Power Quality of Electrical Distribution Systems Considering PVs, EVs and DSM

Abstract

This paper investigates the effect of photovoltaic panels (PVs) and electric vehicles (EVs) on power quality of electrical distribution systems, while proposing an approach of demand-side management (DSM). Electricity generation of PVs is estimated based on technical parameters and weather data, whereas electricity consumption of EVs is evaluated using travel data of conventional cars. Calculations of three-phase power flow are developed in this study to assess the impact of PVs and EVs on voltage magnitude and voltage unbalance of residential grids. Simulation results of different case studies show that additional power generation of PVs increases voltage magnitude. However, uncoordinated electricity consumption of charging EVs degrades voltage unbalance. Therefore, a strategy of DSM is proposed to coordinate EV charging using deterministic programming, while considering historical data of system components. The proposed scheme of DSM is able to improve voltage quality by re-scheduling EV consumption in line with PV generation, postponing upgrading requirements of power grids.

Introduction

The level of penetration of low carbon technologies (LCTs) was recognized to increase in electricity grids (KEMA 2014). Photovoltaic panels (PVs) and electric vehicles (EVs) increase the complexity of monitoring and modeling low-voltage grids (Zakariazadeh et al. 2015). To cope with such difficulty, different trials were initiated in UK Power Networks (2014) to quantify the effect of LCTs on future low carbon electricity networks. Power grids will experience considerable uncertainties because of an increasing level of adopting LCTs. Emerging loads such as EVs amplify power consumption particularly over peak hours. In the meantime, distributed generators (e.g., PVs) intensify voltage magnitudes due to their reverse power flow. Therefore, LCTs are able to affect both suppliers and consumers at different levels of electrical systems. As a result, quality of electricity should be maintained within their limits, while integrating such technologies in power systems (Energy Network Association Technology 2012). Coordinated and uncoordinated charging methods of hybrid EVs were addressed in Clement-nyns et al. (2010), considering voltage profiles and power losses of a low-voltage network. The influence of EVs and PVs on a real electricity feeder was discussed in Agüero et al. (2012) based on daily profiles of voltage and power, considering different penetration levels. Maximum uptakes of renewable energy sources (e.g., PVs) were evaluated in radial distribution systems, while considering voltage profiles and power losses (Rawat and Vadhera 2019). Actual data of energy generation of PVs were considered in Toliyat et al. (2012) to evaluate voltage unbalance in a real utility grid. The impact of EVs on a low-voltage network was analyzed in Putrus et al. (2009), while evaluating possible issues of power quality. EVs were used in Ali et al. (2013) as a moveable energy storage to mitigate the effect of high penetration levels of PVs on distribution networks. A stochastic approach was presented in Shariff et al. (2016) to study the impact of EVs on voltage profiles in power grids. A probabilistic methodology was used in Al Essa and Cipcigan (2016a, b) to study the impact of EVs and PVs on power quality of a distribution system, while evaluating different combinations of such distributed energy resources. Deterministic and stochastic approaches were presented in Al Essa and Cipcigan (2015) and Al Essa (2017) to assess the effect of EVs and PVs on a number of electricity systems. Although three-phase systems were used in Leou et al. (2014) and Sharma et al. (2012) to study the influence of EVs on distribution networks, voltage unbalance was not assessed. In addition, the impact of PV generation on such systems was not evaluated in Leou et al. (2014) and Sharma et al. (2012). Both PVs and EVs were considered in Drude et al. (2014). However, EVs were studied in Drude et al. (2014) based on vehicle-to-grid modes. Though a range of software packages was presented in Gao et al. (2017) to evaluate the effect of LCTs on residential power grids, they were planned based on certain procedures to perform power flow calculations. Therefore, three-phase load flow equations were developed in this paper to monitor grid conditions while integrating LCTs (e.g., PVs and EVs) into residential electricity grids.

