**1. Introduction**

In recent years, with global carbon dioxide emissions hitting record highs, China has proposed a "two-carbon" target to tackle environmental problems. Promoting the development of new energy and the transformation of energy structures has become an important part of global development. Due to abundant reserves and easy access, solar energy has been developing rapidly in recent years, and its proportion in the power grid has been increasing year by year [1]. While improving energy utilization, this has brought a lot of trouble to the power distribution network. With the continuous increase in the penetration rate of photovoltaics integrated into the power distribution network, problems such as voltage collapse may occur, which has a serious impact on the safe and stable operation of the system [2].

Studies have shown that a large number of photovoltaics connected to the distribution network will also increase the number of system equipment, which will bring a burden to the system and easily generate harmonic interference. In addition, the retrograde power generated by the grid connection is prone to exceed the limit of the system node voltage, which not only reduces the power quality but also deteriorates the user experience. When high-penetration photovoltaics are connected to the grid, the uncertainty of output cannot be matched with the load of the distribution network in real-time, which will affect the power balance of the system. When the photovoltaic output fluctuates greatly due to the change in environment and climate, the stability of the system will be affected [3]. In addition, the high-penetration photovoltaic grid connection requires a large number of

**Citation:** Zhang, J.; Zhu, L.; Zhao, S.; Yan, J.; Lv, L. Optimal Configuration of Energy Storage Systems in High PV Penetrating Distribution Network. *Energies* **2023**, *16*, 2168. https:// doi.org/10.3390/en16052168

Academic Editors: Luis Hernández-Callejo, Jesús Armando Aguilar Jiménez and Carlos Meza Benavides

Received: 31 January 2023 Revised: 16 February 2023 Accepted: 20 February 2023 Published: 23 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

power electronic equipment to join the distribution network, which leads to the existence of harmonics and affects the power quality [4], and the dispatching flexibility of the distribution network is greatly reduced, which makes it more difficult for the power system to develop a power generation plan. If such problems cannot be properly solved, it will not only seriously threaten the safe and stable operation of the system but also cause a waste of energy and limit the future development of photovoltaic power generation [5].

The authors in [6–8] analyze the influence of photovoltaic systems from the aspects of voltage fluctuation, voltage amplitude, and frequency. From the perspective of stability, Rasoul proposed a new framework to analyze the influence of different photovoltaic permeability on voltage stability [9]. During the study, Zetty found that in a high permeability renewable energy distribution network, load fluctuation is the main factor leading to the voltage fluctuation of the system, and the realization of various fluctuations in the high-light voltage permeability distribution network is important content to achieve the increase of photovoltaic permeability in the distribution network [10]. The introduction of energy storage devices improves the power quality while improving the photovoltaic stable output [11–13]. Through reasonable regulation and control of a BESS, the absorption of new energy on the power generation side can be completed, the permeability of distributed power supply on the transmission side and distribution side can be improved, and the safe, stable, and economic operation of the system can be ensured [14,15]. The authors in [16–18] studied the working principle and characteristic analysis of different types of energy storage devices and different types of BESSs and discussed the practicability of combining BESS energy storage and generation measurement. From the perspective of photovoltaic and load output prediction, Rahman and Zhao verified the feasibility of combining energy storage optimization configuration with the prediction by comparing scenarios with or without prediction [19,20]. In order to meet the photovoltaic energy storage demand in the distribution network, Wang's multiple operation scenarios of energy storage were divided into grid scenarios to obtain the demand relationship of energy storage capacity under different operating conditions and to complete the calculation of energy storage capacity [21].

Access to energy storage equipment requires considerable capital investment in actual project construction and operation and maintenance. Therefore, the demand response for energy storage capacity is important content in optimizing energy storage configuration. In [22], Balouch proposed an optimization goal of matching demand and supply. Based on the analysis of line planning, low-cost scheduling, and demand response, the energy utilization efficiency and comprehensive operating cost of a smart grid were optimized. The authors in [23,24] introduced the improved optimization algorithm to improve the optimization ability so as to determine the optimal scheme of energy storage optimization configuration and realize a higher degree of response between demand and supply by analyzing various indicators of access to the power grid. In [23], Balouch optimized a response scheduling scheme by introducing the GWCSO algorithm. Higher robustness and computational efficiency of the algorithm make the optimization results more advantageous in power cost and peaking ratio. In [24], Mostafa improves the PSO algorithm, improves the accuracy and effectiveness of the algorithm, and optimizes the location and capacity allocation of energy storage in distributed networks. While the optimization objects are complex and diverse when connecting to the power system, the choice and update of the Pareto optimal solution will determine the quality of the final optimization result [25].

