CN112467746B - Power distribution network optimization method considering out-of-limit risk - Google Patents

Abstract

The present disclosure belongs to the technical field of distribution network optimization operation, and discloses a distribution network optimization method considering the over-limit risk, comprising the following steps: establishing an independent standard normal distribution variable ξ and a node voltage over-limit under the distribution network network The mapping relationship between risks; the probability density function of the node voltage over-limit risk is expressed as a Hermite chaotic polynomial with ξ as the independent variable; the sampling point is selected, according to the model of the sampling point, based on the voltage value of the sampling point, using the voltage safety risk, Obtain the undetermined coefficient of the Hermite chaotic polynomial, and obtain the probability distribution of the output response; use the probability distribution of the output response to establish a risk perception system; use the active power and reactive power of the flexible converter station, distributed photovoltaic reactive power and static reactive power compensation The controller is the control object, and based on the risk perception system, the risk of the voltage exceeding the limit of the distribution network is minimized; it can effectively avoid the voltage exceeding the limit.

Description

A distribution network optimization method considering the risk of transgression

technical field

The invention relates to a distribution network optimization method considering the risk of overrunning, and belongs to the technical field of distribution network optimization operation.

Background technique

The optimal operation of the distribution network refers to the coordinated control and active management of the distribution network, distributed power, reactive power compensation equipment, and flexible loads. For the optimal operation of the distribution network, at present, the optimization goals are mainly based on economy and safety, and based on the deterministic operation information of the distribution network, the intelligent algorithm or the traditional optimization algorithm is used to solve the problem, so as to reduce network loss, reduce voltage deviation, Reduce the three-phase unbalance and reduce the cost of electricity and other effects.

DC power sources such as distributed photovoltaics and energy storage systems must be integrated into the AC distribution network through AC-DC inverters. The operating loss of the inverter directly increases the overall loss of the AC distribution network system. Due to the existence of this shortcoming, power loss A DC distribution network with low power consumption, high power quality, and flexible control methods is proposed. However, the AC distribution network will still be the main form of the distribution network due to its own unique advantages, and the DC distribution network can be connected to the AC distribution network as a supplement, and the AC-DC hybrid distribution network will definitely become a new development trend .

At present, distributed photovoltaic is the main representative form of distributed power in AC and DC distribution networks. In the face of a large number of blowout, small and medium-capacity, decentralized distributed photovoltaic access, the control and operation of the distribution network is faced with various more complex voltages. Safety issues, but the current optimal operation scheme generally only considers rigid constraints such as voltage not exceeding the limit, and does not fully consider the risk of voltage exceeding the limit caused by short-term uncertainties of distributed photovoltaics and loads.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a distribution network optimization method that considers the risk of exceeding the limit. The problem to be solved is to establish a risk awareness system for voltage exceeding Limit the risk, and effectively reduce the risk of voltage over-limit through optimized operation to ensure the voltage safety of the distribution network.

The AC/DC distribution network operation optimization method proposed by the present invention mainly includes the following steps:

(1) Determine the optimal scheduling control object:

The system topology of AC and DC distribution network generally mainly includes three parts: AC distribution network, DC distribution network and flexible converter station. The flexible converter station is usually a voltage source converter (VSC).

The controllable units in the AC and DC distribution network are divided into two types: continuous control type and discrete control type. The continuous control type generally includes energy storage system (ESS), photovoltaic (PV), static var compensator (SVC) and VSC. The control type generally includes a capacitor bank (CB) and an on-load tap changer transformer tap changer (OLTC).

Among them, VSC is used as the energy conversion interface between the AC distribution network and the DC distribution network, and can simultaneously control two state quantities in variables such as active power, reactive power, AC voltage, and DC voltage. According to the different control states, it can be classified into V _dc -Q control, V _dc -V _ac control, PQ control and V _ac -P etc. For the AC-DC hybrid distribution network shown in Figure 1, the VSC generally adopts the master-slave control mode, that is, the master station adopts the V _dc -Q control mode to control the port voltage of the DC distribution network, and the slave station adopts the PQ control mode, which can actively Control its transmission active power and output reactive power. In the master-slave control mode, by controlling the slave station to transmit active power, output reactive power and master station output reactive power, on the one hand, it can change the line flow of the AC and DC distribution network, and on the other hand, it can perform reactive power on the AC distribution network. Power compensation, thereby realizing voltage regulation and loss reduction.