Management strategies were proposed by relevant studies to coordinate power profiles of charging and discharging EVs to mitigate their influence on electricity grids, while considering different techniques and constraints. For instance, various forms of neural networks were used in Moradzadeh and Khaffafi (2017) to achieve an optimal management program of charging and discharging EVs. A genetic algorithm was proposed in Ahmed and Alhialy (2019) to increase the efficiency of PVs, while considering different parameters in residential premises. However, PVs and EVs were separately considered in Ahmed and Alhialy (2019) and Moradzadeh and Khaffafi (2017). Although power quality includes different aspects such as current distortion, voltage unbalance, voltage sag and harmonic (Hosseini 2018), the focus of this paper is associated to voltage issues of magnitude and unbalance, which commonly appear while integrating PVs and EVs into electricity networks. Furthermore, this paper concentrates on small-scale PVs and EVs, which differ from the PV plant and electric transportation presented in Nazir (2019). It is necessary to study the effect of domestic LCTs on distribution networks in terms of their operational characteristics (e.g., voltage magnitude) to avoid instable conditions. Therefore, this article contributes to the existing literature as follows.

  • A grid-to-vehicle mode of EVs is evaluated in residential feeders using driving patterns of conventional cars, while considering PV generation based on historical weather data.

  • Three-phase load flow equations are developed to identify the issues of voltage magnitude and voltage unbalance, while integrating EVs and PVs into power grids.

  • A strategy of demand-side management (DSM) is proposed to mitigate the impact of PVs and EVs on distribution networks by adjusting peak loads. Consequently, the proposed scheme of DSM is able to postpone upgrading needs of power grids, while avoiding considerable costs of reinforcement.

The rest of this article is organized as follows. Section 2 presents power modeling of PVs and EVs. Section 3 gives information of the grid under study, while developing three-phase load flow equations. Section 4 illustrates the algorithm of impact assessment. Meanwhile, a strategy of DSM is proposed in Sect. 4 to alleviate the impact of PVs and EVs on distribution networks. Case studies and simulation results are explained in Sect. 5 and corollaries are given in Sect. 6.

Photovoltaic Panels, Electric Vehicles and Residential Loads

Power generation of PVs is assessed based on solar irradiance while considering manufacturing parameters such as efficiency of solar cells. Meanwhile, the grid-to-vehicle mode of EVs is determined considering a travel survey of conventional cars. In the meantime, load profiles of residential appliances are presented based on IEEE test systems.

System Notation

A summary of main notation utilized in this research is described as follows.

  • \(\alpha\) Solar irradiance in W/m2

  • \(\beta\) Total capacity of the PVs installed in W

  • \(\eta_{1}\) Efficiency of power generation of solar cells

  • \(\eta_{2}\) Efficiency of PV inverter

  • \(A\) Total area of the PVs installed in m2

  • \(N\) Total number of nodes along the feeder

  • \(X\) Total number of residential customers

  • \(Y\) Total number of PVs

  • \(Z\) Total number of EVs

  • \(V_{0}\) Zero sequence components of phase voltages

  • \(V_{1}\) Positive sequence components of phase voltages

  • \(V_{2}\) Negative sequence components of phase voltages

  • \(V_{A}\) System voltage at phase A

  • \(V_{B}\) System voltage at phase B

  • \(V_{C}\) System voltage at phase C

  • \(P_{{{\text{PVP}}}}\) Power generation of a single PV module

  • A, B & C Three phases of electricity system

  • \(V_{A,B,C}\) Three-phase magnitudes of phase voltage

  • \(Z_{A,B,C}\) Three-phase values of impedance

  • \(I_{A,B,C}\) Three-phase values of current

  • \(\emptyset_{A,B,C}\) Three-phase values of phase voltage angles

  • \(\theta_{A,B,C}\) Three-phase values of power factor angles

  • \({\text{VU}}\) Voltage unbalance

  • \(P1_{A,B,C}\) Power consumption of residential loads

  • \(P2_{A,B,C}\) Power generation of PV panels

  • \({\mathbb{P}}3_{A,B,C}\) Charging power of EVs

  • \(P3_{A,B,C}^{^{\prime}}\) Three-phase values of optimized power for charging EVs

