Chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction

Abstract

The invention discloses an opportunity-constrained reactive power optimization method for a distribution network based on random voltage probability prediction, which relates to the field of distribution networks and includes the following steps: based on a linear distribution network power flow model, decomposing the node voltage into three parts: random, controllable, and fixed, where the random part is the action of random source and load powers on the node voltage, and obtaining a calculation model for the random voltage; collecting historical samples of the predicted values and actual values of source and load power points, and constructing historical samples of the predicted values and actual values of the random voltage; constructing a probability prediction model for the random voltage; obtaining the probability prediction results of the random voltage at each node and constructing an opportunity-constrained reactive power optimization model for the distribution network, and solving the optimization model to obtain a reactive power scheduling scheme; the invention does not need to perform probability prediction on random multi-dimensional source and load powers, significantly reduces the difficulty of accurately evaluating the risk of distribution network voltage violation, and realizes the precise and reliable control of the risk of distribution network voltage violation through opportunity-constrained reactive power optimization of the distribution network.

Description

Technical Field

[0001] The invention relates to the field of distribution networks, and in particular to a method for optimizing reactive power of distribution networks based on chance constraints and random voltage probability prediction. Background Art

[0002] The construction of new distribution networks is being vigorously promoted. The distribution networks will be connected to a large number of new sources and loads with random characteristics, such as distributed photovoltaic power sources and electric vehicle loads, which will significantly increase the randomness and volatility of the distribution network voltage. The high risk of voltage exceeding the limit of the distribution network has become a prominent problem. The chance-constrained distribution network reactive power optimization method is an effective means to control the risk of voltage exceeding the limit. The traditional method first predicts the power of sources and loads probabilistically, then establishes a chance-constrained distribution network reactive power optimization model and solves the optimized reactive power dispatching scheme. However, there are many random sources and loads in the new distribution network, and it is extremely difficult to accurately predict the random multi-dimensional source and load power probabilistically. Therefore, it is difficult to reliably optimize and control the risk of voltage exceeding the limit of the distribution network through the chance-constrained reactive power optimization method. Summary of the invention

[0003] The purpose of the present invention is to provide a chance-constrained distribution network reactive power optimization method based on random voltage probability prediction, which does not require probabilistic prediction of random multi-dimensional source and load power, significantly reduces the difficulty of accurately evaluating the risk of voltage over-limit in the distribution network, and achieves accurate and reliable control of the risk of voltage over-limit in the distribution network through chance-constrained distribution network reactive power optimization, so as to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] The method for reactive power optimization of distribution network with chance constraints based on random voltage probability prediction includes the following steps:

[0006] (1) Based on the linear distribution network power flow model, the node voltage is decomposed into three parts: random, controllable, and fixed. The random part is the effect of random source and load power on the node voltage, and the calculation model of random voltage is obtained;

[0007] (2) According to the calculation model of random voltage obtained in step (1), historical samples of point prediction values ​​and actual values ​​of source and load power are collected to construct historical samples of point prediction values ​​and actual values ​​of random voltage;

[0008] (3) constructing a probability prediction model for random voltage based on the point prediction value and actual value historical samples of the random voltage obtained in step (2);

[0009] (4) According to the probability prediction model of random voltage obtained in step (3), the probability prediction results of random voltage at each node are obtained and a chance-constrained distribution network reactive power optimization model is constructed, and the reactive power dispatching scheme is obtained by solving the optimization model.

[0010] As a further embodiment of the present invention:

[0011] The method for obtaining the random voltage calculation model in step (1) is specifically as follows:

[0012] The calculation model of the power injected into the distribution network node is established, specifically:

[0013]

[0014] Where: P l , Q l are the injected active and reactive power of node l respectively; is a random power source set, g is its index number, χ g is the active variable of the g-th random power source; is a random load set, d is its index number, ζ d is the active variable of the dth random load; For fixed power supply assembly, For its index number, For the Active power variables of fixed power sources; is a fixed load set, For its index number, For the The active variable of a fixed load; q j is the reactive power that can be dispatched by the jth node; κ represents the tangent value of the power factor angle of each power source and load that does not participate in reactive power dispatch; η represents whether each power source and load is connected to the corresponding node l, 1 represents connected, otherwise 0;