In the existing studies, it seems obvious for everyone to apply energy storage in highpermeability photovoltaic distribution networks [26–32]. In the case of low photovoltaic permeability, access to energy storage can indeed improve photovoltaic output and power quality. However, few researchers have analyzed whether energy storage can still meet expectations in the scenario of high photovoltaic permeability, and how to rationally allocate energy storage in a distribution network with high photovoltaic permeability. In this paper, the application of energy storage in a high permeability photovoltaic scenario is analyzed, and the energy storage in a high-light volt distribution network is configured by

establishing a two-layer planning model of the distribution network. The optimal size of energy storage was configured considering the fluctuation of power grid voltage and load, economic benefits and energy storage benefits, and the working condition of energy storage in the scenario of high-light voltage permeability, and the improvement of benefits in all aspects of the distribution network were studied. Finally, the feasibility of the proposed method was verified in the IEEE-33 node system.

The main contributions of this study are summarized below:


The rest of this paper is organized as follows: The treatment method for the PV uncertainty and the selection of the PV working curve is introduced in Section 2. In Sections 3 and 4, the bi-level decision-making programming model is constructed and solved to realize the addressing and capacity selection of the energy storage device. At the same time, in the fourth section, the specific content of particle swarm optimization is described. In Section 5, four scenarios are constructed to discuss the benefits generated by energy storage configuration and optimization benefits brought by algorithm improvement. Finally, in Section 6, we summarize the content of the thesis.

#### **2. Analysis of Photovoltaic Output Characteristic**

Due to the great influence of light and the environment, photovoltaic power generation is full of uncertainties. For further analysis, we collected the annual daily output data of photovoltaic power stations (annual output of an operational photovoltaic power station in Henan Province from June 2019 to July 2020), as shown in Figure 1. When considering energy storage benefits, excessive uncertainty in output will lead to uncertainty in energy storage benefits. In order to avoid this influence, this paper will process various output curves by clustering the division method, summarizing the photovoltaic output with high uncertainty into six typical output scenarios and analyzing them, and transforming the uncertainty into a deterministic analysis.

#### *2.1. K-Means Cluster Analysis Method*

The K-means clustering method is a classical clustering analysis method based on the iterative method which has the advantages of high efficiency and convenience in processing large-scale uncertain data [33]. Through the K-means clustering method, a large number of output data can be refined and extracted, and fewer typical output scenarios can be obtained that can represent the output of photovoltaic power stations.

The K-means algorithm sets an initial cluster center in all scenes and iterates clustering for a large number of scenes based on the optimal distance. The iteration is not finished until the clustering presents a steady-state equilibrium. The iteration results are shown in Figure 2. After the whole process is complete, the center of each cluster scene is set as the partition scene, and the probability of each cluster scene is set as the required partition probability *Pr*(*s*).

**Figure 1.** Annual daily output curve of photovoltaic power plants.

**Figure 2.** K-means clustering method results.

Set the number of initial scenarios *ξs*(*s* = 1, 2 . . . *N*) to *Ns*. The number of target scenarios is *Ms*, and the entire calculation procedure is as follows:


$$\text{calculated:} \begin{cases} DT\_{s,s'} = DT \left( \mathfrak{f}\_{\mathfrak{s}}^{\text{Centre}}, \mathfrak{f}\_{\mathfrak{s}}^{\text{Member}} \right) = ||\mathfrak{f}\_{\mathfrak{s}}^{\text{Centre}} - \mathfrak{f}\_{\mathfrak{s}}^{\text{Member}}||\_2\\ s = 1, 2 \dots M\_{\mathfrak{s}}, \mathfrak{s}' = 1, 2 \dots N\_{\mathfrak{s}} - M\_{\mathfrak{s}} \end{cases}$$


the clustering center of the next iteration. This is used to calculate the next iteration cluster center set.

<sup>5</sup> At this point, stable cluster centers and clustering results can be obtained by repeating steps <sup>2</sup> –<sup>4</sup> . The probability number of each type of scenario is the probability number of a single scenario in that type of scenario.