  • \(P3_{Ath,Bth,Cth}\) Threshold values of charging power consumption of EVs

  • \(TT1{ }\& T2\) The margins of the interval excluded in the optimization, while scheduling EV charging consistent with PV generation

  • UV Upper limit of voltage magnitude

  • LV Lower limit of voltage magnitude

  • \({\text{VU}}_{{{\text{TH}}}}\) Threshold value of voltage unbalance

Photovoltaic Panels

Power generation of PVs was evaluated using solar irradiance as shown in the following equation (Al Essa and Cipcigan 2016a, b).

$$ P_{{{\text{PVP}}}} = \alpha \times \beta \times \eta_{1} \times \eta_{2} \times A $$
(1)

where \(P_{{{\text{PVP}}}}\) represents power generation of PVs in Watt. \(\alpha\) represents solar irradiance in W/m2. \(\beta\) is the total capacity of the PVs installed in W. \(\eta_{1} \,\& \,\eta_{2}\) are the efficiency of power generation of solar cells, and the efficiency of PV inverter, respectively. \(A\) is the total area of the PVs installed in m2. Data of solar irradiance were utilized based on European Communities (2017), Saoud et al. (2018) and Huld et al. (2012) to calculate power generation of individual PVs over a day considering a quarter-hourly time series. Equation (1) can be further developed to include additional variables and parameters as presented in Al Essa (2019) while calculating PV power.

Electric Vehicles

The single-phase power of EV charging device was assumed 2.8 kW, while considering a slow charging mode consistent with IEC 61850 standards (Machado et al. 2018). Patterns of departure time of conventional cars were presented in Pasaoglu et al. (2012) during working days (i.e., including intervals of returning homes) in European countries as follows:

  • Virtually 19% of the trips are made before morning.

  • Roughly, 18% of trips are made until noon.

  • Nearly 63% of trips occur between noon and afternoon.

Therefore, starting intervals of charging EVs were diversified based on these data. Furthermore, durations of charging EVs are synthesized in this paper using the percentage of trips, as presented in Pasaoglu et al. (2012). Thus, the peak demand of charging EVs will occur afternoon when the owners of EVs return their homes to recharge their batteries. It is assumed that diurnal power profiles of charging EVs follow quadrilateral patterns considering single-phase power consumption of 2.8 kW for each individual charging device.

Residential Loads

Residential load profiles, which were collected from IEEE Power Energy Society and Power System Analysis Computing and Economics Committee (2015), have been used in this study on a quarter-hourly daily basis. In IEEE Power Energy Society and Power System Analysis Computing and Economics Committee (2015), power consumption of conventional domestic appliances such as washing machines, refrigerators and TVs was included. Although electricity of PVs and EVs was excluded in such daily profiles of domestic loads, they were modeled in this paper as previously illustrated in Sects. 2.2 and 2.3.

Test System and Load Flow

A residential feeder of IEEE European systems is adapted in this study to assess the effect of PVs and EVs on electricity grids in terms of voltage magnitude and voltage unbalance. Three-phase load flow equations are developed in this paper as demonstrated in Sect. 3.2.

Low-Voltage Test Feeder

An electricity feeder of IEEE Power Energy Society and Power System Analysis Computing and Economics Committee (2015) was modified in this paper to study the effect of PVs and EVs on voltage magnitude and voltage unbalance. Figure 1 illustrates the low-voltage feeder used in this study, while considering locations of residential customers across the feeder. It can be seen that the feeder has been divided into four zones to organize the study of PVs and EVs. Fourteen customers are located in Zone 1, whereas forty-two customers are connected to this feeder at Zone 2. Other fourteen customers are connected to the feeder at Zone 3, while fifty residential customers are located in Zone 4.

