Power distribution network reactive power planning method based on improved point estimation method and chance constraint

Abstract

The invention discloses a power distribution network reactive power planning method based on an improved point estimation method and chance constraint, and the method comprises the steps: S1, carrying out the mixing moment calculation and sample point selection of an uncertainty parameter through employing the improved point estimation method, and obtaining an estimation value of the uncertainty parameter; the uncertainty parameters comprise distributed power supply output and load; s2, constructing a power distribution network reactive power planning model based on opportunity constraint, taking the minimum comprehensive operation cost of the power distribution network as a target function, and determining various constraint conditions; the constraint conditions comprise a power flow equation equality constraint of the power distribution network, an inequality constraint of a node voltage amplitude, branch current and reactive compensation equipment capacity, and a chance constraint of the node voltage amplitude and branch power; and S3, substituting the estimated values of the uncertainty parameters into the reactive power planning model, and solving the reactive power planning model by adopting a genetic algorithm combined with quantum behaviors. According to the method, the defects of a traditional point estimation method and deterministic constraints are overcome, and a better reactive power planning scheme is obtained.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network technology, and in particular to a reactive power planning method for distribution networks based on an improved point estimation method and chance constraints. Background Technology

[0002] In the development of smart grids, the stable operation and efficient planning of distribution networks are crucial. Reactive power planning, as a key link in the optimized operation of distribution networks, directly affects the voltage quality, network losses, and power supply reliability of the grid. However, with the large-scale integration of distributed power sources (such as photovoltaic and wind power) into the distribution network and the increasing uncertainty of user-side loads, traditional reactive power planning methods for distribution networks face significant challenges.

[0003] Traditional point estimation methods suffer from insufficient estimation accuracy and difficulty adapting to complex probability distributions when dealing with uncertain parameters, failing to accurately reflect the actual output of distributed generation and load fluctuations in distribution networks. Furthermore, traditional reactive power planning models often employ deterministic constraints, failing to fully consider the risks posed by various uncertainties. This can lead to problems such as voltage exceeding limits and power overload during actual operation, reducing the safety and economy of the distribution network. Therefore, a new method is urgently needed to improve point estimation methods and incorporate chance constraints to construct a more scientific and reasonable reactive power planning model for distribution networks.

[0004] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0005] The purpose of this invention is to provide a reactive power planning method for distribution networks based on an improved point estimation method and chance constraints, so as to overcome the shortcomings of point estimation method and deterministic constraints in traditional reactive power planning schemes for distribution networks.

[0006] To achieve the above objectives, this invention proposes a reactive power planning method for distribution networks based on an improved point estimation method and chance constraints, comprising:

[0007] S1. Using the improved point estimation method, the mixed moments of the uncertainty parameter are calculated and sample points are selected to obtain the estimated value of the uncertainty parameter;

[0008] The uncertain parameters include distributed power output and load;

[0009] S2. Construct a reactive power planning model for the distribution network based on opportunity constraints, with the objective function min F being the minimum comprehensive operating cost of the distribution network, and determine various constraints.

[0010] The constraints include equality constraints of the power flow equations of the distribution network, inequality constraints of node voltage magnitude, branch current and reactive power compensation equipment capacity, and opportunity constraints of node voltage magnitude and branch power.

[0011] S3. Substitute the estimated values ​​of the uncertainty parameters into the reactive power planning model, and use a genetic algorithm that incorporates quantum behavior to solve the reactive power planning model.

[0012] Optionally, step S0 is also included:

[0013] Historical data on uncertainty parameters are collected, preprocessed, and used for uncertainty modeling.

[0014] The distributed power output includes photovoltaic power output. To address the uncertainty of photovoltaic power output, a non-parametric kernel density estimation is used to fit the actual light fluctuation.

[0015] To address the uncertainty of the load, a Gaussian mixture model is used to fit the load fluctuations on the user side.

[0016] Optionally, step S1 includes the following steps:

[0017] S1.1 Calculate the mixed moments of the historical data of the uncertainty parameters to obtain the distribution characteristics of the historical data of the uncertainty parameters;

[0018] S1.2 Adaptive sample point selection: The number and location of sample points are dynamically adjusted based on the distribution characteristics of historical data of uncertainty parameters and the fluctuation of real-time data.

