Reactive power optimization method and computer medium based on distributed interval optimization for power system

Abstract

The present invention discloses a method for reactive power optimization of a power system based on distributed interval optimization, comprising the following steps: S1, constructing a first model; the first model comprises an interval reactive power optimization model of a power system with high renewable energy penetration rate; the interval reactive power optimization model comprises an objective function, a first constraint and an interval power flow equation constraint; S2, obtaining a first state variable interval according to the interval power flow equation constraint combined with a distributed interval power flow algorithm; S3, transforming the first model according to the first state variable interval combined with a safety limit definition method to obtain a second model; the second model comprises a deterministic optimization model; S4, obtaining a reactive voltage control strategy according to the second model combined with an original dual interior point method. The present invention can improve the accuracy, practicality and economy of the reactive power optimization method of a power system with high renewable energy penetration rate.

Description

Technical Field

[0001] The present invention relates to the field of power system optimization, and in particular to a power system reactive power optimization method based on distributed interval optimization and a computer medium. Background Art

[0002] Reactive power optimization of power systems plays a vital role in ensuring grid security, improving voltage quality and reducing power loss. In recent years, the large-scale grid connection of renewable energy such as wind power and photovoltaics, the volatility and intermittency of renewable energy have brought strong uncertainty to the power system. At the same time, the frequent power trading and the diversification of power loads have further increased the uncertainty of the power system. The increase in uncertainty in the power system has made the reactive power optimization problem of the power system more complex and uncertain.

[0003] Most traditional reactive power optimization methods are based on deterministic optimization models, assuming that system parameters are known and determined, which is difficult to apply to the power system in the current context. Therefore, more and more scholars have introduced uncertainty optimization methods into reactive power optimization of power systems, forming three main types of uncertain reactive power optimization methods: stochastic programming, robust optimization, and interval optimization. In the stochastic programming method, the uncertainty parameters are regarded as random variables that follow a specific distribution, so that the reactive power optimization model is transformed into an expectation model or a chance-constrained programming model. In this way, a reactive voltage control scheme that meets the constraints and optimization objectives at a certain confidence level can be obtained. However, the stochastic programming method requires the probability distribution information of uncertain data, and needs to generate a large number of scenarios through historical data statistics or empirical models. The modeling process is rough and the computational efficiency is low. At the same time, it cannot guarantee the safety of the grid voltage under uncertain environments. The robust optimization method does not require the assumption of the probability distribution of uncertain data, but seeks an optimization solution that can meet the constraints in all scenarios based on a given uncertainty set. Although the solution provided by robust optimization is usually more conservative and can cope with various uncertainties in the uncertainty set, it solves the complexity of the stochastic programming method in modeling and computing time, and improves the practical feasibility of the solution, but it is relatively weak in terms of economy. In addition, since reactive power optimization is a non-convex problem, the robust optimization method can only be used for convex optimization, which requires approximate processing and may introduce certain approximation errors.

[0004] In the interval optimization method, the uncertainty data is represented as an interval to establish an optimization model. In the interval optimization model, the state variables are represented as intervals, and the control variables are real numbers. The control variables that make the state variables meet the constraints and the objective function optimal are sought. The interval optimization method is simple to model, does not require approximate convexity processing, and the acquisition strategy can theoretically guarantee the safety of the system. Existing interval optimization methods include: intelligent algorithm solution methods, such as using genetic algorithms and particle swarm algorithms to find the best control variables; approximate optimization methods, such as interval reactive power optimization through interval Taylor expansion, constructing linear or quadratic programming interval reactive power optimization models, and reducing the difficulty of solving; other conversion methods, such as using the safety limit definition method to convert the interval model into a deterministic model for solution. When processing the state variables in the model, the existing interval optimization methods all use the interval power flow algorithm to solve the interval power flow equation to obtain the state variable interval. It can be seen that the solution of the interval power flow equation occupies a vital position in the processing of reactive power optimization models. However, the interval power flow solutions obtained by the existing interval power flow algorithms are all conservative. Since they take into account extreme scenarios with extremely low probability of occurrence, they deviate from the actual range and have little engineering significance. At the same time, the interval reactive power optimization strategy obtained in this case is also less economical.

[0005] Therefore, a new technical solution is urgently needed to solve the technical problem of how to improve the accuracy, practicality and economy of reactive power optimization methods in power systems with high renewable energy penetration rates. Summary of the invention

[0006] The present invention provides a reactive power optimization method for a power system based on distributed interval optimization and a computer medium, which are used to solve the technical problem of how to improve the accuracy, practicality and economy of the reactive power optimization method for a power system with high new energy penetration rate.

[0007] To achieve the above object, the present invention provides a method for optimizing reactive power of a power system based on distributed interval optimization, comprising the following steps:

[0008] S1. Construct a first model; the first model includes an interval reactive power optimization model of a power system with high renewable energy penetration rate; the interval reactive power optimization model includes an objective function, a first constraint and an interval power flow equation constraint.

[0009] S2. Obtain the first state variable interval according to the interval power flow equation constraint combined with the distributed interval power flow algorithm.

[0010] S3. According to the first state variable interval and the safety limit definition method, the first model is transformed to obtain a second model; the second model includes a deterministic optimization model.