Fig. 1
figure1

A single-line diagram of the IEEE European feeder (i.e., adapted from IEEE Power Energy Society and Power System Analysis Computing and Economics Committee 2015)

Three-Phase Load Flow

Unbalanced load flow analysis was used in this study considering a three-phase paradigm of distribution grids. Load flow calculations of radial systems were evaluated in this paper based on the principles presented in Kersting (2002). Such calculations were used because R/X ratio is high in low-voltage distribution network. A comparable algorithm of power flow evaluation was presented in do Nascimento Alves (2019), while integrating distributed generation (e.g., PVs) into radial distribution networks. By using Euler’s technique to represent complex quantities, phase voltages at the most remote end node of radial feeders are calculated using the following equation (Al Essa and Cipcigan 2016a, b).

$$ \begin{aligned} & \left| {V_{A,B,C} \left( t \right)} \right|_{n} e^{{i\emptyset_{A,B,C} \left( t \right)_{n} }} \\ & \quad = \left| {V_{A,B,C} \left( t \right)} \right|_{n - 1} e^{{i\emptyset_{A,B,C} \left( t \right)_{n - 1} }} - \left| {Z_{A,B,C} } \right|_{n\_n - 1} \\ & \quad \quad \times \left| {I_{A,B,C} \left( t \right)} \right|_{n} e^{{i\theta_{A,B,C} \left( t \right)_{n} }} \quad n = \left\{ {1, 2, 3, \ldots ,N} \right\} \\ \end{aligned} $$
(2)

where \(\left| {V_{A,B,C} \left( t \right)} \right|_{n}\) represents the three-phase magnitudes of phase voltage at node (\(n\)) in time step (\(t\)) across the three phases of A, B and C. \(\emptyset_{A,B,C} \left( t \right)_{n}\) represents the three-phase values of phase voltage angles with respect to reference axis at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. \(\left| {Z_{A,B,C} } \right|_{n\_n - 1}\) denotes the three-phase values of the impedance of the feeder segment between the nodes of (\(n\)) and (\(n - 1\)) across the three phases A, B and C. \(\left| {I_{A,B,C} \left( t \right)} \right|_{n}\) denotes the three-phase values of current at node (\(n\)) in time step (\(t\)) across the three phases of A, B and C.\({ }\theta_{A,B,C} \left( t \right)_{n}\) represents the three-phase values of power factor angles at node (\(n\)) in time step (\(t\)) across the three phases of A, B and C. \(N\) is the total number of nodes along the radial feeder. By considering values of current as a function of power data, the following equation is acquired (Al Essa and Cipcigan 2016a, b).

$$ \left| {I_{A,B,C} \left( t \right)} \right|_{n} = f\left( {\left| {P_{A,B,C} \left( t \right)} \right|_{n} } \right)\quad n = \left\{ {1, 2, 3, \ldots ,N} \right\} $$
(3)

where \(\left| {P_{A,B,C} \left( t \right)} \right|_{n}\) represents the three-phase values of power at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. The three-phase values of power are determined as follows (Al Essa and Cipcigan 2016a, b).

$$ \left| {P_{A,B,C} \left( t \right)} \right|_{n} = \mathop \sum \limits_{x = 1}^{X} \left| {P1_{A,B,C} \left( t \right)} \right|_{x} - \mathop \sum \limits_{y = 1}^{Y} \left| {P2_{A,B,C} \left( t \right)} \right|_{y} + \mathop \sum \limits_{z = 1}^{Z} \left| {P3_{A,B,C} \left( t \right)} \right|_{z} $$
(4)

where \(\left| {P1_{A,B,C} \left( t \right)} \right|_{x}\) represents the three-phase values of power consumed by residential customers at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. \(X\) is the total number of residential customers connected to the residential feeder at node (\(n\)). \(\left| {P2_{A,B,C} \left( t \right)} \right|_{y}\) represents the three-phase values of power generated by PVs at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. \(Y\) is the total number of PVs connected to the residential feeder at node (\(n\)).\({ }\left| {P3_{A,B,C} \left( t \right)} \right|_{z}\) represents the three-phase values of power consumed by charging EVs at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. \(Z\) is the total number of EVs connected to the residential feeder at node (\(n\)). Meanwhile, the percentage values of voltage unbalance \({\text{VU}}_{n} \% \left( t \right)\) at node (\(n\)) are calculated as follows (Trichakis et al. 2006).