The process of the clustering algorithm to reduce the scene is shown in Figure 3.

**Figure 3.** Cluster reduction flowchart.

*2.2. Selection of Typical Output Scenarios*

After data processing and division by the K-means clustering method, six output scenarios as shown in Figure 4 can be obtained. The occurrence probability and the number of curves of each output scenario are shown in Table 1.

**Table 1.** Typical scenario probability.


**Figure 4.** Clustering of typical scenarios.

As can be seen from Figure 4 and Table 1, the photovoltaic output power in Scenario 1 is low, while the output in Scenario 2 has great fluctuation and uncertainty. The intermediate level of output in Scenarios 3 and 4 cannot represent photovoltaic output, and Scenarios 5 and 6 have a high probability and good output curve. In contrast, Scenario 5 with the maximum annual output is selected as the typical photovoltaic output curve, which can better reflect the output characteristics of photovoltaic power generation. In order to facilitate the analysis of the combined effect of photovoltaic and energy storage under different permeability, in this paper, we will only select Scenario 5, which is the most representative and has the highest probability of occurrence at the same time, as the analysis object to study the influence of energy storage access to the power grid during daily operation on voltage fluctuation, operation cost, and other benefits of the distribution network.

#### **3. BESS Bi-Level Decision-Making Model Configuration**

Due to the mutual influence between the optimal configuration of the energy storage system and the stable operation of the distribution network, this will bring difficulties to the dispatching of the energy storage devices and will cause the operation stability of the distribution network to decline. Therefore, it is necessary to consider a reasonable location and capacity while taking into account the operation economy of the distribution network. The bi-level decision-making model relies on its own two-level hierarchical structure to optimize the system objectives hierarchically. The upper and lower levels influence each other and seek the overall optimal solution according to the independent objective function and the corresponding constraints [34,35].

#### *3.1. Upper-Level Model Objective Function*

In the upper-level optimization, energy storage configuration location, rated power, and installed capacity are considered to reduce the total cost of the energy storage system and distribution network investment and maintenance. The installation location and capacity of the BESS are optimized. After the optimal configuration of energy storage is obtained, the information is transmitted to the lower level to adjust the charge and discharge power of energy storage.

$$\begin{cases} F\_{\text{min}} = f\_{\text{sto}} + f\_{\text{ope}} \\ \quad \text{s.t.} \mathcal{g}(X) \le 0 \end{cases} \tag{1}$$

where *Fmin* is the minimum daily total cost after the energy storage is connected; *fope* is the total cost of distribution network operation investment. *fsto* is the input costs for energy storage construction. *X* = [*x*1, *x*2, *x*3], and *x*1, *x*2, *x*3, respectively, represent the BESS input node, power, and capacity.

#### *3.2. Lower Objective Function*

In the lower-level optimization, due to the influence of the energy storage installation location and capacity selection on the energy storage life, the lower-level decision-making model fully considers the change of the energy storage charging and discharging power to realize the economical operation mode of the distribution network and achieve the smallest fluctuation range of node voltage and load. The lower optimization objective function is as follows:

$$\begin{cases} \min \left( f\_{\text{opt}}, f\_{2\text{-}} f\_3 \right) \\ \text{s.t.} h(y) \le 0 \end{cases} \tag{2}$$

where *f*<sup>2</sup> is the amplitude of the voltage fluctuation of the distribution network node caused by the access to energy storage, *f*<sup>3</sup> is the amplitude of the load fluctuation of the distribution network, and *y* = [*y*1, *y*1, *y*<sup>2</sup> ... *y*24] is the average hourly charging and discharging power of the energy storage system throughout the day.

(1) The voltage fluctuation of distribution network nodes caused by energy storage access can be expressed as:

$$\min f\_2 = \sum\_{t=1}^{24} \sum\_{k=1}^{N} \left[ \frac{\mu\_k(t) - \mu\_{kn}}{\Delta \mu\_{k\text{max}}} \right]^2 \tag{3}$$

where *N* indicates the number of system nodes, and *uk*(*t*) indicates the voltage value of node *k* at time *t*.

