, and appropriate corrective and improvement actions are taken" [12]. It is a very strategic resource essential for ensuring production capacity, product quality and best lifecycle cost. It is related to Business Continuity and to High-Reliability Organization (HRO) too: the choice of a specific maintenance policy, in

fact, defines a more or less compliant maintenance approach to the HRO paradigm [13].

nance, such as costs and availability [2].

336 System Reliability

on-field service [10].

between costs and benefits for the company profit [6].

proposed by Furlanetto and Mastriforti [11].

important aspects in maintenance management.

Maintenance engineering is one of the three main maintenance organizational processes, as shown in **Figure 2**, adapted from Furlanetto et al. [16].

Maintenance has a unique role also in the latest 4th Generation Industrial Revolution (Industry 4.0), which focuses on intelligent products and production processes [14]. The new digital industrial technology defines a transformation where sensors, machines, workpieces and Information Systems are connected along the value chain: internet allows communication between humans and machines in cyber-physical systems (CPS). The interaction with surrounding systems is able to create self-aware and self-learning machines condition, with consequent improvement of overall performance and maintenance management [15]. It is clear that maintenance processes must be integrated in an effective way in the Industry 4.0 framework. Digitalization and networking, in particular, shall provide an increasing amount of actor and sensor data which can support the continuous monitoring of the process and of the machines conditions. Data, in fact, can be recorded and transmitted in real time to the cloud for predictive maintenance analysis.

Maintenance engineering is strictly connected to maintenance management and maintenance implementation. In fact, the maintenance implementation process gets orders from maintenance management, to which refer on their progress. Maintenance management sends information to maintenance engineering function for reliability and maintenance analysis. Then, maintenance engineering, through tools and specific software, defines maintenance plans to be transferred to maintenance management function and, finally, to maintenance implementation [16].

It is well recognized, however, that in many asset-intensive industries, maintenance costs are an important part of the operational cost [5], both for preventive and for corrective maintenance activities. Even if corrective and preventive maintenance is the most known maintenance

• *R*(*t*): reliability function

element that has survived up to that time t.

• *λ*(*t*): hazard function, defined as the trend of the instantaneous failure rate at time *t* of an

Imperfect Maintenance Models, from Theory to Practice http://dx.doi.org/10.5772/intechopen.69286 339

Hazard function is usually presented as a time depending curve, called the "bathtub" curve, which is useful for determining three main failure types corresponding to three different life stages of a component. The life of a device has a first part with a failure rate relatively high and a descending shape (decreasing failure rate DFR) because of the so-called early failures depending on potential manufacturing defects (design or installation defects, for example); the central part of its life corresponds to the useful life, in which it is usually assumed that the failure rate does not change over time (constant failure rate CFR); finally, the end of life

The reliability properties of a component might be represented with a specific probability distribution model in each one of the main phases (DFR, CFR, IFR): the early stage is modelled through the Weibull distribution, the random failure stage is defined by a negative exponential distribution and finally, for the wear-out failures, the normal distribution is the most suitable one, since its failure rate is always a monotonically increasing function of time (so the normal distribution is an IFR distribution) [18]. Obviously, the most suitable distribution has

The knowledge of the reliability features of a system is the starting point for the definition of the maintenance and replacement models to apply. Many models are shown in the literature [19]: all of them can fall into some categories, such as the age replacement policy, the block replacement policy, the periodic preventive maintenance policy, the failure limit policy, the

Reliability parameters are used in maintenance optimization models, too. For a long time, in fact, the cost was the only parameter considered for their optimization, in line with the old maintenance concept (maintenance as a necessary evil and the only maintenance is corrective). Today, however, both costs and reliability measures (such as availability) are present in maintenance optimization models. In literature, there are many contributions on maintenance optimization models, and the review papers on this topic are really interesting [21, 22]. Some models, for example, try to optimize maintenance activities according to risk management [23]: the main aim is the minimization of the effects of failures on the organization's main objectives.

Maintenance models could be quite difficult to apply because of lack of data on maintenance actions and faults [24]. At the same time, cost data could be harder to have, especially with respect to indirect costs since, for example, it could be very difficult to quantify intangible

Furthermore, models are usually complex to apply since several constraints and several objectives usually affect the optimization of maintenance policies [22]: simulation approach could

In conclusion, we can say that maintenance optimization models could be very useful in a maintenance management process because they allow to consider all the main maintenance objectives (ensuring system function, ensuring system life, ensuring safety, ensuring human

corresponds to the wear-out phase with an increasing failure rate (IFR).

to be selected according to the real failure rate dependency on time.

opportunistic maintenance policy, the inspection policy [20], etc.

aspects like the benefits of maintenance.

be a viable alternative to the analytical one.

**Figure 2.** Role of maintenance engineering in maintenance organization process [16].

types, in the last decades, new kinds of maintenance were identified in the literature, as better explained in the following sections.

#### **1.1. Maintenance and reliability**

Reliability and maintenance are strictly connected: reliability models, in particular, define the main reliability properties of a system, which are essential for maintenance management.

Here, we show a brief summary of the most important reliability considerations useful in maintenance theory.

First of all, reliability is defined as the probability that a component (or an entire system) will perform its function for a specified period of time, when operating in its design environment [17]: reliability definition, therefore, requires an unambiguous criterion for distinguishing operation from non-functioning states and the exact definition of environmental conditions. In this way, reliability will depend only on time.

The most significant reliability parameters are:

• *R*(*t*): reliability function

types, in the last decades, new kinds of maintenance were identified in the literature, as better

**Figure 2.** Role of maintenance engineering in maintenance organization process [16].

Reliability and maintenance are strictly connected: reliability models, in particular, define the main reliability properties of a system, which are essential for maintenance management. Here, we show a brief summary of the most important reliability considerations useful in