$$ VU_{n} \left( t \right)\% = \frac{{V_{2n} \left( t \right)}}{{V_{1n} \left( t \right)}} \times 100\% \quad n = \left\{ {1, 2, 3, \ldots ,N} \right\} $$
(5)

where \(V_{1n} \left( t \right)\) and \(V_{2n} \left( t \right)\) are the positive and negative sequence components of phase voltages at node (\(n\)) in time step (\(t\)). Unbalanced systems are converted to balance system using symmetrical components of positive, negative and zero sequence components. The following equations describe a mathematical conversion of unbalanced three-phase voltages into balanced system (Lee et al. 2014).

$$ \left[ {\begin{array}{*{20}c} {V_{0} } \\ {V_{1} } \\ {V_{2} } \\ \end{array} } \right] = \frac{1}{3} \left[ {\begin{array}{*{20}c} 1 & 1 & 1 \\ 1 & {e^{i2\pi /3} } & {e^{i4\pi /3} } \\ 1 & {e^{i4\pi /3} } & {e^{i2\pi /3} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {V_{A} } \\ {V_{B} } \\ {V_{C} } \\ \end{array} } \right] $$
(6)

where \(V_{0}\), \(V_{1}\), and \(V_{2}\) are the zero, positive and negative sequence components of phase voltages of \(V_{A}\), \(V_{B}\), and \(V_{C}\).

Impact Assessment and Demand-Side Management

An impact study of PVs and EVs was performed on the network under study in terms of voltage magnitude and voltage unbalance. Then, a proposed demand-side management (DSM) scheme was implemented considering the IEEE test feeder. A deterministic programming method was used to activate the proposed scheme by re-scheduling charging power of EVs.

Algorithmic Stages of Impact Assessment

Figure 2 shows the stages that have been adopted to assess the effect of PVs and EVs considering the IEEE residential feeder studied in this paper. Firstly, weather data were gathered from European Communities (2017) and T. Huld et al. (2012) to calculate diurnal power generation of PVs using Eq. (1). Travel data were collected from Pasaoglu et al. (2012) to construct daily power of charging EVs as illustrated in Sect. 2.3, in which driving patterns of conventional cars were used to estimate charging periods. In the meantime, daily residential loads of other appliances (e.g., refrigerators and TVs) were gathered from IEEE Power Energy Society and Power System Analysis Computing and Economics Committee (2015). Specifications of the IEEE test feeder considered in this study were used based on the data presented in IEEE Power Energy Society and Power System Analysis Computing and Economics Committee (2015). The IEEE test feeder was modified by indicating four zones to simplify the visualization of big data that were generated in terms of voltage magnitude and voltage unbalance for each node over a day. Diurnal power data of residential appliances were considered using the number of domestic customers for each zone. Meanwhile, daily power data of PVs and EVs were studied based on different penetration levels of these LCTs in the grid under study. Afterwards, Eqs. (2) to (6) were used to calculate voltage magnitude and voltage unbalance on a daily basis.

Fig. 2
figure2

Algorithm of impact assessment of photovoltaic panels (PVs) and electric vehicles (EVs) on power quality

Demand-Side Management Scheme

An integrated controller was proposed in this paper to coordinate power consumption of charging EVs, while considering PV generation. Mobility features of EVs were included in the proposed DSM scheme as follows. As the majority of trips occurs over daylight hours (Pasaoglu et al. 2012), a relatively high portion of EVs were assumed to be re-charged overnight. Accordingly, electricity consumption of charging EVs was primarily re-scheduled in conjunction with the intervals of PV generation. Thus, the objective function was written using the following equation.