[0011] S4. According to the second model and the original dual interior point method, the reactive voltage control strategy is obtained.

[0012] Preferably, the objective function includes:

[0013] The objective function is the system network loss, including:

[0014] ;

[0015] in, Represents the set of all nodes in the system; and Respectively represent nodes and nodes ; and Respectively represent nodes and nodes The voltage amplitude of is the real part of the system node admittance matrix; , and Respectively represent nodes and nodes The voltage phase angle.

[0016] Preferably, the interval power flow equation constraints include:

[0017] ;

[0018] in, Represents the imaginary part of the system node admittance matrix; Represents the active output range of renewable energy units ; and They represent the lower and upper boundaries of the active output range of renewable energy units respectively; represents the generator nodes excluding the balancing nodes; Indicates a balancing node. Generally, a system includes one balancing node. hour, It represents the active load of the generator node excluding the balancing node; hour, Indicates the active load of the balancing node; Indicates the active output of the balancing unit; hour, and They represent the reactive output and reactive load of the generator nodes excluding the balancing node respectively; hour, and Respectively represent the reactive output and reactive load of the balancing node; the active load and reactive load of the balancing node and the generator node are deterministic data; and Represents the load nodes Active load range and reactive load range ; and They represent the lower and upper boundaries of the active load interval of the load node respectively; and They represent the lower and upper boundaries of the reactive load interval of the load node respectively; represents a load node; Representation Node Reactive power compensation capacity.

[0019] Preferably, the first constraint includes:

[0020] ;

[0021] in, and Respectively represent the lower and upper limits of the node voltage amplitude; and They represent the lower and upper limits of the active output of the balancing unit respectively; hour, and They represent the lower and upper limits of reactive power output of the generator nodes excluding the balancing nodes respectively; hour, and They represent the lower and upper limits of reactive power output of the balancing node respectively; Indicates the transformer ratio; and Respectively represent the lower and upper limits of the transformer ratio; Indicates transformer branch; and Respectively represent the lower limit and upper limit of reactive power compensation capacity; Indicates reactive power compensation node.

[0022] Preferably, S2 comprises:

[0023] The interval power flow equation constraints are processed by the distributed interval power flow algorithm:

[0024] Assume that the total number of nodes in the system is , the total number of generator nodes excluding the balancing nodes is ; The state variables in the interval power flow equation constraints and Represented in affine form; state variables and The first affine expression consists of:

[0025] ;

[0026] ;

[0027] ;

[0028] in, and Respectively and The midpoint of the interval can be obtained by solving the power flow equation at the midpoint of the system injection power interval; and is an affine noise element, and its value range is ; and is the sensitivity coefficient.

[0029] A third model is established according to the first affine expression. The third model includes a scenario optimization model constrained by an interval power flow equation, including:

[0030] ;

[0031] The interior point method is used to solve the third model and obtain the maximum value of the affine noise element and minimum value , and then obtain the high-precision affine expression of the state variable, that is, the state variable and The second affine expression is:

[0032] ;

[0033] ;

[0034] ;

[0035] For affine expressions on intervals, the noise metavariable and If it obeys uniform distribution in the interval, then the second affine expression can be regarded as the superposition of a series of uniform distributions, and each term in each expression is independent of each other, that is, it satisfies the central limit theorem. and The value of approximately obeys the normal distribution; according to the properties of uniform distribution, the variance of each term in the second affine expression is obtained, including:

[0036] ;

[0037] ;

[0038] ;

[0039] in, Indicates from or Choose one of them.

[0040] Get the state variable based on the variance and The standard deviation of

[0041] ;

[0042] ;

[0043] ;

[0044] because and The value of approximately obeys the normal distribution. According to the properties of the normal distribution, the confidence interval of the state variable with a confidence level of 0.9973 is obtained:

[0045] ;

[0046] ;

[0047] ;

[0048] That is, the first state variable interval is obtained.

[0049] Preferably, it also includes:

[0050] Solve for sensitivity coefficients, including:

[0051] ;

[0052] in, and represents the partial derivative of each variable at 0, which can be obtained at the power flow solution at the midpoint of the injected power interval; and denote the active and reactive power injection interval radii respectively, , and They represent the upper and lower limits of the active output range of the generator node respectively; , and They represent the upper and lower limits of the active load demand range of the load node respectively; , and They represent the upper and lower limits of the reactive load demand of the load node respectively.

[0053] Preferably, S3 includes:

[0054] Since the inequality constraints in the first model are all single variable constraints, the variables, objective functions and constraints in the first model are represented by vectors and functions, and the first model can be represented as a compact model:

[0055] ;

[0056] in, Indicates system network loss; The interval form of network loss; represents the interval power flow equation constraint; represents the node injection power interval vector; represents the first state variable interval; represents the control variable; Represents the vector composed of load node voltage and generator reactive output, and Respectively The minimum and maximum values ​​of and Represent the control variable vectors The minimum and maximum values ​​of Indicates the transpose; the voltage phase angle of nodes other than the balance node and the active output of the balance node are expressed as vectors , then the system state variable vector can be expressed as .