(2) The load fluctuation of the distribution network caused by access to energy storage can be expressed as:

$$\min f\_3 = \frac{1}{T} \sum\_{t=1}^{T} \left[ P\_{load}'(t) - P\_{\text{ave}}' \right]^2 \tag{4}$$

where *P ave* represents the average load in a period of time when energy storage is connected.


$$1 \le \varkappa\_1 \le N\_{\max} \tag{5}$$

where *x*<sup>1</sup> are nodes invested in energy storage, and *Nmax* is the maximum number of nodes expressed as energy storage input.

(2) The constraints of power rating and capacity energy storage devices can be expressed as

$$\begin{cases} P\_{\text{ess}}^{\text{min}} \le P\_{\text{essn}} \le P\_{\text{ess}}^{\text{max}}\\ E\_{\text{ess}}^{\text{min}} \le E\_{\text{essn}} \le E\_{\text{ess}}^{\text{max}} \end{cases} \tag{6}$$

where *Pmax ess* and *Pmin ess* is the maximum and minimum value of the rated output of the energy storage, and *Emax ess* and *Emin ess* are the maximum and minimum values of the energy storage input capacity.

(3) Power balance constraints

$$P\_{\rm grid} + P\_{\rm gv} = P\_{\rm load} + P\_{\rm loss} + P\_{\rm css} \tag{7}$$

where *Pgrid* is the power value received by the grid, *Pgv* is the PV output power, *Pload* is the output power, *Ploss* is the network loss, and *Pess* is the BESS input power.

(5) BESS charge and discharge power constraints

$$\begin{cases} \ 0 \le P\_{\text{ess}}^{\text{cha}}(t) \le P\_{\text{essn}}\\ -P\_{\text{essn}} \le P\_{\text{ess}}^{\text{cha}}(t) \le 0 \end{cases} \tag{8}$$

(6) Voltage constraints in distribution network nodes

$$u\_k^{\min} \le u\_k(t) \le u\_k^{\max} \tag{9}$$

where *umin <sup>k</sup>* and *<sup>u</sup>max <sup>k</sup>* are the minimum and maximum voltages of node *k* at time *t*. Energy storage system *SOC* constraints

$$\text{SOC}(t) = \frac{E(t)}{E\_{\text{sn}}} = \text{SOC}\_0 + \frac{\sum\_{k=1}^{t} \left\{ d\_1(t) P\_{\text{crs}}^{\text{cla}}(t) n\_c \right\} \Delta t + \sum\_{k=1}^{t} \left\{ d\_2(t) P\_{\text{crs}}^{\text{cla}}(t) / n\_d \right\} \Delta t}{E\_{\text{sn}}} \tag{10}$$

where *SOC*<sup>0</sup> is the initial state of the energy storage system, including power and capacity. *Essn* is the rated capacity of the energy storage battery.


$$P'\_{\rm ess} = \begin{cases} P\_{\rm esc}(t) \, \text{SOC}\_{\rm min} \le \text{SOC}(t) \le \text{SOC}\_{\rm max} \\ 0 \, \text{otherwise} \end{cases} \tag{11}$$

where *P ess*(*t*) is the energy storage charge and discharge power value that has been processed at time *t*. In this way, the infeasible solution is transformed into an effective feasible solution, and the charging and discharging power that is not within the SOC range of the energy storage is changed to 0.

<sup>2</sup> Using the penalty function method to deal with the constraints that are not within the valid range:

$$F(\mathbf{x}, M) = f(\mathbf{x}) + M \sum\_{i=1}^{r} \max(g\_i(\mathbf{x}), 0) - M \sum\_{i=1}^{s} \min(h\_i(\mathbf{x}), 0) + M \sum\_{i=1}^{t} |k\_i(\mathbf{x})| \tag{12}$$

where *M* is the penalty coefficient. *gi*(*x*) indicates the negative inequality constraint. *hi*(*x*) indicates the positive inequality constraints. *ki*(*x*) indicates the equality constraint at zero. *r*,*s*, *t* are the number of constraints.

#### **4. Solution of Model**

For the bi-level programming model, this paper selects the genetic algorithm (GA) for the optimization of the upper layer and improved multi-objective particle swarm optimization (IMOPSO) for the optimization of the lower level. The calculation process is as follows:


the best scheme is selected and fed back to the upper layer to solve the fitness of the upper layer target.


The calculation process is shown in Figure 5. In the following sections, we will give a specific description of the improvement content of the multi-objective particle swarm optimization.

**Figure 5.** Calculation process.