$$ \begin{aligned} & {\text{minimize}} \mathop \sum \limits_{{T1{ \preccurlyeq }t{ \succcurlyeq }T2}} \\ &\quad \left( {\mathop \sum \limits_{x = 1}^{X} \left| {P1_{A,B,C} \left( t \right)} \right|_{x} - \mathop \sum \limits_{y = 1}^{Y} \left| {P2_{A,B,C} \left( t \right)} \right|_{y} + \mathop \sum \limits_{z = 1}^{Z} \left| {{\mathbb{P}}3_{A,B,C} \left( t \right)} \right|_{z} } \right) \end{aligned} $$
(7)

where \(\left| {{\mathbb{P}}3_{A,B,C} \left( t \right)} \right|_{z}\) represents decision variables of the optimization, considering charging power of EVs (i.e., \(\left| {P3_{A,B,C} \left( t \right)} \right|_{z}\)) across the three phases A, B and C. \(T1\,\& \,T2\) denote the boundaries of the interval excluded in the optimization, while scheduling EVs consistent with PV generation. Equation (7) is subjected to the following constraints.

$$ \mathop \sum \limits_{z = 1}^{Z} \left| {P3_{A,B,C}^{{\prime }} \left( t \right)} \right|_{z} \ge \mathop \sum \limits_{z = 1}^{Z} \left| {P3_{Ath,Bth,Cth} \left( t \right)} \right|_{z} $$
(8)
$$ U\left| {V_{ } } \right| \le \left| {V_{A,B,C} \left( t \right)} \right|_{n} \le L\left| {V_{ } } \right|_{ } $$
(9)
$$ {\text{VU}}_{n} \left( t \right)\% \le {\text{VU}}_{{{\text{TH}}}} \% $$
(10)

where \(\left| {P3_{A,B,C}^{{\prime}} \left( t \right)} \right|\) represents the three-phase values of optimized power for charging EVs at node (\(n\)) in time step (\(t\)) across the three phases A, B and C. \(\left| {P3_{Ath,Bth,Cth} \left( t \right)} \right|\) represents the threshold values of charging power consumption of EVs across the three phases A, B and C. The threshold values were empirically evaluated to provide sufficient amount of charging electricity while maintaining the batteries of EVs within an acceptable level of state of charge. \(U\left| {V_{ } } \right|\) and \(L\left| {V_{ } } \right|\) show the upper and the lower boundaries of voltage magnitude, while \({\text{VU}}_{{{\text{TH}}}} \%\) indicates the limit of voltage unbalance. The values of \(U\left| {V_{ } } \right|\), \(L\left| {V_{ } } \right|\) and \({\text{VU}}_{{{\text{TH}}}} \%\) were considered based on IEEE guide for recognizing quality of voltage in electrical power systems as demonstrated in IEEE Power and Energy Society (2011). The optimization problem of nonlinear characteristics can be deterministically solved using either sequential quadratic regulator (SQR) or generalized reduced gradient (GRG) (Yeniay 2005). In this paper, the latter technique was used to solve the optimization problem by considering fixed parameters of historical power profiles (Clement-nyns et al. 2010). The former technique was previously used in detail in another study (Al Essa 2018) to optimize charging power of grid-connected batteries considering their state of charge and grid constraint. A probabilistic method of optimization is needed when the uncertainties related to forecasting errors are considered (Clement-nyns et al. 2010). Table 1 shows decision variables and constraints of the optimization problem proposed in this paper. Figure 3 shows the algorithm proposed in this paper to re-schedule EV charging power while considering their mobility characteristics, network constraints and PV power profiles. It can be seen that the DSM algorithm proposed in Fig. 3 is able to consider the next day to increase optimization feasibility.

Table 1 A summary of decision variables, constants and constraints of the optimization problem
Fig. 3
figure3

The proposed DSM scheme of re-scheduling electricity consumption of charging EVs in power grids

Case Studies and Results

In this section, different case studies were presented based on penetration levels of PVs and EVs in the test feeder. Simulation results were demonstrated based on the three-phase load flow developed in this paper. Thereafter, impact assessment of PVs and EVs on the IEEE feeder is summarized. Afterwards, the proposed DSM scheme was implemented using the grid under study to coordinate charging loads of EVs.

