CN112467746B

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

Info

Publication number: CN112467746B
Application number: CN202011314544.7A
Authority: CN
Inventors: 窦晓波; 刘之涵
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2020-11-21
Filing date: 2020-11-21
Publication date: 2022-11-01
Anticipated expiration: 2040-11-21
Also published as: CN112467746A

Abstract

The invention belongs to the technical field of optimized operation of a power distribution network, and discloses a power distribution network optimization method considering out-of-limit risks, which comprises the following steps: aiming at a power distribution network, establishing a mapping relation between an independent standard normal distribution variable xi and a node voltage out-of-limit risk; expressing a probability density function of the node voltage out-of-limit risk as a Hermite chaotic polynomial with xi as an independent variable; selecting a sampling point, and acquiring an undetermined coefficient of a Hermite chaotic polynomial by utilizing voltage safety risk according to a model of the sampling point and based on a voltage value of the sampling point to obtain probability distribution of output response; establishing a risk perception system by utilizing the probability distribution of the output response; active power and reactive power of the flexible converter station and the distributed photovoltaic reactive power and static reactive power compensator are taken as regulation and control objects, and the risk perception system is based so that the voltage out-of-limit risk of the power distribution network is minimum; the voltage out-of-limit can be effectively avoided.

Description

Power distribution network optimization method considering out-of-limit risk

Technical Field

The invention relates to a power distribution network optimization method considering out-of-limit risks, and belongs to the technical field of power distribution network optimization operation.

Background

The optimized operation of the power distribution network refers to the coordinated control and active management of regulation and control objects such as a power distribution network, a distributed power supply, reactive compensation equipment, flexible loads and the like. For the optimized operation of a power distribution network, at present, economic efficiency and safety are mainly taken as optimization targets, deterministic operation information of the power distribution network is taken as a basis, and the solution is carried out through an intelligent algorithm or a traditional optimization algorithm, so that the effects of reducing the network loss, reducing the voltage deviation, reducing the three-phase imbalance, reducing the power consumption cost and the like are achieved.

Direct-current power supplies such as distributed photovoltaic systems and energy storage systems must be merged into an alternating-current power distribution network through an alternating-current and direct-current inverter, the running loss of the inverter directly increases the overall loss of the alternating-current power distribution network system, and due to the defects, the direct-current power distribution network is low in electric energy loss, high in electric energy quality and flexible in control mode. However, the alternating current distribution network still has the main form of the distribution network due to the unique advantages of the alternating current distribution network, the direct current distribution network can be used as a supplement to be connected into the alternating current distribution network, and the alternating current and direct current hybrid distribution network is bound to become a new development trend.

At present, distributed photovoltaic is a main representative form of a distributed power supply of an alternating current-direct current power distribution network, and in the face of distributed photovoltaic access with a large number of well-spraying types, medium and small capacities and decentralization, the control operation of the power distribution network faces various more complex voltage safety problems, but the current optimized operation scheme generally only considers rigid constraints such as voltage non-overrun and the like, and does not fully consider the voltage overrun risk caused by short-term uncertainty of the distributed photovoltaic and load.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a power distribution network optimization method considering the out-of-limit risk, and aims to solve the problems that a voltage out-of-limit risk perception system is established to evaluate the voltage out-of-limit risk caused by distributed photovoltaic and load uncertainty, the voltage out-of-limit risk is effectively reduced through optimized operation, and the voltage safety of a power distribution network is ensured.

The invention provides an operation optimization method for an alternating current-direct current power distribution network, which mainly comprises the following steps:

(1) Determining an optimized scheduling control object:

the topology of an AC/DC power distribution network generally comprises three parts: the system comprises an alternating current distribution network, a direct current distribution network and a flexible converter station, wherein the flexible converter station is generally a Voltage Source Converter (VSC).

The controllable units in the AC/DC distribution network are divided into a continuous control type and a discrete control type, the continuous control type generally comprises an Energy Storage System (ESS), a Photovoltaic (PV), a Static Var Compensator (SVC) and a VSC, and the discrete control type generally comprises a Capacitor Bank (CB) and an on-load tap changer (OLTC).