[0019] S1.3 Calculate the mixed moments for the sample points of the uncertainty parameter to obtain the estimated value of the uncertainty parameter.

[0020] Optionally, the mixed moment calculation in step S1 is to combine the lower-order moments with the higher-order moments to obtain the mixed moment;

[0021] The lower-order moments include the mean μ and the variance σ. 2 The higher-order moments include skewness S and kurtosis K;

[0022] The formula for calculating the mean is:

[0023] The formula for calculating variance is:

[0024] The formula for calculating skewness is:

[0025] The formula for calculating kurtosis is:

[0026] In the formula, n is the total amount of data for the uncertainty parameters involved in the calculation, and xi Let i be the i-th data point of the uncertainty parameter.

[0027] Optionally, the comprehensive operating cost of the distribution network includes the investment cost C of reactive power compensation equipment. inv Network loss cost C loss Voltage regulation cost C v The formula for calculating the objective function min F is:

[0028] min F=C inv +C loss +C v ;

[0029] The formula for calculating the investment cost of reactive power compensation equipment is as follows:

[0030]

[0031] In the formula, m represents the number of different types of reactive power compensation equipment, and c j Let q be the unit capacity investment cost of the j-th type of reactive power compensation equipment. j Let be the configuration capacity of the j-th type of reactive power compensation equipment;

[0032] The formula for calculating network loss cost is:

[0033]

[0034] In the formula, λ represents the unit energy loss cost, i and k represent two nodes in the distribution network, (i,k)∈L represents the set of physical lines actually connecting nodes i and k in the distribution network, and r ik Let P be the resistance of the line (i,k). ik Q ik V represents the active power and reactive power transmitted on line (i,k), respectively. i Let be the voltage amplitude at node i;

[0035] The formula for calculating the cost of voltage regulation is:

[0036]

[0037] In the formula, n is the number of nodes, C v,i Let be the voltage regulation cost coefficient for node i. Let be the expected voltage amplitude at node i.

[0038] Optionally, the power flow equations of the distribution network include active power balance equations and reactive power balance equations.

[0039] The active power balance equation is as follows:

[0040]

[0041] The reactive power balance equation is:

[0042]

[0043] In the formula, i represents a node in the distribution network, and P i Q i V represents the injected active power and reactive power at node i, respectively. i V j G represents the voltage magnitudes at nodes i and j, respectively. ij B ij θ represents the conductance and susceptance between node i and node j, respectively. ij Let n be the voltage phase angle difference between node i and node j, and n be the number of nodes.

[0044] Optionally, the inequality constraint on the node voltage amplitude is: V i min ≤V i ≤V i max ,

[0045] In the formula, i represents a node in the distribution network, and V i Let V be the voltage magnitude at node i. i min and V i max These are the lower and upper limits of the voltage amplitude at node i, respectively;

[0046] The inequality constraint for the branch current is: in

[0047] In the formula, i and k represent two nodes in the distribution network, (i,k) represents the physical connection between node i and node k, and I ik Let (i,k) be the current on line (i,k). Let (i,k) be the rated current of the line.

[0048] The inequality constraint on the capacity of the reactive power compensation equipment is:

[0049] In the formula, q j Let the configuration capacity of the j-th type of reactive power compensation equipment be . and These are the lower and upper limits of the configuration capacity of the j-th type of reactive power compensation equipment, respectively.

[0050] Optionally, the opportunity constraint sets the node voltage amplitude and branch power to meet the safe operation conditions at a certain confidence level;

[0051] The chance constraint for the node voltage magnitude is: P{V i min ≤V i ≤V i max}≥α;

[0052] The opportunity constraint for branch power is:

[0053] In the formula, V i Let V be the voltage magnitude at node i. i min and V i max These are the lower and upper limits of the voltage amplitude at node i, respectively. Let P be the apparent power of line (i,k). ik Q ik Let i and k represent the active power and reactive power transmitted on line (i,k), respectively. Let α be the rated apparent power of line (i,k), and β be the confidence levels.

