An Optimized Strategy for the Integration of Photovoltaic Systems and Electric Vehicles into the Real Distribution Grid

Abstract

The increasing spread of photovoltaic systems for private households (PVs) and electric vehicles (EVs) in order to reduce carbon emissions significantly impacts operation conditions in existing distribution networks. Variable and unpredictable PVs can stress distribution network operation, mainly manifested in voltage violations during the day. On the other hand, variable loads such as EV chargers which have battery storage in their configuration have the ability of storying a surplus energy and, if it is necessary, support a distribution network with energy, commonly known as vehicle-to-grid concept (V2G), to help voltage stability network enhancement. This paper proposes an optimal power flow (OPF)-based model for EV charging to minimize power exchange between the superior-10 kV grid and the observed distribution feeder. The optimization procedure is realized using the co-simulation approach that connects power flow analysis software and optimization method. Three different scenarios are observed and analysed. The first scenario is referred to as a base case without optimization. The second and third scenarios include optimal EV charging and discharging patterns under different constraints. To test the optimization model, a 90-bus unbalanced distribution feeder modelled based on real-life examples is used. The obtained results suggest that this optimization model does not only significantly reduce the power exchange between an external network and the distribution feeder but also improves voltage stability and demand curve in the distribution feeder.

1. Introduction

Distributed generation (DG), which is less harmful to the environment, can usually be built closer to consumption centres or at the point of consumption. In some studies, such as [1,2,3], it is assumed that the majority of households have their own PV systems on their roofs. This amount of DG can also have some negative effects, such as voltage increase and line overloads. There are several methods to overcome these issues, and some of them are addressed in [4,5,6]. The use of inverters as a method to reduce overvoltage is presented the example of an unbalanced grid in papers [7,8,9]. One of the most frequently used methods is also the integration of storage systems of different types and sizes. In the paper [10], a buffer storage system is used to reduce the overvoltage during the period of peak generation. The use of storage in low-voltage grids also increases the self-consumption of the loads, as shown in [11,12], which in turn reduces the energy exchange with the superior, upper-voltage grid and the losses [13]. All these methods can be categorized as demand-side management, and some methods are proposed in the paper [14].

EVs, whose use is also part of the recommendations for reducing emissions in transport, can also be used as part of demand management [15,16]. The number of EVs sold is increasing significantly every year, for example, by 14% in the year 2022 compared to the previous year [17]. This increase not only means major changes for the transport sector but also for the distribution grids, which have to provide the infrastructure and satisfy the energy demand for their operation. With the increasing number of DGs and EVs, it is clear that vehicles can have a benefit for the grid by supporting the grid during peak load periods or times of decreased DG generation [16]. As DGs have stochastic generation, V2G can be used to reduce energy swings and to increase the maximum level of integration [18,19,20]. To take full advantage of V2G, the charging and discharging schedule needs to be optimized with different objective functions regarding energy management or pricing. Some optimization methods are presented in papers [21,22]. With an optimized charging schedule, consumers can reduce their dependence on the superior-10 kV grid and lower their costs. V2G not only contributes to energy supply but can also be useful in providing ancillary services such as frequency and voltage regulation [23]. With the high price of electricity, this also gives vehicle owners the opportunity to achieve financial benefits and thus make the best use of their cars, and the fulfilment of these goals can also be achieved by creating energy communities as analysed in papers [24,25,26].

This paper is a continuation of the authors’ earlier work published in [27] on the impact of the V2G concept on the energy management of a low-voltage grid. A realistic urban low-voltage distribution grid with high PV penetration and significant phase imbalance is used to examine the proposed V2G concept with the aim of minimizing the energy exchange with the superior-10 kV grid through three operational scenarios. The first scenario is the baseline scenario in which the impact of high PV penetration is analysed. In the second scenario, the optimal EV battery charging schedule is determined without considering the state of charge (SoC) of the battery at the end of the cycle. In the third scenario, the same charging schedule as in the second scenario is considered, but the SoC at the end of the charging cycle is taken into account. According to all the above, the following list summarizes the key contributions.