The VSC is used as an energy conversion interface of the alternating current distribution network and the direct current distribution network, and can simultaneously control 2 state quantities in variables such as active power, reactive power, alternating current voltage and direct current voltage. According to the difference of control state quantity, it can be classified as V_dc-Q control, V_dc-V_acControl, P-Q control and V_ac-P, etc. For the ac-dc hybrid distribution network shown in fig. 1, the VSC generally adopts a master-slave control mode, that is, the master station adopts V_dcAnd the Q control mode is used for controlling the port voltage of the direct current distribution network, and the slave station adopts the P-Q control mode and can actively control the transmission active power and the output reactive power of the slave station. Under the master-slave control mode, the active power transmitted by the slave station, the reactive power output by the master station and the reactive power output by the master station are controlled, so that the line flow of the alternating-current and direct-current power distribution network can be changed, and the reactive power compensation can be performed on the alternating-current power distribution network, so that the voltage regulation and loss reduction are realized.

(2) Establishing a voltage risk perception system:

the uncertain analysis method of the power system mainly comprises a simulation method represented by a Monte Carlo method, an analytic method represented by a point estimation method and the like, the Monte Carlo method needs to perform a large amount of deterministic load flow calculations, the calculation precision is high but the calculation efficiency is low, the point estimation method is high in calculation speed but difficult to guarantee, and the probability density function of random variables can be obtained by means of various series. The random response surface method is a method which does not depend on the number of stages and can give consideration to both the calculation efficiency and the calculation precision and the randomness analysis, so the method selects the random response surface method to carry out voltage risk perception.

The basic idea of the random response surface is to fit a function relation between an input variable and an output response by using a Hermite chaotic polynomial, wherein the input variable and the output response are random variables.

The random response surface mainly comprises three steps: 1) Input standardization, namely representing input random variables by using a functional relation of a set of standard random variables; 2) Output standardization, namely determining a Hermite chaotic polynomial form of an output response to be solved; 3) And model calculation, namely selecting a proper sampling point, performing model calculation of the sample point, solving undetermined coefficients of a Hermite chaotic polynomial through input and output of the sampling point to obtain probability distribution of output response, and establishing a risk perception system by utilizing the probability distribution of the output response.

Aiming at a power distribution network, for an alternating current-direct current power flow model G, a probability density function of a node voltage out-of-limit risk R (V) and active output random variables X of n photovoltaic and loads = [ X ]₁,x₂,…,x_n]^TThe mapping relationship can be expressed as

R(V)＝G(X)＝G(x₁,x₂,…,x_n)

Firstly, standardizing the photovoltaic and load active power output X, generally selecting an independent standard normal distribution variable as a standard random variable, and establishing a mapping relation between the X and the standard random variable:

X＝F^-1[Φ(ξ)]

in the formula: xi = [ xi ]₁,ξ₂,···,ξ_n]^TIs an n-dimensional independent standard normal distribution variable; f^-1An inverse function of the cumulative distribution function of X; Φ is the cumulative distribution function of the standard random variables.

Secondly, a mapping relation between an independent standard normal distribution variable xi and a node voltage out-of-limit risk R (V) can be established;

and expressing the probability density function of the node voltage out-of-limit risk R (V) as a Hermite chaotic polynomial with ξ as an argument. The higher the Hermite polynomial order m is, the higher the precision of the chaotic polynomial is, but the larger the number N of the coefficients to be determined is. When m is more than or equal to 3, the influence of increasing the order m on improving the precision is not obvious, a 2-order or 3-order Hermite chaotic polynomial is generally adopted, and the 2-order chaotic polynomial is adopted in the invention:

in the formula: a is₀,a₁8230is undetermined coefficient of polynomial and constant term.

Then, selecting proper sampling points, performing model calculation on each sample, and determining a to-be-determined coefficient of the chaotic polynomial;

the sampling selection principle of the random response surface method is as follows: determining a coefficient to be determined of the chaotic polynomial with the highest order of m, selecting roots of Hermite polynomials of 0 order and m +1 order as sampling points, namely, each standard random variable ξ of each sample point_iThe sampled values of (1) are taken as the roots of Hermite polynomials of order 0 or m + 1. For the 2 nd order chaotic polynomial, the one-dimensional 3 rd order Hermite polynomial equation is

The roots are respectively

0,

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

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

When the sampling points are selected, if the linear equation set composed of the sampling points is linearly independent of the row vectors of the coefficient matrix, namely the rank of the coefficient matrix is equal to the row number of the coefficient matrix, the coefficient matrix is a row full-rank matrix, the value of the determinant of the coefficient matrix is constantly unequal to zero, the established linear algebraic equation set has a unique solution, and the equation solving precision is obviously improved. Therefore, the probability distribution point method based on the linear independence principle is adopted, the linearly related distribution points can be removed, the reversibility of the coefficient matrix of the linear equation set is ensured, namely the full rank is reached, and the linear independence between the row vectors of the coefficient matrix of the equation set is ensured.