Case Studies

Four penetration levels of PVs and EVs were studied based on the total number of residential customers connected to the feeder. Table 2 shows the number of PVs and EVs for the penetration levels studied in the test feeder. The percentage of penetration level is calculated by taking the average value of the number of PVs to the number of residential customers across the four zones of the test feeder. The last statement is applicable when the penetration levels of EVs are evaluated. Accordingly, four case studies were considered to study the impact of PVs and EVs on the IEEE test feeder in terms of voltage quality. These case studies are demonstrated as follows.

Table 2 Number of residential customers, PVs and EVs for each zone of the IEEE feeder for each case study
  • Case study 1 calculates voltage magnitude and voltage unbalance of the test system with 0% of PVs and 0% of EVs using the three-phase power flow developed in this paper (i.e., Case study 1 in Table 2).

  • Case study 2 calculates voltage magnitude and voltage unbalance of the test system with 73% of PVs using the three-phase power flow developed in this paper (i.e., Case study 2 in Table 2).

  • Case study 3 calculates voltage magnitude and voltage unbalance of the test system with 50% of EVs using the three-phase power flow developed in this paper (i.e., Case study 3 in Table 2).

  • Case study 4 calculates voltage magnitude and voltage unbalance of the test system with 73% of PVs and 50% of EVs using the three-phase power flow developed in this paper (i.e., Case study 4 in Table 2).

These case studies were designed to assess the impact of different penetration levels of PVs and EVs on the feeder, as compared to business as usual (i.e., 0% of PVs and 0% of EVs). Figure 4 shows the aggregation of residential power on a quarter-hourly basis for each zone of the residential feeder considered in this study. In the meantime, Fig. 5 illustrates the power generated from PVs over a day, considering quarter-hourly resolution for Case study 2 and Case study 4 in all zones. Similarly, Fig. 6 demonstrates the electricity consumed by charging EVs for Case study 3 and Case study 4 on a quarter-hourly basis in all zones of the grid under study.

Fig. 4
figure4

Residential loads on a quarter-hourly basis for each zone of the test feeder (adapted from IEEE Power Energy Society and Power System Analysis Computing and Economics Committee 2015)

Fig. 5
figure5

Power generation of PVs on a quarter-hourly basis for each zone of the test feeder for Case study 2 and Case study 4

Fig. 6
figure6

Charging power of EVs on a quarter-hourly basis for each zone of the test feeder for Case study 3 and Case study 4

Results

After modifying the IEEE feeder to include four zones, the three-phase load flow developed in this paper was utilized to calculate average values of voltage magnitude and voltage unbalance in Zone 1 and Zone 4. Consequently, such values were able to show the variation of voltage magnitude and voltage unbalance across the whole feeder. The test system was firstly evaluated using Case study 1 with 0% penetration of PVs and EVs. In Case study 1, Fig. 7a shows that voltage magnitude is within the limit as indicated in IEEE Power and Energy Society (2011). However, Fig. 7b demonstrates that voltage values exceeded the limit when Case study 2 (i.e., 73% penetration of PVs) was assessed due to the reverse power flow of PVs. Therefore, voltage magnitude increases when PVs reaches their highest generation during mid-day periods by injecting surplus power into the grid. Figure 7c indicates a drop of voltage magnitude in the afternoon, corresponding to the peak demand of charging EVs (see Fig. 6). Nevertheless, this drop of voltage remains above the voltage limit. Figure 7d shows that the integration of both PVs and EVs into the feeder is able to maintain voltage magnitude within the limit. Hence, the reverse power flow of high penetration levels of PVs has capability to increase voltage levels of electricity networks over mid-day hours. A combination of PVs and EVs would mitigate the impact of photovoltaic generation on voltage magnitude if PVs were partially used to re-charge EVs. Such corollaries were identified by Ali et al. (2013) to alleviate the impact of high penetration levels of PVs on electricity networks by considering energy consumption of EVs.