• The urban distribution network is modelled according to the real-life data. Load profiles and EV charging patterns are obtained from conducted real-life measurements.
• Analysis is performed on unbalanced power flows since the distribution feeder is composed up of single-phase loads. Proposed EV charging patterns are presented as a mixed-integer nonlinear programming (MINLP) optimization model, and combined with unbalanced power flows, they represent the most accurate and realistic optimization model.
• The proposed EV charging pattern offers a robust and straightforward procedure that can be generally applied on all levels and types of integration.

The introduction is the first of four sections in this paper. The second section consists of the proposed optimization method and model description. The results of the performed simulations and calculations are presented in the third section. Concluding remarks are given in the fourth section.

2. Proposed Optimization for V2G

The proposed optimization method is based on a general mathematical model of the objective function to minimize the energy exchange between the low-voltage distribution grid with the superior-10 kV grid with following constraints:

○

Unbalanced power flows;

○

Bus voltages;

○

Maximum rating of each system component;

○

Solar irradiance;

○

State of charge of the batteries;

○

Charging/discharging powers of the batteries;

○

Energy exchanges with the external grid.

2.1. Mathematical Formulation of the Proposed Optimization Model

The objective function of the proposed model is written according to Expression (1):

$$\min \{Si{n}_{i,t}-Se{x}_{i,t}\}$$

(1)

where:

$Si{n}_{i,t}$—the apparent power imported from the superior-10 kV grid at the i-th bus in period t;

$Se{x}_{i,t}$—the apparent power exported to the superior-10 kV grid at the i-th bus in period t.

All the constraints considered are detailed below and are shown in Expressions (2)–(11). The power flow equation is described by Expressions (2) and (3).

$$Pi{n}_{i,t}-Pe{x}_{i,t}={\displaystyle \sum }_{i=1}^N\left|V_{i,t}\right|\left|V_{k,t}\right|\left|Y_{ik}\right|\cos \left({\delta }_{i,t}-{\delta }_{k,t}-{\theta }_{ik}\right)$$

(2)

$$Qi{n}_{i,t}-Qe{x}_{i,t}={\displaystyle \sum }_{i=1}^N\left|V_{i,t}\right|\left|V_{k,t}\right|\left|Y_{ik}\right|\sin \left({\delta }_{i,t}-{\delta }_{k,t}-{\theta }_{ik}\right)$$

(3)

where:

$Pi{n}_{i,t}$—the active power imported from the superior-10 kV grid at the i-th bus in period t;

$Pe{x}_{i,t}$—the active power exported to the superior-10 kV grid at the i-th bus in period t;

$Qi{n}_{i,t}$—the reactive power imported from the superior-10 kV grid at the i-th bus in period t;

$Qe{x}_{i,t}$—the reactive power exported to the superior-10 kV grid at the i-th bus in period t;

$V_{i,t}$—the voltage magnitude at the i-th bus in period t;

$V_{k,t}$—the voltage magnitude at the k-th bus in period t;

$Y_{ik}$—the i-th element of the bus admittance matrix ${\mathit{Y}}_{bus}$;

${\delta }_{i,t}$—the voltage phase angle at the i-th bus in period t;

${\delta }_{k,t}$—the voltage phase angle at the k-th bus in period t;

${\theta }_{ik}$—the phase angle i-th element of the bus admittance matrix ${\mathit{Y}}_{bus}$.

Maintaining the voltage within specified limits is described by (4):

$$V_{min} \le V_{i,t} \le V_{max}$$

(4)

where:

$V_{min}$—the lower voltage limit;

V_max—the upper voltage limit.

The thermal limitation of the power system component due to the overload current can be described with Expression (5):

$$0 \le P_{ik,t} \le P_{ik,max}$$

(5)

where:

$P_{ik,t}$—the active power at the ijth element in period t;

$P_{ik,max}$—the active power limit at the ijth element.

