Optimal Scheduling of Battery Energy Storage Systems and Demand Response for Distribution Systems with High Penetration of Renewable Energy Sources ^†

Abstract

The penetration of renewable energy sources (RESs) is increasing in modern power systems. However, the uncertainties of RESs pose challenges to distribution system operations, such as RES curtailment. Demand response (DR) and battery energy storage systems (BESSs) are flexible countermeasures for distribution-system operators. In this context, this study proposes an optimization model that considers DR and BESSs and develops a simulation analysis platform representing a medium-sized distribution system with high penetration of RESs. First, BESSs and DR were employed to minimize the total expenses of the distribution system operation, where the BESS model excluding binary state variables was adopted. Second, a simulation platform based on a modified IEEE 123 bus system was developed via MATLAB/Simulink for day-ahead scheduling analysis of the distribution system with a high penetration of RESs. The simulation results indicate the positive effects of DR implementation, BESS deployment, and permission for electricity sales to the upper utility on decreasing RES curtailment and distribution system operation costs. Noticeably, the RES curtailments became zero with the permission of bidirectional power flow. In addition, the adopted BESS model excluding binary variables was also validated. Finally, the effectiveness of the developed simulation analysis platform for day-ahead scheduling was demonstrated.

1. Introduction

Fossil fuels are major sources of electricity. However, excessive consumption of fossil resources leads to environmental damage [1]. Worldwide, countries are eager to decrease their dependency on fossil fuels [2]; thus, procuring alternative energy sources is vital to meet the growing energy demands and reduce carbon dioxide emissions. Renewable energy sources (RESs), among which solar and wind energy resources have the highest attractiveness [3], are environmentally friendly and are the most promising alternative energy sources [4]. As RES-based generators such as wind turbines (WTs) and photovoltaic panels (PVs) are increasingly being installed, the intermittent nature of these RESs poses many challenges to distribution systems [5]. For example, RES curtailment frequently occurs because of a mismatch between power generation and load demands. RES curtailment causes wastage of free and clean energy, leading to economic losses [6]. As a flexible countermeasure to handle the problem, demand response (DR) can motivate customers to shift their power consumption and reduce load demand during peak hours [7,8]. In addition, battery energy storage systems (BESSs) can be dispatched to absorb RES generation surplus or fulfill peak load demands [9]. Therefore, from the perspective of distribution system operators, an optimization model that considers DR implementation and BESS scheduling is vital for minimizing the total expenses of operating costs and electricity trading.

The existing literature offers several optimization methods for DR and BESSs in power system scheduling. Specifically, the authors in [9] proposed an interval optimization-based coordination approach for DR and BESSs to minimize the total operational costs of the microgrid. In [10], the authors proposed a stochastic framework for optimal charge and discharge scheduling of plug-in electric vehicles in local distribution systems, where plug-in electric vehicles can be considered as mobile BESSs. In [11], an optimal scheduling method for distributed generators, BESSs, tap transformers, and controllable loads of a radial distribution feeder was proposed to minimize total distribution losses. In [12], an optimal operational strategy for a grid-connected microgrid considering distributed energy resources and their interaction with incentive-based DR programs was proposed, and the whale optimization algorithm was adopted to solve the optimization problem. The authors in [13] presented detailed mathematical models of BESSs, PV systems, directly controllable loads, and generation curtailment in the microgrid optimal scheduling problem. An energy management strategy was proposed in [14] to extend the life cycles of hybrid energy storage systems based on the state of charge (SOC). In [15], the authors analyzed the techno-economic impacts of mixed-integer linear programming (MILP)-based dispatch for BESSs deployed within a small residential RES community. In [16], the authors proposed a methodological framework for optimal coordinated scheduling of BESSs with microturbines considering RESs and dynamic electricity prices to maximize the daily utility profit. In [17], the authors presented a two-stage active distribution network management method to deliver the power flexibility that the upper grid requested, where the BESS output was adjusted to mitigate the power imbalance due to RES uncertainty.