[0057] In the compact model, for any control variable , solve the interval power flow equation by using the distributed interval power flow algorithm , get the corresponding ;because is bounded, then there exists a control variable vector Make one of the The interval radius is the largest, denoted by , and each There is one Corresponding; therefore, the definition Maximum radius :

[0058] ;

[0059] in, Represents state variables The radius of the interval.

[0060] Through Monte Carlo simulation, we get The vector consisting of the maximum values ​​of the radius of all variable intervals in ; For the same control variable , is the interval power flow equation The solution, is the deterministic power flow equation The solution is to consider that the deterministic state variable may be anywhere within the maximum state variable interval in the Monte Carlo simulation, and the deterministic state variable The corresponding maximum radius of the state variable interval is , then there is a constraint ,ensure The constraints in the compact model are satisfied; therefore, an absolute safety limit is defined, including:

[0061] ;

[0062] ;

[0063] The absolute safety limit represents the safety margin under the worst scenario, which is highly conservative and introduces the average position ratio. The safety limits are modified to make them less conservative:

[0064] ;

[0065] in, Represents the control variable exist , scene exist Determine the state variables at ; and Respectively expressed in Solve the interval power flow equation The lower and upper bounds of the state variable interval are obtained; assuming The corresponding average position ratio is , , then the modified safety limit can be expressed by the following relationship:

[0066] ;

[0067] ;

[0068] Average position ratio It is defined at the midpoint of the control variable, and in general, the control variable can take any value within its interval, resulting in Deviation , so there is a safety error in the corrected safety limit, and the state variable may exceed the limit; take the state variable The limit is exceeded , the lower limit is , to accurately correct the state variables, including:

[0069] ;

[0070] ;

[0071] If the state variable is still in the over-limit state after precise correction, the precise correction is repeated until the state variable does not exceed the limit and the final safety limit is obtained. According to the final safety limit, the compact model is transformed into the second model, which can be expressed by the following relationship:

[0072] ;

[0073] in, express Any scene within.

[0074] Preferably, S4 includes:

[0075] Solve the second model using the primal-dual interior point method:

[0076] For the second model, we first introduce the Lagrange multiplier And the dual variable and Constructing Lagrangian functions , which can be expressed by the following relationship: ;

[0077] The KKT conditions of the Lagrangian function are established. The KKT conditions include gradient conditions, original feasibility conditions, dual feasibility conditions and complementary relaxation conditions, which can be expressed by the following relationship:

[0078] ;

[0079] Solve the KKT conditions by Newton gradient descent, including:

[0080] Select the starting point , ensuring that the inequality constraints are satisfied; in the In the iteration, based on the current The Newton gradient descent equation is obtained, which can be expressed by the following relationship:

[0081] ;

[0082] in, is the Hessier matrix of the Lagrangian function, is the Newton step, including and ; represents the current gradient; let As the step length, the Newton step variable update scheme is obtained, which can be expressed by the following relationship:

[0083] ;

[0084] in, Indicates A vector of variables for the iterations, containing ; Indicates The variable vector for the iterations, containing .

[0085] Determine whether the convergence condition is met. If so, Newton gradient descent is determined to have converged, the iteration is stopped, and the solution of the second model is output. , that is, the reactive voltage control strategy is obtained; the convergence conditions include the dual gap is smaller than the convergence tolerance, and the primal feasibility condition, the dual feasibility condition, and the complementary slackness condition are all satisfied.

[0086] Preferably, it also includes:

[0087] According to the reactive power and voltage control strategy, the distribution interval power flow is calculated to obtain the control variable value. and the corresponding second state variable interval ,include:

[0088] Reactive voltage control strategy is the solution result The control variables in Including final transformer ratio , Generator terminal voltage and reactive power compensation capacity ; According to the control variables get The distribution interval power flow model under can be expressed by the following relationship:

[0089] ;

[0090] in, and are the final transformer ratios Real and imaginary parts of the lower node admittance matrix.

[0091] according to The distributed interval power flow model under the condition of The corresponding interval of the second state variable of the system , Including load node voltage range , node voltage phase angle interval and generator reactive output range Output and , that is, the control variable value and the corresponding second state variable interval are obtained.

[0092] The present invention also provides a computer medium, comprising a processor, a memory and a computer program for implementing the method of the present invention.

[0093] The present invention has the following beneficial effects:

[0094] The reactive power optimization method of the power system based on distributed interval optimization of the present invention has a state variable interval obtained by processing the interval power flow equation constraints through the distributed interval power flow algorithm with high confidence, so that the method can reduce the conservatism of the interval algorithm and be closer to the actual range, thereby improving the solution accuracy, while reducing the system network loss and improving the economy and practicality of the voltage control strategy; the interval reactive power optimization model is converted into a deterministic optimization model through the safety limit definition method, and the deterministic optimization model is solved through the primal-dual interior point method, so that the method of the present invention solves the convergence problem of the nonlinear interval optimization algorithm and can obtain a safer and more economical interval voltage control strategy.

[0095] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0097] Figure 1 It is a flow chart of a preferred embodiment of the present invention.

[0098] Figure 2 It is a schematic diagram of optimizing the distribution interval and reducing conservatism in a preferred embodiment of the present invention.

