## 1. Introduction

With the rapid development of the distributed photovoltaic (PV) and the wind turbine systems, power system economy and stability are facing great challenges because of the uncertainty and fluctuation of renewable energy [

1,

2,

3]. To solve this problem, distributed energy storage systems are installed to suppress renewable energy outputs fluctuation, reduce the peak and valley difference of a distributed power system, improve the matching degree of daily renewable energy outputs and loads, reduce the installation capacity of distributed fossil power generators, and minimize the total costs of a distributed network [

4,

5]. However, due to the relatively high initial installation cost of the energy storage system, a large-scale installation of an energy storage system is difficult to achieve at present. Therefore, properly configuring energy storage capacity is crucial for improving the economy and stability of distributed power systems [

6,

7].

In recent years, many models have been proposed to optimize the installation capacity of a distributed energy storage system. However, by selecting different simulation time scales and optimization criterion, the results of the optimal capacity are quite different. In [

8,

9,

10,

11,

12], one hour is selected as the simulation time scale to configure the capacity of a distributed energy storage system. Among them, in [

8], the capacity of a distributed energy storage system is configured based on the redundant energy generated by renewable energy generators. In addition, to meet the peak demands of an isolated island, Kaldellis J.K et al [

9] design the optimal energy storage capacity of PV systems according to system stability constraints. Similarly, system spinning reserve and the unit commitment problem are fully considered in [

10] to estimate the ideal energy storage system capacity for both grid-connected and off-grid power systems. Moreover, Lee T. et al. sized system battery capacity, aiming at reducing the average yearly energy costs of users who have participated in time-of-use (TOU) tariffs [

11]. Finally, and crucially, as the mainstream method of configuring energy storage capacity, battery capacity is designed on the basis of the capability of shaving peak demands [

12]. In summary, an hour-based energy storage system configuring is commonly focused on improving system economy and security, but it usually neglects the dynamic characteristic of renewable generation.

To analyze the dynamic characteristic of renewable energy generation systems, one second is selected as the simulation cycle in [

13] to configure the capacity of a flywheel battery hybrid energy storage system. However, Barelli L. et al. do not take system economy into account. Therefore, this paper is the first time that a battery and super-capacitor storage system is configured under multi-time scales while taking system economy, security, and the fluctuation of a renewable energy system into consideration.

After translating distributed energy storage system capacity configuration problems into multi-objective optimization problems, many scholars have applied different algorithms to solve the proposed problems. Chen S.X. et al [

10,

14] use mixed-integer linear programming (MILP) to optimize the capacity and the operation strategy of energy storage systems for microgrids. Additionally, considering the efficiency and operation characteristics of the storage devices, dynamic programming is used in [

15] to determine the optimal capacity of a vanadium redox battery (VRB). Moreover, some scholars use metaheuristic algorithms to find the optimal capacity of distributed system energy storage systems [

16,

17]. The aforementioned papers have good performance on translating energy storage configuration problems into multi-objective optimization problems, generating a relatively high accuracy quantitative analysis, and revealing the best capacity and operation strategy of energy storage systems. However, these papers cannot directly point out the influence of different factors on the energy storage system configuration. Therefore, this paper firstly analyzes the key factors that can affect the installation capacity of distributed energy storage systems, and afterwards intuitively displays the key factors that can affect energy storage system installation capacity in a three-dimensional (3D) graph and carries out quantitative analysis.