[0015] Based on the linear distribution network power flow model, the calculation model of node voltage is established as follows:

[0016]

[0017] Where: i is the voltage of node i; 0 is the root node voltage; R i,l , X i,l The matrices 2FD are r F T 、2FD x F T The element in the i-th row and the l-th column in the graph, F is the inverse matrix of the reduced-order branch-node association matrix, D r , D x are the diagonal matrices of branch resistance and reactance respectively;

[0018] Substituting equation (1) into equation (2), the calculation model of node voltage is further converted into:

[0019]

[0020] Where: b is the sensitivity coefficient of each source and load power to the node voltage, which is given by R i,l , X i,l , η, κ are calculated according to formula (1)-(2);

[0021] According to formula (3), the node voltage is decomposed into three parts:

[0022]

[0023]

[0024]

[0025]

[0026] Where: is a random source, load power χ g , d The effect on voltage is defined as random voltage; is the dispatchable reactive power q j The effect on voltage is defined as controllable voltage; For fixed source and load power The effect on voltage is defined as fixed voltage; equations (5), (6), and (7) are the calculation models of random voltage, controllable voltage, and fixed voltage, respectively.

[0027] As a further embodiment of the present invention:

[0028] The method for constructing historical samples of predicted values ​​and actual values ​​of random voltage points in the distribution network in step (2) is specifically as follows:

[0029] Collect N historical samples of the point prediction value and actual value of each random source and load power of the distribution network, and the kth sample of the predicted value and actual value of the active power of the gth random power source collected are: and X g,k , the kth samples of the predicted value and actual value of the dth random load active power collected are: and Z d,k ;

[0030] Based on the historical samples of the point prediction value and actual value of each random source and load power and the calculation model of the random voltage of the distribution network Constructing distribution network random voltage point prediction values and actual value The historical sample is:

[0031]

[0032] Where: V i,k They are The k-th sample of is calculated from the k-th historical samples of the point prediction value and actual value of each random source and load power.

[0033] As a further embodiment of the present invention:

[0034] The method for establishing the distribution network random voltage probability prediction model in step (3) is specifically as follows:

[0035] According to the predicted value of random voltage point in distribution network and actual value The historical samples are used to obtain the random voltage prediction error e i A sample of:

[0036] The random voltage prediction error e is established by kernel density estimation method. i With the predicted value The joint probability distribution of is:

[0037]

[0038] Where: u i For vector U i,k for u i The kth sample of H i,k For sample U i,k The bandwidth matrix at ; N(·) is the Gaussian kernel function;

[0039] Formula (9) is a Gaussian mixture model containing N Gaussian components. The density-preserving hierarchical expectation maximization algorithm is used to reduce the number of Gaussian components in Formula (9) from N to K, and the result is:

[0040]

[0041]

[0042]

[0043] Where: μ i,k ,Σ i,k ,ω i,k are the mean vector, covariance matrix, and weight coefficient of the kth Gaussian component respectively;

[0044] According to equations (10)-(12), the probability prediction model of random voltage is obtained:

[0045]

[0046]

[0047]

[0048]

[0049] Where: is the random voltage prediction error e i About its point prediction value The conditional probability distribution of ; They are The mean vector, covariance matrix, and weight coefficient of the kth Gaussian component of ; the conditional probability distribution is still a Gaussian mixture model containing K Gaussian components, and the point prediction value of a given random voltage is When , the random voltage prediction error e is obtained by equations (13)-(16): i The probability distribution of .