[0099] Figure 3 It is a schematic diagram of the safety limit definition of the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0100] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0101] See also Figure 1 In a preferred embodiment of the present invention, a method for optimizing reactive power of a power system based on distributed interval optimization is provided, comprising the following steps:

[0102] S1. Construct a first model; the first model includes an interval reactive power optimization model of a power system with high renewable energy penetration rate; the interval reactive power optimization model includes an objective function, a first constraint and an interval power flow equation constraint.

[0103] In a preferred embodiment of the present invention, the objective function includes:

[0104] The objective function is the system network loss, including:

[0105] ;

[0106] in, Represents the set of all nodes in the system; and Respectively represent nodes and nodes ; and Respectively represent nodes and nodes The voltage amplitude of is the real part of the system node admittance matrix; , and Respectively represent nodes and nodes The voltage phase angle.

[0107] In a preferred embodiment of the present invention, the interval power flow equation constraints include:

[0108] ;

[0109] in, Represents the imaginary part of the system node admittance matrix; Represents the active output range of renewable energy units ; and They represent the lower and upper boundaries of the active output range of renewable energy units respectively; represents the generator nodes excluding the balancing nodes; Indicates a balancing node. Generally, a system includes one balancing node. hour, It represents the active load of the generator node excluding the balancing node; hour, Indicates the active load of the balancing node; Indicates the active output of the balancing unit; hour, and They represent the reactive output and reactive load of the generator nodes excluding the balancing node respectively; hour, and They represent the reactive output and reactive load of the balancing node respectively. Since the load of a power plant is generally stable, the active load and reactive load of the balancing node and generator node are deterministic data. and Represents the load nodes Active load range and reactive load range ; and They represent the lower and upper boundaries of the active load interval of the load node respectively; and They represent the lower and upper boundaries of the reactive load interval of the load node respectively; represents a load node; Representation Node Reactive power compensation capacity.

[0110] In a preferred embodiment of the present invention, the first constraint includes:

[0111] ;

[0112] in, and Respectively represent the lower and upper limits of the node voltage amplitude; and They represent the lower and upper limits of the active output of the balancing unit respectively; hour, and They represent the lower and upper limits of reactive power output of the generator nodes excluding the balancing nodes respectively; hour, and They represent the lower and upper limits of reactive power output of the balancing node respectively; Indicates the transformer ratio; and Respectively represent the lower and upper limits of the transformer ratio; Indicates transformer branch; and Respectively represent the lower limit and upper limit of reactive power compensation capacity; Indicates reactive power compensation node.

[0113] S2. Obtain the first state variable interval according to the interval power flow equation constraint combined with the distributed interval power flow algorithm. S2 specifically includes:

[0114] The interval power flow equation constraints are processed by the distributed interval power flow algorithm:

[0115] Assume that the total number of nodes in the system is , the total number of generator nodes excluding the balancing nodes is ; The state variables in the interval power flow equation constraints and Represented in affine form; state variables and The first affine expression consists of:

[0116] ;

[0117] ;

[0118] ;

[0119] in, and Respectively and The midpoint of the interval can be obtained by solving the power flow equation at the midpoint of the system injection power interval; and is an affine noise element, and its value range is ; and is the sensitivity coefficient;

[0120] In a preferred embodiment of the present invention, solving the sensitivity coefficient includes:

[0121] ;

[0122] in, and represents the partial derivative of each variable at 0, which can be obtained at the power flow solution at the midpoint of the injected power interval; and denote the active and reactive power injection interval radii respectively, , and They represent the upper and lower limits of the active output range of the generator node respectively; , and They represent the upper and lower limits of the active load demand range of the load node respectively; , and They represent the upper and lower limits of the reactive load demand of the load node respectively.

[0123] A third model is established according to the first affine expression. The third model includes a scenario optimization model constrained by an interval power flow equation, including:

[0124] ;

[0125] The interior point method is used to solve the third model and obtain the maximum value of the affine noise element and minimum value , and then obtain the high-precision affine expression of the state variable, that is, the state variable and The second affine expression is:

[0126] ;

[0127] ;

[0128] ;

[0129] For affine expressions on intervals, the noise metavariable and If it obeys uniform distribution in the interval, the second affine expression can be regarded as the superposition of a series of uniform distributions, and each term in each expression is independent of each other, that is, it satisfies Lyapunov's central limit theorem. and The value of approximately obeys the normal distribution; according to the properties of uniform distribution, the variance of each term in the second affine expression is obtained, including:

[0130] ;

[0131] ;

[0132] ;

[0133] in, Indicates from or Choose one of the following;

[0134] Get the state variable based on the variance and The standard deviation of

[0135] ;

[0136] ;

[0137] ;

[0138] because and The value of approximately obeys the normal distribution. According to the properties of the normal distribution, the confidence interval of the state variable with a confidence level of 0.9973 is obtained:

[0139] ;

[0140] ;

[0141] ;

[0142] That is, the first state variable interval is obtained.