Finally, N sampling points (xi) are selected_1,1,…,ξ_n,1)、(ξ_1,2,…ξ_n,2)…(ξ_1,N…ξ_n,N) Output response to each sampling pointR＝[R(V₁),…,R(V_N)]^TWith a waiting coefficient A = [ a ]₀,a₁,…,a_ij]^TFor unknown quantities, a linear equation set HA = R is established, where H is the equation set coefficient matrix, in the specific form:

and (3) solving a linear equation system to obtain an undetermined coefficient A, and further obtaining f [ R (V) ] by a Hermite chaotic polynomial.

For the load, because the region range of the same power distribution network supply area is small, the power utilization habit has correlation, the load active power ultra-short time scale follows normal distribution, the average value is a load predicted value, and the standard deviation is a certain percentage of the average value. For photovoltaic, because strong correlation exists in illumination intensity in the same power distribution network supply area, correlation also exists in photovoltaic active output, but no correlation exists between load and photovoltaic. Obeying Beta distribution on the ultra-short time scale of the photovoltaic active output probability density, wherein the probability density function of the Beta distribution can be expressed as follows:

in the formula: alpha and Beta are shape parameters of Beta distribution, gamma is Gamma function, P is photovoltaic active power output, and P is_maxAnd the maximum value of the photovoltaic active power output is obtained.

The random response surface can be directly applied to the situation that the input variable has no correlation, and for the input variable with the correlation, the input variable needs to be standardized through a Nataf transformation.

Setting correlation coefficient matrix C of n photovoltaic and load active power output X_XExpressed as:

in the formula: rho is the correlation coefficient between random variables.

Introducing a standard normal distribution vector Y = [ Y = [)₁,y₂,…,y_n]^TThe random variables in Y have correlation, and the correlation coefficient matrix C thereof_YCan be expressed as:

according to the principle of equal probability, x_iAnd y_iCan be expressed as:

Φ_Y(y_i)＝F(x_i)

in the formula: phi_YIs a standard normal distribution variable cumulative distribution function.

For an inter-load correlation coefficient that follows a normal distribution, ρ = ρ';

for inter-photovoltaic correlation coefficients that do not follow a normal distribution, ρ and ρ' are related as follows:

in the formula:

and

respectively represent random variables x_iAnd x_jThe average value of (a) is calculated,

and

representing a random variable x_iAnd x_jStandard deviation of (2).

According to Gauss-Hermite double integral theory, the relationship between ρ and ρ' can be further expressed as follows:

in the formula: g is the Gauss point and omega is a constant coefficient.

In the case of Beta distribution, ρ_ijAnd ρ_i′_jThe relation between the p and the p can not be expressed by using a direct explicit expression, and the p can be obtained by adopting a dichotomy method_i′_j。

In the known C_XOn the basis, solving for C_YAnd the intermediate photovoltaic correlation coefficient part completes the conversion from the dependent Beta distribution vector to the dependent standard normal distribution vector. Next, the conversion to the independent standard normal distribution vector needs to be further completed.

C is to be_YCholesky factorization to give C_Y＝BB^TWhere B is a lower triangular matrix, then

ξ＝B^-1Y

Thus, input variable standardization processing of photovoltaic and load active power output is completed, and when sampling is carried out on a random response surface, sample values of distributed photovoltaic active power output of each station can be determined according to xi sampling point values.

Therefore, a flow chart of sensing the voltage out-of-limit risk by a random response surface method based on the Nataf transformation is shown in FIG. 1.

(3) Determining optimized operational objective functions and constraints

The active power and reactive power of the flexible convertor station and the distributed photovoltaic reactive and static reactive compensators are taken as regulation and control objects in the optimized operation, the calculation result is based on the voltage risk perception technology, the minimum out-of-limit risk of the voltage of the power distribution network is taken as a target, and the objective function is as follows:

in the formula: r denotes a distribution network node, V_r,upAnd V_r,downThe maximum and minimum values of the voltage of the r-th node are respectively, and f is a probability density function.

