# Maximization Approach of Hosting Capacity Based on Uncertain Renewable Energy Resources Using Network Reconfiguration and Soft Open Points

Authors: Ahmed S. Abbas; Adel A. Abou El-Ela; Ragab A. El-Sehiemy
Journal: International Transactions on Electrical Energy Systems
 (2022)

---

## Abstract

Nowadays, the continuous increase of renewable energy integration in power systems has become a global demand, especially after the urgent need to reduce the greenhouse gases resulting from fossil fuel fuels. Therefore, various methods have been presented to increase the hosting capacity (HC) that increases the system's ability to integrate more renewable energy resources (RERs) without exceeding the system's operational limits. In this paper, an optimization-based approach is proposed for assessing and maximizing the HC via network reconfiguration (NR) and/or soft open points (SOPs) techniques. The uncertain nature related to photovoltaic (PV) and wind turbine (WT) is considered and simulated based on hourly historical data in addition to taking into account the load variability. Various case studies are considered to evaluate the impact of the NR and SOPs combination on maximizing the system HC. The proposed approach has been tested with the standard IEEE 33-bus and IEEE 69-bus distribution systems. The obtained results confirmed the effectiveness of the proposed approach in maximizing the hosting capacity.


---

## Body

## 1. Introduction

### 1.1. Motivation and Incitement

The global trend of maximizing the integration of RERs, in order to reduce the greenhouse gases faces many technical challenges. These challenges include power quality issues, reliability, and energy loss issues. Many research work has been presented on finding the maximum limit for RERs integration in distribution systems without exceeding any of the considered operational limits or the performance limits [1].


### 1.2. Literature Review

Some studies addressed the RERs hosting capacity (HC) determination for the distribution system without using any enhancement techniques as in [2–4]. Other studies focused on developing techniques and methodologies to enhance the HC of the RERs, such as reactive power control techniques, active power curtailment techniques, network reconfiguration, etc. Many factors can affect the HC enhancement issue, such as the uncertainty consideration, the performance limits considered, the types of RERs considered, and the enhancement technique.Considering the uncertain nature of the RERs output power in addition to the load demand uncertainty increases the problem complexity. Therefore, a lot of HC studies ignore generation and/or load uncertainties, but this minimizes the accuracy and robustness of the presented methods. In [5], the uncertainty of PV was considered while enhancing its HC using a static voltage compensator (SVC). In [6], The uncertainties of both WT and load demand were taken into consideration while presenting a hybrid HC enhancement technique using an on-load tap changing (OLTC) transformer and voltage regulators. In [7–9], the authors presented various stochastic scenarios for representing and reducing the uncertainty of WT, PV, and load demand.The second factor that can affect the HC is the considered performance limits that must be kept within their allowable boundaries while determining the HC. Various performance limits have been considered in HC problems, such as overvoltage [10, 11], voltage unbalance [12, 13], overloading of the transmission lines [14, 15], harmonic distortion [4, 16], and line current carrying capacity [17]. Authors in [18] addressed the impact of different performance limits on the HC value by assessing the HC by considering single and multiple performance limits without any enhancement techniques. Another factor that affects the HC calculations is the type of the RERs considered, where considering more than one type of RERs increases the problem complexity due to the conflicting characteristics of each type, especially when the uncertainty is considered [19].The type of the HC enhancement technique plays an effective role in maximizing the HC of the distribution system. In [14], the conductor reinforcement method was employed to improve the HC and reduce the annual energy losses. In [11], the HC of wind turbines (WTs) in distribution networks was enhanced by using active network management (ANM) technique. The optimal capacitor banks allocation technique was presented in [10] to increase the integration of RERs and enhance the system performance. In [20], DSTATCOM was integrated along with PV systems to enhance HC and reduce system losses. The optimal NR was usually used for distribution systems to minimize the system power losses and improve the system performance as in [21, 22]. Recently, the impact of NR on enhancing the performance of the active distribution systems was studied through different methodologies [15]. In [23], the optimal planning of both DGs and reclosures was presented to improve the system reliability using two metaheuristic algorithms considering the uncertain nature of both WTs and PVs. In [24], a graphical-based method was introduced to optimally reconfigure the distribution system to minimize the system power losses without the need to check the system radiality, where the introduced method was tested on different scales of distribution systems. In [25], the combination between the optimal placement of DGs and optimal NR was presented as an effective technique for maximizing the HC, where a multiperiod linear programming was utilized to solve the optimization problem. Authors in [23, 26] presented various heuristic techniques to get the optimal network topology using NR to enhance the integration of the RERs. The effect of total load variation on determining the optimal system configuration with DGs planning was introduced in [27]. In [28], coordination between the RERs penetration and system reconfiguration was addressed, where different mathematical and heuristic methods were employed during enhancing the RERs penetration in distribution systems.Soft open points (SOPs) are considered the latest techniques, which are able to provide active and reactive power control, and are employed to enhance the HC in distribution systems. In [29], an approach was proceeded to find the adequate management of RERs in distribution systems supported by SOPs. In [30], the authors considered different typologies of SOPs to evaluate their effectiveness in enhancing the HC of distributed generation units (DGs). In [31], SOP technology was employed to improve the system controllability and reduce the uncertainty effect of high PV integration. In [32], the authors presented a method for improving the HC depending on the active and reactive power control through the optimal planning of the SOP, where a bilevel optimization formulation was considered. Also, the optimal placement and sizing of SOPs were investigated on standard and real distribution networks using a mixed integer programming model based on probability scenarios in [33]. In [34], the impact of integrating three predefined SOP sizes on the system HC was quantified using second-order programming, where the system loads variability was simulated using Monte Carlo Simulation (MCS). The authors in [35] presented a deterministic method for maximizing the system HC using SOPs without exceeding the thermal and voltage limits where the load variability was ignored.A few research work is presented to evaluate the combination of both NR and SOPs for improving the RERs integration. Authors in [5, 36] presented optimization-based methods to increase the DGs integration using both NR and SOP techniques in small-scale distribution systems without considering the DGs uncertainty. In [37], an optimization-based sequential approach was presented to optimize the benefits of both NR and SOPs in maximizing the HC. The authors considered the load balancing and the voltage stability as the performance limits while ignoring the uncertain nature of the DGs’ output power and load demand. Authors in [38] introduced a multiscenarios approach while the incorporation between NR and SOPs for enhancing the HC. The problem was formulated as a single objective optimization model considering different load levels and without taking into consideration the uncertainty output of the DGs. Also, in [39], the same combination between NR and SOP was presented using deterministic and probabilistic cases while ignoring the RERs uncertainties. From the presented literature review, there is a gap either in the uncertainty consideration or in the performance limits or in the RERs type.


### 1.3. Contribution and Paper Organization

Motivated by the research gap in the presented literature review, the salient contributions of this paper are summarized as follows:(1)
An optimization-based approach is proposed to evaluate and enhance the HC of the distribution systems considering uncertainties of both PV, WT, and the load demand variation.(2)
A comparative study between three optimization algorithms is presented while assessing the HC.(3)
The impact of the SOP number on maximizing the HC is evaluated.(4)
NR, SOPs, and a combination of NR and SOPs techniques are proposed and compared to obtain an effective approach for maximizing the system HC.(5)
The optimal allocation of RERs is obtained along with maximizing the HC through determining the optimal location, size, number, type, and power factor of both PV and WT.The rest parts of this paper are ordered as follows: Section2 presents the modeling of various types of RERs and loads. Section 3 presents the optimization algorithm that will be used to optimize the hosting capacity. Section 4 presents the proposed techniques for enhancing the HC. Section 5 presents the mathematical representation of the target problem. Section 6 presents the applications of the proposed techniques. The conclusions of the paper are represented in Section 7.


