Multi-objective reactive power planning considering uncertainty of dynamic voltage regulation of SVGs

Abstract

The present application relates to a kind of considering SVG dynamic voltage regulating ability's uncertainty multi-objective reactive power planning configuration method, comprising: considering source, load injection power uncertainty, construct considering SVG voltage regulating characteristic affine power flow model, to affine noise element association each uncertainty factor, obtain the output power interval required for SVG to suppress node voltage fluctuation;Using the affine power flow algorithm considering SVG capacity constraint, according to the over-limit situation of each equipment output power, interval correction is carried out to power flow state variable;Double-layer reactive power planning model is constructed, considering the suppression effect of reactive power equipment on voltage fluctuation under each load scenario, obtain the optimal planning scheme.The present application comprehensively considers the network loss and voltage quality in the process of grid operation scheduling of planning scheme, reasonably configures the grid-connected position and capacity of SVG and capacitor bank, avoids the problem that planning scheme cost is too high due to redundant reactive power equipment capacity configuration.

Description

Technical Field

[0001] This invention relates to the field of reactive power planning for power grids, and specifically to an uncertain multi-objective reactive power planning configuration method that considers the dynamic voltage regulation capability of SVG. Background Technology

[0002] Reactive power planning, which rationally allocates the grid connection location and capacity of reactive power compensation equipment, is an important means to improve the economy of the power grid and ensure voltage quality. The increasing proportion of distributed renewable energy and stochastic loads such as electric vehicles will lead to uncertainties in power system operation. Complex and variable grid conditions affect the compensation effect of reactive power equipment, thus reducing the accuracy of planning models in evaluating equipment configuration schemes. Therefore, it is necessary to construct a reasonable reactive power planning configuration model that can comprehensively consider the economic benefits of reactive power equipment configuration schemes and the uncertainties of power grid operation. Furthermore, Static Var Generators (SVGs) can effectively improve the controllability of power flow scheduling and suppress the impact of source and load uncertainties on distribution network voltage. Deterministic power flow algorithms cannot accurately calculate the power range of SVG dynamic voltage regulation output, causing the planning model to be unable to rationally allocate the capacity of each reactive power equipment according to voltage fluctuation levels.

[0003] Currently, the main methods for handling uncertainty in power grid reactive power planning problems are stochastic programming and robust optimization.

[0004] Stochastic programming is mainly based on probabilistic statistical models of uncertain quantities. It uses chance constraints to process random parameters and then transforms them into deterministic models for solution. However, in reality, it is often impossible to accurately obtain the probabilistic statistical distribution of uncertain parameters such as photovoltaic and wind power output and load, resulting in low engineering applicability of reactive power planning schemes.

[0005] Robust optimization methods seek the maximum investment return of a planning scheme while meeting the safety indicators of the worst-case operating conditions of the power grid, which aligns with the important reliability requirements of power system planning. However, robust optimization makes decisions based on the worst-case scenarios within the set of uncertain parameter intervals, which can easily lead to overly aggressive or conservative equipment configuration schemes.

[0006] Furthermore, traditional reactive power planning models do not consider the dynamic voltage regulation capability of SVG, and cannot accurately obtain the output power range of SVG to smooth out node voltage fluctuations, and thus cannot use this range for reactive power planning, weighing the effect of reactive power equipment configuration schemes on reducing grid operation losses and suppressing voltage uncertainty.

[0007] In summary, existing reactive power planning and configuration methods that take into account the uncertainties of power grid operation have the following shortcomings: 1. Stochastic programming requires high accuracy of the model with injected uncertainty parameters and has low engineering applicability; 2. Robust optimization has the problem of overly conservative decision results; 3. The above two planning methods do not consider the suppression effect of SVG on voltage fluctuations and fail to perform reactive power planning and configuration for the uncertainties of power grid operation voltage. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a multi-objective reactive power planning configuration method that considers the uncertainty of SVG dynamic voltage regulation capability, in order to solve the above-mentioned problems.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] An uncertain multi-objective reactive power planning configuration method considering the dynamic voltage regulation capability of SVG includes:

[0011] Considering the uncertainty of source and load injected power, an affine power flow model that takes into account the voltage regulation characteristics of SVG is constructed. The affine noise element is used to associate each uncertainty factor to obtain the output power range required by SVG to smooth node voltage fluctuations.

[0012] An affine power flow algorithm that takes into account SVG capacity constraints is adopted to perform interval correction on the power flow state variables based on the over-limit status of each device's output power;

[0013] A two-layer reactive power planning model is constructed to consider the suppression effect of reactive power equipment on voltage fluctuations under various load scenarios, and to obtain the optimal planning scheme.

