A Coordinated Two-Level Voltage Control Method for AC / DC Systems Considering the Stochasticity of Wind Power

Abstract

This invention discloses a coordinated two-stage voltage control method for AC / DC systems that considers the stochasticity of wind power, comprising the following steps: 1) analyzing the characteristics of random fluctuations in wind power; 2) selecting characteristic time periods of wind power fluctuations; 3) compressing the original wind power scenario into a typical scenario using the k-means clustering method; 4) establishing a coordinated two-stage voltage control model for AC / DC systems that considers the stochasticity of wind power; 5) solving the coordinated two-stage voltage control model for AC / DC systems that considers the stochasticity of wind power, obtaining the minimum expected value of the scenario for the dual objectives of central point voltage deviation and generator reactive power balance. This invention has significant advantages during periods of large wind power fluctuations, can adapt to various possible output conditions of wind power in the future, significantly reduces central point voltage deviation, and lowers the risk of exceeding limits at the central point and generator terminal voltages, thus possessing significant engineering value.

Description

Technical Field

[0001] This invention relates to the field of power system dispatch automation, specifically to a coordinated two-stage voltage control method for AC / DC systems that takes into account the randomness of wind power. Background Technology

[0002] With the increasing development of power system voltage and reactive power control technology, graded voltage control has become a core function of the energy management system of provincial power grid control centers in my country. Secondary voltage control, situated in the middle layer of graded voltage control, plays an indispensable role. Given the current context of large-scale long-distance power transmission from wind power via DC lines in my country, there will be periods of significant short-term fluctuations in wind power. This renders the assumption of constant power flow distribution within the calculation period in secondary voltage control invalid, making it difficult to guarantee the effectiveness of existing deterministic AC / DC coordinated secondary voltage control in sending-end grids with large-scale centralized wind power integration. To address the large-scale changes in power flow and converter bus voltage disturbances caused by random wind power fluctuations, further impacting the frequency of additional operations of discrete equipment in converter stations, this invention proposes a coordinated secondary voltage control method for AC / DC systems that considers the randomness of wind power. Due to the random and intermittent fluctuations in wind power, the centralized integration of large-scale wind power significantly increases the difficulty and complexity of power system voltage and reactive power control. Therefore, it is necessary to analyze the random fluctuations of wind power to provide a reference for deciding whether to consider wind power randomness in secondary voltage control decisions. Wind power fluctuations can be represented by minute-level components separated by first-order difference and moving average methods, the difference in average output between two adjacent days, the content of fluctuation harmonics, and the fluctuation smoothing effect. However, no relevant research has been found that analyzes the randomness of wind power fluctuations within 5-15 minutes from the perspective of secondary voltage control. Summary of the Invention

[0003] The purpose of this invention is to provide a coordinated two-stage voltage control method for AC / DC systems that takes into account the randomness of wind power, comprising the following steps:

[0004] 1) Analyze the characteristics of random fluctuations in wind power.

[0005] This study analyzes the spatial correlation between wind power fluctuation characteristics and wind power output from three perspectives: single wind turbine, wind farm, and wind farm cluster.

[0006] Parameters describing the random fluctuation characteristics of wind power include relative power deviation.

[0007] The relative power deviation ρ% is shown below:

[0008]

[0009] In the formula, t0 is the initial moment of the control period. t is the control period. P is the wind power, which is the sum of the measured wind power at the current moment and the random power deviation. ΔP is the fluctuating wind power value within the control period.

[0010] The wind power P(t0) at the initial moment of the control period and the fluctuating wind power ΔP during the control period are shown below:

[0011]

[0012] In the formula, This represents random power deviation.

[0013] 2) Select the characteristic time period of wind power fluctuation.

[0014] The characteristic period of wind power fluctuation includes the period in which the number of times of significant wind power fluctuation is greater than a set threshold t. max % of the time period.