To model renewable energy resource uncertainty and improve the accuracy of optimization results, the Monte Carlo method is extensively applied to study problems related to power system uncertainty. Liu W. et al. [

18] use the pseudo-sequential Monte Carlo simulation to model the uncertainty of PV outputs, and it also combines the intelligent state space reduction to evaluate the economic performance of a power system with PV installation. In addition, based on the state sampling non-sequential Monte Carlo simulation and the DC load flow-based load curtailment model, Bakkiyaraj R.A. et al. simulated the random fault of the power system, and put forward a power system reliability evaluation method [

19]. Also, by using the Monte Carlo method to simulate unbalanced voltage and then analyzing the effects of unbalanced voltage on PV hosting capacity, the hosting capacity of PV in different regions was shown in [

20]. Moreover, the Monte Carlo method was used to simulate the uncertainty of wind power generation and users’ electric vehicle charging behaviors in [

21]. In this paper, a joint operation model is proposed to decrease the high uncertainty of a wind power system by centralizing electric vehicle charging stations. In [

18,

19,

20,

21], the Monte Carlo method was successfully used to model the uncertainty of power systems, but this method has some limitations, such as for example, high complexity and low computation efficiency. In order to avoid the limitations of the Monte Carlo method, factors (excluding the uncertainty of renewable energy resource) that can affect energy storage system installation capacity are comprehensively considered when sizing hybrid energy storage systems. Then, by defining two indexes, wind speed volatility and solar irradiance volatility, the influence of renewable energy resource uncertainty on the proposed storage system is evaluated. This approach significantly reduces computation complexity. The main contributions of this article can be summarized as follows. (1) In the view of different time scales, this paper analyzes the renewable generation and load characteristics of a distributed power system, puts forward a high-precision storage capacity configuration method for a place with relatively stable meteorology, and optimizes the proposed model by using the genetic algorithm (GA). (2) By comprehensively considering the limitations of carbon emissions, costs, and the hybrid energy storage system installation capacity, this paper shows the relationship among the super-capacitor installation capacity, the battery installation capacity, and the average daily energy costs of the system in a 3D graph. Then, it generates a region of feasible hybrid energy storage system installation capacity in the 3D graph, and meanwhile reveals the influence of carbon emissions and daily energy cost on energy storage system installation capacity in a straightforward way. (3) The volatility of wind speed and solar irradiance are introduced at last to evaluate the anti-interference capability of the proposed hybrid energy storage system.

## 4. Case Study

In this paper, a small community in China with a peak demand of 4.5 MW is analyzed. In this community, a distributed PV generation system, a wind turbine system, and diesel generators are installed. Additionally, this community works on the off-grid operation mode. Moreover, in order to meet the basic requirements of the operational cost of the community, smooth the renewable generation and the loads curves, reduce the carbon emissions, and improve the system security (reduce the LOLP rate), this paper focuses on optimizing the installation capacity of a battery super-capacitor energy storage system.

Figure 3 shows the average yearly load curve of the proposed community on an hour-based time scale.

Figure 4 is the meteorological data of this region, which includes the average yearly wind speed and solar irradiance. It is worth noting that the main body of

Figure 4 (hour-based) shows the variation tendency of wind speed and solar irradiance, and two peripheral diagrams in

Figure 4 (minute-based) are used to illustrate the uncertainty of renewable energy.

According to the LCOE published by State Electricity Regulatory Commission,

C_{W},

C_{PV}, and

C_{d} are assigned the value of 10 US cents/kWh, 14 US cents/kWh, and 6 US cents/kWh in this paper, respectively [

36]. Considering the constraint of space, the installation capacity of the PV and wind turbine systems should be no more than 2 MW and 1 MW, respectively. In addition, in order to reduce the LOLP rate, the

LOLP_{max} is set as 5%. Moreover, in order to extend the battery lifespan, the maximum discharge current coefficient of the battery

β is assigned to 1, the nominal cycle efficiency of the battery system is set as 90% [

27], SDR is set as 0.1%, and the nominal efficiency of the power conversion system is set as 99%. Finally, the energy efficiency of the diesel generators is 40% [

37]. The following results are acquired by implementing MATLAB (R2016b, MathWorks company, Nettie, MA, USA) Simulation.