[0014] Furthermore, the affine power flow model that takes into account the voltage regulation characteristics of SVG is specifically as follows:

[0015] Uncertainties in the power flow model are described using affine form. When the distribution network structure and parameters remain unchanged, the fluctuation characteristics of state variables such as voltage and power in the power flow equations are described using affine form as the main source of uncertainty. The affine model of node injected power is constructed as follows:

[0016]

[0017] In the formula: A complex affine model for injecting power into node i, to inject active and reactive power. It is composed of a combination of real affine numbers; ε j Let be a noise element, representing the j-th uncertainty factor; n is the total number of noise elements.

[0018] The specific parameters of the affine power model, including the noise element ε, are determined based on the source and magnitude of the source and charge fluctuations. jand its corresponding noise element coefficient P i,j Q i,j ;

[0019] When node injected power fluctuates, its uncertainties will affect all state variables in the reactive power planning model, including node voltage, system network losses, and reactive power output of the SVG. The state variables affected by uncertainties are described in affine form, as shown in the following equation:

[0020]

[0021]

[0022]

[0023] In the formula: The affine phasor expression for the voltage at node i is derived from the real affine expressions for voltage magnitude and phase angle. constitute; Let U be the real affine expression for the system network loss and the reactive power output of the SVG, respectively; where U i,0 θ i,0 P L,0 Q S,0 U is the affine center value; i,j θ i,j P L,j Q S,j Let be the coefficient of the j-th affine noise element corresponding to each power flow state quantity.

[0024] Furthermore, the affine power flow algorithm that takes into account SVG capacity constraints is specifically as follows:

[0025] The Ybus affine power flow iterative equations for the grid node voltages are constructed based on the block matrix form of the voltage equations, as follows:

[0026]

[0027]

[0028] In the formula: node t is the equilibrium node; Y ot and Y to Y is the block matrix of mutual admittance formed between node t and other nodes; tt U is the self-admittance coefficient of node t; Y is the node admittance matrix composed of all nodes in the power grid except the slack node; U t I t U and I respectively balance the voltage and injected current of node t with those of other nodes;

[0029] Considering that the SVG operates with a constant voltage control strategy, the compensation calculations for the SVG reactive power output and node voltage are as follows:

[0030]

[0031] In the formula: U represents the voltage amplitude offset of the i-th SVG grid-connected node during the m-th iteration; set,i Set the amplitude setting value for the i-th SVG dynamic voltage regulator; The magnitude and affine number of the voltage phasor at the m-th iteration; Let X be the affine form of the reactive power output of the SVG in the m-th iteration and its correction; -1 Let be the Thevenin equivalent nodal reactance matrix.

[0032] Furthermore, the two-layer reactive power planning model includes a planning and configuration model for SVG and capacitor banks and a scheduling optimization model for power grid operation. The planning and configuration model for SVG and capacitor banks is the planning layer, which optimizes the configuration scheme of SVG and capacitor banks with the minimum equivalent annual total cost and voltage fluctuation index as the optimization objective. The scheduling optimization model for power grid operation is the operation layer, which optimizes the operation scheduling scheme of distribution network voltage regulating device with the minimum system operation network loss and voltage deviation under typical load levels as the optimization objective, and returns the network loss and voltage uncertainty index of the optimal operation scheme under each typical load level to the upper layer.

[0033] Furthermore, the planning and configuration model for the SVG and capacitor bank is as follows: with the objective function of minimizing the equivalent annual total cost and voltage fluctuation index, the installation node locations and capacities of the SVG and switchable capacitor bank are optimized.

[0034] (1) Objective function 1: Equivalent annual total cost;

[0035] The equivalent annual total cost C1 of the reactive power planning scheme is derived from the equivalent annual investment cost C of the equipment. In Annual maintenance cost C M Decommissioning and disposal costs C D And system operating costs C L Composition, objective function construction:

[0036] minC1=C In +C M +C L +C D (8)

[0037]

[0038] C M =C LA +CT +C E (10)

[0039]

[0040]

[0041]

[0042] In the formula: The annual conversion factor is used for SVG and switchable capacitor banks; K is the set of reactive power equipment, including SVG and capacitor banks; n S n C C represents the total number of SVG and capacitor bank installations; SVG C CB The installation cost per unit capacity of SVG and capacitor bank; The capacity configured for the i-th SVG and the number of switchable groups configured for the i-th capacitor bank, Q CB For the capacitance of a single capacitor bank; C LA C T C E These are the labor costs for routine equipment maintenance, the costs of regular testing, and the costs of equipment failure. The network loss for the optimal operating scheme under this load level is returned by the lower-level operation optimization model; the specific formula is given in Section 2.2. e The electricity price is represented by b; b and c are the percentage coefficients of the residual value of scrapped assets and the proportion of scrapping disposal management costs to the initial investment, respectively, which are taken as 2% and 5% in this paper; h g Let r be the equivalent duration hours of the g-th load level, r be the discount rate, and T be the equipment lifespan.