[0143] In a preferred embodiment of the present invention, the distribution interval theory is used to process the interval power flow equation constraints, and a high-confidence state variable interval result is obtained through the central limit theorem. That is, the first state variable interval calculated by the distribution interval power flow algorithm has a high confidence level, which can reduce the conservatism of the interval algorithm and is beneficial to improving the accuracy of the method of the present invention.

[0144] S3. According to the first state variable interval and the safety limit definition method, the first model is transformed to obtain a second model; the second model includes a deterministic optimization model. S3 specifically includes:

[0145] Since the inequality constraints in the first model are all single variable constraints, the variables, objective functions and constraints in the first model are represented by vectors and functions, and the first model can be represented as a compact model:

[0146] ;

[0147] in, Indicates system network loss; The interval form of network loss; represents the interval power flow equation constraint; represents the node injection power interval vector; represents the first state variable interval; represents the control variable; Represents the vector composed of load node voltage and generator reactive output, and Respectively The minimum and maximum values ​​of and Represent the control variable vectors The minimum and maximum values ​​of Indicates the transpose; the voltage phase angle of nodes other than the balance node and the active output of the balance node are expressed as vectors , then the system state variable vector can be expressed as ;

[0148] In the compact model, for any control variable , solve the interval power flow equation by using the distributed interval power flow algorithm , get the corresponding , the state variable is a high confidence distribution interval result; due to is bounded, then there exists a control variable vector Make one of the The interval radius is the largest, denoted by , and each There is one Corresponding; therefore, the definition Maximum radius :

[0149] ;

[0150] in, Represents state variables The radius of the interval;

[0151] Through Monte Carlo simulation, we get The vector consisting of the maximum values ​​of the radius of all variable intervals in ; For the same control variable , is the interval power flow equation The solution, is the deterministic power flow equation The solution is to consider that the deterministic state variable may be anywhere within the maximum state variable interval in the Monte Carlo simulation, and the deterministic state variable The corresponding maximum radius of the state variable interval is , then there is a constraint ,ensure The constraints in the compact model are satisfied; therefore, an absolute safety limit is defined, including:

[0152] ;

[0153] ;

[0154] The absolute safety limit represents the safety margin under the worst scenario, which is highly conservative and introduces the average position ratio. The safety limits are modified to make them less conservative:

[0155] ;

[0156] in, Represents the control variable exist , scene exist Determine the state variables at ; and Respectively expressed in Solve the interval power flow equation The lower and upper bounds of the state variable interval are obtained; assuming The corresponding average position ratio is , , then the modified safety limit can be expressed by the following relationship:

[0157] ;

[0158] ;

[0159] Average position ratio It is defined at the midpoint of the control variable, and in general, the control variable can take any value within its interval, resulting in Deviation , so there is a safety error in the corrected safety limit, and the state variable may exceed the limit; take the state variable The limit is exceeded , the lower limit is , to accurately correct the state variables, including:

[0160] ;

[0161] ;

[0162] If the state variable is still in the over-limit state after precise correction, the precise correction is repeated until the state variable does not exceed the limit and the final safety limit is obtained. According to the final safety limit, the compact model is transformed into the second model, which can be expressed by the following relationship:

[0163] ;

[0164] in, express Any scene within.

[0165] S4. According to the second model combined with the original dual interior point method, a reactive voltage control strategy is obtained. S4 specifically includes:

[0166] The transformed deterministic optimization model, i.e., the second model, is a nonlinear model and can be solved by the primal-dual interior point method. Solving the second model by the primal-dual interior point method includes:

[0167] For the second model, we first introduce the Lagrange multiplier And the dual variable and Constructing Lagrangian functions , which can be expressed by the following relationship:

[0168] ;

[0169] The KKT conditions of the Lagrangian function are established. The KKT conditions include gradient conditions, original feasibility conditions, dual feasibility conditions and complementary relaxation conditions, which can be expressed by the following relationship:

[0170] ;

[0171] Solve the KKT conditions by Newton gradient descent, including:

[0172] Select the starting point , ensuring that the inequality constraints are satisfied; in the In the iteration, based on the current The Newton gradient descent equation is obtained, which can be expressed by the following relationship:

[0173] ;

[0174] in, is the Hessier matrix of the Lagrangian function, is the Newton step, including and ; represents the current gradient; let As the step length, the Newton step variable update scheme is obtained, which can be expressed by the following relationship:

[0175] ;

[0176] in, Indicates A vector of variables for the iterations, containing ; Indicates The variable vector for the iterations, containing ;

[0177] Determine whether the convergence condition is met. If so, Newton gradient descent is determined to have converged, the iteration is stopped, and the solution of the second model is output. , that is, the reactive voltage control strategy is obtained; the convergence conditions include the dual gap Less than the convergence tolerance, and the primal feasibility condition, dual feasibility condition and complementary relaxation condition are all satisfied. The convergence tolerance is generally a very small value close to 0.

[0178] In a preferred embodiment of the present invention, for the overall interval reactive power optimization model, the interval model is converted into a deterministic model by adopting the safety limit definition, and the solution is solved by establishing the KKT condition, thereby solving the convergence problem of the nonlinear interval optimization algorithm and obtaining a safer and more economical interval voltage control strategy.