## 1.1. Motivation and Incitement

The global trend of maximizing the integration of RERs, in order to reduce the greenhouse gases faces many technical challenges. These challenges include power quality issues, reliability, and energy loss issues. Many research work has been presented on finding the maximum limit for RERs integration in distribution systems without exceeding any of the considered operational limits or the performance limits [1].


## 1.2. Literature Review

Some studies addressed the RERs hosting capacity (HC) determination for the distribution system without using any enhancement techniques as in [2–4]. Other studies focused on developing techniques and methodologies to enhance the HC of the RERs, such as reactive power control techniques, active power curtailment techniques, network reconfiguration, etc. Many factors can affect the HC enhancement issue, such as the uncertainty consideration, the performance limits considered, the types of RERs considered, and the enhancement technique.Considering the uncertain nature of the RERs output power in addition to the load demand uncertainty increases the problem complexity. Therefore, a lot of HC studies ignore generation and/or load uncertainties, but this minimizes the accuracy and robustness of the presented methods. In [5], the uncertainty of PV was considered while enhancing its HC using a static voltage compensator (SVC). In [6], The uncertainties of both WT and load demand were taken into consideration while presenting a hybrid HC enhancement technique using an on-load tap changing (OLTC) transformer and voltage regulators. In [7–9], the authors presented various stochastic scenarios for representing and reducing the uncertainty of WT, PV, and load demand.The second factor that can affect the HC is the considered performance limits that must be kept within their allowable boundaries while determining the HC. Various performance limits have been considered in HC problems, such as overvoltage [10, 11], voltage unbalance [12, 13], overloading of the transmission lines [14, 15], harmonic distortion [4, 16], and line current carrying capacity [17]. Authors in [18] addressed the impact of different performance limits on the HC value by assessing the HC by considering single and multiple performance limits without any enhancement techniques. Another factor that affects the HC calculations is the type of the RERs considered, where considering more than one type of RERs increases the problem complexity due to the conflicting characteristics of each type, especially when the uncertainty is considered [19].The type of the HC enhancement technique plays an effective role in maximizing the HC of the distribution system. In [14], the conductor reinforcement method was employed to improve the HC and reduce the annual energy losses. In [11], the HC of wind turbines (WTs) in distribution networks was enhanced by using active network management (ANM) technique. The optimal capacitor banks allocation technique was presented in [10] to increase the integration of RERs and enhance the system performance. In [20], DSTATCOM was integrated along with PV systems to enhance HC and reduce system losses. The optimal NR was usually used for distribution systems to minimize the system power losses and improve the system performance as in [21, 22]. Recently, the impact of NR on enhancing the performance of the active distribution systems was studied through different methodologies [15]. In [23], the optimal planning of both DGs and reclosures was presented to improve the system reliability using two metaheuristic algorithms considering the uncertain nature of both WTs and PVs. In [24], a graphical-based method was introduced to optimally reconfigure the distribution system to minimize the system power losses without the need to check the system radiality, where the introduced method was tested on different scales of distribution systems. In [25], the combination between the optimal placement of DGs and optimal NR was presented as an effective technique for maximizing the HC, where a multiperiod linear programming was utilized to solve the optimization problem. Authors in [23, 26] presented various heuristic techniques to get the optimal network topology using NR to enhance the integration of the RERs. The effect of total load variation on determining the optimal system configuration with DGs planning was introduced in [27]. In [28], coordination between the RERs penetration and system reconfiguration was addressed, where different mathematical and heuristic methods were employed during enhancing the RERs penetration in distribution systems.Soft open points (SOPs) are considered the latest techniques, which are able to provide active and reactive power control, and are employed to enhance the HC in distribution systems. In [29], an approach was proceeded to find the adequate management of RERs in distribution systems supported by SOPs. In [30], the authors considered different typologies of SOPs to evaluate their effectiveness in enhancing the HC of distributed generation units (DGs). In [31], SOP technology was employed to improve the system controllability and reduce the uncertainty effect of high PV integration. In [32], the authors presented a method for improving the HC depending on the active and reactive power control through the optimal planning of the SOP, where a bilevel optimization formulation was considered. Also, the optimal placement and sizing of SOPs were investigated on standard and real distribution networks using a mixed integer programming model based on probability scenarios in [33]. In [34], the impact of integrating three predefined SOP sizes on the system HC was quantified using second-order programming, where the system loads variability was simulated using Monte Carlo Simulation (MCS). The authors in [35] presented a deterministic method for maximizing the system HC using SOPs without exceeding the thermal and voltage limits where the load variability was ignored.A few research work is presented to evaluate the combination of both NR and SOPs for improving the RERs integration. Authors in [5, 36] presented optimization-based methods to increase the DGs integration using both NR and SOP techniques in small-scale distribution systems without considering the DGs uncertainty. In [37], an optimization-based sequential approach was presented to optimize the benefits of both NR and SOPs in maximizing the HC. The authors considered the load balancing and the voltage stability as the performance limits while ignoring the uncertain nature of the DGs’ output power and load demand. Authors in [38] introduced a multiscenarios approach while the incorporation between NR and SOPs for enhancing the HC. The problem was formulated as a single objective optimization model considering different load levels and without taking into consideration the uncertainty output of the DGs. Also, in [39], the same combination between NR and SOP was presented using deterministic and probabilistic cases while ignoring the RERs uncertainties. From the presented literature review, there is a gap either in the uncertainty consideration or in the performance limits or in the RERs type.


## 1.3. Contribution and Paper Organization

Motivated by the research gap in the presented literature review, the salient contributions of this paper are summarized as follows:(1)
An optimization-based approach is proposed to evaluate and enhance the HC of the distribution systems considering uncertainties of both PV, WT, and the load demand variation.(2)
A comparative study between three optimization algorithms is presented while assessing the HC.(3)
The impact of the SOP number on maximizing the HC is evaluated.(4)
NR, SOPs, and a combination of NR and SOPs techniques are proposed and compared to obtain an effective approach for maximizing the system HC.(5)
The optimal allocation of RERs is obtained along with maximizing the HC through determining the optimal location, size, number, type, and power factor of both PV and WT.The rest parts of this paper are ordered as follows: Section2 presents the modeling of various types of RERs and loads. Section 3 presents the optimization algorithm that will be used to optimize the hosting capacity. Section 4 presents the proposed techniques for enhancing the HC. Section 5 presents the mathematical representation of the target problem. Section 6 presents the applications of the proposed techniques. The conclusions of the paper are represented in Section 7.