[0043] (2) Objective function 2: Voltage fluctuation index;

[0044] To characterize the degree to which node voltage is affected by uncertainty, a voltage uncertainty index E is defined. U as follows,

[0045]

[0046] In the formula: Let wid() be the affine form of the voltage at node i, where wid() is the width of the affine interval, and U max U min These are the upper and lower limits that the node voltage can be allowed, respectively.

[0047] Therefore, the voltage fluctuation index C2 represents the expected value of the node voltage uncertainty index under typical load levels. The objective function is:

[0048]

[0049] In the formula: G is the set of load levels; N is the number of system nodes; p g This represents the equivalent percentage of the duration of the g-th load level. The voltage uncertainty index of node i under the g-th load level is returned by the grid operation scheduling optimization model;

[0050] (3) The constraints are as follows:

[0051]

[0052] In the formula: x SVG x CB For the grid connection location of the SVG and the switchable capacitor bank; Q SVG N represents the configuration capacity of a single SVG unit. CB N represents the number of capacitor banks configured. ch Q is the set of reactive power devices to be connected; SVGmax Limit the SVG capacity allocated to nodes; N CBmax N CBmin The upper and lower limits for the number of switchable capacitor banks to be connected at the node; Q CBmax Configure the total capacity limit for the capacitor bank.

[0053] Furthermore, the scheduling optimization model for power grid operation is specifically as follows:

[0054] With minimizing system operation network loss and voltage deviation as the optimization objective, and using the adjustable transformer ratio, SVG equipment voltage setting value, and the number of capacitor banks in operation at each load level as decision variables, the objective function expression F of the lower-level optimization model is as follows:

[0055]

[0056] in,

[0057]

[0058] In the formula: The on-load adjustable transformer tap position, SVG operating voltage setting value, and number of capacitor banks in operation under the g-th load level are used as control variables for lower-level operation optimization. For affine network loss The center value and noise element coefficient, To balance the affine forms of the voltage vectors at nodes s and j respectively, Let ΔU be the affine form of the load demand of node j. g This is the voltage deviation value. node voltage The center value of the affine amplitude, U w g The voltage setting value for the node is the voltage setting value for the SVG grid-connected node. 'a' is the voltage deviation weighting coefficient.

[0059] The constraints of the lower-level operation optimization model at each load level are as follows:

[0060] (1) Equality constraints

[0061] When optimizing the operation of reactive power regulation equipment in the system, each node must satisfy power balance constraints in affine form, that is:

[0062]

[0063] In the formula: The active and reactive power injected into the nodes for generators and loads; Let be the voltage amplitude at node i. The voltage phase angle difference between nodes i and j; Q C,i The reactive power injected into the SVG and capacitor bank at node i.

[0064] (2) Inequality constraints

[0065] Inequality constraints are divided into control variable constraints and state variable constraints. Among them, the control variables are the scheduling schemes of the power grid equipment under each load level, including adjustable transformer ratios, SVG setting values, etc., which are deterministic scheduling schemes. The state variables of the system power flow are affected by the uncertainty of the source loads. The state variables must ensure that the upper and lower boundaries of the interval of the affine number can satisfy the constraints. The specific formulas are shown in equations 1 and 2.

[0066]

[0067]

[0068] In the formula: T R,k T SVG,k G k These represent the turns ratio setting of the k-th transformer, the SVG operating voltage setting, and the number of operable capacitor banks, respectively. T Number of on-load adjustable transformers; T Rmax T Rmin T Smax T Smin These are the upper and lower limits for the transformer turns ratio setting and the SVG operating voltage setting, respectively. U k These are the upper and lower boundaries of the affine interval for the voltage of the k-th node, respectively. QS k These represent the upper and lower boundaries of the affine output range of the k-th SVG; U max U min These are the upper and lower limits of the allowable node voltage, respectively; Configure the upper and lower limits of reactive power capacity for the k-th SVG respectively.

[0069] Furthermore, the planning and configuration model of the SVG and capacitor bank is solved using the NSGA-II algorithm for multi-objective optimization; the NSGA-II algorithm for multi-objective optimization is solved using the DPSO algorithm.