(2) Establish a voltage risk perception system:

Uncertain analysis methods for power systems mainly include simulation methods represented by the Monte Carlo method and analytical methods represented by the point estimation method. Low, the point estimation method has fast calculation speed but the calculation accuracy is difficult to guarantee, and the above two methods need to use various series to obtain the probability density function of random variables. The stochastic response surface method is a method that does not depend on series, and can take into account the calculation efficiency, calculation accuracy and randomness analysis method. Therefore, the present invention chooses the stochastic response surface method for voltage risk perception.

The basic idea of stochastic response surface is to use Hermite chaotic polynomials to fit the functional relationship between input variables and output responses, where both input variables and output responses are random variables.

The stochastic response surface mainly includes three steps: 1) Input standardization, the input random variable is represented by a set of standard random variable functional relationships; 2) Output standardization, the Hermite chaotic polynomial form of the output response to be obtained is determined; 3) Model calculation, Select the appropriate sampling point, carry out the model calculation of the sample point, solve the undetermined coefficient of the Hermite chaotic polynomial through the input and output of the sampling point, obtain the probability distribution of the output response, and use the probability distribution of the output response to establish a risk perception system.

For the distribution network, for the AC-DC power flow model G, the probability density function of the node voltage out-of-limit risk R(V) and the random variable X=[x ₁ ,x ₂ ,…, x _n ] ^T mapping relationship can be expressed as

R(V)＝G(X)＝G(x ₁ ,x ₂ ,…,x _n )

First, standardize the active output X of photovoltaics and loads, usually choose independent standard normal distribution variables as standard random variables, and establish the mapping relationship between X and standard random variables:

X＝F ^-1 [Φ(ξ)]

In the formula: ξ=[ξ ₁ ,ξ ₂ ,...,ξ _n ] ^T is an n-dimensional independent standard normal distribution variable; F ^-1 is the inverse function of the cumulative distribution function of X; Φ is the accumulation of standard random variables Distribution function.

Secondly, the mapping relationship between the independent standard normal distribution variable ξ and the node voltage cross-limit risk R(V) can be established;

The probability density function of node voltage over-limit risk R(V) is expressed as a Hermite chaotic polynomial with ξ as an independent variable. The higher the order m of the Hermite polynomial is, the higher the precision of the chaotic polynomial is, but at the same time the number N of undetermined coefficients is also larger. When m ≥ 3, the impact of increasing the order m on improving the accuracy is not obvious. Generally, the second-order or third-order Hermite chaotic polynomials are used, and the present invention adopts the second-order chaotic polynomials:

In the formula: a ₀ , a ₁ ,… are undetermined coefficients of the polynomial, which are constant items.

Then, select the appropriate sampling points, carry out the model calculation of each sample, and determine the undetermined coefficients of the chaotic polynomial;

其根分别为

0,

The sampling selection principle of the random response surface method is: to determine the undetermined coefficients of the chaotic polynomial with the highest order of m order, and to select the root of the Hermite polynomial of order 0 and m+1 as the sampling point, that is, each standard random variable ξ _i of each sample point The sampled values of all take the roots of Hermite polynomials of order 0 or m+1. For the 2nd-order chaotic polynomial, the one-dimensional 3rd-order Hermite polynomial equation is

its roots are

0,

The number N of undetermined coefficients of the chaotic polynomial is:

In the formula: n is the number of input variables, so N sampling points need to be selected.

When selecting sampling points, if the coefficient matrix row vectors of the linear equation system composed of sampling points are linearly independent, that is, the rank of the coefficient matrix is equal to the number of rows of the coefficient matrix, the coefficient matrix is a full-rank matrix, and the value of the determinant of the coefficient matrix is constant is not equal to zero, the established linear algebraic equations have a unique solution, and the accuracy of solving the equations will be significantly improved. Therefore, the probability collocation method based on the principle of linear independence can be used to remove the collocation points that are linearly related, to ensure that the coefficient matrix of the linear equation system is reversible, that is, to achieve full rank, and to ensure that the row vectors of the coefficient matrix of the system of equations are linearly independent.