[0054] Optionally, step S3 includes the following steps:

[0055] S3.1 Initialize the quantum population so that each individual in the quantum population has a quantum state probability amplitude representation;

[0056] S3.2 Observing the generation of classical solutions from quantum states;

[0057] S3.3 Decode and evaluate fitness;

[0058] S3.4 Determine whether the result converges. If it converges, output the optimal solution; if it does not converge, proceed to step S3.5.

[0059] S3.5, Quantum Revolving Door Update;

[0060] S3.6, Adaptive Quantum Mutation;

[0061] S3.7, Quantum crossover operation;

[0062] S3.8. Dynamically adjust the parameters and return to step S3.2.

[0063] Optionally, step S4 is also included:

[0064] Scheme evaluation and optimization involves simulating and evaluating the reactive power planning scheme obtained from the solution, analyzing the voltage quality, network loss, and operating cost indicators of the reactive power planning scheme, and adjusting and optimizing the scheme based on the evaluation results until the optimal reactive power planning scheme that meets the actual needs of the project is obtained.

[0065] Compared with the prior art, the present invention has at least the following beneficial effects:

[0066] 1. High-precision parameter estimation: The improved point estimation method, through hybrid moment estimation and adaptive sample point selection, can more accurately characterize the distribution characteristics of uncertain parameters in the distribution network, providing more reliable input data for reactive power planning and improving the accuracy of reactive power planning schemes.

[0067] 2. Effectively addressing uncertainty: The opportunity-constrained reactive power planning model fully considers the uncertainties in the operation of the distribution network, ensuring the safe and stable operation of the distribution network under a given confidence level and reducing the operational risks caused by uncertainty.

[0068] 3. Optimize economic operation level: With the goal of minimizing the overall operating cost, the optimization of reactive power planning scheme effectively reduces the costs of reactive power compensation equipment investment, network loss and voltage regulation, thereby improving the economic operation level of the distribution network.

[0069] 4. High efficiency in solving problems: It adopts a genetic algorithm that combines quantum behavior, which has powerful global search and local optimization capabilities. It can quickly and accurately solve complex reactive power planning models, providing an efficient solution method for practical engineering applications. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating the construction of a reactive power planning model for a power distribution network according to the present invention.

[0071] Figure 2 This is a flowchart of the present invention, which uses a genetic algorithm incorporating quantum behavior to solve a reactive power planning model. Detailed Implementation

[0072] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the reactive power planning method for distribution networks based on the improved point estimation method and chance constraints proposed in this invention. The advantages and features of this invention will become clearer from the following description. It should be noted that the accompanying drawings are in a very simplified form and use non-precise scales, used only to facilitate and clearly illustrate the embodiments of this invention. Please refer to the accompanying drawings to make the objectives, features, and advantages of this invention more apparent and understandable. It should be understood that the structures, scales, sizes, etc., depicted in the accompanying drawings are only for illustrative purposes to aid those skilled in the art and are not intended to limit the implementation conditions of this invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in scale, or adjustments to the size, without affecting the effects and objectives achieved by this invention, should still fall within the scope of the technical content disclosed in this invention.

[0073] This invention proposes a reactive power planning method for distribution networks based on an improved point estimation method and chance constraints, comprising the following steps:

[0074] S0. Data acquisition and preprocessing, specifically including the following steps:

[0075] S0.1 Collect historical data of the original uncertainty parameters, perform preprocessing operations such as filtering and interpolation on the historical data to remove noise and abnormal data, fill in missing data, and provide an accurate data foundation for subsequent model construction. The uncertainty parameters include the output of distributed power sources (such as photovoltaic power generation and wind power generation) and user-side load.

[0076] S0.2, Perform uncertainty modeling to obtain the probability distribution characteristics of uncertainty parameters;

[0077] Specifically, for the uncertainty of photovoltaic power output, nonparametric kernel density estimation (KDE) is used to fit the actual irradiance fluctuations to generate a probability distribution;

[0078] To address the uncertainty of user-side load, a Gaussian mixture model (GMM) is established to fit the user-side load fluctuations and generate a probability distribution.