[0070] Compared with the prior art, the present invention has the following advantages:

[0071] 1. This invention constructs a two-level planning model that combines planning and operation, which can balance improving economic benefits and reducing operational uncertainty;

[0072] 2. This invention comprehensively considers network losses and voltage quality during the grid operation and dispatching process of the planning scheme, and rationally configures the grid connection location and capacity of SVG and capacitor banks to avoid the problem of excessive planning scheme cost caused by redundant reactive power equipment capacity configuration;

[0073] 3. Based on affine theory, this invention proposes an uncertainty power flow calculation method that considers the voltage regulation characteristics of SVG. It can effectively track the impact of source and load injection power uncertainty on node voltage, accurately describe the voltage fluctuation range under SVG capacity constraints, and quantitatively evaluate the uncertainty of different reactive power planning schemes.

[0074] 4. This invention uses a non-dominated sorting genetic algorithm and a discrete particle swarm optimization algorithm to solve the upper and lower level models respectively, thereby improving the utilization rate of voltage regulating equipment such as SVG equipment while ensuring the economical operation of the power grid, and providing a reasonable reactive power planning scheme for power grid dispatch. Attached Figure Description

[0075] Figure 1 This is a flowchart of power flow range correction considering SVG capacity constraints in one embodiment of the present invention;

[0076] Figure 2 This is a flowchart of the affine power flow algorithm in one embodiment of the present invention.

[0077] Figure 3 This is a flowchart of the solution process for a two-layer reactive power planning model in one embodiment of the present invention. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0079] Please refer to Figure 1-3 This invention provides a multi-objective reactive power planning configuration method considering the uncertainty of SVG dynamic voltage regulation capability, comprising:

[0080] Considering the uncertainty of source and load injected power, an affine power flow model that takes into account the voltage regulation characteristics of SVG is constructed. The affine noise element is used to associate each uncertainty factor to obtain the output power range required by SVG to smooth node voltage fluctuations.

[0081] An affine power flow algorithm that takes into account SVG capacity constraints is adopted to perform interval correction on the power flow state variables based on the over-limit status of each device's output power;

[0082] A two-layer reactive power planning model is constructed to consider the suppression effect of reactive power equipment on voltage fluctuations under various load scenarios, and to obtain the optimal planning scheme.

[0083] In this embodiment, the affine power flow model taking into account the voltage regulation characteristics of SVG is specifically as follows:

[0084] Uncertainties in the power flow model are described using affine form. When the distribution network structure and parameters remain unchanged, the fluctuation characteristics of state variables such as voltage and power in the power flow equations are described using affine form as the main source of uncertainty. The affine model of node injected power is constructed as follows:

[0085]

[0086] In the formula: A complex affine model for injecting power into node i, to inject active and reactive power. It is composed of a combination of real affine numbers; ε j Let be a noise element, representing the j-th uncertainty factor; n is the total number of noise elements.

[0087] The specific parameters of the affine power model, including the noise element ε, are determined based on the source and magnitude of the source and charge fluctuations. j and its corresponding noise element coefficient P i,j Q i,j；

[0088] When node injected power fluctuates, its uncertainties will affect all state variables in the reactive power planning model, including node voltage, system network losses, and reactive power output of the SVG. The state variables affected by uncertainties are described in affine form, as shown in the following equation:

[0089]

[0090]

[0091]

[0092] In the formula: The affine phasor expression for the voltage at node i is derived from the real affine expressions for voltage magnitude and phase angle. constitute; Let U be the real affine expression for the system network loss and the reactive power output of the SVG, respectively; where U i,0 θ i,0 P L,0 Q S,0 U is the affine center value; i,j θ i,j P L,j Q S,j Let be the coefficient of the j-th affine noise element corresponding to each power flow state quantity.

[0093] It is worth noting that SVG provides reactive power to the power system by controlling the reactive power output current and achieves dynamic compensation of the grid's reactive power based on the droop control of the grid-connected voltage. When there are uncertainties in the distribution network, the output reactive power required for SVG dynamic voltage regulation will change according to voltage fluctuations, thereby suppressing the impact of uncertainties in source and load injected power on the voltage. Therefore, in the affine model of electrical parameters, the noise element coefficient Q S,j U represents the reactive power output required by the SVG to smooth out voltage fluctuations caused by the j-th uncertainty factor. i,0 θ i,0 and P L,0 These represent the degree to which the voltage of each node and the network loss of the system are affected by uncertainties under SVG dynamic voltage regulation.