The aforementioned studies have demonstrated the wide use of DR and BESSs for the optimal scheduling of distribution systems or microgrids. However, the investigated distribution systems or microgrids in those studies are very small (at most 30–40 nodes). Besides, a convenient simulation platform for distribution systems with a high penetration of RESs has not been developed to observe the effects of the obtained scheduling plans. Furthermore, most BESS models employed in [9,10,11,12,13,14,15] introduced binary variables to describe the charging and discharging states. Those BESS binary variables are unnecessary if BESS operation costs are considered and all generation costs in the objective are positive [18]. Fewer integer variables can contribute to a simpler optimization model to save time. In this context, this study proposes an optimization model that considers DR and BESSs and develops a simulation analysis platform representing a medium-sized distribution system with high penetration of RESs. First, BESSs and DR are employed to minimize the total operating expenses, which is formulated as an MILP problem. Note that although the BESS models in this study do not contain integers, binary variables for DR models are still required. Second, a simulation platform based on a modified IEEE 123 bus system penetrated by WTs, PVs, and BESSs was developed via MATLAB/Simulink for the practical operation analysis of distribution systems. A modified complex load module was added at each bus so the distribution operator can mark a BESS (or PV, WT) at any bus as they like and implement simulation. The simulation results indicate that BESSs and DRs are crucial for decreasing RES curtailment and system operation costs. The positive effects of bidirectional power flow between the utility and the distribution system on RES curtailment and operation costs are illustrated. In addition, the adopted BESS model, excluding binary variables, was also validated. Furthermore, the effectiveness of the developed platform for day-ahead scheduling simulations is demonstrated. Compared to our previous work [19], our current paper incorporates the following new features: (1) the BESS model excludes unnecessary binary variables; (2) the utility grid can buy redundant electricity from the distribution system operator; and (3) additional voltage variation results obtained via the developed MATLAB/Simulink platform are presented.

The remainder of this paper is organized as follows. Section 2 introduces the proposed MILP model for distribution system optimization. In Section 3, the developed Simulink-based simulation platform is described. The simulation results of the modified IEEE 123 bus system are presented in Section 4, and Section 5 concludes the paper.

2. Mathematical Models for Optimization

This section describes the proposed mathematical models for distribution system optimization from the perspective of distribution system operators. The distribution system is penetrated by customer-owned WTs and PVs, and the operator buys the RES generation from customers. RESs may be curtailed when the load demand is low and BESSs cannot consume RES surplus power because of capacity limits. In this situation, the operator does not pay RES utilization fees, but the compensation of RES curtailments to customers. The operator purchases electricity from the utility grid and sells it to customers. Note that the distribution system operator can also sell redundant power to the utility grid. In addition, the operator implements DR and dispatches BESSs installed in the system to tackle RES uncertainty problems and facilitate energy management. The DR strategy is to use price signals to change the customer loads. Specifically, by decreasing customer load prices when power generation is redundant, customers will be motivated to increase load consumption, so power generation and consumption are balanced again, and vice versa.

2.1. The Objective Function

The total operation costs can be represented as follows:

$$min F=C^{\mathrm{UTIL}}+C^{\mathrm{RES},\mathrm{buy}}+C^{\mathrm{RES},\mathrm{cut}}+C^{\mathrm{BESS}}-C^{\mathrm{CTM}}$$

(1)

$$C^{\mathrm{UTIL}}={{\displaystyle \sum }}_{t\in T}\left(C_t^{\mathrm{UTIL},\mathrm{buy}}{P}_t^{\mathrm{UTIL},\mathrm{buy}}-C_t^{\mathrm{UTIL},\mathrm{sell}}{P}_t^{\mathrm{UTIL},\mathrm{sell}}\right)\tau$$

(2)

$$C_t^{\mathrm{UTIL},\mathrm{sell}}={\omega }^{\mathrm{UTIL},\mathrm{sell}}{C}_t^{\mathrm{UTIL},\mathrm{buy}}$$

(3)

$$C^{\mathrm{RES},\mathrm{buy}}={{\displaystyle \sum }}_{t\in T}{C}_t^{\mathrm{RES},\mathrm{buy}}{P}_t^{\mathrm{RES},\mathrm{buy}}\tau$$

(4)

$$C_t^{\mathrm{RES},\mathrm{buy}}={\omega }^{\mathrm{RES},\mathrm{buy}}{C}_t^{\mathrm{UTIL},\mathrm{buy}}$$