[0079] For coastal environments, considering coastal environmental factors, a probability model for line parameter drift caused by salt spray corrosion is introduced to correct the probability distribution of uncertain parameters.

[0080] S1. Based on the probability distribution characteristics obtained in step S0, the improved point estimation method is used to calculate the mixed moments and select sample points. Since the output and load of distributed generation in the distribution network are uncertain, the fluctuation of these uncertain parameters is the main object of the improved point estimation method. Specifically, it includes the following steps:

[0081] S1.1 Introduce mixed moment estimation to estimate the probability distribution characteristics of the uncertainty parameters;

[0082] Specifically, the moments of the overall uncertainty parameters are calculated using a large amount of historical data preprocessed in step S0, abandoning the traditional single moment estimation method and incorporating the lower-order moments (mean μ, variance σ). 2 The mixed moments are obtained by combining the mixed moments with higher-order moments (skewness S, kurtosis K).

[0083] The formula for calculating the mean is:

[0084] The formula for calculating variance is:

[0085] The formula for calculating skewness is:

[0086] The formula for calculating kurtosis is:

[0087] In the formula, n is the total amount of data for the uncertainty parameters involved in the calculation, and xi This represents the i-th data point of the uncertainty parameter;

[0088] Mixed moment estimation can more comprehensively and accurately describe the probability distribution characteristics of uncertain parameters. Compared with the traditional point estimation method, it significantly improves the estimation accuracy of parameters with complex distribution characteristics.

[0089] S1.2 Adaptive sample selection to determine the sample points required for point estimation;

[0090] Specifically, an adaptive sample point selection algorithm is designed to select sample points from historical and real-time data of uncertain parameters. Based on the distribution characteristics of historical data calculated in step S1.1 and combined with the fluctuation of real-time data, the number and location of sample points are dynamically adjusted to ensure that the sample points are representative. When the data fluctuates greatly or the distribution changes significantly, the number of sample points is increased and their distribution is optimized to ensure that the distribution characteristics and changing trends of uncertain parameters can be accurately captured. When the data is relatively stable, the number of sample points is reduced to improve computational efficiency.

[0091] Finally, as few sample points as possible are selected to represent the distribution characteristics of the uncertainty parameters for subsequent calculations.

[0092] S1.3 Calculate the estimated values ​​of uncertainty parameters based on sample points;

[0093] Specifically, the sample points determined in step S1.2 are used to calculate the mixed moment estimates of uncertainty parameters, such as the mean μ and variance σ of distributed generation output and load. 2 This provides input for the reactive power planning model.

[0094] S2. Based on the actual structure and operation requirements of the distribution network, construct a reactive power planning model for the distribution network based on opportunity constraints, and determine the objective function and various constraints. This includes the following steps:

[0095] S2.1 Construct the objective function;

[0096] The objective function is min F, which takes the minimum overall operating cost of the power distribution network as its objective function. The overall operating cost includes the investment cost C of reactive power compensation equipment. inv Network loss cost C loss Voltage regulation cost C v ,

[0097] The formula for calculating the objective function is:

[0098] min F=C inv +C loss +C v ;

[0099] The formula for calculating the investment cost of reactive power compensation equipment is as follows:

[0100]

[0101] In the formula, m represents the number of different types of reactive power compensation equipment, and c j Let q be the unit capacity investment cost of the j-th type of reactive power compensation equipment. j Let be the configuration capacity of the j-th type of reactive power compensation equipment;

[0102] The formula for calculating network loss cost is:

[0103]

[0104] In the formula, λ represents the unit energy loss cost, i and k represent two nodes in the distribution network, (i,k) represents a physical line connecting node i and node k, and ∈L indicates that this line belongs to the set L of all actual physical lines in the distribution network. Therefore, (i,k)∈L represents the set of actual physical lines connecting node i and node k in the distribution network. ik Let P be the resistance of the line (i,k). ik Q ik V represents the active power and reactive power transmitted on line (i,k), respectively. i Let be the voltage amplitude at node i;

[0105] The formula for calculating the cost of voltage regulation is:

[0106]

[0107] In the formula, n is the number of nodes, C v,i Let be the voltage regulation cost coefficient for node i. Let be the expected voltage amplitude at node i.