## 2. Renewable Energy Resources and Loads Modeling

Many studies have considered the RERs’s output as a fixed value or deal with the worst-case scenarios, which lacks accuracy. However, the output power from renewable resources (PV and WT) do not have a certain value over the time as it depends on uncertain weather parameters such as wind speedVW and solar irradiance G , which are changing continuously so that to represent a robust approach, the variance of the weather parameters should be simulated effectively.Therefore, this paper uses the hourly recorded data of VW and G to model the uncertainty of the PV and WT output power. Also, to present a model that simulates the actual, various load demand levels are considered along with the RERs uncertainty as follows:(1)
Loading real historical data forG and VW for one year (2016) from the Zaafarana region, Egypt [40].(2)
Assuming 5 loading levels as a percentage of the total demand, representing the variation of loading as follows: (10, 30, 50, 70, 90) % from total load demand (TLD).(3)
Determining the boundaries of theVW and G from the loaded data in step 1. The lowest and highest values for VW and G are 1.106, 8.754, 0.1103, and 0.992, respectively.(4)
Equally dividing the range between each parameter (G and VW) boundaries into four regions. This results in representing each parameter with five values representing the whole variation region of the uncertainty parameter as shown in Table 1.(5)
Generating the probability scenarios by permutation using the five representing values of the three uncertainty parameters (G, VW and load demand). The generated uncertainty scenarios equal 53=125 scenarios.(6)
Using the actual parameters' values from step 1 to represent each value to each corresponding one from the five calculated values in step 4. So, the number of reputations for every scenario is computed as in Table1.Table 1
Summary of the uncertainty analysis cases.
G0.11030.33080.55130.77180.992LR0.9000001.106VW0.7000000.5100000.3305515762220.14913200.9000003.0180.71012100.511471327250.31545194190190730.118835810.93001044.930.716531329350.5367325755660.318752142581431030.114033320.93412036.8420.7107111429470.5162384655700.34951041381431400.11110340.9501208.7540.7154910120.51733140.352262835190.111010After that, the resulting uncertainty scenarios are used for computing the corresponding generated power from the RERs as follows:(1)PWT=PrWT×VW−VoVr−Vo,Vo≤VW≤Vr,0,Vr≥VWorVW≥Vm,PrWT,Vr≤VW≤Vm.The values ofVr,Vo,Vm are considered to be 10 m/s, 3 m/s, and 17 m/s, respectively. The output power of the PV plant PPV is determined as follows:(2)PPV=PrPVG2Gstd×GC,0≤G≤GC,PrPVGGstd,GC≤G.The values ofGstd,Gc are considered to be 1000 W/m2 and 120 W/m2, respectively.


## 3. Proposed Optimization Algorithm

This paper proposed the manta ray foraging optimization (MRFO) algorithm presented by Zhao et al. in 2020 [41]. It follows the behavior of the manta ray while searching for its food (Plankton) in the sea. The foraging process is achieved through three types of foraging; chain, somersault, and cyclone foraging. The mathematical representations of the different foraging types are illustrated as follows:


### 3.1. Chain Foraging

Following chain foraging, each population updates its position by the best solution obtained around its position. This process goes behind the following equation:(3)xit+1=r.xbestt−xit+ωxbestt−xit+xitr.xi−1t−xit+ωxbestt−xit+xit,ω=2rlogr.


### 3.2. Cyclone Foraging

The manta ray has two types of motion in the cyclone foraging, the first toward the plankton and the other one in the direction of the manta ray in front of it. This mechanism helps in enhancing the algorithm exploration, and it can be represented mathematically as follows:(4)xit+1=r.xbestt−xit+ρxbestt−xit+xbest,r.xbestt−xit+ρxbestt−xit+xbest,ρ=2er1T−t+1/T×sin2πr1.The exploration process is expressed by the next equations:(5)xrand=LB+r×UB−LB,xit+1=xrand+r.xrandt−xit+ρxrandt−xit,xrand+r.xi−1t−xit+ρxrandt−xit.


### 3.3. Somersault Foraging

The aim of the somersault foraging is to generate a set of manta rays circulating around the plankton as follows:(6)xit+1=xit+λ×r2×xbest−r3×xit.


## 3.1. Chain Foraging

Following chain foraging, each population updates its position by the best solution obtained around its position. This process goes behind the following equation:(3)xit+1=r.xbestt−xit+ωxbestt−xit+xitr.xi−1t−xit+ωxbestt−xit+xit,ω=2rlogr.


## 3.2. Cyclone Foraging

The manta ray has two types of motion in the cyclone foraging, the first toward the plankton and the other one in the direction of the manta ray in front of it. This mechanism helps in enhancing the algorithm exploration, and it can be represented mathematically as follows:(4)xit+1=r.xbestt−xit+ρxbestt−xit+xbest,r.xbestt−xit+ρxbestt−xit+xbest,ρ=2er1T−t+1/T×sin2πr1.The exploration process is expressed by the next equations:(5)xrand=LB+r×UB−LB,xit+1=xrand+r.xrandt−xit+ρxrandt−xit,xrand+r.xi−1t−xit+ρxrandt−xit.


## 3.3. Somersault Foraging

The aim of the somersault foraging is to generate a set of manta rays circulating around the plankton as follows:(6)xit+1=xit+λ×r2×xbest−r3×xit.


## 4. Enhancement of the Hosting Capacity

### 4.1. Network Reconfiguration (NR)

There are two types of network reconfiguration, namely static and dynamic. Static reconfiguration is preferred in this study rather than the dynamic one because all the system switches are available to be controlled in the static reconfiguration. On the other side, the remotely controlled switches are only available in the dynamic reconfiguration, which limits the available configurations and also needs automatized distribution system infrastructure. Static reconfiguration is proposed and employed to enhance the system HC by changing the status of the system lines, either sectionalized lines or tie lines, to obtain the optimal configuration of the network that enhances the HC. So, the distribution system reconfiguration can be formulated as an optimization problem that can be solved by using the proposed metaheuristic optimization algorithm.To keep the distribution system radial after the reconfiguration process, two radiality checks are considered to ensure the system radiality during each obtained reconfiguration solution. The first radiality check is to ensure that the number of tie lines is still the same as before and after the reconfiguration. But sometimes, this check is not sufficient to ensure the system's radiality, so the second check is performed to ensure that the power flow throughout the system is converged.


### 4.2. Soft Open Points (SOPs)

A soft open point (SOP) is a power electronic device that can be used in radial distribution networks instead of normally open points (NOPs) to provide a better system performance as it can exchange active and reactive power between the system feeders plus control the system voltage by a fast and effective way. SOPs have various topologies, such as two terminals SOP, multiterminal SOP, and SOP with energy storage. In this paper, two terminals’ Back-to-Back Voltage Source Converters (B2B VSC) topology are considered, as shown in Figure1 Due to the existence of the DC bus between the two converters, the output reactive power of the two converters is independent, which is considered as an extra advantage.Figure 1
Two terminals Back-to-Back Voltage Source Converters (B2B VSC) topology.The considered SOP topology can be modeled by the following equations:(7)PISOP+PJSOP+LISOP×PISOP+LJSOP×PJSOP=0,(8)QminSOP≤QISOP≤QmaxSOP,(9)QminSOP≤QJSOP≤QmaxSOP,(10)QISOP2+PISOP2≤SISOP,(11)QJPISOP2+PJPISOP2≤SJPISOP.


## 4.1. Network Reconfiguration (NR)

There are two types of network reconfiguration, namely static and dynamic. Static reconfiguration is preferred in this study rather than the dynamic one because all the system switches are available to be controlled in the static reconfiguration. On the other side, the remotely controlled switches are only available in the dynamic reconfiguration, which limits the available configurations and also needs automatized distribution system infrastructure. Static reconfiguration is proposed and employed to enhance the system HC by changing the status of the system lines, either sectionalized lines or tie lines, to obtain the optimal configuration of the network that enhances the HC. So, the distribution system reconfiguration can be formulated as an optimization problem that can be solved by using the proposed metaheuristic optimization algorithm.To keep the distribution system radial after the reconfiguration process, two radiality checks are considered to ensure the system radiality during each obtained reconfiguration solution. The first radiality check is to ensure that the number of tie lines is still the same as before and after the reconfiguration. But sometimes, this check is not sufficient to ensure the system's radiality, so the second check is performed to ensure that the power flow throughout the system is converged.