Finally, select N sampling points (ξ _1,1 ,...,ξ _n,1 ), (ξ _1,2 ,...ξ _n,2 )...(ξ _1,N ...ξ _n,N ), to each sampling point The output response R=[R(V ₁ ),…,R(V _N )] ^T , with the undetermined coefficient A=[a ₀ ,a ₁ ,…,a _ij ] ^T as the unknown quantity, establish a linear equation system HA= R, where H is the coefficient matrix of the equation system, the specific form is:

The undetermined coefficient A is obtained by solving the linear equation system, and f[R(V)] is further obtained by the Hermite chaotic polynomial.

For the load, due to the small area of the same distribution network supply area, the electricity consumption habit has correlation, the load active power obeys the normal distribution on the ultra-short time scale, the mean is the load prediction value, and the standard deviation is a certain percentage of the mean. For photovoltaics, due to the strong correlation of light intensity in the same distribution network supply area, there is also a correlation between photovoltaic active output, but there is no correlation between load and photovoltaic. The probability density of photovoltaic active power output obeys the Beta distribution on an ultra-short time scale, and the probability density function of the Beta distribution can be expressed as:

In the formula: α and β are the shape parameters of the Beta distribution, Γ represents the Gamma function, P is the photovoltaic active output, and P _max is the maximum value of the photovoltaic active output.

The random response surface can be directly applied to the case where the input variables have no correlation, but for the input variables with correlation, it needs to be standardized by Nataf transformation.

Let the correlation coefficient matrix C _X of n photovoltaic units and load active output X be expressed as:

In the formula: ρ is the correlation coefficient between random variables.

Introducing a standard normal distribution vector Y=[y ₁ ,y ₂ ,…,y _n ] ^T , each random variable in Y has correlation, and its correlation coefficient matrix C _Y can be expressed as:

According to the principle of equal probability, the relationship between x _i and y _i can be expressed as:

Φ _Y (y _i )＝F(x _i )

In the formula: Φ _Y is the cumulative distribution function of the standard normal distribution variable.

For the correlation coefficient between loads subject to normal distribution, ρ=ρ';

For the photovoltaic inter-correlation coefficients that do not obey the normal distribution, the relationship between ρ and ρ′ is as follows:

和

分别表示随机变量x_i和x_j的均值，

和

表示随机变量x_i和x_j的标准差。In the formula:

and

represent the mean values of random variables x _i and x _j respectively,

and

Indicates the standard deviation of the random variables x _i and x _j .

According to the Gauss-Hermite double integral theory, the relationship between ρ and ρ' can also be expressed by the following formula:

In the formula: g is Gauss point, ω is a constant coefficient.

In the case of Beta distribution, the relationship between ρ _ij and ρ _i ′ _j cannot be expressed by direct explicit expressions, and ρ _i ′ _j can be obtained by using the dichotomy method.

On the basis of known C _X , the correlation coefficient between photovoltaics in C _Y is solved, and the conversion of the non-independent Beta distribution vector to the non-independent standard normal distribution vector is completed. Next, a further transformation to an independent standard normal distribution vector needs to be done.

Carry out Cholesky factorization of C _Y to get C _Y =BB ^T , where B is a lower triangular matrix, then

ξ=B ^-1 Y

So far, the input variable standardization of photovoltaic and load active output has been completed. When sampling in the random response surface, the sample value of each distributed photovoltaic active output can be determined according to the value of the ξ sampling point.

Therefore, the flow chart of the random response surface method based on Nataf transformation to perceive the risk of voltage violation is shown in Figure 1.

(3) Determine the objective function and constraints of optimization operation

The optimal operation takes the active power and reactive power of the flexible converter station, distributed photovoltaic reactive power and static var compensator as the control object, and based on the calculation results of voltage risk perception technology, the goal is to minimize the risk of voltage over-limit in the distribution network. The objective function is:

In the formula: r represents the node of the distribution network, V _r,up and V _r,down are the maximum and minimum voltages of the rth node, respectively, and f is the probability density function.

When the distribution network is running, there is a situation that the voltage is about to exceed the limit, that is, when the voltage is close to the safe operation boundary but has not reached the boundary threshold, there is the possibility of the voltage exceeding the limit, and there is a risk of the voltage exceeding the limit. The present invention sets the upper and lower thresholds of the voltage safe operation boundary as 0.95p.u. and 1.05p.u. When the voltage exceeds 1.04p.u. or is lower than 0.96p.u., there is a risk of voltage exceeding the limit, and when the voltage is between 0.96p.u. and 1.04p.u., there is no voltage exceeding the limit risk.