[0179] In a preferred embodiment of the present invention, after the reactive voltage control strategy is obtained, the method further includes:

[0180] According to the reactive power and voltage control strategy, the distribution interval power flow is calculated to obtain the control variable value. and the corresponding second state variable interval ,include:

[0181] Reactive voltage control strategy is the solution result The control variables in Including final transformer ratio , Generator terminal voltage and reactive power compensation capacity , that is, the optimal reactive power control strategy corresponding to the first model; according to the control variable get The distribution interval power flow model under can be expressed by the following relationship:

[0182] ;

[0183] in, and are the final transformer ratios The real and imaginary parts of the lower node admittance matrix;

[0184] according to The distributed interval power flow model under the condition of The corresponding interval of the second state variable of the system , Including load node voltage range , node voltage phase angle interval and generator reactive output range Output and , that is, the control variable value and the corresponding second state variable interval are obtained.

[0185] In a preferred embodiment of the present invention, the second state variable interval is calculated by the reactive voltage control strategy, so that the method of the present invention can more intuitively show the lower conservatism of the state variable interval, thereby further verifying the ability of the present invention in improving the accuracy of model solution.

[0186] In a preferred embodiment of the present invention, a computer medium is also provided, including a processor, a memory, and a computer program for implementing the method of the present invention.

[0187] In order to evaluate the effectiveness and superiority of the power system reactive power optimization method based on distributed interval optimization of the present invention, the following three examples are used for verification.

[0188] (1) The distributed interval power flow algorithm is compared with the interval power flow algorithm based on the optimization scenario method, and the IEEE30-node test system is used to verify the ability of distributed interval optimization to reduce conservatism. The IEEE30-node example used includes 6 generators, 37 transmission lines, 4 transformers and 2 reactive compensation capacitors. All parameters are in per-unit values, and the reference power is 100MVA. The generators in the system (except the balancing machine) are all new energy generators with fluctuating output. The range of the generator active output range and related variables is set in Table 1. The ratio range of all transformers is 0.9~1.1pu, and the step size is 0.05. The parameter setting of the reactive compensation capacitor is set in Table 2. The load node voltage range is 0.95~1.05pu. It is assumed that the load fluctuates within the range of ±20% on the initial load. In this example, refer to Figure 2 The interval range of the power flow state variables obtained by the distributed interval optimization algorithm is narrower than that obtained by the optimization scenario method, and is closer to the interval range of the state variables obtained by the actual Monte Carlo simulation. The results obtained by the distributed interval power flow algorithm are better. Figure 2 middle, Represents the nodes obtained through Monte Carlo simulation Voltage and nodes Voltage The range of all possible values, Represents the nodes obtained by the distribution interval power flow calculation Voltage range and nodes Voltage range The scope of composition, Represents the nodes obtained by optimizing the scenario method power flow calculation Voltage range and nodes Voltage range The scope of composition.

[0189] ;

[0190] ;

[0191] (2) The reactive power optimization method of the power system based on distributed interval optimization of the present invention is compared with the interval reactive power optimization algorithm based on intelligent algorithm (particle swarm algorithm). In the intelligent algorithm, the optimization scenario method is used to process the interval power flow equation constraints, and the superiority of the reactive power optimization method of the power system based on distributed interval optimization in terms of convergence and optimization is verified. The example used is the same as the IEEE30 node example used in (1). In addition, the parameters of the interior point method in the example are set as: convergence accuracy , center parameter When solving the maximum radius of the state variable interval, the number of Monte Carlo sampling is set to 100 to ensure the solution efficiency. After verification and comparison, the power system reactive power optimization method based on the distribution interval has a faster calculation speed, avoids local convergence, and obtains a more economical voltage control strategy. The power system reactive power optimization method based on the distribution interval optimization has a better optimization effect.

[0192] (3) The reactive power optimization method of the power system based on distributed interval optimization of the present invention is compared with the interval reactive power optimization method based on safety limit definition, wherein the reactive power optimization method of the power system based on distributed interval optimization of the present invention includes distributed interval power flow analysis and safety limit definition, while the interval reactive power optimization method based on safety limit definition uses the optimization scenario method to process the interval power flow equation constraint, wherein the safety limit definition is referred to in Figure 3 . The IEEE118 node system is used to verify the superiority and economy of the method of the present invention, and to verify the application ability of the method of the present invention in large node systems and under different output fluctuation conditions. The IEEE118 node example used includes 54 generators, 64 load nodes, 169 transmission lines, 9 transformers and 9 reactive compensation capacitors. All parameters are in per-unit value, and the reference power is 100MVA. The generators in the system (except the balancing machine) are all new energy generators with fluctuating output. The transformer ratio range is 0.9~1.1pu, the adjustment step is 0.05, and the reactive compensation capacitor parameter settings are shown in Table 3. The generator node voltage range is 0.9~1.1pu, and the load node voltage range is 0.95~1.05pu. It is assumed that the generator active output and load fluctuate by ±10% and ±20% on the initial output and load, respectively. The interior point method parameter settings are the same as those in (2). After verification and comparison, the reactive power optimization method of the power system based on distributed interval optimization can obtain a more economical voltage control strategy, reduce the conservatism of the interval reactive power optimization method based on safety limit definition, and make the system network loss smaller. The reactive power optimization method of the power system based on distributed interval optimization is more economical.