## 4.2. Soft Open Points (SOPs)

A soft open point (SOP) is a power electronic device that can be used in radial distribution networks instead of normally open points (NOPs) to provide a better system performance as it can exchange active and reactive power between the system feeders plus control the system voltage by a fast and effective way. SOPs have various topologies, such as two terminals SOP, multiterminal SOP, and SOP with energy storage. In this paper, two terminals’ Back-to-Back Voltage Source Converters (B2B VSC) topology are considered, as shown in Figure1 Due to the existence of the DC bus between the two converters, the output reactive power of the two converters is independent, which is considered as an extra advantage.Figure 1
Two terminals Back-to-Back Voltage Source Converters (B2B VSC) topology.The considered SOP topology can be modeled by the following equations:(7)PISOP+PJSOP+LISOP×PISOP+LJSOP×PJSOP=0,(8)QminSOP≤QISOP≤QmaxSOP,(9)QminSOP≤QJSOP≤QmaxSOP,(10)QISOP2+PISOP2≤SISOP,(11)QJPISOP2+PJPISOP2≤SJPISOP.


## 5. Mathematical Representation of the Target Problem

Maximizing the HC of RERs is formulated as an optimization problem with three performance limits (overvoltage, undervoltage, and line current capacity). Both PV and WT are considered renewable based DGs, which give rise to the control variables and thus further increase the problem complexity. Table2 shows the control variables of the formulated optimization problem. The power factor of each DG unit is considered to be flexible and not fixed at unity. So, the DG’s power factor is regarded as to be one of the problem control variables that must be determined. Also, the value of the substation voltage is considered to be a control variable that can help in maximizing the HC.Table 2
Optimization problem control variables.
Renewable based DGsSOPsNRSubstationType, location, size, and power factorLocation (from-to), size (P, Q)Sectionalized lines, tie linesSubstation voltageThe optimization problem objective function and constraints are described as follows:


### 5.1. Objective Function

Maximizing the HC of the RERs in the distribution system is considered to be the objective function of the optimization problem, which is considered as a percentage of the TLD as described in the following equation:(12)HC=max∑PDGiTLD.


### 5.2. Constraints

#### 5.2.1. Over- and UnderVoltage

(13)Vmaxi≤Vi≤Vmini.This constraint guarantees that the voltage at any system bus will not exceed its upper and lower permissible limits at any generation or loading condition.


#### 5.2.2. Line Current Capacity

This constraint is considered to guarantee that none of the system lines exceeds its thermal limit at any generation or loading condition.(14)IL,imax≤IL,i.


#### 5.2.3. Generation Constraints

(15)PGimin≤PGi≤PGimax,(16)QGimin≤QGi≤QGimin.These constraints are in addition to the constraints related to the enhancement techniques mentioned in Section4.


## 5.1. Objective Function

Maximizing the HC of the RERs in the distribution system is considered to be the objective function of the optimization problem, which is considered as a percentage of the TLD as described in the following equation:(12)HC=max∑PDGiTLD.


## 5.2. Constraints

### 5.2.1. Over- and UnderVoltage

(13)Vmaxi≤Vi≤Vmini.This constraint guarantees that the voltage at any system bus will not exceed its upper and lower permissible limits at any generation or loading condition.


### 5.2.2. Line Current Capacity

This constraint is considered to guarantee that none of the system lines exceeds its thermal limit at any generation or loading condition.(14)IL,imax≤IL,i.


### 5.2.3. Generation Constraints

(15)PGimin≤PGi≤PGimax,(16)QGimin≤QGi≤QGimin.These constraints are in addition to the constraints related to the enhancement techniques mentioned in Section4.


## 5.2.1. Over- and UnderVoltage

(13)Vmaxi≤Vi≤Vmini.This constraint guarantees that the voltage at any system bus will not exceed its upper and lower permissible limits at any generation or loading condition.


## 5.2.2. Line Current Capacity

This constraint is considered to guarantee that none of the system lines exceeds its thermal limit at any generation or loading condition.(14)IL,imax≤IL,i.


## 5.2.3. Generation Constraints

(15)PGimin≤PGi≤PGimax,(16)QGimin≤QGi≤QGimin.These constraints are in addition to the constraints related to the enhancement techniques mentioned in Section4.


## 6. Applications

### 6.1. Test Distribution System

The proposed procedure is applied to the IEEE 33-bus and 69-bus distribution systems. The IEEE 33-bus system substation voltage is 12.66 kV, and active and reactive load demands are 3.715 MW and 2.3 MVAr, respectively [22], Where the IEEE 69-bus system substation voltage is 12.66 kV. The total active and reactive load demands are 3.802 MW and 2.694 MVAr. The systems configurations are shown in Figures 2 and 3.Figure 2
Single line diagram of 33-bus distribution network.Figure 3
Single line diagram of 69-bus distribution network.


### 6.2. Simulation Scenarios

The simulation scenarios implemented via four cases are considered in this paper as follows:Case 1: this case aims to assess the HC of the system at the initial case without using any enhancement techniques. So that, the objective function of this case is maximizing the HC as in equation (13) with respect to the constraints in equations (14)–(16) where this can be achieved by determining the optimal siting, sizing, type, power factor, and number of DGs in the system.Case 2: this case aims to maximize the HC using SOP only. In this case, the effect of the SOPs number is evaluated by considering one, two, and three SOPs in three subcases. So that, the objective function of this case is maximizing the HC as in equation (12) with respect to the constraints in equations (13)–(16) and the SOP constraints in equations (7)–(11), where this can be achieved by determining the optimal siting, sizing, type, and number of DGs in the system in addition to the optimal planning of the SOPs.Case 3: maximizing HC of the system is implemented using NR only. So that, in this case, the RERs sites obtained in case 1 are considered to be the candidate buses in this case. Therefore, the control variables of this case are siting, sizing, type, and number of DGs in addition to the system lines that will be opened and the tie lines that will be connected.Case 4: a combination between NR and SOP in a bistage approach is proposed for maximizing the HC, where NR is carried out as described in case 2, then based on the newly obtained reconfiguration, SOP is optimally planned and configured, where the SOP number is selected to be the number at which the best results in case 3 are obtained.The procedure of the proposed approach is represented by the flowchart shown in Figure4. To prove the effectiveness of the proposed MRFO algorithm, a comparative study between the MRFO algorithm and two other known algorithms (Equilibrium optimization algorithm (EO) [42], Jaya optimization algorithm (JO) [43]) is performed on case 1. For a fair comparison, the initial solutions matrix is considered to be the same for the three algorithms in the first iteration. Also, the population and iterations number of the three algorithms are considered to be 100 and 50, respectively. The problem is formulated in a MATLAB m-file code and executed under the MATLAB R2016 environment. Power flow analyses are performed for every uncertainty scenario in each population based on the backward/forward sweeping technique [35]. The limits of the control variables are assumed, as illustrated in Table 3.Figure 4
The flow chart of the proposed HC maximization approach.Table 3
Control variables’ limits.
Control variableLimitsControl variableLimits33-Bus69-Bus33-Bus69-BusSubstation voltage0.97–1.03SOP power factor0.9–1RERs rating (MW)0–1SOP rating (MW)0–0.25RERs power factor0.9–1SOP locationAll sectionalized and tie linesRERs location2–332–69Many studies assume that all the system buses are candidate buses and suitable for RERs integration. However, this assumption is not accurate practically because of the presence of many inappropriate system buses for PV and/or WT integration due to weather and geographical reasons. Therefore, to establish a model close to reality, the candidate buses for the RERs integration are shown in Table4.Table 4
The considered candidate buses for the two test systems.
RERs typePVWT33-bus systemBus 6Bus 12Bus 24Bus 17Bus 21Bus 3269-bus systemBus 25Bus 61Bus 44Bus 53Bus 16Bus 34