[0050] As a further embodiment of the present invention:

[0051] The method for establishing the chance-constrained distribution network voltage-reactive power optimization model in step (4) is specifically as follows:

[0052] The original model of reactive power optimization of chance-constrained distribution network is constructed as follows:

[0053]

[0054] st

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Where: It is the set of other nodes in the distribution network excluding the root node; is the set of dispatchable reactive resources, Pr{·} is the probability operator; τ is the confidence level, 1-τ is the upper limit of the expected voltage over-limit risk; the decision variable is the dispatchable reactive output q j ; The objective function is to minimize the cost of reactive power dispatch, c j Qj The cost coefficient of for q j The absolute value of q; Formula (20)-(21) is j The dispatchable range; Equations (22)-(23) are the opportunity constraints of node voltage; Equation (24) represents the power flow constraints of the linear distribution network;

[0062] Transform the chance constraints (22)-(23) into:

[0063]

[0064]

[0065] Where: VaR τ (·) is the risk value operator with confidence level τ;

[0066] According to step (1) That is, the node voltage is decomposed into three parts: random voltage, controllable voltage, and fixed voltage. The constraints (25)-(26) are converted into:

[0067]

[0068]

[0069] Random Voltage Equal to its point forecast value and the prediction error e i The sum of , further transforms constraints (27)-(28) into:

[0070]

[0071]

[0072] According to the probability density function obtained in step (2) and Newton iteration method and

[0073] The iterative calculation formula is as follows:

[0074]

[0075] Where: is the cumulative distribution function of the conditional probability distribution of random voltage prediction error, given by The cumulative distribution function of each Gaussian component is obtained by weighted summation according to the weight coefficient of the corresponding Gaussian component. They are The initial value calculation formula for the w-th and w+1-th iterations is:

[0076]

[0077]

[0078] Where: Φ -1 (·) is the inverse cumulative distribution function of the standard normal distribution; E(·) is the expectation operator; Var(·) is the variance operator;

[0079] The iterative calculation formula is as follows:

[0080]

[0081] Where: They are The initial value calculation formula for the w-th and w+1-th iterations is:

[0082]

[0083] The original model of reactive power optimization of chance-constrained distribution network is converted into the following linear programming model:

[0084]

[0085] st

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] As a further solution of the present invention: the method for solving the opportunity-constrained distribution network reactive power optimization model established in step (4) is specifically as follows:

[0094] The linear programming solver is used to solve the models (36)-(44) and obtain the decision variables The optimization result is that the reactive power dispatch optimization scheme with minimum cost and able to meet the expected voltage over-limit risk level is obtained.

[0095] Compared with the prior art, the beneficial effects of the present invention are as follows: the scheme of the present invention breaks through the technical route of the existing chance-constrained distribution network reactive optimization relying on source and load power probability prediction, avoids the difficulty of accurately predicting the joint probability distribution containing many random sources and load powers, and obtains accurate risk assessment of random voltage through the proposed random voltage probability prediction method. Compared with the prior art scheme, the present invention realizes the precise and reliable control of the distribution network voltage over-limit risk by chance-constrained distribution network reactive optimization, and the time consumption for solving the optimization problem is slightly lower than that of the prior art scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 Flow chart of the reactive power optimization method for distribution network with chance constraints based on random voltage probability prediction. DETAILED DESCRIPTION

[0097] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0098] See also Figure 1 In an embodiment of the present invention, a method for optimizing reactive power of a distribution network with opportunity constraints based on random voltage probability prediction includes the following steps:

[0099] (1) Based on the linear distribution network power flow model, the node voltage is decomposed into three parts: random, controllable, and fixed. The random part is the effect of random source and load power on the node voltage, and the calculation model of random voltage is obtained;

[0100] (2) According to the calculation model of random voltage obtained in step (1), historical samples of point prediction values ​​and actual values ​​of source and load power are collected to construct historical samples of point prediction values ​​and actual values ​​of random voltage;

[0101] (3) constructing a probability prediction model for random voltage based on the point prediction value and actual value historical samples of the random voltage obtained in step (2);

[0102] (4) According to the probability prediction model of random voltage obtained in step (3), the probability prediction results of random voltage at each node are obtained and a chance-constrained distribution network reactive power optimization model is constructed, and the reactive power dispatching scheme is obtained by solving the optimization model.