For the fixed value of the node voltage, as the voltage value approaches the boundary threshold of normal operation, the smaller the voltage is, the easier the voltage will exceed the limit, and the greater the risk of exceeding the limit. Referring to the utility function of the risk utility theory, the voltage risk R(V ) as a utility, and the voltage deviation W is compared to the income, then R(V) can use the following quadratic function to evaluate the system voltage over-limit risk:

R(W)＝q _i W ² +W

In the formula: V is the per unit value of the node voltage amplitude, and q _i is the function parameter.

The operational constraints for the optimization run are as follows:

Constraints on the expected value of distributed photovoltaic operation:

Distributed photovoltaics have the ability to adjust active and reactive power, but this invention considers not reducing the active output of distributed photovoltaics to ensure the complete consumption of new energy, and only uses its reactive power adjustment ability. The reactive power adjustment constraints are as follows:

和

分别为t时刻第i个分布式光伏输出的有功功率和无功功率；

为光伏最小功率因数。In the formula: Ω ^PV represents the distributed photovoltaic collection;

and

are the active power and reactive power of the i-th distributed photovoltaic output at time t, respectively;

is the minimum photovoltaic power factor.

Static var compensator operating expectations constraints:

和

分别为第i个静止无功补偿器无功补偿最大最小值，

为第i个静止无功补偿器在t时刻无功补偿功率。In the formula: Ω ^SVC represents the set of static var compensators;

and

are the maximum and minimum reactive power compensation values of the i-th static var compensator, respectively,

The reactive compensation power for the ith static var compensator at time t.

Operating expectation constraints of flexible converter station:

和

分别为t时刻第i个柔性换流站的有功功率和无功功率，

为柔性换流站的最大容量，

和

分别为第i个柔性换流站的有功功率和无功功率的最小以及最大功率。In the formula: Ω ^VSC represents the set of static var compensators;

and

are the active power and reactive power of the ith flexible converter station at time t, respectively,

is the maximum capacity of the flexible converter station,

and

are the minimum and maximum power of the active power and reactive power of the i-th flexible converter station, respectively.

System security operation expectations constraints:

V _i,min ≤V _i,t ≤V _i,max ,i∈Ω ^DN

In the formula: Ω ^DN represents the node set of distribution network; V _i,max and V _i,min are the allowable maximum and minimum values of the i-th node voltage, and V _i,t is the voltage amplitude of the i-th node at time t. S _i,max is the maximum transmission capacity of the line, P _i,t and Q _i,t are the active power and reactive power transmitted by the i-th line.

In addition, in order to ensure the normal operation of the distribution network, the power flow balance constraints of the distribution network are also considered. The specific situation is described in detail in the optimization operation solution model below.

(4) Establish a solution model for the optimal operation plan

The AC and DC power flow model is the distribution network power flow balance constraint. The distflow power flow model of the AC distribution network is as follows:

和

表示t时刻节点e注入有功无功功率；U_i,t和U_j,t分别表示t时刻节点i和节点j电压幅值的平方。In the formula: the subscript e indicates the node; the subscript i and j respectively indicate the starting node and the ending node of the branch; k(e,:) indicates the branch k with node e as the head end; k(:,e) indicates the Node e is the branch k at the end; P _k,t and Q _k,t represent the active and reactive power at the head end of line k at time t; I _k,t represents the square of the current amplitude of line k at time t;

and

Indicates the active and reactive power injected into node e at time t; U _i,t and U _j,t represent the square of the voltage amplitudes of node i and node j at time t, respectively.

The distflow power flow model of the DC distribution network is as follows:

The power flow equivalent circuit model of the flexible converter station is shown in Fig. 2, which is composed of equivalent impedance and ideal converter. In the figure, P _AC,t and Q _AC,t are the active power and reactive power of the AC line at time t, respectively; P _c,t and Q _c,t are the active power and reactive power of the AC side of the ideal converter at time t, respectively; P _DC,t is the active power of the DC line at time t; R _c and X _c are the equivalent circuit resistance and impedance of VSC; U _AC,t is the AC voltage measurement at time t; U _DC,t is the DC side voltage at time t; U _{c , t} is the AC fundamental phase voltage of the converter at time t.

The power flow model of the flexible converter station is as follows:

P _AC,t -I _c,t R _c ＝P _DC,t

Q _AC,t -I _c,t X _c ＝-Q _c,t

The voltage constraints on both sides of the ideal converter in the flexible converter station are:

In the formula: μ is the DC voltage utilization rate, and M is the modulation degree.