### 6.3. Results and Discussion

#### 6.3.1. 33-Bus Distribution System Results

The aim of case 1 is to determine the HC of the system without using any improvement techniques. The proposed procedure for case 1 is applied using the three competitive algorithms, i.e., MRFO, EO, and JO. The obtained comparative results are shown in Table5. The results revealed that the system HC at the initial case obtained using MRFO, EO, and JO algorithms equal 1.8275 MW, 1.4282 MW, and 1.6004 MW, respectively. From the obtained results, it is clear that the MRFO resulted in higher HC compared with EO and JO algorithms. Also, the convergence curves of the three algorithms are shown in Figure 5, which illustrate the superior convergence characteristics of the MRFO algorithm.Table 5
Results of HC evaluation (case 1)
AlgorithmVsubHC (%)RERsPVWTMRFO1.0249.19Bus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.06140.42240.49900.15970.49900.1861Power factor−0.9−0.9−0.9−0.9−0.9−0.9EO1.0238.44Power (MW)0.06170.38520.03430.49900.36180.0863Power factor−0.9−0.9−0.9−0.9−0.90.9JO1.0243.08Power (MW)0.14320.24160.43760.17140.46290.1437Power factor−0.9−0.9−0.9−0.9−0.9−0.9Figure 5
MRFO convergence curve for case 1.In case 2, various numbers of SOPs are tested and optimally planned to show the effect of the SOPs number on maximizing the HC. As demonstrated in Table6, the maximum HC is obtained by using one, two, three, and four SOPs, while Table 7 illustrates the data of the RERs integrated into the system. From the obtained results, it is clear that the HC value increases with increasing the number of SOPs until reaching the knee point (two SOPs); the HC decreases with increasing the number of SOPs, where the HC reached 56.3% and 61.3% in case of using one and two SOPs, respectively, and it decreased to 58% and 55.3% after increasing the number of SOPs to three and four units, respectively.Table 6
HC results in case 2 for the the 33-bus system.
SOP no.HC (%)SOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR156.3%16–260.02059−0.025950.01977−0.024910.95171.0500261.3%10–280.02904−0.036590.02787−0.035130.95031.050018–190.05203−0.101180.04995−0.06295358%32–330.03689−0.046480.035410.044621.049924–200.01027−0.012940.009860.0124219–220.02316−0.029190.02224−0.028020.9505455.3%18–250.008250.010400.07920.09980.95091.049824–210.03580−0.045110.03437−0.0433132–330.05208−0.065630.049990.0630031–180.04389−0.055310.04214−0.05310Table 7
RERs specifications in case 2 for the 33-bus system.
SOP No.ParameterPVWTBus 12Bus 24Bus 6Bus 32Bus 21Bus 171Power (MW)—0.59310.53750.14140.58160.2395Power factor—0.90.90.90.90.92Power (MW)—0.7000.38060.24730.70000.2501Power factor—0.90.90.90.90.93Power (MW)—0.58910.64200.08380.64520.1934Power factor—−0.9000−0.9028−0.9000−0.9000−0.90694Power (MW)—0.63460.18120.40980.56450.2661Power factor—−0.9000−0.9044−0.9033−0.9000−0.9000In case 3, by applying the proposed NR technique to enhance the system HC, the results in Table8 are obtained. The results show that NR raised the HC percentage from 47.3% at the initial state to 79.3% by changing the network configuration to the configuration shown in Figure 6. The total capacity of the installed PV and WT plants equals 1.4309 MW and 1.515 MW, respectively. Also, the results confirmed that using NR is more effective than using SOPs for improving the HC.Table 8
RERs specifications in case 3 for the 33-bus system.
RERs TypePVWTBus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.47750.70890.24450.72490.43730.3549Power factor−0.0921−0.0915−0.9220−0.9167−0.9517−0.9360ParameterHC (%)Opened linesAdded linesVsubVminVmaxValue79.3%10 to 1121 to 111.00.95381.0499Figure 6
33-bus single line diagram after reconfiguration.In case 4, one, two, three, and four SOPs are optimally planned along with NR and RERs planning to maximize the system HC. The obtained results are provided in Tables9 and 10, where the planning of the PV, WT, SOPs, and the new tie line is shown. The obtained results declare that the hybrid technique in case 4 has a superior effect on maximizing the HC than using NR or SOPs techniques separately as in case 2 and case 3. Also, it is noticed that the results in case 4 follow the same behavior as in case 2, where the HC achieved 86.8%, 94.4%, 83.6%, and 80.7% with applying one, two, three, and four SOPs, respectively, with the NR. Figure 7 shows voltage profiles of case 4 with 2 SOPs for all the uncertainty scenarios, where all the buses’ voltages are within their limits. Also, Figure 8 shows the single line diagram of the system after applying case 4 with two SOPs.Table 9
RERs specifications in case 4 for the 33-bus system.
SOPs no.HC (%)VsubRERs TypePVWTPlaceBus 12Bus 24Bus 6Bus 32Bus 21Bus 17186.81.0Capacity (MW)0.66870.62940.18680.63180.73070.3776Power factor−0.9−0.90.9−0.9−0.9−0.9294.41.0Capacity (MW)0.44860.67350.62500.50710.74370.5114Power factor−0.9107−0.9−0.9−0.9−0.9−0.9383.61.0Capacity (MW)0.50840.75000.75000.16450.27690.6555Power factor−0.9−0.9−0.9−0.9−0.9−0.9003480.71.0Capacity (MW)0.62730.46110.54640.45040.36290.5564Power factor−0.9023−0.9−0.9−0.9−0.9−0.9015Table 10
HC results in case 4 for the 33-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR110 to 1121 to 1129–160.064150.080840.06682−0.084210.95231.0494210 to 1121 to 1124–170.01746−0.022000.018180.022910.95671.050030–180.04128−0.052010.04300−0.05418310 to 1121 to 1113–240.08223−0.103620.08565−0.107940.95671.048510–230.051660.065100.5381−0.0678110–110.106700.134460.11114−0.14006410 to 1121 to 1112–180.05588−0.070410.05820−0.073350.95731.047014–210.06122−0.077140.063770.0803631–270.05380−0.067800.05605−0.0706326–170.051300.064640.05343−0.06733Figure 7
Voltage profiles for the 33-bus system resulted from case 4 with two SOPs.Figure 8
33-bus single line diagram in case 4 with two SOPs.