[0108] Wherein, the line resistance r ik Number of nodes n, voltage regulation cost coefficient C v,i Unit capacity investment cost of reactive power compensation equipment c j Node expected voltage amplitude It can be obtained through actual distribution network topology data, equipment parameter manuals, and historical operation data collection;

[0109] The configuration capacity q of the reactive power compensation equipment j Active power P transmitted through the line ik and reactive power Q ik Node voltage amplitude V i The optimal value is obtained by solving the model using subsequent algorithms and various constraints. The optimal value is a set of values ​​that minimizes the objective function min F.

[0110] S2.2. Set constraints, including the following three types of constraints:

[0111] (1) Equality constraints, specifically the power flow equations of the distribution network, including active power balance equations and reactive power balance equations.

[0112] The active power balance equation is:

[0113]

[0114] The reactive power balance equation is:

[0115]

[0116] In the formula, P i Q i V represents the injected active power and reactive power at node i, respectively. i V j G represents the voltage magnitudes at nodes i and j, respectively. ij B ij θ represents the conductance and susceptance between node i and node j, respectively. ij Let n be the voltage phase angle difference between node i and node j, and n be the number of nodes.

[0117] (2) Inequality constraints, including node voltage magnitude constraints, branch current constraints and reactive power compensation equipment capacity constraints;

[0118] The node voltage amplitude constraint is: V i min ≤V i ≤V i max ,

[0119] In the formula, V i min and V i max These are the lower and upper limits of the voltage amplitude at node i, respectively;

[0120] Branch current constraints are: in

[0121] In the formula, I ik Let (i,k) be the current on line (i,k). Let (i,k) be the rated current of the line.

[0122] The capacity constraint of the reactive power compensation equipment is:

[0123] In the formula and These are the lower and upper limits of the configuration capacity of the j-th type of reactive power compensation equipment, respectively.

[0124] (3) Opportunity constraints: For node voltage over-limit and branch power overload problems, opportunity constraints are introduced. Opportunity constraints include node voltage amplitude opportunity constraints and branch power opportunity constraints.

[0125] The chance constraint for node voltage amplitude is: P{V i min ≤V i ≤V i max}≥α,

[0126] The branch power opportunity constraint is:

[0127] In the formula, Let be the apparent power of line (i,k). Let α be the rated apparent power of line (i,k), and β be the confidence levels.

[0128] Among them, the lower limit of voltage amplitude V i min and upper limit V i max According to the IEEE 1547 standard (Distributed Power Generation Grid Connection Voltage Requirements), the voltage is typically specified to be within ±5% of the rated voltage, i.e., V. i min and V i max They are 0.95 pu and 1.05 pu respectively; The engineering margin is determined based on the capacitor bank configuration (2×300kVar) in the example; the confidence levels α and β are taken according to power system safety criteria (such as the N-1 criterion), with a typical set of values ​​being α = 0.95 and β = 0.99;

[0129] When solving the reactive power planning model, the estimated values ​​of the uncertainty parameters obtained in step S1 (such as the mean and variance of distributed generation output and load) are input into the chance constraints to quantify the probability of node voltage exceeding limits and branch power overload; the estimated value of distributed generation output corresponds to the injected active power P of the node. i and reactive power Q i The estimated load values ​​correspond to the active and reactive load demands of the nodes, both of which affect the active power P transmitted through the power flow equations. ik Reactive power Q ik and node voltage V i .

[0130] S3. Substitute the estimated values ​​of the uncertainty parameters obtained by the improved point estimation method into the reactive power planning model, and use a genetic algorithm combined with quantum behavior to solve the reactive power planning model.