(5)

$$P_t^{\mathrm{RES},\mathrm{buy}}=P_t^{\mathrm{WT}}+P_t^{\mathrm{PV}}-P_t^{\mathrm{RES},\mathrm{cut}}$$

(6)

$$C^{\mathrm{RES},\mathrm{cut}}={{\displaystyle \sum }}_{t\in T}{C}_t^{\mathrm{RES},\mathrm{cut}}{P}_t^{\mathrm{RES},\mathrm{cut}}\tau$$

(7)

$$C_t^{\mathrm{RES},\mathrm{cut}}={\omega }^{\mathrm{RES},\mathrm{cut}}{C}_t^{\mathrm{RES},\mathrm{buy}}$$

(8)

$$C^{\mathrm{BESS}}={{\displaystyle \sum }}_{t\in T}\left(C_t^{\mathrm{BESS}}{P}_t^{\mathrm{dis}}+C_t^{\mathrm{BESS}}{P}_t^{\mathrm{ch}}\right)\tau$$

(9)

$$C^{\mathrm{CTM}}={\displaystyle \sum }_{t\in T}{\displaystyle \sum }_{j\in J}{\gamma }_{j}P{r}_0{P}_t^{\mathrm{LD}}{\alpha }_{j,t}{L}_j\tau$$

(10)

2.2. The DR Constraints

The DR model can be represented as follows:

$$P_t^{{\mathrm{LD}}_{\mathrm{DR}}}=P_t^{\mathrm{LD}}{\displaystyle \sum }_{j\in J}{\alpha }_{j,t}{L}_j$$

(11)

$${\displaystyle \sum }_{j\in J}{\alpha }_{j,t}=1$$

(12)

$$C^{\mathrm{CTM}}\le {\displaystyle \sum }_{t\in T}P{r}_0{P}_t^{\mathrm{LD}}\tau$$

(13)

$${\displaystyle \sum }_{t\in T}{\displaystyle \sum }_{j\in J}{P}_t^{\mathrm{LD}}{\alpha }_{j,t}{L}_j\tau \ge {\displaystyle \sum }_{t\in T}{P}_t^{\mathrm{LD}}\tau$$

(14)

where Equation (11) calculates the customer load power after DR, Equation (12) indicates that only one DR level can be achieved in each hour, Equation (13) indicates that customers’ electricity expenses after DR cannot exceed the original expenses, and Equation (14) indicates that the implementation of DR cannot have a negative effect on customers’ power consumption.

2.3. The Generation and Consumption Constraint

Instant power generation and consumption should be equal:

$$P_t^{\mathrm{RES},\mathrm{cut}}+P_t^{{\mathrm{LD}}_{\mathrm{DR}}}=P_t^{\mathrm{PV}}+P_t^{\mathrm{WT}}+P_t^{\mathrm{UTIL}}+P_t^{\mathrm{BESS}}$$

(15)

where the total generated power must be equal to the power consumed at any time t.

2.4. The Power Exchange Constraints

Here, the bidirectional power flow between the utility and distribution system is considered as follows:

$$P_t^{\mathrm{UTIL}}=P_t^{\mathrm{UTIL},\mathrm{buy}}-P_t^{\mathrm{UTIL},\mathrm{sell}}$$

(16)

$$P_t^{\mathrm{UTIL},\mathrm{buy}}\ge 0, P_t^{\mathrm{UTIL},\mathrm{sell}}\ge 0$$

(17)

2.5. The BESS Charging/Discharging Behaviors and SOC Constraints

The BESS model is described as follows:

$$0\le P_t^{\mathrm{ch}}\le P_{rated}^{\mathrm{BESS}}$$

(18)

$$0\le P_t^{\mathrm{dis}}\le P_{rated}^{\mathrm{BESS}}$$

(19)

$$P_t^{\mathrm{BESS}}=P_t^{\mathrm{dis}}-P_t^{\mathrm{ch}}$$

(20)

$$SO{C}_t=SO{C}_{t-1}+{\eta }^{\mathrm{ch}}\frac{P_t^{\mathrm{ch}}\tau }{E^{\mathrm{BESS}}}\times 100-\frac{1}{{\eta }^{\mathrm{dis}}}\frac{P_t^{\mathrm{dis}}\tau }{E^{\mathrm{BESS}}}\times 100$$

(21)

$$SO{C}_{min}\le SO{C}_t\le SO{C}_{max}$$

(22)

$$SO{C}_{end}=SO{C}_0$$

(23)

It can be seen that the BESS model excludes unnecessary binary variables; therefore, all BESS variables are continuous.