There is a quadratic equality constraint in the AC-DC power flow model, which is subjected to second-order cone relaxation and used as the power flow balance constraint of the distribution network.

The objective function of the optimal operation plan is an integral nonlinear function, and its physical meaning is the expected value of the probability density function of the voltage safety risk R(V). For the probability density function expressed by the Hermite chaotic polynomial, the expected value of the function is a ₀ , F ₂ can also be represented by the following formula:

At the same time, parameters q ₁ and q ₂ can be set reasonably to eliminate the primary term of V, so that the node voltage appears only as a square term in the solution model. Through the above processing, it can be guaranteed that the optimal operation plan is a convex optimization problem, and the operation plan can be solved by using the second-order cone-relaxed Distflow model.

In the AC/DC power flow Distflow model, referring to the idea of alternating iteration method to calculate the power flow, the AC/DC power flow is constrained by the equal transmission power on both sides of the ideal converter in the flexible converter.

Beneficial effect:

1) When the flexible converter participates in the optimal operation of the distribution network as a flexible response unit, it can not only improve the reactive power distribution of the distribution network, but also adjust the transmission power direction of the line to be small, and improve the overall system economy and safety.

2) The present invention proposes a voltage risk perception technology, which can evaluate the risk of voltage violation through the probability flow based on the stochastic response surface and use it as the objective function of optimal operation, which can effectively avoid voltage violation;

3) The present invention converts the objective function of the integral form into a non-integral form based on the characteristics of the Hermite chaotic polynomial, and combines the mixed integer second-order cone model and the Distflow power flow model to solve the scheduling scheme, which reduces the complexity of the solution and ensures the accuracy of the scheme. Optimal solution.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art In other words, other drawings can also be obtained from these drawings on the premise of not paying creative work.

Figure 1 is a flow chart of voltage over-limit risk perception;

Figure 2 is the equivalent circuit diagram of the power flow of the flexible converter station;

Figure 3 is a topology diagram of the AC-DC hybrid distribution network;

Figure 4 is a graph of the voltage probability density function before and after optimization of No. 4 and No. 24 photovoltaic nodes;

Fig. 5 is the voltage cumulative distribution function graph before and after optimization of No. 4 and No. 24 photovoltaic nodes;

Fig. 6 is a diagram of the mean value of the overall voltage of the system and a confidence interval with a confidence level of 95%.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present disclosure with reference to the accompanying drawings in the embodiments of the present disclosure. Apparently, the described embodiments are only some of the embodiments of the present disclosure, not all of them. Based on the embodiments in the present disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present disclosure.

Example 1:

The present invention takes the modified IEEE33 node AC-DC hybrid distribution network as an example, the topology parameters and predicted load are shown in Table 1 and Table 2 respectively, and the rated voltage of the distribution network is 12.66kV. The specific topology is shown in Figure 3. The dispatching scheme of the present invention is programmed on MATLAB, and is solved by using the YALMIP toolkit and the GUROBI solver.

Table 1 Topological parameters

Table 2 Load parameters

Among them, nodes 25 and 30 are respectively equipped with static var compensators, and the adjustment range is ±200kVar. 300kW, 200kW, 900kW and 500kW photovoltaic power stations are respectively configured at nodes 4, 7, 24 and 28, and their minimum power factors are all 0.95. Configure flexible converter stations between nodes 5 and 6, and between nodes 10 and 11. Among them, the converter station between nodes 5 and 6 is the main station. The active power transmission range of the two flexible converter stations is ±2MW, and the reactive power adjustment range is ±0.3MVar, the equivalent impedance of the flexible converter station is (0.5+0.7j)Ω. The distribution network loss cost is 0.2 yuan/kWh.

The mean of the load normal distribution is set as the load prediction value, the standard deviation is 10% of the mean, and the correlation coefficients are all 0.2. Set the shape parameters of the photovoltaic Beta distribution to 2.06 and 2.5 respectively, and the correlation coefficient matrix is:

The diagonal elements of the matrix correspond to photovoltaics No. 4, 7, 24 and 28 respectively. After Nataf transformation, the correlation coefficient matrix is as follows:

When setting constant parameters of q ₁ and q ₂ , when V 0.96pu, q ₁ =-1/1.92; when V 1.04pu, q ₂ =1/2.08.