[0094] In this embodiment, the affine power flow algorithm that takes into account SVG capacity constraints is specifically as follows:

[0095] The Ybus affine power flow iterative equations for the grid node voltages are constructed based on the block matrix form of the voltage equations, as follows:

[0096]

[0097]

[0098] In the formula: node t is the equilibrium node; Y ot and Y to Y is the block matrix of mutual admittance formed between node t and other nodes; tt U is the self-admittance coefficient of node t; Y is the node admittance matrix composed of all nodes in the power grid except the slack node; U t I t U and I respectively balance the voltage and injected current of node t with those of other nodes;

[0099] Considering that the SVG operates with a constant voltage control strategy, the compensation calculations for the SVG reactive power output and node voltage are as follows:

[0100]

[0101] In the formula: U represents the voltage amplitude offset of the i-th SVG grid-connected node during the m-th iteration; set,i Set the amplitude setting value for the i-th SVG dynamic voltage regulator; The magnitude and affine number of the voltage phasor at the m-th iteration; Let X be the affine form of the reactive power output of the SVG in the m-th iteration and its correction; -1 Let be the Thevenin equivalent nodal reactance matrix.

[0102] Furthermore, if the reactive power range of the SVG dynamic voltage regulation output exceeds its own capacity limit, it is considered that the device has exceeded the power limit. The SVG will lose its dynamic voltage regulation capability and output the rated reactive power, resulting in the grid voltage of the device being unable to be compensated to the set value.

[0103] In this embodiment of the invention, the over-limit situation of the output power of each SVG is addressed by performing interval boundary correction on each power flow state variable. The flowchart of the interval correction and the overall flowchart of the affine power flow algorithm can be found in the appendix. Figure 1 , 2 As shown.

[0104] In this embodiment, the two-layer reactive power planning model includes a planning and configuration model for SVG and capacitor banks, and a scheduling optimization model for power grid operation. The upper-layer model is the planning layer, which optimizes the configuration scheme of SVG and capacitor banks with the goal of minimizing the equivalent annual total cost and voltage fluctuation index. The lower-layer model is the operation layer, which optimizes the operation and scheduling scheme of the distribution network voltage regulating device with the goal of minimizing the system operation network loss and voltage deviation under typical load levels, and returns the network loss and voltage uncertainty index of the optimal operation scheme under each typical load level to the upper layer. The upper-layer model is a multi-objective combinatorial search optimization problem. The genetic algorithm has good global search capabilities, and the NSGA-II algorithm is used for multi-objective optimization, determining the connection location and capacity of reactive power equipment. The lower-layer operation model is a multi-constraint nonlinear model. This paper uses the DPSO algorithm, which has efficient search capabilities, to optimize the transformer ratio, voltage setting value of SVG equipment, and number of capacitor banks switched on and off under different load levels. The reactive power planning solution process is shown in the appendix. Figure 3 .

[0105] Preferably, the planning and configuration model of SVG and capacitor bank optimizes the installation node location and capacity of SVG and switchable capacitor bank with the objective function of minimizing the equivalent annual total cost and voltage fluctuation index.

[0106] (1) Objective function 1: Equivalent annual total cost;

[0107] The equivalent annual total cost C1 of the reactive power planning scheme is derived from the equivalent annual investment cost C of the equipment. In Annual maintenance cost C M Decommissioning and disposal costs C D And system operating costs C L Composition, objective function construction:

[0108] minC1=C In +C M +C L +C D (8)

[0109]

[0110] C M =C LA +C T +C E (10)

[0111]

[0112]

[0113]

[0114] In the formula: The annual conversion factor for SVG and switchable capacitor banks; K is the set of reactive power equipment, including SVG and capacitor banks; nS, n C C represents the total number of SVG and capacitor bank installations; SVG C CB The installation cost per unit capacity of SVG and capacitor bank; The capacity configured for the i-th SVG and the number of switchable groups configured for the i-th capacitor bank, Q CB For the capacitance of a single capacitor bank; C LA C T C E These are the labor costs for routine equipment maintenance, the costs of regular testing, and the costs of equipment failure. The network loss for the optimal operating scheme under this load level is returned by the lower-level operation optimization model; the specific formula is given in Section 2.2. e The electricity price is represented by b; b and c are the percentage coefficients of the residual value of scrapped assets and the proportion of scrapping disposal management costs to the initial investment, respectively, which are taken as 2% and 5% in this paper; h g Let r be the equivalent duration hours of the g-th load level, r be the discount rate, and T be the equipment lifespan.