2.6. The RES Curtailment and Purchase Constraints

The values of RES curtailment and purchase are both non-negative:

$$P_t^{\mathrm{RES},\mathrm{cut}}\ge 0$$

(24)

$$P_t^{\mathrm{RES},\mathrm{buy}}\ge 0$$

(25)

The values of RES curtailment and purchase are both non-negative.

Objective function (1) and the corresponding constraints Equations (2)–(25) constitute the MILP problem. The detailed descriptions of the DR model and BESS model can be found in [9,18], respectively. The control variables for the optimization are DR variables ${\alpha }_{j,t}$, BESS variables $P_t^{\mathrm{ch}/\mathrm{dis}}$ and the power traded with the utility $P_t^{\mathrm{UTIL},\mathrm{buy}/\mathrm{sell}}$.

3. The Matlab/Simulink-Based Developed Simulation Platform

In this section, a simulation platform based on a modified IEEE 123 bus system penetrated by WTs, PVs, and BESSs is developed using the MATLAB/Simulink software. IEEE 123 represents a medium-sized medium-voltage distribution system. The data for the original IEEE 123 bus system were obtained from the IEEE PES official website [20], and the corresponding original MATLAB/Simulink models were retrieved from [21]. A topological diagram of the modified system is shown in Figure 1. In the MATLAB/Simulink model files, every original load module of the IEEE 123 bus system was replaced by the modified complex load module shown in Figure 2. The modified complex load module consists mainly of a PV module, WT module, BESS module, and customer load module. All modules were modeled as controlled current sources in Simulink. Figure 3 shows the BESS charging/discharging behaviors and SOC constraints shown in Equations (18)–(23).

Although Figure 1 indicates specific locations of PVs, WTs, and BESSs, as shown in

Table 1. Locations and rated power of PVs, WTs, and BESSs.

Type	Location	Rated Power at Each Location
PV	Bus 71, 100, 104, 107, 114	200 kW
WT	Bus 75, 88, 90, 92, 96	200 kW
BESS	Bus 79	400 kW

, the distribution operator can mark a BESS (or PV, WT) at any bus they like because of the modified complex load module added at each bus. Then, the operator inputs the corresponding optimization results into the simulation platform after running the optimization models Equations (1)–(25). If a bus contains only one type among the PV, WT, or BESS, the input operation data for the other two types becomes zero. Finally, the operator obtains the temporal simulation results (such as bus voltages) throughout the optimization horizon based on the developed platform. Therefore, it is convenient for the operator to test the effect of BESSs (also PVs and WTs) in different buses and quantities. The flow chart of the utilization of the optimization model and simulation platform is depicted in Figure 4. In this study, the proposed optimization problem is solved by Gurobi [22] on a PC with a 3.70 GHz i5-9600k CPU and 16 GB RAM, and Yalmip [23] is employed as the interface between Gurobi and MATLAB.

4. Case Study

The first subsection presents the optimization results of the models shown in Section 2, where two types of load profiles are considered in the modified IEEE 123 bus system. The effects of DR and BESSs on RES curtailment and operational costs are illustrated. The impact of whether the distribution system sells power to the utility is also analyzed. In addition, the adopted BESS model, which does not include binary variables, was validated. In the second subsection, the simulation results of the developed MATLAB/Simulink-based platform are presented, and the effectiveness of the platform for day-ahead scheduling simulations is demonstrated.

4.1. Optimization Results

Table 1 lists the locations and rated power of the PVs, WTs, and BESSs. The other necessary parameters for the BESSs are listed in

Table 2. BESS parameters.