The limitation of electricity generation from the PV is defined in Expression (6):

$$Sp{v}_{pv,t}\le \sqrt{Pp{v}_{pv,t}^2+Qp{v}_{pv,t}^2}$$

(6)

where:

$Sp{v}_{pv,t}$—the apparent power of the PV inverter in period t;

$Pp{v}_{pv,t}$—the active power of the PV inverter in period t;

$Qp{v}_{pv,t}$—the reactive power of the PV inverter in period t.

The state-of-charge limitations of EV batteries are shown in Expression (7):

$$SOCe{v}_{ev,min}\le SOCe{v}_{ev,t}\le SOCe{v}_{ev,max}$$

(7)

$SOCe{v}_{ev,t}$—SOCev of EV batteries in period t;

$SOCe{v}_{ev,min}$—the lower limit of SOCev of EV batteries;

$SOCe{v}_{ev,max}$—the upper limit of SOCev of EV batteries.

Limitations regarding the energy exchanged with the superior grid are shown in Expressions (8) and (9):

$$0\le Pi{n}_{i_t}\le Pi{n}_{i_t}$$

(8)

$$0\le Pe{x}_{i_t}\le Pe{x}_{i_t}$$

(9)

The limitations of EV batteries regarding the charging and discharging power are given in Expressions (10) and (11):

$$0\le Pchre{v}_{ev,t}\le Pchre{v}_{ev,t}$$

(10)

$$0\le Pdise{v}_{ev,t}\le Pdise{v}_{ev,t}$$

(11)

where:

$Pchre{v}_{ev,t}$—EV batteries charging power in period t;

$Pdise{v}_{ev,t}$—EV batteries discharging power in period t.

2.2. Applied Optimization Procedure

The applied optimization procedure is presented in Figure 1. It represents a co-simulation methodology that interfaces an optimization method with a power system analysis program. In this setup, the optimization method generates a set of decision variables, which serve as input for the power system analysis program. These decision variables may include variables such as PV power plant set points, load allocations, or other controllable variables related to the power system. Once these inputs are processed, the power system analysis program performs power flow analysis, simulating the power system’s response to the obtained inputs. This simulation produces results that reflect the power system’s operational state, such as voltage levels, power losses, system stability metrics, etc. The resulting data from this simulation represent the objective function value, which is then returned to the optimization method. The optimization method uses this objective function value to assess the effectiveness of the current set of decision variables, iteratively testing the variables until convergence ensues. Convergence depends on settings for the optimization method, and it is usually chosen by the trial-and-error method. Because this approach incorporates AC power flow simulations, it provides a comprehensive and realistic representation of the power system’s behaviour, thereby enhancing the reliability and accuracy of the results. Since the optimization problem is presented as an optimal-power-flow-based problem, it is defined as nonlinear and nonconvex, which means it is hard to solve with an analytical optimization method. Otherwise, the original problem should be transformed to a level where the analytical method can be applied. These procedures reduce the degree of accuracy of the optimization model.

This methodology frames the optimization problem as a black-box problem, as the internal relationships between input and output variables in the power system model are not explicitly known or defined. Consequently, this co-simulation approach enables a realistic optimization model, even in the absence of an analytically defined relationship between decision variables and objective function values.

Figure 2 illustrates a flowchart diagram derived from the proposed optimization framework. Solar irradiance, EV charging pattern, loads, and network parameters represent inputs for the optimization procedure. Decision variables are obtained by the optimization process and represent the input for power flow analysis, which gives the objective function value as its output. If the obtained objective function values satisfy all constraints, the optimization procedure ends. Otherwise, the whole procedure is repeated.

The optimization problem is coded in Python 3.10. DIgSilent Power Factory performs power flow analysis. The PyGMO package 2.19, with built-in solution methods, solves the optimization problem. This paper uses particle swarm optimization (PSO) as the solution method, although any method embedded in the PyGMO package can be applied.