[0115] (2) Objective function 2: Voltage fluctuation index;

[0116] To characterize the degree to which node voltage is affected by uncertainty, a voltage uncertainty index E is defined. U as follows,

[0117]

[0118] In the formula: Let wid() be the affine form of the voltage at node i, where wid() is the width of the affine interval, and U max U min These are the upper and lower limits that the node voltage can be allowed, respectively.

[0119] Therefore, the voltage fluctuation index C2 represents the uncertainty index of node voltage under typical load levels. The objective function is:

[0120]

[0121] In the formula: G is the set of load levels; N is the number of system nodes; p g This represents the equivalent percentage of the duration of the g-th load level. The voltage uncertainty index of node i under the g-th load level is returned by the grid operation scheduling optimization model;

[0122] (3) The constraints are as follows:

[0123]

[0124] In the formula: x SVG x CB For the grid connection location of the SVG and the switchable capacitor bank; Q SVG N represents the configuration capacity of a single SVG unit. CB N represents the number of capacitor banks configured. ch Q is the set of reactive power devices to be connected; SVGmax Limit the SVG capacity allocated to nodes; N CBmax N CBmin The upper and lower limits for the number of switchable capacitor banks to be connected at the node; Q CBmax Configure the total capacity limit for the capacitor bank.

[0125] The preferred scheduling optimization model for power grid operation is as follows:

[0126] With minimizing system operation network loss and voltage deviation as the optimization objective, and using the adjustable transformer ratio, SVG equipment voltage setting value, and the number of capacitor banks in operation at each load level as decision variables, the objective function expression F of the lower-level optimization model is as follows:

[0127]

[0128] in,

[0129]

[0130] In the formula: T R g , The on-load adjustable transformer tap position, SVG operating voltage setting value, and number of capacitor banks in operation under the g-th load level are used as control variables for lower-level operation optimization. For affine network loss The center value and noise element coefficient, To balance the affine forms of the voltage vectors at nodes s and j respectively, Let ΔU be the affine form of the load demand of node j. g This is the voltage deviation value. node voltage The center value of the affine amplitude, U w g The voltage setting value for the node is the voltage setting value for the SVG grid-connected node. 'a' is the voltage deviation weighting coefficient.

[0131] The constraints of the lower-level operation optimization model at each load level are as follows:

[0132] (1) Equality constraints

[0133] When optimizing the operation of reactive power regulation equipment in the system, each node must satisfy power balance constraints in affine form, that is:

[0134]

[0135] In the formula: The active and reactive power injected into the nodes for generators and loads; Let be the voltage amplitude at node i. The voltage phase angle difference between nodes i and j; Q C,i The reactive power injected into the SVG and capacitor bank at node i.

[0136] (2) Inequality constraints

[0137] Inequality constraints are divided into control variable constraints and state variable constraints. Among them, the control variables are the scheduling schemes of the power grid equipment under each load level, including adjustable transformer ratios, SVG setting values, etc., which are deterministic scheduling schemes. The state variables of the system power flow are affected by the uncertainty of the source loads. The state variables must ensure that the upper and lower boundaries of the interval of the affine number can satisfy the constraints. The specific formulas are shown in equations 1 and 2.

[0138]

[0139]

[0140] In the formula: T R,k T SVG,k G k These represent the turns ratio setting of the k-th transformer, the SVG operating voltage setting, and the number of operable capacitor banks, respectively. T Number of on-load adjustable transformers; T Rmax T Rmin T Smax T Smin These are the upper and lower limits for the transformer turns ratio setting and the SVG operating voltage setting, respectively. U k These are the upper and lower boundaries of the affine interval for the voltage of the k-th node, respectively. Q S k These represent the upper and lower boundaries of the affine output range of the k-th SVG; U max U min These are the upper and lower limits of the allowable node voltage, respectively; Configure the upper and lower limits of reactive power capacity for the k-th SVG respectively.

[0141] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made within the scope of the claims of the present invention should be included in the scope of the present invention.