${\mathit{E}}^{\mathbf{BESS}}$ (kWh)	${\mathit{C}}_{\mathit{t}}^{\mathbf{BESS}}$ ($/kWh)	$\mathit{S}\mathit{O}{\mathit{C}}_0 (\%)$	$\mathit{S}\mathit{O}{\mathit{C}}_{\mathit{m}\mathit{i}\mathit{n}} (\%)$	$\mathit{S}\mathit{O}{\mathit{C}}_{\mathit{m}\mathit{a}\mathit{x}} (\%)$
400	0.01	50	10	90

. For the system parameters, the temporal variations in PVs and WTs can be found in [24]. The electricity market prices were taken from [25], which indicates the situation of Victoria, Australia, on 11 January 2021. Customer electricity prices before DR were obtained from [26]. The DR price levels are listed in

Table 3. DR levels.

Price Level	Price Rate	DR Rate
1	0.8	1.09
2	1.0	1.0
3	1.2	0.93

[9]. In addition, ${\omega }^{\mathrm{RES},\mathrm{buy}}$ was set to 0.57 [27] and ${\omega }^{\mathrm{RES},\mathrm{cut}}$ was set to 0.15 [28].

4.1.1. The Effects of DR and BESSs

In this part, the effects of DR and BESSs on RES curtailment and operation costs are illustrated. Here, it is assumed that the distribution operator cannot sell electricity to the utility grid, which was also assumed in our previous study [19]. Figure 5 shows the PV and WT total output variations, which show a high-power output in the afternoon. Figure 6 and Figure 7 show the variations in load demand, real-time prices, and RES curtailment for two different types of load profiles, respectively. It is obvious that for both load profiles, DR decreases the RES curtailment via lower customer electricity prices during RES high-output periods. Therefore, DR facilitates RES utilization efficiency.

Two additional BESSs were added to the system (one at Bus 66 and another at Bus 85). With DR implementation, Figure 8 and Figure 9 show the comparison of BESS power variations and RES curtailments for load types A and B, respectively. As the quantity of BESSs increased, the RES curtailment for both load profiles decreased. Thus, it is demonstrated that BESSs can facilitate RES utilization efficiency.

The total operational costs calculated before DR (one BESS), after DR (one BESS), and after DR (three BESSs) are compared in

Table 4. Comparison of the total operation costs in terms of DR implementation and different quantities of BESSs (the distribution operator cannot sell electricity to the utility grid).

Load Type	Costs before DR (One BESS) ($)	Costs after DR (One BESS) ($)	Costs after DR (Three BESSs) ($)
A	−2763.39	−2781.24	−2794.21
B	−2646.26	−2665.65	−2679.02

. The costs after DR are all smaller than those before DR; therefore, the positive effect of DR on operation costs is demonstrated. In addition, the costs decreased as the quantity of BESSs increased, which indicates the positive effect of BESSs. It should be noted that negative costs indicate that the operator earns profits after scheduling.

Overall, the positive effects of DR and BESSs on RES curtailment and operational costs are illustrated. Therefore, from the perspective of the distribution operator, DR implementation and BESS utilization are economically beneficial.

4.1.2. The Effect of Bi-Directional Power Flow between the Utility and the Distribution System

In this part, the bi-directional power flow between the utility and the distribution system was assumed, and ${\omega }^{\mathrm{UTIL},\mathrm{sell}}$ was set to 0.6. Figure 10 and Figure 11 show the variations in load demand, real-time prices, and RES curtailment for load types A and B, respectively. Compared with the results of Figure 6 and Figure 7, the RES curtailments for both load types became zero (from the highest 600 kW to zero for type A and from the highest 400 kW to zero for type B), which indicates that the electricity sales to the utility decreased the RES curtailments to the largest extent. Similarly, compared to the results in Figure 8 and Figure 9, Figure 12 and Figure 13 also demonstrate the positive effects of the electricity sales to the utility on RES utilization.

In addition, the total operation costs that are calculated before DR (one BESS), after DR (one BESS), and after DR (three BESSs), when electricity sales to the utility are permitted, are shown in

Table 5. Comparison of the total operation costs in terms of DR implementation and different quantities of BESSs (the distribution operator is able to sell electricity to the utility grid).

Load Type	Costs before DR (One BESS) ($)	Costs after DR (One BESS) ($)	Costs after DR (Three BESSs) ($)
A	−2772.52	−2787.88	−2800.74
B	−2652.02	−2669.12	−2682.29

. The operation costs in Table 5 all decrease compared to the counterparts in Table 4, which indicates that the permission of bi-directional power flow between the utility and the distribution system reduced the distribution system operation costs.