[0103] Preferably, the method for obtaining the random voltage calculation model in step (1) is specifically as follows:

[0104] The calculation model of the power injected into the distribution network node is established, specifically:

[0105]

[0106] Where: P l , Q l are the injected active and reactive power of node l respectively; is a random power source set, g is its index number, χ g is the active variable of the g-th random power source; is a random load set, d is its index number, ζ d is the active variable of the dth random load; For fixed power supply assembly, For its index number, For the Active power variables of fixed power sources; is a fixed load set, For its index number, For the The active variable of a fixed load; q j is the reactive power that can be dispatched by the jth node; κ represents the tangent value of the power factor angle of each power source and load that does not participate in reactive power dispatch; η represents whether each power source and load is connected to the corresponding node l, 1 represents connected, otherwise 0;

[0107] Based on the linear distribution network power flow model, the calculation model of node voltage is established as follows:

[0108]

[0109] Where: i is the voltage of node i; 0 is the root node voltage; R i,l , X i,l The matrices 2FD are r F T 、2FD x F T The element in the i-th row and the l-th column in the graph, F is the inverse matrix of the reduced-order branch-node association matrix, D r , D x are the diagonal matrices of branch resistance and reactance respectively;

[0110] Substituting equation (1) into equation (2), the calculation model of node voltage is further converted into:

[0111]

[0112] Where: b is the sensitivity coefficient of each source and load power to the node voltage, which is given by R i,l , X i,l , η, κ are calculated according to formula (1)-(2);

[0113] According to formula (3), the node voltage is decomposed into three parts:

[0114]

[0115]

[0116]

[0117]

[0118] Where: is a random source, load power χ g , d The effect on voltage is defined as random voltage; is the dispatchable reactive power q j The effect on voltage is defined as controllable voltage; For fixed source and load power The effect on voltage is defined as fixed voltage; equations (5), (6), and (7) are the calculation models of random voltage, controllable voltage, and fixed voltage, respectively.

[0119] Preferably, the method for constructing historical samples of predicted values ​​and actual values ​​of random voltage points in the distribution network in step (2) is specifically as follows:

[0120] Collect N historical samples of the point prediction value and actual value of each random source and load power of the distribution network, and the kth sample of the predicted value and actual value of the active power of the gth random power source collected are: and X g,k , the kth samples of the predicted value and actual value of the dth random load active power collected are: and Z d,k ;

[0121] Based on the historical samples of the point prediction value and actual value of each random source and load power and the calculation model of the random voltage of the distribution network Constructing distribution network random voltage point prediction values and actual value The historical sample is:

[0122]

[0123] Where: V i,k They are The k-th sample of is calculated from the k-th historical samples of the point prediction value and actual value of each random source and load power.

[0124] Preferably, the method for establishing the distribution network random voltage probability prediction model in step (3) is specifically as follows:

[0125] According to the predicted value of random voltage point in distribution network and actual value The random voltage prediction error e is obtained by using historical samples i A sample of:

[0126] The random voltage prediction error e is established by kernel density estimation method. i With the predicted value The joint probability distribution of is:

[0127]

[0128] Where: u i For vector U i,k for u i The kth sample of H i,k For sample U i,k The bandwidth matrix at ; N(·) is the Gaussian kernel function;

[0129] Formula (9) is a Gaussian mixture model containing N Gaussian components. The density-preserving hierarchical expectation maximization algorithm is used to reduce the number of Gaussian components in Formula (9) from N to K, and the result is:

[0130]

[0131]

[0132]

[0133] Where: μ i,k ,Σ i,k ,ω i,k are the mean vector, covariance matrix, and weight coefficient of the kth Gaussian component respectively;

[0134] According to equations (10)-(12), the probability prediction model of random voltage is obtained:

[0135]

[0136]

[0137]

[0138]

[0139] Where: is the random voltage prediction error ei About its point prediction value The conditional probability distribution of ; They are The mean vector, covariance matrix, and weight coefficient of the kth Gaussian component of ; the conditional probability distribution is still a Gaussian mixture model containing K Gaussian components, and the point prediction value of a given random voltage is When , the random voltage prediction error e is obtained by equations (13)-(16): i The probability distribution of .

