Abstract A high proportion of photovoltaic power generation will have adverse effects on the stability of power system, and energy storage is considered to be one of the effective means to eliminate these effects. This paper analyzes the influence of photovoltaic power generation on the power system from the perspective of power flow, and then analyzes the effect of energy storage on restraining the influence. Firstly, the probability distribution model and energy storage model of components in power system are introduced, and the Latin hypercube sampling method and gram-Schmidt sequence normalization method are introduced. Secondly, a multi-objective optimization model was established, which considered the cost of the energy storage system, the off-limit probability of branch power flow and the network loss of the power grid. The optimal solution of the objective function was obtained by genetic algorithm. Finally, the simulation is carried out in IEEE24 node test system to analyze the influence of different photovoltaic access capacity and access location on the power system and the effect of energy storage on the power system, and the optimal energy storage configuration corresponding to different photovoltaic capacity is obtained.

Key words photovoltaic power generation; Energy storage system; Optimized configuration; Probability power flow; Genetic algorithm (ga)

Photovoltaic power generation has the advantages of green environmental protection and renewable, and is considered to be one of the most potential renewable energy. By 2020, China’s cumulative installed capacity of photovoltaic power generation has reached 253 million kw. The intermittency and uncertainty of large-scale PV power affect the power system, including issues of peak shaving, stability and light discarding, and the grid needs to adopt more flexible measures to cope with these issues. Energy storage is considered to be an effective way to solve these problems. The application of energy storage system brings a new solution for large-scale photovoltaic grid connection.

At present, there are many researches on photovoltaic power generation, energy storage system and probability power flow at home and abroad. A large number of literature studies show that energy storage can improve the utilization rate of photovoltaic and solve the stability of photovoltaic grid connection. In the configuration of energy storage system in new energy power station, attention should be paid not only to the control strategy of optical storage and wind storage, but also to the economy of energy storage system. In addition, for the optimization of multiple energy storage power stations in the power system, it is necessary to study the economic model of the operation of energy storage power stations, the site selection of the starting point and end point of photovoltaic transmission channels and the site selection of energy storage. However, the existing research on optimal configuration of energy storage system does not consider the specific impact on power system, and the research on multi-point system does not involve large-scale optical storage operation characteristics.

With the large-scale development of uncertain new energy power generation such as wind power and photovoltaic, it is necessary to calculate the power flow of the power system in the operation planning of the power system. For example, the literature studies the optimal location and capacity allocation of energy storage in the power system with wind power. In addition, the correlation between multiple new energy sources should also be considered in the calculation of power flow. However, all the above studies are based on deterministic power flow methods, which do not consider the uncertainty of new energy generation. The literature considers the uncertainty of wind power and applies the probabilistic optimal power flow method to optimize the site selection of energy storage system, which improves the operation economy.

At present, different probabilistic power flow algorithms have been proposed by scholars, and data mining methods of nonlinear probabilistic power flow based on Monte Carlo simulation method have been proposed in literatures, but the timeliness of Monte Carlo method is very poor. It is proposed in the literature to use the probabilistic optimal power flow to study the location of energy storage, and 2 m point method is used, but the calculation accuracy of this method is not ideal. The application of Latin hypercube sampling method in power flow calculation is studied in this paper, and the superiority of Latin hypercube sampling method is illustrated by numerical examples.

Based on the above research, this paper uses the probabilistic power flow method to study the optimal allocation of energy storage in the power system with large-scale photovoltaic power generation. Firstly, the probability distribution model and Latin hypercube sampling method of components in power system are introduced. Secondly, a multi-objective optimization model is established considering the energy storage cost, power flow over limit probability and network loss. Finally, the simulation analysis is carried out in IEEE24 node test system.

1. Probabilistic power flow model

1.1 Uncertainty model of components

Photovoltaic, load and generator are all random variables with uncertainty. In the calculation of probabilistic power flow of distribution network, the probabilistic model is explained in the literature. Through the analysis of historical data, the output power of photovoltaic power generation follows BETA distribution. By fitting the probability distribution of load power, it is assumed that load follows normal distribution, and its probability density distribution function is

Picture (1)

Where, Pl is the load power; μ L and σ L are the expectation and variance of load respectively.

The probability model of generator usually adopts two-point distribution, and its probability density distribution function is

(2)

Where, P is the probability of normal operation of generator; PG is the output power of the generator.

When the light is sufficient at noon, the active power of the photovoltaic power station is large, and the power that is difficult to use in time will be stored in the energy storage battery. When the load power is high, the energy storage battery will release the stored energy. The instantaneous energy balance equation of the energy storage system is

When charging

(3)

When the discharge

(4)

The constraint

Pictures,

Pictures,

Picture, picture

Where, St is the energy stored at time T; Pt is the charge and discharge power of energy storage; SL and SG are the energy of charging and discharging respectively. η C and η D are charging and discharging efficiency respectively. Ds is the self-discharge rate of energy storage.