2.3. Distribution Grid Model Data

The proposed optimization procedure was examined using a realistic low-voltage urban distribution grid (radial low-voltage feeder) modelled in DIgSILENT Power Factory 2022 software (Figure 3). The grid consists of 89 household consumers with PV systems installed on roofs and is connected to the superior-10 kV grid via a 0.63 MVA 10/0.4 kV transformer. The single-phase PV systems with an apparent power of 3.68 kVA are connected to approximately every second consumer node, while the three-phase PV systems with an apparent power of 10 kVA are connected to nodes 2, 20, and 28, respectively. The PV generation curve(s) (Figure 4) were determined by continuous power quality measurements over a period of 24 h in summer weather conditions (early August in the Central Europe South area) at a consumer node with an installed PV system [28]. The consumer load characteristic is determined within 24 h power quality measurements at several consumer nodes [28]. Since the load patterns for households do not differ significantly, the load curve resulting from averaging all of the measured values for each hour was adopted for all consumers (Figure 5).

All of the nodes of the low-voltage grid are connected via the cable with parameters given in

Table 1. Cable parameters.

Parameter	Type 1	Type 2
Cable resistance, Ω/km	0.2542	0.443
Cable reactance, Ω/km	0.080424	0.072256
Cable capacitance, µF/km	0.84	0.52
Neutral resistance, Ω/km	0.1271	0.235
Neutral reactance, Ω/km	0.04	0.036
Neutral capacitance, µF/km	0.84	0.52

and a length of 0.877 km.

The EV charging stations are integrated into the grid according to the optimization procedure as three-phase 11 kW symmetric active power loads (P_EVCS = 11 kW). The integration of the EV charging stations at the nodes in the low-voltage grid where PV systems are already installed is supported by the tariff system (Croatia, European Union), which promotes efficient energy management based on the same location of generation, consumption, and storage of the electrical energy [29].

The power flow, generation–consumption–storage, and energy exchange with external network time-sweep calculations are performed according to proposed optimization framework.

2.4. Scenario Description

Simulation scenarios are followed with the voltage profiles of the whole observed low-voltage grid as well as daily voltage curves shown for node 89 (the furthest node from the superior-10 kV grid) and the energy exchange with the superior-10 kV grid:

• Scenario 1—the unbalanced power flow analysis of the actual topology of the observed low-voltage grid.
• Scenario 2—determination of EV charging stations locations and EV battery charge–discharge pattern according to the optimization procedure. There is no additional constraint on the SoC of the EV battery at the end of the observation period. It is assumed that the EV battery with any SoC value can be used for grid support.
• Scenario 3—repeated procedure of Scenario 2 but with an additional constraint on the SoC value of the EV battery at the end of the observation period. It is assumed that the SoC value of the EV battery at the end of the observation period is 30% of its full capacity, which means that EV batteries with a lower SoC value than 30% cannot be used for grid support.

3. Results and Discussion

3.1. Scenario 1

The voltage profile of the feeder was observed during the peaks of PV generation and load imbalance; the voltage value at the last node of the feeder is higher than at the beginning (Figure 6). The voltage profile is determined for the point of the highest production in the system, more precisely at 14:00. Since there are no other specific points, this one is selected as critical with respect to system load and system voltage conditions.

The highest voltage value—1043 p.u.—occurs during the daily generation peak at node 89. However, the voltage is within the specified limits for all three phases, with the lowest value during the night (Figure 7). However, the lowest value is 1 p.u., which is a preferable value.

During the 24 h, an active electrical energy of 305.56 kWh was consumed in the low-voltage grid. The total active energy losses were 36 kWh, while the total PV generation was 341.73 kWh. Figure 8 shows the energy exchange with the superior-10 kV grid, where the red area represents the energy import from the superior-10 kV grid, the yellow area represents the PV generation, while the orange area represents the PV generation surplus exported to the superior-10 kV grid. The household demands during the night-time and during periods of the daytime when the PV generation is low are covered by the energy import from the superior-10 kV grid. PV generation is approximately equal to household demands during 24 h time period.