[0140] Preferably, the method for establishing the chance-constrained distribution network voltage-reactive power optimization model in step (4) is specifically as follows:

[0141] The original model of reactive power optimization of chance-constrained distribution network is constructed as follows:

[0142]

[0143] st

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] Where: It is the set of other nodes in the distribution network excluding the root node; is the set of dispatchable reactive resources, Pr{·} is the probability operator; τ is the confidence level, 1-τ is the upper limit of the expected voltage over-limit risk; the decision variable is the dispatchable reactive output q j ; The objective function is to minimize the cost of reactive power dispatch, c j Q j The cost coefficient of Q j The absolute value of q; Formula (20)-(21) is j The dispatchable range; Equations (22)-(23) are the opportunity constraints of node voltage; Equation (24) represents the power flow constraints of the linear distribution network;

[0151] Transform the chance constraints (22)-(23) into:

[0152]

[0153]

[0154] Where: VaR τ (·) is the risk value operator with confidence level τ;

[0155] According to step (1) That is, the node voltage is decomposed into three parts: random voltage, controllable voltage, and fixed voltage. The constraints (25)-(26) are converted into:

[0156]

[0157]

[0158] Random Voltage Equal to its point forecast value and the prediction error e i The sum of , further transforms constraints (27)-(28) into:

[0159]

[0160]

[0161] According to the probability density function obtained in step (2) and Newton iteration method and

[0162] The iterative calculation formula is as follows:

[0163]

[0164] Where: is the cumulative distribution function of the conditional probability distribution of random voltage prediction error, given by The cumulative distribution function of each Gaussian component is obtained by weighted summation according to the weight coefficient of the corresponding Gaussian component. They are The initial value calculation formula for the w-th and w+1-th iterations is:

[0165]

[0166]

[0167] Where: Φ -1 (·) is the inverse cumulative distribution function of the standard normal distribution; E(·) is the expectation operator; Var(·) is the variance operator;

[0168] The iterative calculation formula is as follows:

[0169]

[0170] Where: They are The initial value calculation formula for the w-th and w+1-th iterations is:

[0171]

[0172] The original model of reactive power optimization of chance-constrained distribution network is converted into the following linear programming model:

[0173]

[0174] st

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] Preferably, the method for solving the chance-constrained distribution network reactive power optimization model established in step (4) is specifically as follows:

[0183] The linear programming solver is used to solve the models (36)-(44) and obtain the decision variables The optimization result is that the reactive power dispatch optimization scheme with minimum cost and able to meet the expected voltage over-limit risk level is obtained.

[0184] Simulation Case Study

[0185] The scheme of the present invention is verified by using an IEEE 123 node system containing 9 distributed photovoltaic power sources and 85 loads. 4 years of hourly power data were collected in the real system, of which the first 70% were used as a training set to build a prediction model, and the latter 30% were used as a test set to test the accuracy of the reactive power optimization of the opportunity-constrained distribution network, and compared with the existing reactive power optimization results of the opportunity-constrained distribution network based on the probability prediction of source and load power. Since the existing technical methods based on the probability prediction of source and load power are affected by different probability prediction methods, the existing technical methods are implemented based on three probability prediction models of long short-term memory network (LSTM), temporal convolutional network (TCN), and Transformer network. The program of the method of the present invention was developed in Matlab R2020a, and the random voltage probability prediction model was established based on the results obtained by the source and load power point prediction method based on LSTM. The final optimization problem was solved by Gurobi on a laptop computer configured with Intel i7-10510U 1.8GHz CPU and 16GB memory.

[0186] 1 Comparison of voltage over-limit risk control accuracy

[0187] Table 1 shows the comparison of the maximum frequency of voltage exceeding the limit of each node in each hour period after implementing the reactive power optimization of the opportunistic constrained distribution network in different methods in the IEEE 123 node, where the upper and lower limits of voltage are 0.95 and 1.05 respectively, and the expected risk level is set to 5%, that is, the target of the maximum frequency exceeding the limit does not exceed 0.05. It can be seen from Table 1 that the scheme of the present invention can reliably ensure that the upper and lower limit frequencies are within the expected risk level range at the same time, while the existing technical scheme using different power probability prediction models can only ensure that the maximum frequency of voltage exceeding the upper limit is within the expected risk level range, while the lower limit frequency obviously exceeds the expected risk level.