## 5. Results and Analysis

#### 5.1. Optimization Results of Battery Super-Capacitor Installation Capacity

Figure 5a shows the relationship among the battery installation capacity, the super-capacitor installation capacity, and the average daily generation cost of the distributed power system. In order to clearly reveal the factors that can affect the installation capacity of the hybrid energy storage system,

Figure 5b magnifies the surface of

Figure 5a for further analysis.

As shown in

Figure 5a, with the increase of battery and super-capacitor installation capacity, the more electrical energy can be provided by renewable generators to reduce carbon emissions. However, with the increase of renewable generation, the daily energy cost of the distributed power system will increase correspondingly. This is because the power generated by the renewable system has a higher LCOE compared with the diesel generator. Additionally,

Figure 5a shows that by increasing the hybrid energy installation capacity, the average daily generation cost of the system increases from 5166.1 U.S. dollars to 5864.9 dollars, which is a 13.5% increase.

Figure 5b shows the constraints of the carbon emissions, the average daily generation cost, the renewable energy fluctuation, and the LOLP rate when sizing the battery and super-capacitor capacity.

L_{1} shows that the minimum capacity of the super-capacitor is limited by the fluctuation of renewable energy. To smooth the outputs of renewable generation, the capacity of the super-capacitor should be no less than

L_{1}.

L_{2} mainly reflects that the battery needs to provide enough spinning reserve to reduce the LOLP rate of the system.

L_{3} and

L_{4} reveal that the total capacity of the hybrid energy storage can be tremendously limited by the maximum allowance of the average daily generation cost and the carbon emissions. Due to the aforementioned limitations, the green area in

Figure 5b is the only feasible scope of the hybrid energy storage system capacity. Finally, considering that the installation costs of super-capacitor is far more expensive than that of the battery, it is preferable to choose point P as the best capacity of the hybrid energy storage system.

#### 5.2. System Optimal Operation Strategy of Point P

Table 1 is the optimization results of the battery and super-capacitor installation capacity, the average daily carbon emissions, and the average daily generation cost of the proposed system at point P.

Figure 6 and

Figure 7 show the optimal operation strategy of the distributed power system. More specifically,

Figure 6 illustrates the output curves of all of the energy generators, and

Figure 7 reveals the output of the energy storage system and the equivalent demands of the proposed community after installing the battery.

As shown in

Table 1, given that the terminal voltage of the hybrid energy storage system is 220 V, the optimal capacity of the battery and super-capacitor are 10.92 kAh and 495.87 F, respectively. In this situation, the minimum daily energy cost and the carbon emissions of the proposed community can be successfully limited to under 5800 U.S. dollars and 1.7 ton, respectively. Compared with point Q (shown in

Figure 5b), the average daily generation cost of the system increases by about 10%, but meanwhile, the carbon emissions of the system reduce by 42%.

Figure 6 reveals that with the increase of the battery capacity, the installation capacity of the distributed PV and wind turbine systems increase as well. At point P, the installation capacity of the PV and the wind turbine systems have reached their saturation values, which are 2 MW and 1 MW, respectively. In addition, the installed battery system can cooperate with diesel generators to shave system peak demands and fill system valleys, which can reduce diesel generator installation capacity and make full use of the capacity. Moreover, the installed super-capacitor system has a good ability to suppress the fluctuation of renewable energy generation, and thus effectively reduces the frequency and the amplitude of the renewable energy output fluctuation (as shown by

Z_{1} and

Z_{2} in

Figure 6).

Comparing

Figure 7 with

Figure 3 shows that the peak-valley difference of the network reduces from 3 MW (at point Q) to 2.3 MW (at point P), which is a 23.3% reduction. This proves that system demands can be smoothed by increasing the battery capacity. Meanwhile,

Figure 7 also shows that the off-grid mode and the insufficient capacity of energy generators can lead to system loss-of-load, but the newly designed hybrid energy storage system can control the LOLP rate within 5%, which can meet the requirements of the community.