Taking No. 4 and No. 24 nodes as examples, analyze the probability information of their voltage safety risks. Figure 4 shows the voltage probability density functions of No. 4 and No. 24 photovoltaic nodes before and after optimization. It can be seen that before optimization, the voltage probability density of the two nodes is There are non-zero values in the interval greater than 1.04p.u., indicating that both nodes have the risk of voltage exceeding the limit. After intraday scheduling, the value range of the voltage probability density of the two nodes is basically below 1.04p.u., which effectively reduces the voltage. Limit risk.

Further, Figure 5 shows the voltage cumulative distribution function diagrams of PV nodes No. 4 and No. 24 before and after optimization. From the value of the four cumulative distribution function voltages at 1.04p.u., it can be seen that the probabilities of approaching limit violations before optimization are 59.3% and 47.48%, and the optimized probabilities are 2.49% and 0.95%, respectively, which shows that the method proposed in the present invention can effectively reduce the probability of the voltage approaching the limit and avoid the voltage exceeding the limit.

Figure 6 shows the mean value of the overall voltage of the system and the confidence interval with a confidence level of 95%. The rectangle corresponds to the upper and lower limits of the confidence interval of the node voltage. It can be seen from the figure that the mean value of all node voltages and their confidence intervals are between 0.96p.u.～1.04 Between p.u., the system does not have the situation that the voltage is about to exceed the limit.

Table 3 shows the control quantity of the control object of the optimized operation plan, where the negative reactive power means the consumption of inductive reactive power. It can be seen from the table that in order to reduce the risk of voltage exceeding the limit, each photovoltaic, static var compensator, and flexible converter station Both the master station and the slave station consume inductive reactive power, and the coordination of photovoltaics, static var compensators and flexible converter stations effectively reduces the risk of voltage overruns.

Table 3 Optimizing operation scheme control object control quantity

In the description of this specification, descriptions referring to the terms "one embodiment", "example", "specific example" and the like mean that specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one of the present disclosure. In an embodiment or example. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

The basic principles, main features and advantages of the present disclosure have been shown and described above. Those skilled in the industry should understand that the present disclosure is not limited by the above-mentioned embodiments. The above-mentioned embodiments and descriptions only illustrate the principle of the present disclosure. Various changes and improvements are intended, which fall within the scope of the claimed disclosure.

Claims (6)

1. A distribution network optimization method considering transgression risk, characterized in that, comprising the following steps: For the distribution network, based on the probability density function of the risk of node voltage exceeding the limit and the random variables of the active output of n units of photovoltaics and loads, the active output of photovoltaics and loads is standardized, and the independent standard normal distribution variable ξ and the node voltage exceeding the limit are established. The mapping relationship between limited risks; Express the probability density function of node voltage over-limit risk as a Hermite chaotic polynomial with ξ as an independent variable; Select the sampling point, according to the model of the sample point, based on the voltage value of the sampling point, use the voltage safety risk to obtain the undetermined coefficient of the Hermite chaotic polynomial, and obtain the probability distribution of the output response; Use the probability distribution of the output response to establish a risk perception system; Determine the optimization operation objective function and constraints, including: The optimal operation takes the active power and reactive power of the flexible converter station, distributed photovoltaic reactive power and static var compensator as the control object, and based on the risk perception system, the goal is to minimize the risk of the distribution network voltage exceeding the limit. The objective function is :

In the formula: r represents the node of the distribution network, V _r,up and V _r,down are the maximum and minimum voltage of the rth node respectively, and f is the probability density function; Set the upper and lower thresholds of the voltage safe operation boundary to 0.95p.u. and 1.05p.u. When the voltage exceeds 1.04p.u. or is lower than 0.96p.u., there is a risk of voltage exceeding the limit. When the voltage is between 0.96p.u. and 1.04p.u., there is no risk of voltage exceeding the limit; Taking the probability density function R(V) of the voltage risk that the voltage is about to exceed the limit as the utility, and comparing the voltage deviation W as the income, then R(V) can use the following quadratic function to evaluate the risk of voltage exceeding the limit: R(W)＝q _i W ² +W

In the formula: V is the per unit value of the node voltage amplitude, and q _i is a function constant parameter; The operational constraints for the optimization run are as follows: Constraints on the expected value of distributed photovoltaic operation:

In the formula: Ω ^PV represents the distributed photovoltaic collection;

and

are the active power and reactive power of the i-th distributed photovoltaic output at time t, respectively;

is the minimum photovoltaic power factor; Static var compensator operating expectations constraints:

In the formula: Ω ^SVC represents the set of static var compensators;

and

are the maximum and minimum reactive power compensation values of the i-th static var compensator, respectively,

is the reactive compensation power of the ith static var compensator at time t; Operating expectation constraints of flexible converter station:

In the formula: Ω ^VSC represents the set of flexible converter stations;

and

are the active power and reactive power of the ith flexible converter station at time t, respectively,

is the maximum capacity of the flexible converter station,

and

are the minimum and maximum power of the active power and reactive power of the i-th flexible converter station, respectively; System security operation expectations constraints: V _{i, min} ≤ V _{i, t} ≤ V _{i, max} , i∈Ω ^DN

In the formula: Ω ^DNL represents the distribution network node set; V _i,max and V _i,min are the allowable maximum and minimum values of the i-th node voltage, V _i,t is the voltage amplitude of the i-th node at time t; S _{i, max} is the maximum transmission capacity of the line, P _i,t and Q _i,t are the active power and reactive power transmitted by the i-th line; Establish a solution model for the optimal operation plan, including: The AC and DC power flow model is the power flow balance constraint of the distribution network; the distflow power flow model of the AC distribution network is as follows:

The distflow power flow model of the DC distribution network is as follows:

In formulas (7) and (8): the subscript e represents the node; the subscript i and j represent the starting node and the ending node of the branch respectively; k(e,:) represents the branch k with node e as the head end; k (:,e) represents the branch k with node e as the end; P _k,t and Q _k,t represent the active and reactive power at the head end of line k at time t; I _k,t represents the current amplitude of line k at time t squared;

and

Indicates the active and reactive power injected into node e at time t; U _i,t and U _j,t respectively represent the squares of the voltage amplitudes of node i and node j at time t; Composition of an ideal converter; The power flow model of the flexible converter station is as follows: P _AC,t -I _c,t R _c =P _c,t Q _AC,t -I _c,t X _c =-Q _c,t (9) The voltage constraints on both sides of the ideal converter in the flexible converter station are:

In the formula: μ is the DC voltage utilization rate, M is the modulation degree; P _AC,t and Q _AC,t are the active power and reactive power of the AC line at time t respectively; P _c,t and Q _c,t are respectively the time t Active power and reactive power on the AC side of the ideal converter; R _c and X _c are the resistance and reactance of VSC equivalent impedance; U _AC,t is the AC side voltage at time t; U _DC,t is the DC side voltage at time t; U _c,t is the AC fundamental wave phase voltage of the converter at time t; There is a quadratic equation constraint in the AC-DC power flow model, which is subjected to second-order cone relaxation and used as the power flow balance constraint of the distribution network;

The objective function of the optimal operation plan is an integral nonlinear function, and its physical meaning is the expected value of the voltage safety risk probability density function R(V). For the probability density function expressed by the Hermite chaotic polynomial, the expected value of the function is a ₀ , F ₂ can also be represented by the following formula:

2. The optimization method according to claim 1, wherein the standardization of the photovoltaic and load active output X includes: selecting an independent standard normal distribution variable as a standard random variable, and establishing a mapping relationship between X and the standard random variable: X＝F ^-1 [Φ(ξ)] (13) In the formula: ξ=[ξ ₁ ,ξ ₂ ,…,ξ _n ] ^T is an n-dimensional independent standard normal distribution variable; F ^-1 is the inverse function of the cumulative distribution function of X; Φ is the cumulative distribution function of the standard random variable . 3. optimization method according to claim 2, is characterized in that, described Hermite chaotic polynomial adopts 2nd order chaotic polynomial:

In the formula: a ₀ , a ₁ ,… are undetermined coefficients of the polynomial, which are constant items. 4. The optimization method according to claim 3, characterized in that, the undetermined coefficients are determined by the stochastic response surface method. 5. optimization method according to claim 4, it is characterized in that, described utilize stochastic response surface method to carry out undetermined coefficient to determine, comprise: for 2 order chaotic polynomial, one-dimensional 3 order Hermite polynomial equation is

its roots are

0,

The number N of undetermined coefficients of the chaotic polynomial is:

In the formula: n is the number of input variables, so N sampling points need to be selected. 6. The optimization method according to claim 5, characterized in that the sampling points are selected by using a probability collocation method based on the principle of linear independence.

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