[0188] Table 1 Comparison of the frequency of voltage exceeding the limit under different methods

[0189]

[0190]

[0191] 2. Comparison of time consumption for optimization solution

[0192] Table 2 shows the time consumption comparison of different methods for solving chance-constrained reactive power optimization. The time consumption of the solution of the present invention is slightly lower than that of the prior art solution. This is because the chance-constrained reactive power optimization problem model established by the solution of the present invention does not require the step of calculating voltage risk from power probability distribution, and the calculation process is simpler than that of the prior art solution.

[0193] Table 2 Comparison of solution time of different methods

[0194]

[0195] In summary, the solution of the present invention breaks through the existing technical route of relying on the probability prediction of source and load power for the reactive optimization of the distribution network with chance constraints, avoids the difficulty of accurately predicting the joint probability distribution of many random sources and load powers, and obtains accurate risk assessment of random voltage through the proposed random voltage probability prediction method. Compared with the existing technical solutions, the present invention realizes the precise and reliable control of the voltage over-limit risk of the distribution network by the reactive optimization of the distribution network with chance constraints, and the time consumption of solving the optimization problem is slightly lower than that of the existing technical solutions.

[0196] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0197] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. Chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction, characterized in that, it includes the following steps: (1) Based on the linear distribution network power flow model, decompose the node voltage into three parts: random, controllable, and fixed. The random part is the action of random source and load power on the node voltage, and obtain the calculation model of random voltage; (2) According to the calculation model of random voltage obtained in step (1), collect historical samples of predicted values and actual values of source and load power points, and construct historical samples of predicted values and actual values of random voltage; (3) According to the historical samples of predicted values and actual values of random voltage obtained in step (2), construct the probability prediction model of random voltage; (4) According to the probability prediction model of random voltage obtained in step (3), obtain the probability prediction results of random voltage at each node and construct the chance-constrained reactive power optimization model for the distribution network, and solve the optimization model to obtain the reactive power scheduling scheme; In step (1), the node voltage is decomposed into three parts: (4) (5) (6) (7) Wherein: is the random source and load power , The effect on voltage is defined as random voltage; is the adjustable reactive power The effect on voltage is defined as controllable voltage; is the fixed source and load power , The effect on voltage is defined as fixed voltage; Equations (5), (6), and (7) are the calculation models of random voltage, controllable voltage, and fixed voltage respectively; In step (3), the method for establishing the probability prediction model of random voltage in the distribution network is specifically: Probability prediction model of random voltage: (13) (14) (15) (16) Wherein: is the random voltage prediction error with respect to its point prediction value conditional probability distribution; , , are respectively the k -th mean vector, covariance matrix, and weight coefficient of the Gaussian component of K ; the conditional probability distribution is still a Gaussian mixture model containing Gaussian components. When the point prediction value of the random voltage is given, the probability distribution of the random voltage prediction error is obtained from equations (13)-(16).

2. The chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction according to claim 1, characterized in that, In step (1), the method for obtaining the random voltage calculation model is specifically: Establish the calculation model of node injection power in the distribution network: (1) In the formula: and are the active and reactive power injected into node respectively; Node is the set of stochastic power sources, is its index number, is the active power variation of the th stochastic power source; is the set of stochastic loads, is its index number, is the active power variation of the th stochastic load; is the set of fixed power sources, is its index number, is the active power variation of the th fixed power source; is the set of fixed loads, is its index number, is the active power variation of the th fixed load; is the reactive power that can be dispatched at the jth node; represents the tangent value of the power factor angle of each power source and load that does not participate in reactive power dispatch; represents whether each power source and load is connected to the corresponding node , taking 1 means connected, otherwise taking 0; Based on the linear distribution network power flow model, establish the calculation model of node voltage as: (2) Where: is the voltage of node ; is the voltage of the root node; , are the elements in the -th row and -th column of matrices and respectively, is the inverse matrix of the reduced incidence matrix, , are the diagonal matrices of branch resistance and reactance respectively; Substitute equation (1) into equation (2), and the calculation model of node voltage is converted to: (3) In the formula: is the sensitivity coefficient of each source and load power to the node voltage, which is calculated from , , , according to formulas (1)-(2).