[0131] The algorithm's initial parameters are set, and through iterative evolution, a reactive power planning scheme that satisfies the constraints and minimizes the objective function is found. This determines the configuration scheme (installation location, capacity) of reactive power compensation equipment and the reactive power output strategy of distributed power sources, etc. Figure 2 As shown, the specific steps include the following:

[0132] S3.1 Initialize the quantum population;

[0133] Specifically, a quantum chromosome encoding is set up, and the chromosome Qi of each individual in the quantum population is represented as... Where n is the number of nodes in the distribution network, α ij β is the real part of the quantum state probability amplitude of the i-th individual at node j. ij It is the imaginary part of the quantum state probability amplitude of the i-th individual at node j;

[0134] The states of reactive power devices (capacitor banks, static var generators, SVG) are mapped to qubits through variable mapping.

[0135] S3.2 Observing the generation of classical solutions from quantum states;

[0136] Specifically, a collapse operation is performed, generating a random number r ~ U(0, 1) for each qubit, based on the quantum state probability amplitude α. ij β ij Mapping quantum states to binary strings (e.g., r≤|α) ij | 2 If the condition is met, use "0"; otherwise, use "1".

[0137] Despace mapping is performed to convert binary strings into state parameters of reactive power equipment according to preset rules. For example, the value of the binary number corresponds to the switching capacity of the capacitor bank (e.g., "101" corresponds to 500kVar) or the reactive power output level of the SVG, thus realizing the mapping from binary code to physical device state.

[0138] S3.3 Decode and evaluate fitness;

[0139] Specifically, the mapping results are decoded, the objective function value is calculated, and constraint processing is performed to evaluate the fitness.

[0140] S3.4 Determine whether the result converges. If it converges, output the optimal solution; if it does not converge, proceed to step S3.5.

[0141] S3.5, Quantum Revolving Door Update;

[0142] Specifically, the quantum rotation gate operation matrix U(θ) is generated guided by the current optimal solution. i )(θ i(The rotation angle is calculated for the current optimal solution); this matrix is ​​applied to manipulate the qubits, ultimately updating the quantum state: In the formula, α i and β i Let α represent the real part and the imaginary part of the quantum state probability amplitude of the i-th individual, respectively. i 'and β i 'represent the real part and imaginary part of the new quantum state probability amplitude of the i-th individual after updating with the rotation operation.

[0143] S3.6, Adaptive Quantum Mutation;

[0144] Specifically, the mutation trigger condition is detected; if the condition is met, a NOT gate operation is performed on the qubit; then the mutation rate is adjusted using the following strategy: In the formula, p m p represents the current mutation rate. m0 Let t be the initial mutation rate, t be the current generation, and T be the total number of generations.

[0145] S3.7, Quantum crossover operation;

[0146] Specifically, a two-point interference crossover method is used to exchange qubits; the crossover result is normalized to maintain |α|. 2 +|β| 2 =1, where α and β represent the real part and imaginary part of the quantum state probability amplitude, respectively.

[0147] S3.8. Dynamically adjust the parameters, and then return to step S3.2;

[0148] Specifically, the following parameters are dynamically adjusted:

[0149] Rotation angle step size Δθ, Δθ(t) = θ min +(θ max -θ min )e -kt In the formula, θ min and θ max These are the minimum and maximum boundaries of the rotation angle step, respectively; k is the decay rate constant; and t is the current algebra.

[0150] Penalty coefficient λ, In the formula, λ0 is the initial value of the penalty coefficient, t is the current algebra, i.e. the number of iterations the algorithm has executed, and T is the total number of algebras, i.e. the maximum number of iterations;

[0151] Weighting factor w i Adjusted dynamically according to the Pareto frontier;

[0152] After the adjustment is completed, return to step S3.2 and recalculate the optimal solution.

[0153] In summary, step S3 introduces the concept of quantum behavior on the basis of traditional genetic algorithms, enabling individuals to have a probability amplitude representation of quantum states in the solution space, thereby enhancing the algorithm's global search capability. At the same time, adaptive crossover and mutation probabilities are designed to dynamically adjust the crossover and mutation probabilities according to the evolutionary state of the population. In the early stage of the search, the crossover probability is increased to accelerate the population evolution speed, and in the later stage of the search, the mutation probability is increased to avoid the algorithm getting trapped in local optima, thus efficiently solving the constructed reactive power planning model.