When the power distribution network operates, the voltage is close to the out-of-limit condition, namely when the voltage is close to the safe operation boundary but does not reach the boundary threshold value, the voltage is possible to be out-of-limit, and the risk of out-of-limit of the voltage exists. The upper threshold value and the lower threshold value of the safe operation boundary of the voltage are set to be 0.95p.u and 1.05p.u, the voltage is out-of-limit risk exists when the voltage exceeds 1.04p.u or is lower than 0.96p.u, and the voltage is not out-of-limit risk exists when the voltage is between 0.96p.u and 1.04p.u.

For the node voltage determination value, as the voltage value approaches the threshold degree of the normal operation boundary, the voltage is easier to exceed the limit, the out-of-limit risk is larger, a utility function of a risk utility theory is used for reference, the voltage risk R (V) of the voltage approaching the out-of-limit is taken as the utility, the voltage deviation W is compared with the profit, and then the R (V) can adopt the following quadratic function to evaluate the out-of-limit risk of the system voltage:

R(W)＝q_iW²+W

in the formula: v is the per unit value of the node voltage amplitude, q_iAre function parameters.

The operational constraints for the optimization run are as follows:

distributed photovoltaic operation desired value constraint:

the distributed photovoltaic has active and reactive power regulation capability, but the invention considers that the active output of the distributed photovoltaic is not reduced to ensure the complete consumption of new energy, only the reactive power regulation capability is utilized, and the reactive power regulation constraint is as follows:

in the formula: omega^PVRepresenting a distributed photovoltaic collection;

and

respectively the active power and the reactive power output by the ith distributed photovoltaic at the moment t;

is the photovoltaic minimum power factor.

And (3) restraining the operation expected value of the static reactive compensator:

in the formula: omega^SVCRepresenting a static var compensator set;

and

respectively the maximum and minimum values of reactive compensation of the ith static var compensator,

and performing reactive compensation on power for the ith static var compensator at the time t.

And (3) restricting the operation expected value of the flexible converter station:

in the formula: omega^VSCRepresenting a set of static var compensators;

and

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

for the maximum capacity of the flexible converter station,

and

the minimum and maximum power of the active power and the reactive power of the ith flexible converter station respectively.

And (3) system safe operation expected value constraint:

V_i,min≤V_i,t≤V_i,max,i∈Ω^DN

in the formula: omega^DNRepresenting a power distribution network node set; v_i,maxAnd V_i,minAllowing the maximum minimum value, V, for the ith node voltage_i,tThe ith node voltage amplitude at time t. S. the_i,maxFor maximum transmission capacity of the line, P_i,tAnd Q_i,tActive and reactive power transmitted for the ith line.

In addition, in order to ensure normal operation of the power distribution network, power flow balance constraint of the power distribution network is also considered, and specific conditions are introduced in detail in an optimized operation solving model below.

(4) Establishing solution model of optimized operation scheme

The alternating current-direct current power flow model is power distribution network power flow balance constraint. The distflow power flow model of the alternating-current power distribution network is as follows:

in the formula: subscript e represents a node; subscripts i and j denote the start and end nodes of the branch, respectively; k (e,: indicates a branch k with a node e as a head end; k (: e) represents a branch k ending with the node e; p is_k,tAnd Q_k,tThe active power and the reactive power of the head end of the line k at the moment t are represented; I.C. A_k,tRepresents the square of the k current amplitude of the line at the time t;

and

indicating that active and reactive power is injected into a node e at the moment t; u shape_i,tAnd U_j,tRepresenting the square of the voltage magnitude at node i and node j, respectively, at time t.

The distflow power flow model of the direct-current power distribution network is as follows:

flexible power flow in converter stationThe value circuit model is shown in fig. 2 and consists of equivalent impedance and an ideal inverter. In the figure P_AC,tAnd Q_AC,tRespectively setting the t time as active power and reactive power of the alternating current circuit; p_c,tAnd Q_c,tRespectively the active power and the reactive power of the alternating current side of the ideal converter at the time t; p_DC,tThe active power of the direct current line at the moment t; r is_cAnd X_cResistance and impedance of the VSC equivalent circuit; u shape_AC,tMeasuring voltage for t moment alternating current; u shape_DC,tIs the direct current side voltage at the time t; u shape_c,tThe AC fundamental phase voltage of the inverter at the time t.

The flexible converter station power flow model 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 two sides of the ideal current converter of the flexible converter station are as follows:

in the formula: mu is the direct current voltage utilization rate, and M is the modulation degree.