[0193] ;

[0194] In summary, the reactive power optimization method of the power system based on distributed interval optimization of the present invention has a high confidence level in the state variable interval obtained by processing the interval power flow equation constraints through the distributed interval power flow algorithm, so that the method can reduce the conservatism of the interval algorithm and be closer to the actual range, thereby improving the solution accuracy, while reducing the system network loss and improving the economy and practicality of the voltage control strategy; the interval reactive power optimization model is converted into a deterministic optimization model through the safety limit definition method, and the deterministic optimization model is solved through the primal-dual interior point method, so that the method of the present invention solves the convergence problem of the nonlinear interval optimization algorithm and can obtain a safer and more economical interval voltage control strategy.

[0195] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for reactive power optimization of a power system based on distributed interval optimization, characterized in that: The following steps are involved: S1. Construct a first model; the first model includes an interval reactive power optimization model of a power system with high renewable energy penetration rate; the interval reactive power optimization model includes an objective function, a first constraint and an interval power flow equation constraint; The objective function includes the system network loss: ； in, Represents the set of all nodes in the system; and Respectively represent nodes and nodes ; and Respectively represent nodes and nodes The voltage amplitude; is the real part of the system node admittance matrix; , and Respectively represent nodes and nodes The voltage phase angle; S2. Obtaining a first state variable interval according to the interval power flow equation constraint combined with a distributed interval power flow algorithm; The S2 includes: The interval power flow equation constraints are processed by the distributed interval power flow algorithm: Assume that the total number of nodes in the system is , the total number of generator nodes excluding the balancing nodes is ; The state variables in the interval power flow equation constraints , and Represented in affine form; state variables , and The first affine expression consists of: ； ； ； in, and Respectively and The midpoint of the interval is obtained by solving the power flow equation at the midpoint of the system injection power interval; and is an affine noise element, and its value range is ; and is the sensitivity coefficient; represents a load node; represents the generator nodes excluding the balancing nodes; A third model is established according to the first affine expression, wherein the third model includes a scenario optimization model constrained by an interval power flow equation, including: ； in, and They represent the lower and upper boundaries of the active output range of renewable energy units respectively; hour, It represents the active load of the generator node excluding the balancing node; and They represent the lower and upper boundaries of the active load interval of the load node respectively; and They represent the lower and upper boundaries of the reactive load interval of the load node respectively; Representation Node Reactive power compensation capacity; hour, and They represent the reactive output and reactive load of the generator nodes excluding the balancing nodes respectively; The third model is solved by the interior point method to obtain the maximum value of the affine noise element and minimum value , and then obtain the high-precision affine expression of the state variable, that is, the state variable and The second affine expression is: ； ； ； For affine expressions on intervals, the noise metavariable and In the interval, it obeys uniform distribution, then the second affine expression is regarded as the superposition of a series of uniform distributions, and each term in each expression is independent of each other, that is, it satisfies the central limit theorem. , and The value of approximately obeys the normal distribution; according to the properties of uniform distribution, the variance of each term in the second affine expression is obtained, including: ； ； ； in, Indicates from or Choose one of the following; The state variable is obtained according to the variance and The standard deviation of ； ； ； because and The value of approximately obeys the normal distribution. According to the properties of the normal distribution, the confidence interval of the state variable with a confidence level of 0.9973 is obtained: ； ； ； That is, the first state variable interval is obtained; S3, transforming the first model according to the first state variable interval combined with the safety limit definition method to obtain a second model; the second model includes a deterministic optimization model; S4. Obtain a reactive voltage control strategy based on the second model combined with the original dual interior point method.

2. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 1, characterized in that: The interval power flow equation constraints include: ； in, Represents the imaginary part of the system node admittance matrix; Represents the active output range of renewable energy units ; and They represent the lower and upper boundaries of the active output range of renewable energy units respectively; represents the generator nodes excluding the balancing nodes; Indicates a balancing node. The system includes one balancing node. hour, It represents the active load of the generator node excluding the balancing node; hour, Indicates the active load of the balancing node; Indicates the active output of the balancing unit; hour, and They represent the reactive output and reactive load of the generator nodes excluding the balancing nodes respectively; hour, and Respectively represent the reactive output and reactive load of the balancing node; the active load and reactive load of the balancing node and the generator node are deterministic data; and Represents the load nodes Active load range and reactive load range ; and They represent the lower and upper boundaries of the active load interval of the load node respectively; and They represent the lower and upper boundaries of the reactive load interval of the load node respectively; represents a load node; Representation Node Reactive power compensation capacity.

3. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 2, characterized in that: The first constraint includes: ； in, and Respectively represent the lower and upper limits of the node voltage amplitude; and They represent the lower and upper limits of the active output of the balancing unit respectively; hour, and They represent the lower and upper limits of reactive power output of the generator nodes excluding the balancing nodes; hour, and They represent the lower and upper limits of reactive power output of the balancing node respectively; Indicates the transformer ratio; and Respectively represent the lower and upper limits of the transformer ratio; Indicates transformer branch; and Respectively represent the lower limit and upper limit of reactive power compensation capacity; Indicates reactive power compensation node.

4. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 3, characterized in that: Also includes: Solving the sensitivity coefficient includes: ； in, and represents the partial derivative of each variable at 0, obtained at the power flow solution at the midpoint of the injected power interval; and denote the active and reactive power injection interval radii respectively, , and They represent the upper and lower limits of the active output range of the generator node respectively; , and They represent the upper and lower limits of the active load demand range of the load node respectively; , and They represent the upper and lower limits of the reactive load demand of the load node respectively.

5. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 4, characterized in that: The S3 includes: Since the inequality constraints in the first model are all single variable constraints, the variables, objective functions and constraints in the first model are represented by vectors and functions, and the first model is represented as a compact model: ； in, Indicates system network loss; The interval form of network loss; represents the interval power flow equation constraint; represents the node injection power interval vector; represents the first state variable interval; represents the control variable; Represents the vector composed of load node voltage and generator reactive output, and Respectively The minimum and maximum values ​​of and Represent the control variable vectors The minimum and maximum values ​​of Indicates the transpose; the voltage phase angle of nodes other than the balance node and the active output of the balance node are expressed as vectors , then the system state variable vector is expressed as ; In the compact model, for any control variable , solve the interval power flow equation by using the distributed interval power flow algorithm , get the corresponding ;because is bounded, then there exists a control variable vector Make one of the The interval radius is the largest, denoted by , and each There is one Corresponding; therefore, the definition Maximum radius : ； in, Represents state variables The radius of the interval; Through Monte Carlo simulation, we get The vector consisting of the maximum values ​​of the radius of all variable intervals in ; For the same control variable , is the interval power flow equation The solution, is the deterministic power flow equation The solution is to consider that the deterministic state variable may be anywhere within the maximum state variable interval in the Monte Carlo simulation, and the deterministic state variable The corresponding maximum radius of the state variable interval is , then there is a constraint ,ensure The constraints in the compact model are satisfied; therefore, an absolute safety limit is defined, including: ； ； The absolute safety limit represents the safety margin under the worst scenario, which is conservative and introduces the average position ratio. The safety limits are modified to make them less conservative: ； in, Represents the control variable exist , scene exist Determine the state variables at ; and Respectively expressed in Solving the interval power flow equation The lower and upper bounds of the state variable interval are obtained; assuming The corresponding average position ratio is , , then the modified safety limit is expressed by the following relationship: ； ； Average position ratio The control variable is defined at the midpoint of the control variable, and the control variable takes any value within its interval, resulting in Deviation , so the modified safety limit has a safety error, and the state variable may exceed the limit; take the state variable The limit is exceeded , the lower limit is , to accurately correct the state variables, including: ； ； If the state variable is still in an over-limit state after precise correction, the precise correction is repeated until the state variable does not exceed the limit, and the final safety limit is obtained; according to the final safety limit, the compact model is converted into a second model, and the second model is represented by the following relationship: ； in, express Any scene within.

6. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 5, characterized in that: The S4 includes: The second model is solved by the primal-dual interior point method: For the second model, we first introduce the Lagrange multiplier And the dual variable and Constructing Lagrangian functions , which is expressed by the following relationship: ； The KKT condition of the Lagrangian function is established, and the KKT condition includes a gradient condition, a primal feasibility condition, a dual feasibility condition, and a complementary relaxation condition, which are expressed by the following relationship: ； The KKT condition is solved by Newton gradient descent, including: Select the starting point , ensuring that the inequality constraints are satisfied; in the In the iteration, based on the current The Newton gradient descent equation is obtained and expressed by the following relationship: ； in, is the Hessier matrix of the Lagrangian function, is the Newton step, including and ; represents the current gradient; let As the step length, the Newton step variable update scheme is obtained, which is expressed by the following relationship: ； in, Indicates A vector of variables for the iterations, containing ; Indicates The variable vector for the iterations, containing ; Determine whether the convergence condition is met. If so, determine that Newton gradient descent has converged, stop iteration, and output the solution result of the second model , that is, the reactive voltage control strategy is obtained; the convergence condition includes the dual gap is smaller than the convergence tolerance, and the primal feasibility condition, the dual feasibility condition, and the complementary slackness condition are all satisfied.

7. The method for reactive power optimization of a power system based on distributed interval optimization according to claim 6, characterized in that: Also includes: According to the reactive voltage control strategy, the distribution interval power flow is calculated to obtain the control variable value. and the corresponding second state variable interval ,include: The reactive voltage control strategy is the solution result The control variables in Including final transformer ratio , Generator terminal voltage and reactive power compensation capacity ; According to the control variables get The distribution interval power flow model under , is expressed by the following relationship: ； in, and are the final transformer ratios The real and imaginary parts of the lower node admittance matrix; According to the The distributed interval power flow model under the condition of The corresponding interval of the second state variable of the system , Including load node voltage range , node voltage phase angle interval and generator reactive output range Output and , that is, the control variable value and the corresponding second state variable interval are obtained.

8. A computer medium, characterized in that The invention comprises a processor, a memory and a computer program for implementing the method according to any one of claims 1 to 7.

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