[0154] S4. Solution evaluation and optimization;

[0155] Specifically, the reactive power planning scheme obtained by the solution is simulated and evaluated. Under different operating scenarios and uncertainties, the voltage quality, network loss, operating cost and other indicators of the scheme are analyzed. Based on the evaluation results, the scheme is appropriately adjusted and optimized until the optimal reactive power planning scheme that meets the actual needs of the project is obtained.

[0156] In one specific embodiment, the reactive power planning scheme obtained using the present invention is evaluated by comparing it with traditional deterministic programming (worst-case scenario) and conventional Monte Carlo method (10,000 samplings). The comparison results are as follows:

[0157] index This patented method Deterministic Programming Monte Carlo Total investment cost (ten thousand yuan) 138.5 210.2 142.1 Average annual loss (MWh) 155.7 201.9 188.3 Voltage over-limit probability 2.8％ 4.6％ 5.1％ Calculation time (h) 0.8 1.5 36.5

[0158] It is evident that this invention reduces the cost of deterministic planning by 34% while keeping the voltage exceedance probability below 2.8%, which is better than the national standard requirement of 5%. Furthermore, its computational efficiency is more than 40 times higher than that of the Monte Carlo method, thus verifying the practical value of this invention in high-fluctuation photovoltaic scenarios.

[0159] In summary, this invention improves the estimation accuracy of uncertain parameters by modifying the point estimation method, rationally handles uncertainties by utilizing chance constraints, and employs a genetic algorithm incorporating quantum behavior to quickly and accurately solve the reactive power planning model, thereby obtaining a better reactive power planning scheme for the distribution network, reducing the operating cost of the distribution network, and improving the operating performance and reliability of the distribution network.

[0160] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0161] In the description of this invention, it should be understood that the terms "center," "height," "thickness," "upper," "lower," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0162] In the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0163] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0164] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A reactive power planning method for distribution networks based on an improved point estimation method and chance constraints, characterized in that, include: S1. Using the improved point estimation method, the mixed moments of the uncertainty parameter are calculated and sample points are selected to obtain the estimated value of the uncertainty parameter; The uncertain parameters include distributed power output and load; S2. Construct a reactive power planning model for the distribution network based on opportunity constraints, with the objective function min F being the minimum comprehensive operating cost of the distribution network, and determine various constraints. The constraints include equality constraints of the power flow equations of the distribution network, inequality constraints of node voltage magnitude, branch current and reactive power compensation equipment capacity, and opportunity constraints of node voltage magnitude and branch power. S3. Substitute the estimated values ​​of the uncertainty parameters into the reactive power planning model, and use a genetic algorithm that incorporates quantum behavior to solve the reactive power planning model.

2. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, It also includes step S0: Historical data on uncertainty parameters are collected, preprocessed, and used for uncertainty modeling. The distributed power output includes photovoltaic power output. To address the uncertainty of photovoltaic power output, a non-parametric kernel density estimation is used to fit the actual light fluctuation. To address the uncertainty of the load, a Gaussian mixture model is used to fit the load fluctuations on the user side.

3. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, Step S1 includes the following steps: S1.1 Calculate the mixed moments of the historical data of the uncertainty parameters to obtain the distribution characteristics of the historical data of the uncertainty parameters; S1.2 Adaptive sample point selection: The number and location of sample points are dynamically adjusted based on the distribution characteristics of historical data of uncertainty parameters and the fluctuation of real-time data. S1.3 Calculate the mixed moments for the sample points of the uncertainty parameter to obtain the estimated value of the uncertainty parameter.

4. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, The mixed moment calculation in step S1 is to combine the lower-order moments with the higher-order moments to obtain the mixed moment; The lower-order moments include the mean μ and the variance σ. 2 The higher-order moments include skewness S and kurtosis K; The formula for calculating the mean is: The formula for calculating variance is: The formula for calculating skewness is: The formula for calculating kurtosis is: In the formula, n is the total amount of data for the uncertainty parameters involved in the calculation, and x i Let i be the i-th data point of the uncertainty parameter.

5. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, The comprehensive operating cost of the power distribution network includes the investment cost of reactive power compensation equipment (C). inv Network loss cost C loss Voltage regulation cost C v The formula for calculating the objective function min F is: min F=C inv +C loss +C v ; The formula for calculating the investment cost of reactive power compensation equipment is as follows: In the formula, m represents the number of different types of reactive power compensation equipment, and c j Let q be the unit capacity investment cost of the j-th type of reactive power compensation equipment. j Let be the configuration capacity of the j-th type of reactive power compensation equipment; The formula for calculating network loss cost is: In the formula, λ represents the unit energy loss cost, i and k represent two nodes in the distribution network, (i,k)∈L represents the set of physical lines actually connecting nodes i and k in the distribution network, and r ik Let P be the resistance of the line (i,k). ik Q ik V represents the active power and reactive power transmitted on line (i,k), respectively. i Let be the voltage amplitude at node i; The formula for calculating the cost of voltage regulation is: In the formula, n is the number of nodes, C v,i Let be the voltage regulation cost coefficient for node i. Let be the expected voltage amplitude at node i.

6. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, The power flow equations of the distribution network include active power balance equations and reactive power balance equations. The active power balance equation is as follows: The reactive power balance equation is: In the formula, i represents a node in the distribution network, and P i Q i V represents the injected active power and reactive power at node i, respectively. i V j G represents the voltage magnitudes at nodes i and j, respectively. ij B ij θ represents the conductance and susceptance between node i and node j, respectively. ij Let n be the voltage phase angle difference between node i and node j, and n be the number of nodes.

7. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, The inequality constraint on the node voltage magnitude is: V i min ≤V i ≤V i max , In the formula, i represents a node in the distribution network, and V i Let V be the voltage magnitude at node i. i min and V i max These are the lower and upper limits of the voltage amplitude at node i, respectively; The inequality constraint for the branch current is: in In the formula, i and k represent two nodes in the distribution network, (i,k) represents the physical connection between node i and node k, and I ik Let (i,k) be the current on line (i,k). Let (i,k) be the rated current of the line. The inequality constraint on the capacity of the reactive power compensation equipment is: In the formula, q j Let the configuration capacity of the j-th type of reactive power compensation equipment be . and These are the lower and upper limits of the configuration capacity of the j-th type of reactive power compensation equipment, respectively.

8. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, The opportunity constraint sets the node voltage amplitude and branch power to meet the safe operation conditions at a certain confidence level. The chance constraint for the node voltage magnitude is: P{V i min ≤V i ≤V i max }≥α; The opportunity constraint for branch power is: In the formula, V i Let V be the voltage magnitude at node i. i min and V i max These are the lower and upper limits of the voltage amplitude at node i, respectively. Let P be the apparent power of line (i,k). ik Q ik Let i and k represent the active power and reactive power transmitted on line (i,k), respectively. Let α be the rated apparent power of line (i,k), and β be the confidence levels.

9. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, Step S3 includes the following steps: S3.1 Initialize the quantum population so that each individual in the quantum population has a quantum state probability amplitude representation; S3.2 Observing the generation of classical solutions from quantum states; S3.3 Decode and evaluate fitness; S3.4 Determine whether the result converges. If it converges, output the optimal solution; if it does not converge, proceed to step S3.

5. S3.5, Quantum Revolving Door Update; S3.6, Adaptive Quantum Mutation; S3.7, Quantum crossover operation; S3.

8. Dynamically adjust the parameters and return to step S3.

2.

10. The reactive power planning method for distribution networks based on the improved point estimation method and chance constraints as described in claim 1, characterized in that, It also includes step S4: Scheme evaluation and optimization involves simulating and evaluating the reactive power planning scheme obtained from the solution, analyzing the voltage quality, network loss, and operating cost indicators of the reactive power planning scheme, and adjusting and optimizing the scheme based on the evaluation results until the optimal reactive power planning scheme that meets the actual needs of the project is obtained.

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