And (4) secondary equality constraint exists in the alternating current-direct current power flow model, second-order cone relaxation is carried out on the secondary equality constraint, and the secondary equality constraint is used as power flow balance constraint of the power distribution network.

The objective function of the optimized operation scheme is an integral nonlinear function, the physical meaning of the integral nonlinear function is the expected value of a probability density function of voltage safety risk R (V), and for the probability density function expressed by Hermite chaotic polynomial, the function expected value is a₀，F₂It can also be represented by the following formula:

q can be reasonably set simultaneously₁And q is₂The parameter eliminates the first order term of V, so that the node voltage only appears as a square term in the solution model. By the processing, the optimized operation scheme can be guaranteed to be a convex optimization problem integrally, and the operation scheme can be solved by using a Distflow model with a relaxed second-order cone.

In the alternating current-direct current flow Distflow model, the idea of calculating the current by an alternating iteration method is used for reference, and the alternating current-direct current flow is constrained by equal transmission power on two sides of an ideal current converter in the flexible current converter.

Has the advantages that:

1) When the flexible converter is used as a flexible response unit to participate in the optimized operation of the power distribution network, the reactive power distribution condition of the power distribution network can be improved, the transmission power direction of a line can be adjusted to be small, and the economical efficiency and safety of the system are integrally improved.

2) The invention provides a voltage risk perception technology, which can evaluate the voltage out-of-limit risk through the probability tide based on the random response surface and take the voltage out-of-limit risk as an objective function for optimizing operation, thereby effectively avoiding the voltage out-of-limit;

3) The method converts the target function in the integral form into the non-integral form based on the Hermite chaotic polynomial characteristic, and solves the scheduling scheme by combining the mixed integer second-order cone model and the Distflow power flow model, thereby reducing the solving complexity and ensuring the optimal solution of the scheme.

Drawings

In order to more clearly illustrate the embodiments or technical solutions of the present disclosure, the drawings used in the embodiments or technical solutions of the present disclosure will be briefly described below, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.

FIG. 1 is a flow chart of voltage threshold risk sensing;

FIG. 2 is a power flow equivalent circuit diagram of the flexible converter station;

FIG. 3 is a topological diagram of an AC/DC hybrid power distribution network;

FIG. 4 is a graph of voltage probability density functions before and after optimization of photovoltaic nodes No. 4 and No. 24;

FIG. 5 is a graph of cumulative distribution functions of voltage before and after optimization of photovoltaic nodes No. 4 and No. 24;

fig. 6 is a graph of the mean voltage and confidence interval with a confidence level of 95% for the system as a whole.

Detailed Description

The technical solutions in the embodiments of the present disclosure will be described clearly and completely with reference to the drawings in the embodiments of the present disclosure, and it is obvious that the embodiments described are only some embodiments of the present disclosure, rather than all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.

Example 1:

in the invention, an improved IEEE33 node alternating current-direct current hybrid power distribution network is taken as an example, topological parameters and predicted loads are respectively shown in tables 1 and 2, and the rated voltage of the power distribution network is 12.66kV. The specific topology is shown in fig. 3. The scheduling scheme of the invention is programmed on MATLAB and solved by using YALMIP toolkit and GUROBI solver.

TABLE 1 topological parameters

TABLE 2 load parameters

Wherein, the number 25 and the number 30 nodes are respectively provided with a static var compensator, and the adjusting ranges are +/-200 kVar. 4. The 7, 24 and 28 nodes are respectively provided with 300kW, 200kW, 900kW and 500kW photovoltaic power stations, and the minimum power factors of the photovoltaic power stations are all 0.95. And flexible converter stations are configured between

nodes

5 and 6 and between

nodes

10 and 11, wherein the converter station between the

nodes

5 and 6 is a main station, the active power transmission ranges of the two flexible converter stations are +/-2 MW, the reactive power regulation ranges are +/-0.3 MVar, and the equivalent impedance of the flexible converter stations is (0.5 +0.7 j) omega. The network loss cost of the power distribution network is 0.2 yuan/kWh.