[0015] The criteria for significant fluctuations in wind power are as follows:

[0016] ΔQ>D'Q c (20)

[0017] In the formula, ΔQ represents the reactive power deviation of wind power. D' is the dead zone coefficient of the compensation capacitor. c This refers to the capacitance of a group of capacitors.

[0018] 3) Use the k-means clustering method to compress the original wind power scenario into a typical scenario.

[0019] The steps to compress the original wind power scenario into a typical scenario using the k-means clustering method include:

[0020] 3.1) Let the sample size be N, the observation index of each sample be M, and the amount of data to be clustered be Z. N×M The number of clusters is k. At the initial time t=1, k samples are selected as the initial clustering points Z. j (t). j = 1, 2, ..., K.

[0021] 3.2) Calculate the Euclidean distance D(Z) from each sample to the initial cluster center. i Z j The data is then classified according to Euclidean distance. The classification criterion is to minimize the Euclidean distance from the sample to the initial cluster center. i = 1, 2, ..., N. Each sample is iterated over, and a clustering operation is performed on all samples. Each cluster contains n samples. j Samples. Minimum Euclidean distance D(Z) i Z m (t) is shown below:

[0022] D(Z i Z m (t))=min{D(Z i Z j (t),i=1,2,…,N)},m∈[1,L] (21)

[0023] 3.3) Update K new cluster centers Z j (t+1), that is:

[0024]

[0025] In the formula, Z i (j) This represents the cluster center of the j-th class. n is the number of spatial objects.

[0026] 3.4) Determine Z j (t+1)=Z j If (t) is true, then the clustering ends and a typical scenario is generated; otherwise, return to step 3.2.

[0027] The typical scenario probability P of the generated typical scenario i As shown below:

[0028] P i =N i / N (23)

[0029] In the formula, N i Let be the number of samples included in the i-th typical scenario.

[0030] The metrics for evaluating the effectiveness of the optimal number of clusters are as follows:

[0031]

[0032] In the formula, F is the distance cost function, representing the sum of inter-class distance and intra-class distance. The distance cost function is negatively correlated with the effectiveness of the optimal number of clusters. L is the inter-class distance, representing the distance from all cluster centers to the spatial center. D is the intra-class distance, representing the sum of the distances from samples within each cluster to their cluster centers. m is the average of all samples. i For cluster C i The mean of the included samples. k is the number of clusters, and p is any sample in the space.

[0033] 4) Establish a coordinated two-level voltage control model for AC / DC systems that takes into account the randomness of wind power.

[0034] The objective function of the AC / DC system coordinated two-stage voltage control model considering the stochasticity of wind power is shown below:

[0035]

[0036]

[0037] In the formula, s represents the scene, and ρ s Let W be the probability of scene s, N be the number of scenes, and W be the probability of scene s. a and W q Let W be the weights of the two objectives. a >W q . and V ref These are vectors representing the current and reference voltage values ​​of the central node, both with dimension n. p ×1. C p and C pw These are the sensitivity matrices of the central point voltage to the generator terminal voltage and the reactive power of wind power, respectively, with dimensions n. p ×n g and n p ×n w ΔQ w,s Let n be the wind power reactive power deviation vector in scenario s, with dimension n. w ×1. μ g,s and ΔV g,s Let n be the vector of generator reactive power output ratio and generator terminal voltage regulation under scenario s, with dimension n. g ×1. ||μ g,s || represents the generator reactive power balancing factor, where the i-th component is μ. gi,s . and These are the current value, lower limit, and upper limit vectors of the generator's reactive power output, each with dimension n. g ×1. They are respectively and The i-th line. C g and C gw These are the sensitivity matrices of generator reactive power output to generator terminal voltage and wind power reactive power, respectively, with dimensions n. p ×n g and n p ×n w C gi and C gwi C respectively g and C gw The i-th row. n p n g n w n d Does it indicate the number of central points, generators, wind turbines, and converters?

[0038] The constraints of the AC / DC system coordinated two-level voltage control model considering the stochasticity of wind power include generator control capability constraints, converter firing angle upper and lower limit constraints, central bus voltage upper and lower limit constraints, and converter station gate reactive power constraints.