Fig. 7
figure7

Voltage magnitude of a Case study 1, b Case study 2, c Case study 3 and d Case study 4

Figure 8a illustrates the profiles of voltage unbalance for Case study 1. It can be seen that voltage unbalance is within the limit as reported in IEEE Power and Energy Society (2011). Figure 8b shows that voltage unbalance would not exceed its limit even if a relatively high penetration of PVs was integrated in residential feeders. Comparable results of voltage unbalance were presented in Toliyat et al. (2012). This is because PVs have a quasi-alike pattern of electricity generation over the day, while considering a uniform distribution of PVs across the three phases. However, a dramatic influence on voltage unbalance was recorded when EVs were connected to the feeder under study, as shown in Fig. 8c, d due to unbalanced power consumption of charging EVs.

Fig. 8
figure8

Voltage unbalance of a Case study 1, b Case study 2, c Case study 3 and d Case study 4

The proposed scheme of DSM is illustrated by considering the penetration level of PVs and EVs in Case study 4, as shown in Table 2. Thus, voltage magnitude was calculated in Zone 1 and Zone 4 with and without the proposed scheme of DSM. Figure 9a, b shows that the proposed strategy is able to maintain voltage magnitude within its limit by adjusting electricity consumption of charging EVs over peak periods. Meanwhile, voltage unbalance was evaluated in Zone 1 and Zone 4 with and without the proposed DSM strategy, as shown in Fig. 9c, d. It can be remarked that the proposed DSM has capability to re-schedule charging loads of EVs using deterministic programming based on fixed parameters of Eq. (7), while maintaining the constrictions of Eqs. (8)–(10). Table 3 shows a summary of the results evaluated in the IEEE feeder of European systems, considering different penetration levels of PVs and EVs. Table 4 shows the considerations evaluated in relevant studies as compared to the aspects presented in this paper.

Fig. 9
figure9

Voltage magnitude of a Zone 1 and b Zone 4 with voltage unbalance of c Zone 1 and d Zone 4, considering the proposed scheme of demand-side management (DSM) for Case study 4

Table 3 A summary of data resulted in terms of voltage magnitude and voltage unbalance for each case study
Table 4 The considerations presented in this paper as compared to relevant phases existing in other references

Conclusions

Three-phase load flow equations were developed in this paper to study the impact of PVs and EVs on power quality, performing quarter-hourly calculations of voltage magnitude and voltage unbalance. Four case studies were designed to assess the impact of different penetration levels of PVs and EVs on the residential feeder adapted from the IEEE European systems. Simulation results demonstrated that the reverse power flow of high penetration levels of PVs has capability to increase voltage levels of electricity networks over mid-day hours, as shown in Fig. 7b. Uncoordinated charging power of EVs deteriorates voltage unbalance, as illustrated in Fig. 8c. A dual connection of both PVs and EVs to a residential grid moderates their influence on voltage unbalance, as shown in Fig. 8d. Moreover, a combination of PVs and EVs would alleviate the impact of PV generation on voltage magnitude if PVs were partially used to re-charge EVs, as demonstrated in Fig. 7d.

A strategy of demand-side management (DSM) was proposed to re-schedule charging loads of EVs using deterministic programming based on historical data of system components to maintain network constrictions within their limits as shown in Fig. 9.

The proposed DSM scheme is able to mitigate the impact of PVs and EVs on distribution networks by adjusting peak loads accordingly. As a result, the DSM strategy proposed in this paper has capability to postpone upgrading needs of power grids, avoiding considerable costs of reinforcement.

Stochastic programming will be considered in future work to include uncertainties of forecasting errors, while evaluating additional representative scenarios of coordinating power profiles of PVs and EVs.

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Al Essa, M.J.M. Power Quality of Electrical Distribution Systems Considering PVs, EVs and DSM. J Control Autom Electr Syst (2020). https://doi.org/10.1007/s40313-020-00637-1

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Keywords

  • Demand-side management
  • Electric vehicles
  • Optimization
  • Photovoltaic panels
  • Power quality
  • Three-phase load flow