Claims

1. A multi-objective reactive power planning configuration method considering the uncertainty of SVG dynamic voltage regulation capability, characterized in that, include: Considering the uncertainties of source injection power and charge injection power, an affine power flow model that takes into account the voltage regulation characteristics of SVG is constructed. The affine noise element is used to associate each uncertainty factor to obtain the output power range required by SVG to smooth node voltage fluctuations. An affine power flow algorithm that takes into account SVG capacity constraints is adopted to perform interval correction on the power flow state variables based on the over-limit status of each device's output power; A two-layer reactive power planning model is constructed to consider the suppression effect of reactive power equipment on voltage fluctuations under various load scenarios, and to obtain the optimal planning scheme. Specifically, the construction of the affine power flow model considering the voltage regulation characteristics of SVG is as follows: Uncertainties in the power flow model are described using affine form. When the distribution network structure and parameters remain unchanged, the fluctuation characteristics of voltage and power state variables in the power flow equations are described using affine form, which is the main source of uncertainty. The affine model of node injected power is constructed as follows: In the formula: A complex affine model for injecting power into node i, to inject active power. and reactive power It is composed of a combination of real affine numbers; ε j Let be a noise element, representing the j-th uncertainty factor; n is the total number of noise elements. The specific parameters of the affine power model, including the noise element ε, are determined based on the source and magnitude of the source and charge fluctuations. j The noise element coefficient P corresponding to source fluctuations and charge fluctuations i,j Q i,j ; When node injected power fluctuates, the resulting uncertainties will affect all state variables in the reactive power planning model, including node voltage, system network losses, and reactive power output of the SVG. The state variables affected by these uncertainties can be described in affine form, as shown in the following equation: In the formula: The affine phasor expression for the voltage at node i is derived from the real affine expressions for voltage magnitude and phase angle. constitute; Let U be the real affine expression for the system network loss and the reactive power output of the SVG, respectively; where U i,0 θ i,0 P L,0 Q S,0 U is the affine center value; i,j θ i,j P L,j Q S,j For each tidal state quantity, the j-th affine noise element coefficient is denoted; Specifically, the affine power flow algorithm that takes into account SVG capacity constraints is as follows: The Ybus affine power flow iterative equations for the grid node voltages are constructed based on the block matrix form of the voltage equations, as follows: In the formula: node t is the equilibrium node; Y ot and Y to Y is the block matrix of mutual admittance formed between node t and other nodes; tt U is the self-admittance coefficient of node t; Y is the node admittance matrix composed of all nodes in the power grid except the slack node; U t I t U and I respectively balance the voltage and injected current of node t with those of other nodes; Considering that the SVG operates with a constant voltage control strategy, the compensation calculations for the SVG reactive power output and node voltage are as follows: In the formula: U represents the voltage amplitude offset of the i-th SVG grid-connected node during the m-th iteration; set,i Set the amplitude setting value for the i-th SVG dynamic voltage regulator; Let be the affine number of the voltage phasor magnitude at the m-th iteration; Let f(x) be the affine number of the phase angle of the voltage phasor at the m-th iteration. Let be the affine form of the reactive power output of the SVG in the m-th iteration; X is the affine form of the reactive power correction of the SVG in the m-th iteration; -1 The Thevenin equivalent nodal reactance matrix; The two-layer reactive power planning model includes a planning and configuration model for SVG and capacitor banks and a scheduling optimization model for power grid operation. The planning and configuration model for SVG and capacitor banks is the planning layer, which optimizes the configuration scheme of SVG and capacitor banks with the goal of minimizing the equivalent annual total cost and voltage fluctuation index. The scheduling optimization model for power grid operation is the operation layer, which optimizes the operation and scheduling scheme of distribution network voltage regulating devices with the goal of minimizing the system operation network loss and voltage deviation under typical load levels, and returns the network loss and voltage uncertainty index of the optimal operation scheme under each typical load level to the upper layer. The planning and configuration model for the SVG and capacitor bank is as follows: with the objective function of minimizing the equivalent annual total cost and voltage fluctuation index, the installation node locations and capacities of the SVG and switchable capacitor bank are optimized. (1) Objective function 1: equivalent annual total cost; The equivalent annual total cost C1 of the reactive power planning scheme is derived from the equivalent annual investment cost C of the equipment. In Annual maintenance cost C M Decommissioning and disposal costs C D And system operating costs C L Composition, objective function construction: minC1=C In +C M +C L +C D (8) C M =C LA +C T +C E (10) In the formula: The annual conversion factor is used for SVG and switchable capacitor banks; K is the set of reactive power equipment, including SVG and capacitor banks; n S n C C represents the total number of SVG and capacitor bank installations; SVG C CB The installation cost per unit capacity of SVG and capacitor bank; The capacity configured for the i-th SVG and the number of switchable groups configured for the i-th capacitor bank, Q CB For the capacitance of a single capacitor bank; C LA C T C E These are the labor costs for routine equipment maintenance, the costs of regular testing, and the costs of equipment failure. The network loss for the optimal operating scheme under this load level is returned by the lower-level operation optimization model; λ e a) is the electricity price; b) is the ratio of the residual value of scrapped assets to the initial investment, taken as 2%; c) is the ratio of scrapping disposal management costs to the initial investment, taken as 5%; h) g Let r be the equivalent duration hours of the g-th load level, r be the discount rate, and T be the equipment lifespan. (2) Objective function 2: Voltage fluctuation index; To characterize the degree to which node voltage is affected by uncertainty, a voltage uncertainty index E is defined. U as follows, In the formula: Let wid() be the affine form of the voltage at node i, where wid() is the width of the affine interval, and U max U represents the upper limit of the node voltage allowed. min This represents the lower limit of the allowable node voltage. Therefore, the voltage fluctuation index C2 is the expected value of the node voltage uncertainty index under typical load levels; the objective function is: In the formula: G is the set of load levels; N is the number of system nodes; p g This represents the equivalent percentage of the duration of the g-th load level. The voltage uncertainty index of node i under the g-th load level is returned by the grid operation scheduling optimization model; (3) The constraints are as follows: In the formula: x SVG For the grid connection location of the SVG, x CB For the grid connection location of switchable capacitor banks; Q SVG N represents the configuration capacity of a single SVG unit. CB N represents the number of capacitor banks configured. ch Q is the set of reactive power devices to be connected; SVGmax Limit the SVG capacity allocated to nodes; N CBmax N is the upper limit of the number of switchable capacitor banks that can be connected to a node. CBmin The lower limit for the number of switchable capacitor banks that can be connected to a node; Q CBmax Configure the total capacity limit for the capacitor bank.