3. The chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction according to claim 2, characterized in that, In step (3), the method for establishing the probability prediction model of random voltage in the distribution network is specifically: According to the predicted values of random voltage points in the distribution network and the actual values to obtain the samples of random voltage prediction errors : ; Establish the joint probability distribution of the random voltage prediction error and the predicted value using the kernel density estimation method: (9) where: is a vector ; is the k-th sample of, that is ; is the bandwidth matrix at the sample ; is the Gaussian kernel function Equation (9) is a Gaussian mixture model containing N Gaussian components. Use the density-preserving hierarchical expectation-maximization algorithm to reduce the number of Gaussian components in equation (9) from N to K, and obtain: (10) (11) (12) Wherein: , , are respectively the mean vector, covariance matrix, and weight coefficient of the k-th Gaussian component; At the point prediction value of the given random voltage the probability distribution of the random voltage prediction error is obtained from equations (13)-(16).

4. The chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction according to claim 3, characterized in that, In step (2), the method for constructing the historical samples of predicted values and actual values of random voltage in the distribution network is specifically: Collect the point prediction values and actual values of the random sources and loads in the distribution network N historical samples, and the th sample of the predicted and actual active power of the k th random power source are respectively: and , and the th sample of the predicted and actual active power of the k th random load are respectively: and ; According to the historical samples of the point prediction values and actual values of each random source and load power, and the calculation model of the random voltage of the distribution network , construct the historical samples of the point prediction value and the actual value of the random voltage of the distribution network as follows: (8) Wherein: and are respectively and the k th sample, calculated from the historical samples of the predicted values and actual values of the k th points of each random source and load power.

5. The chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction according to claim 4, characterized in that, In step (4), the method for establishing the chance-constrained reactive power optimization model for the distribution network is specifically: The original model of chance-constrained reactive power optimization for the distribution network is constructed as: (17) s.t. (18) (19) (20) (21) (22) (23) (24) In the formula: is the set of other nodes except the root node in the distribution network; is the set of schedulable reactive power resources, is the probability operator; is the confidence level, is the upper limit of the expected voltage violation risk; The decision variable is the dispatchable reactive power output ; The objective function is to minimize the cost of reactive power dispatch, which is the cost coefficient; Equations (18)-(19) represent which is the absolute value of; Equations (20)-(21) are the adjustable range of; Equations (22)-(23) are the chance constraints of node voltage; Equation (24) represents the power flow constraint of the linear distribution network; Convert the chance constraints (22)-(23) to: (25) (26) Wherein: is the value-at-risk operator with a confidence level of ; According to the in step (1), that is, the node voltage is decomposed into three parts: random voltage, controllable voltage, and fixed voltage, convert the constraints (25)-(26) into: (27) (28) Random voltage equals its point prediction value and the prediction error The sum of which further transforms constraints (27)-(28) into: (29) (30) The probability density function obtained according to step (2) and calculated by the Newton iteration method and ; The iterative calculation formula is as follows: (31) where: is the cumulative distribution function of the conditional probability distribution of the random voltage prediction error, which is obtained by weighted summation of the cumulative distribution functions of the respective Gaussian components according to the weight coefficients of the corresponding Gaussian components, , are respectively at the w , w values of the +1-th iteration, and the initial value calculation formula is: (32) (33) Wherein: is the inverse cumulative distribution function of the standard normal distribution; is the expectation operator; is the variance operator; The iterative calculation formula is as follows: (34) Where: , are respectively at the w , w values of the +1-th iteration, and their initial value calculation formula is: (35) The original model of chance-constrained reactive power optimization for the distribution network is converted into the following linear programming model: (36) s.t. (37) (38) (39) (40) (41) (42) (43) (44)。 6. The chance-constrained reactive power optimization method for distribution network based on random voltage probability prediction according to claim 5, characterized in that, The method for solving the chance-constrained reactive power optimization model established in step (4) is specifically: Solve the model (36)-(44) using a linear programming solver to obtain the optimization results of each decision variable That is, a reactive power dispatch optimization plan that minimizes costs and meets the expected voltage violation risk level is obtained.

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