#### 6.3.2. 69-Bus Distribution System Results

After applying case 1 to the IEEE 69-bus system, it is obtained that the system failed to integrate any RERs without using enhancement techniques. As the system’s voltage profile at the initial case is out of boundaries and remains out of boundaries with any integration from the RERs as shown in Figure9, the proposed bistage method is employed with two SOPs. The proposed approach aims not only to maximize the HC but also to obtain the optimal allocation of the integrated PV and WT plants. In the first stage, the optimal system reconfiguration is obtained, where in the second stage, the optimal allocation and configuration of SOPs are determined along with deciding the optimal allocation of the RERs as well as adjusting the substation voltage. The obtained results from the bistage approach are shown in Tables 11 and 12. It is clear that the proposed bistage approach succeeded in maximizing the system HC to 91.1%. The figure shows the 69-bus system topology after applying the proposed bistage approach. Also, Figure 10 shows the single line diagram of the system after applying case 4 with two SOPs.Figure 9
69-bus voltage profiles at different loading ratios (LR) at the initial case.Table 11
RERs specifications in case 4 for the 69-bus system.
SOPs No.HC (%)VsubRERs TypePVWTPlaceBus 25Bus 61Bus 44Bus 53Bus 16Bus 34291.10.99Capacity (MW)0.63350.59290.39920.65070.48770.7Power factor−0.9−0.90.9−0.9−0.90560.9Table 12
HC results in case 4 for the 69-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR255–5655–5614–640.00298−0.003760.00286−0.003610.95171.045323–2465–2746–370.0575−0.072490.05522−0.06959Figure 10
69-bus single line diagram in case 4 with two SOPs.


## 6.1. Test Distribution System

The proposed procedure is applied to the IEEE 33-bus and 69-bus distribution systems. The IEEE 33-bus system substation voltage is 12.66 kV, and active and reactive load demands are 3.715 MW and 2.3 MVAr, respectively [22], Where the IEEE 69-bus system substation voltage is 12.66 kV. The total active and reactive load demands are 3.802 MW and 2.694 MVAr. The systems configurations are shown in Figures 2 and 3.Figure 2
Single line diagram of 33-bus distribution network.Figure 3
Single line diagram of 69-bus distribution network.


## 6.2. Simulation Scenarios

The simulation scenarios implemented via four cases are considered in this paper as follows:Case 1: this case aims to assess the HC of the system at the initial case without using any enhancement techniques. So that, the objective function of this case is maximizing the HC as in equation (13) with respect to the constraints in equations (14)–(16) where this can be achieved by determining the optimal siting, sizing, type, power factor, and number of DGs in the system.Case 2: this case aims to maximize the HC using SOP only. In this case, the effect of the SOPs number is evaluated by considering one, two, and three SOPs in three subcases. So that, the objective function of this case is maximizing the HC as in equation (12) with respect to the constraints in equations (13)–(16) and the SOP constraints in equations (7)–(11), where this can be achieved by determining the optimal siting, sizing, type, and number of DGs in the system in addition to the optimal planning of the SOPs.Case 3: maximizing HC of the system is implemented using NR only. So that, in this case, the RERs sites obtained in case 1 are considered to be the candidate buses in this case. Therefore, the control variables of this case are siting, sizing, type, and number of DGs in addition to the system lines that will be opened and the tie lines that will be connected.Case 4: a combination between NR and SOP in a bistage approach is proposed for maximizing the HC, where NR is carried out as described in case 2, then based on the newly obtained reconfiguration, SOP is optimally planned and configured, where the SOP number is selected to be the number at which the best results in case 3 are obtained.The procedure of the proposed approach is represented by the flowchart shown in Figure4. To prove the effectiveness of the proposed MRFO algorithm, a comparative study between the MRFO algorithm and two other known algorithms (Equilibrium optimization algorithm (EO) [42], Jaya optimization algorithm (JO) [43]) is performed on case 1. For a fair comparison, the initial solutions matrix is considered to be the same for the three algorithms in the first iteration. Also, the population and iterations number of the three algorithms are considered to be 100 and 50, respectively. The problem is formulated in a MATLAB m-file code and executed under the MATLAB R2016 environment. Power flow analyses are performed for every uncertainty scenario in each population based on the backward/forward sweeping technique [35]. The limits of the control variables are assumed, as illustrated in Table 3.Figure 4
The flow chart of the proposed HC maximization approach.Table 3
Control variables’ limits.
Control variableLimitsControl variableLimits33-Bus69-Bus33-Bus69-BusSubstation voltage0.97–1.03SOP power factor0.9–1RERs rating (MW)0–1SOP rating (MW)0–0.25RERs power factor0.9–1SOP locationAll sectionalized and tie linesRERs location2–332–69Many studies assume that all the system buses are candidate buses and suitable for RERs integration. However, this assumption is not accurate practically because of the presence of many inappropriate system buses for PV and/or WT integration due to weather and geographical reasons. Therefore, to establish a model close to reality, the candidate buses for the RERs integration are shown in Table4.Table 4
The considered candidate buses for the two test systems.
RERs typePVWT33-bus systemBus 6Bus 12Bus 24Bus 17Bus 21Bus 3269-bus systemBus 25Bus 61Bus 44Bus 53Bus 16Bus 34