3.2. Scenario 2—Minimization of Energy Exchange with the Superior-10 kV Grid

As can be seen from Figure 8, most of the PV generation in the baseline scenario was exported to the superior-10 kV grid; the high PV generation resulted in a voltage increase at node 89. Therefore, the total consumption of the low-voltage grid is increased by integrating EV charging stations in this operational scenario. The locations of integration and the charging curve are determined following the optimization procedure and constraints set in Section 2.1, which implies the minimization of energy exchange with the superior-10 kV grid while keeping the voltage values within the specified limits. The optimization procedure indicates that preferable locations for integration of EV charging stations are nodes 4, 16, 28, 40, 52, 60, and 88, with no additional constraints. Each EV battery has capacity of 70 kWh, which was obtained by directly surveying owners of EVs by the authors of [30]. The charging curve is shown in Figure 9. Positive values indicate the period when the battery provides energy to the network, while the negative period is the battery charging time.

The EV battery charging process changes the voltage profile of the low-voltage grid. The voltages are lower in comparison with the baseline scenario (Figure 10); the lowest voltage appears during the 16th hour and represents the new peak load in the system, and therefore the peak of the 16th hour was chosen to show that even under high load conditions, the voltage remains within acceptable limits. The previous voltage peak during the 14th hour is lower than in the baseline scenario, with values between 1 p.u. in phase C and 0.974 p.u in phase A, and it is shown that during the highest consumption in the system, the voltage manages to be maintained within acceptable limits. The voltage profile during the peak production period is shown in Appendix A with Figure A1.

The voltage profile changes when EV charging stations are implemented in the feeder. The PV generation peak is between the 12th and 14th hour, but with charging of EVs during the peak production period, voltage decreases, reaching its maximum—1.0225 p.u. (phase B)—during the 11th hour (Figure 11). After charging begins, the charging current increases, and the voltage drops to its daily minimum, which occurs during the 16th hour. The lowest voltage in phase A is 0.974 p.u., while phases C and B have higher voltages, 0.9825 p.u. and 0.99 p.u., respectively, which means that the voltages are within the specified limits.

The energy exchange for the second scenario is shown in Figure 12. The household consumption remains equal, as in Scenario 1, while the total consumption is increased with the charging of EVs. PV generation (yellow) also remains the same as in Scenario 1. During the night, the EVs (blue) are used to support the grid, and the total consumption of the feeder is partially covered by the EV batteries. During the short period between the 9th and 10th hour and between the 19th and 21st hour, electrical energy was received from the superior grid (red for energy imported from the superior grid). Surplus energy—in the period between the 10th and 12th hour and the 18th and 19th hour—was exported to the superior grid (red indicates energy imported from the superior grid, and yellow indicates energy generated by PV and used for household consumption). The remaining energy obtained from PV generation was used to charge EVs (combination of blue and yellow characteristics). Also, between the 13th and 18th hour, energy was imported from the superior grid and used for charging EV batteries (blue for EV battery charging and red for energy imported from the superior grid). In total, 48.42 kWh was received from the superior grid, while 82.38 kWh was exported to the superior grid in the observed period. If we assume that the battery has a capacity of 70 kWh, which was determined by a direct survey of electric vehicle owners by the authors of [27], the SoC value at the end of the cycle is below 30%, which is the minimum preferred by the owners.

3.3. Scenario 3—Minimizing Energy Exchange with Limited Battery SoC at the End of the Cycle

In the third scenario, the proposed optimization procedure from Section 2 is performed with an additional constraint related to the SoC of the vehicle battery at the end of the cycle. In this scenario, the EV’s batteries were charged at night when the household consumption is low. The SoC of the batteries has been kept above the set limit of 30%, and the charging pattern is shown in Figure 13.

With this adjustment, the voltage profile during the peak generation of PVs remains the same as in the previous scenario, while the phase imbalance is less noticeable than in the previous scenarios. The voltage profile for the point of the peak load is identical to Scenario 2. Therefore, the voltage profile at a third time point is observed here, i.e., the 21st hour when the battery supports the grid (Figure 14). The lowest voltage value during this period is 1 p.u., and the highest is 1.015 p.u. in phases A and C. In this scenario, the voltage imbalance is reduced.