2. The multi-objective reactive power planning and configuration method considering the uncertainty of SVG dynamic voltage regulation capability according to claim 1, characterized in that, The scheduling optimization model for power grid operation is specifically as follows: With the goal of minimizing network losses and voltage deviations during system operation, and with the adjustable transformer ratio, SVG equipment voltage setting value, and the number of capacitor banks in operation at each load level as decision variables, the aim is to find the optimal dispatch scheme that balances the economic efficiency of power grid operation and power quality. The objective function expression F of the lower-level optimization model is as follows: in, In the formula: T R g For the on-load adjustable transformer tap position under the g-th load level, This is the set value for the SVG operating voltage. The number of capacitor banks in operation is used as a control variable for lower-level operation optimization. For affine network loss The central value, For affine network loss The noise element coefficient; The affine form of the voltage vector at the s-node is given. To represent the affine form of the voltage vector at node j, Let ΔU be the affine form of the load demand of node j. g This is the voltage deviation value. node voltage The center value of the affine amplitude, U w g The voltage setting value for the node is the voltage setting value for the SVG grid-connected node. α is the voltage deviation weighting coefficient; The constraints of the lower-level operation optimization model at each load level are as follows: (1) Equality constraints When optimizing the operation of reactive power regulation equipment in the system, each node must satisfy power balance constraints in affine form, that is: In the formula: The active and reactive power injected into the nodes for generators and loads; Let be the voltage amplitude at node i. The voltage phase angle difference between nodes i and j; Q C,i Inject reactive power into SVG and capacitor bank at node i; (2) Inequality constraints Inequality constraints are divided into control variable constraints and state variable constraints. Among them, the control variables are the scheduling schemes of the power grid equipment under each load level, including the adjustable transformer ratio, SVG setting value, etc., which are deterministic scheduling schemes. The state variables of the system power flow are affected by the uncertainty of the source load. The state variables need to ensure that the upper and lower boundaries of the interval of the affine number can satisfy the constraint conditions. The specific formulas are shown in equations (20) and (21). In the formula: T R,k T SVG,k G k These represent the turns ratio setting of the k-th transformer, the SVG operating voltage setting, and the number of operable capacitor banks, respectively. T Number of on-load adjustable transformers; T Rmax T Rmin T Smax T Smin These are the upper and lower limits for the transformer turns ratio setting and the SVG operating voltage setting, respectively. These are the upper and lower boundaries of the affine interval for the voltage of the k-th node, respectively. These represent the upper and lower boundaries of the affine output range of the k-th SVG; U max U min These are the upper and lower limits of the allowable node voltage, respectively; Configure the upper and lower limits of reactive power capacity for the k-th SVG respectively.

3. The multi-objective reactive power planning and configuration method considering the uncertainty of SVG dynamic voltage regulation capability according to claim 1, characterized in that, The planning and configuration model of the SVG and capacitor bank is solved using the NSGA-II algorithm for multi-objective optimization; the NSGA-II algorithm for multi-objective optimization is solved using the DPSO algorithm.

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