#### 5.3. The Influence of Renewable Energy Volatility on the Proposed Energy Storage System

In order to demonstrate the influence of renewable energy volatility on the proposed energy storage system, the red and blue solid lines shown in

Figure 8 are used to represent the system average daily generation cost under different renewable energy volatility rates for the best case (i.e., the wind speed and light intensity tend to increase at most of time during the day) and the worst case (i.e., the wind speed and light intensity tend to decrease at most of the time during the day), respectively. Similarly, the red and blue dashed lines are used to represent system LOLP under different renewable energy volatility rates for the best case and the worst case, respectively.

As shown by the red lines, for the best case, with the increase of the renewable generation volatility coefficients, the outputs of the renewable energy and the average daily generation cost will gradually increase as well. However, due to the capability limitation of the renewable generation system, most of the time, the outputs of the renewable generation system can reach saturation value, after the fluctuation rate reaches 30%. Meanwhile, the average daily generation cost is close to saturation, and its growth rate will reduce. In addition, as the renewable generation increases, the system can improve its ability to cope with the system’s peak load, which eventually reduces the system’s LOLP.

Similarly, as shown by the blue lines, for the worst case, with the increase of the renewable generation volatility coefficients, the outputs of renewable energy will reduce, and more electrical power will be provided by diesel generators. Since the LCOE of the diesel generators is much lower than that of the renewable energy generators, the average daily generation cost of the system will reduce significantly. It is worth noting that the average daily generation cost reduces faster after the volatility reaches 40%. This is because when the wind speed and solar irradiance are less than their threshold values, the outputs of renewable energy will reduce to zero immediately, rather than realizing a smaller value. In addition, due to the rapid reduction of renewable generation, the system’s peak demands cannot be supplied by diesel generators, which results in a significant increase of system LOLP.

Therefore, the designed capacity of the hybrid energy storage system can properly cope with climatic change. In other words, if the renewable energy volatility rate can be limited to within 10%, the stability and economy of the distributed network will not be significantly affected. However, when the renewable energy volatility rate increases to more than 20%, the optimal capacity of the energy storage system presented in this paper cannot guarantee the reliability of the off-grid system.

## 6. Conclusions

In order to suppress the fluctuation of the distributed renewable generation system and reduce the influence of its uncertainty on distributed power systems, this paper comprehensively considers system economy, stability, carbon emissions, and renewable energy fluctuation, and then calculates the theoretical feasible installation capacity of the hybrid distributed energy storage system. Meanwhile, based on the genetic algorithm and the manufacturing prices of the super-capacitor and battery, this paper selects the best capacity for the hybrid energy storage system. After that, this paper shows the optimal operation strategy for the distributed generation system, the energy storage system, and the loads under the condition of the theoretical best energy storage capacity. Finally, this paper analyzes the influence of renewable energy volatility (i.e., renewable energy volatility coefficient α) on system economic and stable operation under the proposed hybrid energy storage capacity.

The simulation results show that for a region with a relatively stable climate, with the increase of the hybrid energy storage capacity, the installation capacity of the renewable energy system also increases, which will reduce the carbon emissions and increase the average daily generation cost. However, due to the space limitation of the community, the average daily generation cost tends to be saturated when the installation capacity of the renewable energy is saturated. For the proposed off-grid power system, the average daily generation cost can increase by 13.5% if the installed storage capacity varies from zero to its saturation value. Moreover, compared with not installing an energy storage system, the average daily generation cost can increase by 10% for a properly sized energy storage system. However, after installing an appropriate energy storage system, system carbon emissions reduce by 42%, and the peak valley gap reduces by 23.3%. In addition, the renewable energy fluctuation rate and system loss of load probability are successfully limited in an allowable range. Finally, if the renewable energy volatility rate can be limited to within 10%, the theoretical best energy storage capacity will not be seriously affected. On the contrary, if the renewable energy volatility rate exceeds 20%, the optimal capacity of the energy storage system presented in this paper cannot guarantee the reliability of the off-grid system.