Setting the average value of the normal distribution of the load as a predicted value of the load, setting the standard deviation as 10 percent of the average value, and setting the correlation coefficient of the standard deviation as 0.2. Setting the shape parameters of photovoltaic Beta distribution as 2.06 and 2.5 respectively, wherein a correlation coefficient matrix is as follows:

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

setting q₁And q is₂Constant parameter, V0.96p.u. time, q₁= -1/1.92; v1.04p.u. time, q₂＝1/2.08。

Taking nodes No. 4 and No. 24 as examples, probability information of voltage safety risks of the nodes No. 4 and No. 24 is analyzed, and a voltage probability density function before and after optimization of the photovoltaic nodes No. 4 and No. 24 is shown in FIG. 4, so that before optimization, the voltage probability densities of the two nodes are both nonzero values in an interval larger than 1.04p.u., the two nodes are both subjected to voltage out-of-limit risks, and after scheduling in the day, voltage probability density value intervals of the two nodes are both basically 1.04p.u., and the voltage out-of-limit risks are effectively reduced.

Further, figure 5 shows the voltage cumulative distribution function graphs before and after the photovoltaic node 4 and the photovoltaic node 24 are optimized, and values of four cumulative distribution function voltages are 1.04p.u. It can be seen that the adjacent threshold probabilities before optimization are 59.3% and 47.48% respectively, and the adjacent threshold probabilities after optimization are 2.49% and 0.95% respectively, which shows that the method provided by the invention can effectively reduce the probability of the adjacent threshold of the voltage and avoid the threshold of the voltage.

Fig. 6 shows the confidence interval with 95% confidence level and the overall voltage mean value of the system, wherein the rectangle corresponds to the upper and lower limits of the confidence interval of the node voltage, and it can be seen from the figure that all the node voltage mean values and the confidence intervals thereof are between 0.96p.u. to 1.04p.u., and there is no situation that the voltage approaches the out-of-limit in the system.

Table 3 shows the control quantity of the control object of the optimized operation scheme, wherein reactive power is negative and represents consumption inductive reactive power, and as can be seen from the table, in order to reduce the voltage out-of-limit risk, each of the photovoltaic static var compensator, the flexible converter station master station and the slave station consumes inductive reactive power, and the voltage out-of-limit risk is effectively reduced through the coordination of the photovoltaic static var compensator and the flexible converter station.

TABLE 3 control of the Regulation and control of the optimized operating scenarios

In the description herein, references to the description of "one embodiment," "an example," "a specific example," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the disclosure. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

The foregoing illustrates and describes the general principles, principal features, and advantages of the present disclosure. It will be understood by those skilled in the art that the present disclosure is not limited to the embodiments described above, which are presented solely for purposes of illustrating the principles of the disclosure, and that various changes and modifications may be made to the disclosure without departing from the spirit and scope of the disclosure, which is intended to be covered by the claims.

Claims

1. A power distribution network optimization method considering out-of-limit risks is characterized by comprising the following steps:

aiming at a power distribution network, standardizing the active output of the photovoltaic and the load based on a probability density function of node voltage out-of-limit risks and n active output random variables of the photovoltaic and the load, and establishing a mapping relation between an independent standard normal distribution variable xi and the node voltage out-of-limit risks;

expressing a probability density function of the node voltage out-of-limit risk as a Hermite chaotic polynomial with xi as an independent variable;

selecting a sampling point, and acquiring undetermined coefficients of a Hermite chaotic polynomial by using voltage safety risks according to a model of the sampling point and based on a voltage value of the sampling point to obtain probability distribution of output response;

establishing a risk perception system by utilizing the probability distribution of the output response;

determining an optimized operation objective function and constraint, comprising:

the active power and reactive power of the flexible convertor station and the distributed photovoltaic reactive power and static reactive power compensator are used as regulation and control objects in the optimized operation, the risk perception system is based, the minimum out-of-limit risk of the voltage of the power distribution network is used as a target, and the target function is as follows:

in the formula: r denotes a distribution network node, V_r,upAnd V_r,downThe maximum and minimum values of the voltage of the r node are respectively, and f is a probability density function;

setting upper and lower thresholds of a safe voltage operation boundary to be 0.95p.u and 1.05p.u, wherein the voltage is out-of-limit when the voltage exceeds 1.04p.u or is lower than 0.96p.u, and the voltage is between 0.96p.u and 1.04p.u;

taking the probability density function R (V) of the voltage risk of the voltage approaching the out-of-limit as the utility, and comparing the voltage deviation W as the profit, then R (V) can adopt the following quadratic function to evaluate the voltage out-of-limit risk:

R(W)＝q_iW²+W

in the formula: v is the per unit value of the node voltage amplitude, q_iIs a function constant parameter;

the operational constraints for the optimization run are as follows:

distributed photovoltaic operation desired value constraint:

in the formula: omega^PVRepresenting a distributed photovoltaic collection;

and

is the photovoltaic minimum power factor;

and (3) restraining the running expected value of the static reactive compensator:

in the formula: omega^SVCRepresenting a set of static var compensators;

and

are respectively the ithThe static var compensator reactive compensation maximum and minimum values,

reactive compensation power of the ith static reactive compensator at the time t;

and (3) constraint of operation expected value of the flexible converter station:

in the formula: omega^VSCRepresenting a set of flexible converter stations;

and

for the maximum capacity of the flexible converter station,

and

the minimum and maximum power of the active power and the reactive power of the ith flexible converter station are respectively;

and (3) system safe operation expected value constraint:

V_i，min≤V_i，t≤V_i，max，i∈Ω^DN

in the formula: omega^DNLRepresenting a power distribution network node set; v_i,maxAnd V_i,minAllowing the maximum minimum value, V, for the ith node voltage_i,tThe voltage amplitude of the ith node at the time t; s. the_i,maxFor maximum transmission capacity, P, of the line_i,tAnd Q_i,tActive power and reactive power transmitted for the ith line;

establishing a solution model of an optimized operation scheme, comprising the following steps:

the alternating current-direct current power flow model is power distribution network power flow balance constraint; the distflow power flow model of the alternating-current power distribution network is as follows:

in equations (7) and (8): subscript e represents a node; subscripts i and j denote the start and end nodes of the branch, respectively; k (e,: indicates a branch k with a node e as a head end; k (: e) represents a branch k ending with the node e; p is_k,tAnd Q_k,tThe active power and the reactive power of the head end of the line k at the moment t are represented; i is_k,tRepresents the square of the amplitude of the line k current at time t;

and

indicating that active power and reactive power are injected into a node e at the moment t; u shape_i,tAnd U_j,tRespectively representing the squares of the voltage amplitudes of the node i and the node j at the time t; the flexible converter station tidal current equivalent circuit model consists of equivalent impedance and an ideal converter;

the flexible converter station power flow model is as follows:

P_AC，t-I_c，tR_c＝P_c，t

Q_AC，t-I_c，tX_c＝-Q_c，t (9)

in the formula: mu is the direct current voltage utilization rate, and M is the modulation degree; p is_AC,tAnd Q_AC,tRespectively setting the t time as active power and reactive power of the alternating current circuit; p is_c,tAnd Q_c,tRespectively the active power and the reactive power of the alternating current side of the ideal converter at the time t; r_cAnd X_cResistance and reactance of VSC equivalent impedance; u shape_AC,tIs the AC side voltage at time t; u shape_DC,tIs the direct current side voltage at the time t; u shape_c,tThe AC fundamental phase voltage of the converter at the time t;

secondary equality constraint exists in the alternating current-direct current power flow model, second-order cone relaxation is carried out on the secondary equality constraint, and the secondary equality constraint is used as power flow balance constraint of the power distribution network;

the objective function of the optimized operation scheme is an integral nonlinear function, the physical meaning of the integral nonlinear function is the expected value of a voltage safety risk probability density function R (V), and for the probability density function expressed by Hermite chaotic polynomial, the function expected value is a₀，F₂It can also be represented by the following formula:

2. the optimization method according to claim 1, wherein the photovoltaic and load active power output X is normalized and comprises: selecting an independent standard normal distribution variable as a standard random variable, and establishing a mapping relation between X and the standard random variable:

X＝F^-1[Φ(ξ)] (13)

in the formula: xi = [ xi ]₁,ξ₂,…,ξ_n]^TIs an n-dimensional independent standard normal distribution variable; f^-1An inverse function of the cumulative distribution function of X; Φ is the cumulative distribution function of the standard random variables.

3. The optimization method according to claim 2, wherein the Hermite chaotic polynomial is a 2 nd order chaotic polynomial:

in the formula: a is a₀,a₁And 8230, undetermined coefficients of a polynomial and constant terms.

4. The optimization method according to claim 3, wherein the undetermined coefficient is determined by using a random response surface method.

5. The optimization method according to claim 4, wherein the undetermined coefficient determination by using a random response surface method comprises: for the 2 nd order chaotic polynomial, the one-dimensional 3 rd order Hermite polynomial equation is

The roots are respectively

0，

6. The optimization method according to claim 5, wherein the sampling points are selected by a probability matching method based on a linear independence principle.