The voltage values at node 89 (Figure 15) have changed compared to the previous scenarios, as they drop significantly in the periods between the 2nd and 4th hour and again between the 22nd and 24th hour. During these periods, the EV’s batteries are not needed to maintain the voltage, so they are charged to keep the SoC value in the specified range. During the day, the charging profile remains the same as in the previous scenarios. The voltage in phase A reaches its minimum (0.97 p.u.) after the 16th hour, while the voltage values in phases B and C are 0.99 p.u. and 0.983 p.u., respectively. The voltage profile for Scenario 3 during the peak production period (14th hour) is given in Appendix A, Figure A2.

The highest voltage values occur in the 11th hour and reach values between 1.01 p.u. (phase A) and 1.0225 p.u. (phase B).

With an additional constraint on SoC, the EV’s batteries are charged independently of PV generation (Figure 16). In this way, with the same PV generation and household consumption, the energy imported from the external grid increases to 189.30 kWh to fulfil the storage of 224.81 kWh in the EV batteries. Maintaining the desired SoC resulted in a much higher energy exchange with the superior-10 kV grid.

Energy exported to the superior-10 kV grid is marked in blue, while the red area is the energy supplied by the grid. Red and blue characteristics represent EV charging from the superior grid. PV production is marked in yellow. During the maximum generation period, the EV is charged and the energy used for the charging is marked with blue and yellow. Since charging EV and PV generation profiles do not match completely, between the 12th and 18th hour, batteries are charged from energy taken from the external grid (red and blue characteristic).

4. Conclusions

A review of the recent scientific literature revealed many papers dealing with achieving optimal technical and economic conditions when integrating renewable energy sources and EVs into distribution grids. The integration of PV systems and the use of EVs are recommended as part of the measures to reduce the environmental impact caused by the burning of fossil fuels. PV power plants can be integrated anywhere, most often on the roofs of buildings and houses directly at the point of energy consumption, reducing the dependence of consumers on external energy sources. The increasing integration of PV systems leads to an increase in voltage along the feeder. The overall PV integration is limited by the ratings of the existing grid components. The use of vehicles as V2G can mitigate this problem to some extent. In order to take full advantage of V2G, this paper optimizes the vehicle charging and discharging patterns with the goal of reducing active power losses as well as energy received from the external grid and keeping voltage values within specified limits.

In this paper, results in Scenario 1 showed negative aspects of high PV integration levels in the distribution grid and significant energy exchange with the superior grid. The total PV generation was 341.73 kWh, while the total electrical energy consumption was 305.56 kWh in the low-voltage grid. Also, most of the PV generation in Scenario 1 was exported to the superior-10 kV grid. On the other hand, the minimum energy exchange with the external grid is achieved in Scenario 2, where EV batteries are used to support the grid without SoC as a constraint. Providing constant grid support would be a more appropriate solution in this context, as in this scenario, only 82.38 kWh was exported to the superior grid, and 48.42 kWh was imported from the superior grid. However, the more realistic solution is presented in Scenario 3. It is the nature of vehicle owners to want to use their vehicles at all times, which is only possible with SoC constraining the EV battery in V2G operation, thus increasing the energy exchange with the external grid. Therefore, the SoC value of the EV battery that satisfies both V2G operation and driver autonomy was set at approximately 30%. This SoC value is similar to a conventional car’s approximated reserve tank fuel capacity. The impact of external conditions, such as battery sensitivity, on weather conditions is also considered. In Scenario 3, 189.30 kWh was imported from the superior grid to fulfil the storage of 224.81 kWh in the EV batteries.

The advantages of the proposed optimization procedure are ensuring optimal locations for EV charging stations and obtaining optimal electric vehicle charging patterns. The proposed optimization procedure is suitable for application to the distribution system operator in order to take into account the capability of modern control mechanisms to improve operation and power quality in distribution grids. Also, the proposed optimization procedure can be applied in more complex grid configurations to achieve the above objectives.

In the future, it is necessary to carry out additional research in order to integrate a larger amount of renewable energy sources and EVs into the distribution grid with different load conditions and grid configurations, taking into account the technical aspect on the one hand and the economic aspect on the other hand, respecting the behaviour of users.