Overall, the positive effects of bidirectional power flow between the utility and the distribution system on RES curtailment and operation costs are illustrated. As RES penetration levels increase, these positive effects may become more noticeable. The interaction coordination between the utility and distribution system will be the subject of our future research.

4.1.3. The Validation of the BESS Model

In this part, the adopted BESS model excluding binary variables is validated. DR implementation, one BESS, and electricity sales to the utility are considered herein. Figure 14 depicts the BESS charging/discharging power variations for both load types A and B, indicating that, at most, one variable of $P_t^{\mathrm{dis}}$ and $P_t^{\mathrm{ch}}$ can be nonzero, and simultaneous charging and discharging never occur. This is because when the BESS total output $P_t^{\mathrm{BESS}}$ is determined by Equation (15), simultaneous charging and discharging can never achieve the optimal operation cost according to Equation (9).

4.2. Simulation Results of the Developed Matlab/Simulink Platform

After optimization, the operator conducts a module simulation to check whether the scheduling decisions can be implemented without operational violation. The simulation results for the developed MATLAB/Simulink platform are presented in this subsection. DR implementation, one BESS, and electricity sales to the utility are considered. Note that the simulations under other conditions can be similarly completed by simply revising the parameters.

The MATLAB/Simulink simulation was implemented every 2 s, and the entire-day voltage variations at Buses 1, 71, 79, and 88 for load type A are shown in Figure 15. The voltages for the other buses exhibited similar variation trends and are omitted here for simplification. The permitted voltage range [0.9, 1.1] p.u., as shown in [29,30], was adopted here. The voltage variations were within the tolerance range at all times, which indicates that the scheduling decisions can be implemented without operational violation. Similar conclusions can be drawn from Figure 16, where the voltage variations for load type B are shown.

In addition, the average CPU time for these two simulations was only 652.87 s, which is sufficiently fast for the operator to formulate a day-ahead scheduling plan in reality. Thus, the effectiveness of the developed platform for day-ahead scheduling simulations is demonstrated.

Overall, DR implementation, BESS employment, and the permission of bidirectional power flow between the utility and the distribution system all led to decreasing RES curtailment and distribution system operation costs. Thus, the positive effects of DR implementation, BESS employment, and the permission of bidirectional power flow were demonstrated. It is worth noticing that the RES curtailments for both load types became zero (from the highest 600 kW to zero for type A and from the highest 400 kW to zero for type B) with the permission of bi-directional power flow. This indicates that the electricity sales to the utility decreased the RES curtailments to the largest extent. In addition, the BESS charging/discharging power variations cannot be simultaneously nonzero, which justified the adopted BESS model that excludes the binary variables. Finally, the effectiveness of the developed platform for day-ahead scheduling simulations is demonstrated, as the voltages were within the limit and the CPU time was short.

5. Conclusions

This paper proposes an optimization model that considers DR and BESSs and develops a simulation analysis platform representing a medium-sized distribution system with high penetration of RESs. First, BESSs and DR were deployed to minimize the total expenses of the distribution system operation. Second, a simulation platform based on a modified IEEE 123 bus system was developed via MATLAB/Simulink for practical day-ahead scheduling analysis of a distribution system with a high penetration of RESs. The simulation results indicate the positive effects of DR implementation, BESS employment, and the permission of bidirectional power flow between the utility and the distribution system on decreasing RES curtailment and distribution system operation costs. Specifically, the RES curtailments for both load types became zero (from the highest 600 kW to zero for type A and from the highest 400 kW to zero for type B) with the permission of bidirectional power flow. This indicates that the electricity sales to the utility decrease the RES curtailments to the largest extent. In addition, the BESS charging/discharging power variation results justified the adopted BESS model that excludes the binary variables. Finally, the effectiveness of the developed platform for day-ahead scheduling simulations was demonstrated.

One weakness of this study is the neglect of distribution system power flow. In future studies, the power flow formulation should be considered. Besides, as the operation of WTs will be affected by the system frequency, the frequency stability should also be verified. Furthermore, the optimal locations and corresponding number and rated powers of BESSs in the distribution system highly penetrated by RESs can be studied based on the proposed optimization method and simulation platform, considering the initial investment and maintenance of the BESSs.