## 6.3. Results and Discussion

### 6.3.1. 33-Bus Distribution System Results

The aim of case 1 is to determine the HC of the system without using any improvement techniques. The proposed procedure for case 1 is applied using the three competitive algorithms, i.e., MRFO, EO, and JO. The obtained comparative results are shown in Table5. The results revealed that the system HC at the initial case obtained using MRFO, EO, and JO algorithms equal 1.8275 MW, 1.4282 MW, and 1.6004 MW, respectively. From the obtained results, it is clear that the MRFO resulted in higher HC compared with EO and JO algorithms. Also, the convergence curves of the three algorithms are shown in Figure 5, which illustrate the superior convergence characteristics of the MRFO algorithm.Table 5
Results of HC evaluation (case 1)
AlgorithmVsubHC (%)RERsPVWTMRFO1.0249.19Bus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.06140.42240.49900.15970.49900.1861Power factor−0.9−0.9−0.9−0.9−0.9−0.9EO1.0238.44Power (MW)0.06170.38520.03430.49900.36180.0863Power factor−0.9−0.9−0.9−0.9−0.90.9JO1.0243.08Power (MW)0.14320.24160.43760.17140.46290.1437Power factor−0.9−0.9−0.9−0.9−0.9−0.9Figure 5
MRFO convergence curve for case 1.In case 2, various numbers of SOPs are tested and optimally planned to show the effect of the SOPs number on maximizing the HC. As demonstrated in Table6, the maximum HC is obtained by using one, two, three, and four SOPs, while Table 7 illustrates the data of the RERs integrated into the system. From the obtained results, it is clear that the HC value increases with increasing the number of SOPs until reaching the knee point (two SOPs); the HC decreases with increasing the number of SOPs, where the HC reached 56.3% and 61.3% in case of using one and two SOPs, respectively, and it decreased to 58% and 55.3% after increasing the number of SOPs to three and four units, respectively.Table 6
HC results in case 2 for the the 33-bus system.
SOP no.HC (%)SOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR156.3%16–260.02059−0.025950.01977−0.024910.95171.0500261.3%10–280.02904−0.036590.02787−0.035130.95031.050018–190.05203−0.101180.04995−0.06295358%32–330.03689−0.046480.035410.044621.049924–200.01027−0.012940.009860.0124219–220.02316−0.029190.02224−0.028020.9505455.3%18–250.008250.010400.07920.09980.95091.049824–210.03580−0.045110.03437−0.0433132–330.05208−0.065630.049990.0630031–180.04389−0.055310.04214−0.05310Table 7
RERs specifications in case 2 for the 33-bus system.
SOP No.ParameterPVWTBus 12Bus 24Bus 6Bus 32Bus 21Bus 171Power (MW)—0.59310.53750.14140.58160.2395Power factor—0.90.90.90.90.92Power (MW)—0.7000.38060.24730.70000.2501Power factor—0.90.90.90.90.93Power (MW)—0.58910.64200.08380.64520.1934Power factor—−0.9000−0.9028−0.9000−0.9000−0.90694Power (MW)—0.63460.18120.40980.56450.2661Power factor—−0.9000−0.9044−0.9033−0.9000−0.9000In case 3, by applying the proposed NR technique to enhance the system HC, the results in Table8 are obtained. The results show that NR raised the HC percentage from 47.3% at the initial state to 79.3% by changing the network configuration to the configuration shown in Figure 6. The total capacity of the installed PV and WT plants equals 1.4309 MW and 1.515 MW, respectively. Also, the results confirmed that using NR is more effective than using SOPs for improving the HC.Table 8
RERs specifications in case 3 for the 33-bus system.
RERs TypePVWTBus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.47750.70890.24450.72490.43730.3549Power factor−0.0921−0.0915−0.9220−0.9167−0.9517−0.9360ParameterHC (%)Opened linesAdded linesVsubVminVmaxValue79.3%10 to 1121 to 111.00.95381.0499Figure 6
33-bus single line diagram after reconfiguration.In case 4, one, two, three, and four SOPs are optimally planned along with NR and RERs planning to maximize the system HC. The obtained results are provided in Tables9 and 10, where the planning of the PV, WT, SOPs, and the new tie line is shown. The obtained results declare that the hybrid technique in case 4 has a superior effect on maximizing the HC than using NR or SOPs techniques separately as in case 2 and case 3. Also, it is noticed that the results in case 4 follow the same behavior as in case 2, where the HC achieved 86.8%, 94.4%, 83.6%, and 80.7% with applying one, two, three, and four SOPs, respectively, with the NR. Figure 7 shows voltage profiles of case 4 with 2 SOPs for all the uncertainty scenarios, where all the buses’ voltages are within their limits. Also, Figure 8 shows the single line diagram of the system after applying case 4 with two SOPs.Table 9
RERs specifications in case 4 for the 33-bus system.
SOPs no.HC (%)VsubRERs TypePVWTPlaceBus 12Bus 24Bus 6Bus 32Bus 21Bus 17186.81.0Capacity (MW)0.66870.62940.18680.63180.73070.3776Power factor−0.9−0.90.9−0.9−0.9−0.9294.41.0Capacity (MW)0.44860.67350.62500.50710.74370.5114Power factor−0.9107−0.9−0.9−0.9−0.9−0.9383.61.0Capacity (MW)0.50840.75000.75000.16450.27690.6555Power factor−0.9−0.9−0.9−0.9−0.9−0.9003480.71.0Capacity (MW)0.62730.46110.54640.45040.36290.5564Power factor−0.9023−0.9−0.9−0.9−0.9−0.9015Table 10
HC results in case 4 for the 33-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR110 to 1121 to 1129–160.064150.080840.06682−0.084210.95231.0494210 to 1121 to 1124–170.01746−0.022000.018180.022910.95671.050030–180.04128−0.052010.04300−0.05418310 to 1121 to 1113–240.08223−0.103620.08565−0.107940.95671.048510–230.051660.065100.5381−0.0678110–110.106700.134460.11114−0.14006410 to 1121 to 1112–180.05588−0.070410.05820−0.073350.95731.047014–210.06122−0.077140.063770.0803631–270.05380−0.067800.05605−0.0706326–170.051300.064640.05343−0.06733Figure 7
Voltage profiles for the 33-bus system resulted from case 4 with two SOPs.Figure 8
33-bus single line diagram in case 4 with two SOPs.


### 6.3.2. 69-Bus Distribution System Results

After applying case 1 to the IEEE 69-bus system, it is obtained that the system failed to integrate any RERs without using enhancement techniques. As the system’s voltage profile at the initial case is out of boundaries and remains out of boundaries with any integration from the RERs as shown in Figure9, the proposed bistage method is employed with two SOPs. The proposed approach aims not only to maximize the HC but also to obtain the optimal allocation of the integrated PV and WT plants. In the first stage, the optimal system reconfiguration is obtained, where in the second stage, the optimal allocation and configuration of SOPs are determined along with deciding the optimal allocation of the RERs as well as adjusting the substation voltage. The obtained results from the bistage approach are shown in Tables 11 and 12. It is clear that the proposed bistage approach succeeded in maximizing the system HC to 91.1%. The figure shows the 69-bus system topology after applying the proposed bistage approach. Also, Figure 10 shows the single line diagram of the system after applying case 4 with two SOPs.Figure 9
69-bus voltage profiles at different loading ratios (LR) at the initial case.Table 11
RERs specifications in case 4 for the 69-bus system.
SOPs No.HC (%)VsubRERs TypePVWTPlaceBus 25Bus 61Bus 44Bus 53Bus 16Bus 34291.10.99Capacity (MW)0.63350.59290.39920.65070.48770.7Power factor−0.9−0.90.9−0.9−0.90560.9Table 12
HC results in case 4 for the 69-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR255–5655–5614–640.00298−0.003760.00286−0.003610.95171.045323–2465–2746–370.0575−0.072490.05522−0.06959Figure 10
69-bus single line diagram in case 4 with two SOPs.