1.2 Latin hypercube sampling method

There are simulation method, approximate method and analytical method which can be used to analyze system power flow under uncertain factors. Monte Carlo simulation is one of the most accurate methods in probabilistic power flow algorithms, but its timeliness is low compared with high precision. In the case of low sampling times, this method usually ignores the tail of the probability distribution curve, but in order to improve the accuracy, it needs to increase the sampling times. Latin hypercube sampling method avoids this problem. It is a hierarchical sampling method, which can ensure that the sampling points reflect the probability distribution effectively and reduce the sampling times effectively.

Figure 1 shows the expectation and variance of Latin hypercube sampling method and Monte Carlo simulation method with sampling times ranging from 10 to 200. The overall trend of results obtained by the two methods is decreasing. However, the expectation and variance obtained by monte Carlo method are very unstable, and the results obtained by multiple simulations are not the same with the same sampling times. The variance of Latin hypercube sampling method decreases steadily with the increase of sampling times, and the relative error decreases to less than 5% when the sampling times are more than 150. It is worth noting that the sampling point of the Latin hypercube sampling method is symmetric about the Y-axis, so its expected error is 0, which is also its advantage.

The picture

FIG. 1 Comparison of different sampling times between MC and LHS

Latin hypercube sampling method is a layered sampling method. By improving the sample generation process of input random variables, the sampling value can effectively reflect the overall distribution of random variables. The sampling process is divided into two steps.

(1) Sampling

Xi (I = 1, 2,… ,m) is m random variables, and the sampling times are N, as shown in FIG. 2. The cumulative probability distribution curve of Xi is divided into N interval with equal spacing and no overlap, the midpoint of each interval is selected as the sampling value of probability Y, and then the sampling value Xi= p-1 (Yi) is calculated by using inverse function, and the calculated Xi is the sampling value of random variable.

The picture

Figure 2 schematic diagram of LHS

(2) Permutations

The sampling values of random variables obtained from (1) are sequentially arranged, so the correlation between m random variables is 1, which cannot be calculated. The gram-Schmidt sequence orthogonalization method can be adopted to reduce the correlation between the sampling values of random variables. Firstly, a matrix of K×M order I=[I1, I2…, IK]T is generated. Elements in each row are randomly arranged from 1 to M, and they represent the position of the sampling value of the original random variable.

Positive iteration

The picture

A reverse iterative

The picture

“Picture” represents assignment, takeout(Ik,Ij) represents calculation of residual value in linear regression Ik=a+bIj, rank(Ik) represents new vector formed by the sequence number of elements in orientation Ik from small to large.

After bidirectional iteration until the RMS value ρ, which represents the correlation, does not decrease, the position matrix of each random variable after permutation is obtained, and then the permutation matrix of random variables with the least correlation can be obtained.

(5)

Where, the picture is correlation coefficient between Ik and Ij, cov is covariance, and VAR is variance.

2. Multi-objective optimization configuration of energy storage system

2.1 Objective function

In order to optimize the power and capacity of the energy storage system, a multi-objective optimization function is established considering the cost of the energy storage system, the power off-limit probability and the network loss. Due to the different dimensions of each indicator, deviation standardization is carried out for each indicator. After deviation standardization, the value range of observed values of various variables will be between (0,1), and the standardized data are pure quantities without units. In the actual situation, there may be differences in the emphasis on each indicator. If each indicator is given a certain weight, different emphases can be analyzed and studied.

(6)

Where, w is the index to be optimized; Wmin and wmax are the minimum and maximum of the original function without standardization.

The objective function is

(7)

In the formula, λ1 ~ λ3 are weight coefficients, Eloss, PE and CESS are standardized branch network loss, branch active power crossing probability and energy storage investment cost respectively.

2.2 Genetic algorithm

Genetic algorithm is a kind of optimization algorithm established by imitating the genetic and evolutionary laws of survival of the fittest and survival of the fittest in nature. It first to coding, initial population each coding on behalf of an individual (a feasible solution of the problem), so each feasible solution is from for genotype phenotype transformation, to undertake choosing according to the laws of nature for each individual, and selected in each generation to the next generation of computing environment to adapt to the strong individual, until the most adaptable to the environment of the individual, After decoding, it is the approximate optimal solution of the problem.

In this paper, the power system including photovoltaic and energy storage is firstly calculated by the probabilistic power flow algorithm, and the obtained data is used as the input variable of the genetic algorithm to solve the problem. The calculation process is shown in Figure 3, which is mainly divided into the following steps:

The picture

FIG. 3 Algorithm flow

(1) Input system, photovoltaic and energy storage data, and perform Latin hypercube sampling and Gram-Schmidt sequence orthogonalization;

(2) Input the sampled data into the power flow calculation model and record the calculation results;

(3) The output results were encoded by chromosome to generate the initial population corresponding to the sampling value;

(4) Calculate the fitness of each individual in the population;

(5) select, cross and mutate to produce a new generation of population;

(6) Judge whether the requirements are met, if not, return step (4); If yes, the optimal solution is output after decoding.

3. Example analysis

The probabilistic power flow method is simulated and analyzed in the IEEE24-node test system shown in FIG. 4, in which the voltage level of 1-10 nodes is 138 kV, and that of 11-24 nodes is 230 kV.

The picture

Figure 4 IEEE24 node test system

3.1 Influence of photovoltaic power station on power system

Photovoltaic power station in power system, the location and capacity of power system will be affect the node voltage and branch power, therefore, before the analysis of the influence of the energy storage system for power grid, this section first analyzes the influence of photovoltaic power station on the system, photovoltaic access the system in this paper, the trend of the limit of the probability, the network loss and so on has carried on the simulation analysis.

As can be seen from FIG. 5(a), after photovoltaic power station is connected, nodes with smaller branch power flow overlimit are as follows: 11, 12, 13, 23, 13 to balance the node node, the node voltage and the phase Angle is given, have the effect of stable power grid power balance, 11, 12 and 23 instead of directly connected, as a result, several nodes connected to the limit the probability of smaller and more power, photovoltaic power station will access the node with balance effect is less on the impact of power system.

The picture

Figure 5. (a) sum of power flow off-limit probability (b) node voltage fluctuation (c) total system network loss of different PV access points

In addition to the exceedance of power flow, this paper also analyzes the influence of photovoltaic on node voltage, as shown in FIG. 5(b). The standard deviations of voltage amplitudes of nodes 1, 3, 8, 13, 14, 15 and 19 are selected for comparison. On the whole, the connection of photovoltaic power stations to the power grid does not have a great influence on the voltage of nodes, but the photovoltaic power stations have a great influence on the voltage of a-Nodes and their nearby nodes. In addition, in the system adopted by the calculation example, through comparison, it is found that photovoltaic power station is more suitable for access to the node types: ① nodes with higher voltage grade, such as 14, 15, 16, etc., the voltage almost does not change; (2) nodes supported by generators or adjusting cameras, such as 1, 2, 7, etc.; (3) in the line resistance is large at the end of the node.

In order to analyze the influence of PV access point on the total network loss of power system, this paper makes a comparison as shown in Figure 5(c). It can be seen that if some nodes with large load power and no power supply are connected to pv power station, the network loss of the system will be reduced. On the contrary, nodes 21, 22 and 23 are the power supply end, which is responsible for centralized power transmission. The photovoltaic power station connected to these nodes will cause large network loss. Therefore, the pv power station access point should be selected at the receiving end of power or the node with large load. This access mode can make the power flow distribution of the system more balanced and reduce the network loss of the system.

Based on the three factors in the analysis of the above results, node 14 is taken as the access point of photovoltaic power station in this paper, and then the influence of the capacity of different photovoltaic power stations on the power system is studied.

Figure 6(a) analyzes the influence of photovoltaic capacity on the system. It can be seen that the standard deviation of the active power of each branch increases with the increase of photovoltaic capacity, and there is a positive linear relationship between the two. Except for several branches shown in the figure, the standard deviations of other branches are all less than 5 and show a linear relationship, which are ignored for the convenience of drawing. It can be seen that photovoltaic grid connection has a great influence on the power of directly connected with photovoltaic access point or adjacent branches. Because of limited power transmission line transmission, the transmission lines of quantities of construction and investment is huge, so installing a photovoltaic power station, should consider the limitation of transportation capacity, choose the smallest influence on line access to the best location, in addition, selecting the best capacity of photovoltaic power station will play an important part to reduce this effect.

The picture

Figure 6. (a) Branch active power standard deviation (b) branch power flow out-of-limit probability (c) total system network loss under different photovoltaic capacities

FIG. 6(b) compares the probability of active power exceeding the limit of each branch under different pv power station capacities. Except for the branches shown in the figure, the other branches did not exceed the limit or the probability was very small. Compared with FIG. 6(a), it can be seen that the probability of off-limit and standard deviation are not necessarily related. The active power of a line with large standard deviation fluctuation does not necessarily off-limit, and the reason is related to the transmission direction of photovoltaic output power. If it is in the same direction as the original branch power flow, small photovoltaic power may also cause off-limit. When the pv power is very large, the power flow may not exceed the limit.

In FIG. 6(c), the total network loss of the system increases with the increase of photovoltaic capacity, but this effect is not obvious. When the photovoltaic capacity increases by 60 MW, the total network loss only increases by 0.5%, i.e. 0.75 MW. Therefore, when installing pv power stations, network loss should be taken as a secondary factor, and factors that have a greater impact on the stable operation of the system should be considered first, such as transmission line power fluctuation and out-of-limit probability.

3.2 Impact of energy storage access on the system

Section 3.1 The access position and capacity of photovoltaic power station depend on the power system