## 6.3.1. 33-Bus Distribution System Results

The aim of case 1 is to determine the HC of the system without using any improvement techniques. The proposed procedure for case 1 is applied using the three competitive algorithms, i.e., MRFO, EO, and JO. The obtained comparative results are shown in Table5. The results revealed that the system HC at the initial case obtained using MRFO, EO, and JO algorithms equal 1.8275 MW, 1.4282 MW, and 1.6004 MW, respectively. From the obtained results, it is clear that the MRFO resulted in higher HC compared with EO and JO algorithms. Also, the convergence curves of the three algorithms are shown in Figure 5, which illustrate the superior convergence characteristics of the MRFO algorithm.Table 5
Results of HC evaluation (case 1)
AlgorithmVsubHC (%)RERsPVWTMRFO1.0249.19Bus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.06140.42240.49900.15970.49900.1861Power factor−0.9−0.9−0.9−0.9−0.9−0.9EO1.0238.44Power (MW)0.06170.38520.03430.49900.36180.0863Power factor−0.9−0.9−0.9−0.9−0.90.9JO1.0243.08Power (MW)0.14320.24160.43760.17140.46290.1437Power factor−0.9−0.9−0.9−0.9−0.9−0.9Figure 5
MRFO convergence curve for case 1.In case 2, various numbers of SOPs are tested and optimally planned to show the effect of the SOPs number on maximizing the HC. As demonstrated in Table6, the maximum HC is obtained by using one, two, three, and four SOPs, while Table 7 illustrates the data of the RERs integrated into the system. From the obtained results, it is clear that the HC value increases with increasing the number of SOPs until reaching the knee point (two SOPs); the HC decreases with increasing the number of SOPs, where the HC reached 56.3% and 61.3% in case of using one and two SOPs, respectively, and it decreased to 58% and 55.3% after increasing the number of SOPs to three and four units, respectively.Table 6
HC results in case 2 for the the 33-bus system.
SOP no.HC (%)SOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR156.3%16–260.02059−0.025950.01977−0.024910.95171.0500261.3%10–280.02904−0.036590.02787−0.035130.95031.050018–190.05203−0.101180.04995−0.06295358%32–330.03689−0.046480.035410.044621.049924–200.01027−0.012940.009860.0124219–220.02316−0.029190.02224−0.028020.9505455.3%18–250.008250.010400.07920.09980.95091.049824–210.03580−0.045110.03437−0.0433132–330.05208−0.065630.049990.0630031–180.04389−0.055310.04214−0.05310Table 7
RERs specifications in case 2 for the 33-bus system.
SOP No.ParameterPVWTBus 12Bus 24Bus 6Bus 32Bus 21Bus 171Power (MW)—0.59310.53750.14140.58160.2395Power factor—0.90.90.90.90.92Power (MW)—0.7000.38060.24730.70000.2501Power factor—0.90.90.90.90.93Power (MW)—0.58910.64200.08380.64520.1934Power factor—−0.9000−0.9028−0.9000−0.9000−0.90694Power (MW)—0.63460.18120.40980.56450.2661Power factor—−0.9000−0.9044−0.9033−0.9000−0.9000In case 3, by applying the proposed NR technique to enhance the system HC, the results in Table8 are obtained. The results show that NR raised the HC percentage from 47.3% at the initial state to 79.3% by changing the network configuration to the configuration shown in Figure 6. The total capacity of the installed PV and WT plants equals 1.4309 MW and 1.515 MW, respectively. Also, the results confirmed that using NR is more effective than using SOPs for improving the HC.Table 8
RERs specifications in case 3 for the 33-bus system.
RERs TypePVWTBus no.Bus 12Bus 24Bus 6Bus 32Bus 21Bus 17Power (MW)0.47750.70890.24450.72490.43730.3549Power factor−0.0921−0.0915−0.9220−0.9167−0.9517−0.9360ParameterHC (%)Opened linesAdded linesVsubVminVmaxValue79.3%10 to 1121 to 111.00.95381.0499Figure 6
33-bus single line diagram after reconfiguration.In case 4, one, two, three, and four SOPs are optimally planned along with NR and RERs planning to maximize the system HC. The obtained results are provided in Tables9 and 10, where the planning of the PV, WT, SOPs, and the new tie line is shown. The obtained results declare that the hybrid technique in case 4 has a superior effect on maximizing the HC than using NR or SOPs techniques separately as in case 2 and case 3. Also, it is noticed that the results in case 4 follow the same behavior as in case 2, where the HC achieved 86.8%, 94.4%, 83.6%, and 80.7% with applying one, two, three, and four SOPs, respectively, with the NR. Figure 7 shows voltage profiles of case 4 with 2 SOPs for all the uncertainty scenarios, where all the buses’ voltages are within their limits. Also, Figure 8 shows the single line diagram of the system after applying case 4 with two SOPs.Table 9
RERs specifications in case 4 for the 33-bus system.
SOPs no.HC (%)VsubRERs TypePVWTPlaceBus 12Bus 24Bus 6Bus 32Bus 21Bus 17186.81.0Capacity (MW)0.66870.62940.18680.63180.73070.3776Power factor−0.9−0.90.9−0.9−0.9−0.9294.41.0Capacity (MW)0.44860.67350.62500.50710.74370.5114Power factor−0.9107−0.9−0.9−0.9−0.9−0.9383.61.0Capacity (MW)0.50840.75000.75000.16450.27690.6555Power factor−0.9−0.9−0.9−0.9−0.9−0.9003480.71.0Capacity (MW)0.62730.46110.54640.45040.36290.5564Power factor−0.9023−0.9−0.9−0.9−0.9−0.9015Table 10
HC results in case 4 for the 33-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR110 to 1121 to 1129–160.064150.080840.06682−0.084210.95231.0494210 to 1121 to 1124–170.01746−0.022000.018180.022910.95671.050030–180.04128−0.052010.04300−0.05418310 to 1121 to 1113–240.08223−0.103620.08565−0.107940.95671.048510–230.051660.065100.5381−0.0678110–110.106700.134460.11114−0.14006410 to 1121 to 1112–180.05588−0.070410.05820−0.073350.95731.047014–210.06122−0.077140.063770.0803631–270.05380−0.067800.05605−0.0706326–170.051300.064640.05343−0.06733Figure 7
Voltage profiles for the 33-bus system resulted from case 4 with two SOPs.Figure 8
33-bus single line diagram in case 4 with two SOPs.


## 6.3.2. 69-Bus Distribution System Results

After applying case 1 to the IEEE 69-bus system, it is obtained that the system failed to integrate any RERs without using enhancement techniques. As the system’s voltage profile at the initial case is out of boundaries and remains out of boundaries with any integration from the RERs as shown in Figure9, the proposed bistage method is employed with two SOPs. The proposed approach aims not only to maximize the HC but also to obtain the optimal allocation of the integrated PV and WT plants. In the first stage, the optimal system reconfiguration is obtained, where in the second stage, the optimal allocation and configuration of SOPs are determined along with deciding the optimal allocation of the RERs as well as adjusting the substation voltage. The obtained results from the bistage approach are shown in Tables 11 and 12. It is clear that the proposed bistage approach succeeded in maximizing the system HC to 91.1%. The figure shows the 69-bus system topology after applying the proposed bistage approach. Also, Figure 10 shows the single line diagram of the system after applying case 4 with two SOPs.Figure 9
69-bus voltage profiles at different loading ratios (LR) at the initial case.Table 11
RERs specifications in case 4 for the 69-bus system.
SOPs No.HC (%)VsubRERs TypePVWTPlaceBus 25Bus 61Bus 44Bus 53Bus 16Bus 34291.10.99Capacity (MW)0.63350.59290.39920.65070.48770.7Power factor−0.9−0.90.9−0.9−0.90560.9Table 12
HC results in case 4 for the 69-bus system.
SOPs No.Opened linesAdded linesSOP placeSOP input powerSOP output powerVminVmaxMWMVARMWMVAR255–5655–5614–640.00298−0.003760.00286−0.003610.95171.045323–2465–2746–370.0575−0.072490.05522−0.06959Figure 10
69-bus single line diagram in case 4 with two SOPs.


## 7. Conclusion

In this paper, an optimization-based approach has been proposed for assessing and maximizing the HC of both PV and WT in the distribution systems. Unlike most of the previous studies, in the proposed approach, the uncertainty of the PV and WT has been considered in addition to considering the load demand variation. The uncertainty modeling has been simulated using probability uncertainty scenarios based on historical data. A comparative study between MRFO, EO, and JO algorithms has been presented to show the effectiveness of the proposed MRFO algorithm. Network reconfiguration and soft open points have been proposed as a bistage approach to maximize the HC of RERs. Different case studies have been formulated to study the effect of SOPs number and NR for maximizing the HC. Overvoltage and current line capacity have been considered as two performance limits. The proposed bistage approach achieved a superior increase in the HC (94.4%) compared with NR (79.3%) and SOPs (61.3%) approaches with the IEEE 33-bus system. Increasing the number of SOPs results in enhancing the obtained HC until reaching its maximum point with two SOPs; after that, the HC decreased with increasing the SOPs number. Also, the proposed bistage method succeeded in raising the HC up to 91.1% with the IEEE 69-bus system, which failed in integrating any RERs in the initial case of bad voltage profile characteristics. For all the proposed techniques, the optimal location, size, number, type, and power factor of both PV and WT are obtained along with the HC solution. The obtained results indicate that operating the RERs inverters at a lagging power factor, instead of a unity power factor, helps in maximizing the HC.



---

*Source: 2947965-2022-09-02.xml*