[0039] The control capability constraints of the generator include single-step adjustment constraints of the power plant bus, upper and lower limit constraints of the voltage of the high-voltage side bus of the power plant, upper and lower limit constraints of the generator reactive power output, and upper and lower limit constraints of the generator terminal voltage.

[0040] The single-step adjustment constraint for the power plant busbar is shown below:

[0041] ΔV h =C h ΔV g,s +C hw ΔQ w,s (27)

[0042]

[0043] In the formula, ΔV h and The single-step adjustment of the bus voltage on the high-voltage side of the power plant and its maximum allowable value, with a dimension of n. g ×1. C h and C hw These are the sensitivity matrices of the high-voltage bus voltage of the power plant to the generator terminal voltage and the reactive power output of wind power, respectively, with dimensions n. g ×n g and n g ×n w ΔV h These are decision variables.

[0044] The upper and lower limits of the high-voltage bus voltage at the power plant are constrained as follows:

[0045]

[0046] In the formula, and These represent the current, upper, and lower limits of the voltage on the high-voltage side bus of the power plant, respectively, each with dimension n. g ×1.

[0047] The upper and lower limits of the central bus voltage are constrained as follows:

[0048]

[0049] In the formula, and The upper and lower limits of the central point voltage are both n in dimension. p ×1. α p The confidence level of this constraint.

[0050] The upper and lower limits of generator reactive power output are constrained as follows:

[0051]

[0052] The upper and lower limits of the generator terminal voltage are constrained as follows:

[0053]

[0054] In the formula, and The generator terminal voltage has current, upper, and lower limits, each with dimension n. g ×1, α g The confidence level of this constraint.

[0055] The upper and lower limits of the converter firing angle are constrained as follows:

[0056]

[0057] In the formula, and Let n be the current value, upper limit, and lower limit of the cosine of the converter firing angle. d ×1. C d and C dw These are the sensitivity matrices of the converter firing angle cosine to the generator terminal voltage and the reactive power output of wind power, respectively, with dimensions n. d ×n g and n d ×n w .

[0058] The upper and lower limits of reactive power at the converter gate are constrained as follows:

[0059]

[0060] In the formula, and Let n be the current value, upper limit, and lower limit of reactive power at the converter station gateway, each with dimension n. d ×1. C n and C nw The sensitivity matrices for reactive power at the converter station gate to generator terminal voltage and reactive power output of wind power are given, with dimensions n respectively. d ×n g and n d ×n w .

[0061] 5) Solve the AC / DC system coordinated two-level voltage control model considering the randomness of wind power, and obtain the minimum expected value of the dual objectives of central point voltage deviation and generator reactive power balance.

[0062] Tools for solving coordinated two-stage voltage control models of AC / DC systems that take into account the stochasticity of wind power include the quadprog function on the Matlab software platform.

[0063] It is worth noting that this invention, from the perspective of DC near-area coordinated secondary voltage control, uses data from an actual wind farm throughout the year with a sampling period of 1 minute as the entire scenario to represent the randomness of wind power fluctuations. The scenario is compressed using the K-means clustering method, and the number of clusters is specified according to the distance cost function, compressing the scenario of the characteristic time period into multiple typical scenarios to achieve scenario simulation of wind power fluctuations. For the selected characteristic time periods, based on the coordinated secondary voltage control model considering the discrete equipment operation requirements of the converter station, a coordinated secondary voltage control model for AC / DC systems considering the randomness of wind power is proposed. The uncertainty optimization problem is solved using the chance-constrained programming method.

[0064] This invention describes the degree of wind power fluctuation by defining relative power deviation, and selects characteristic periods in which wind power fluctuations cannot be ignored in secondary voltage control. It uses k-means clustering to obtain typical scenarios of wind power output during these characteristic periods; employs a probabilistic scenario method to represent the randomness of wind power; and utilizes a chance constraint method to solve the uncertainty optimization problem. Finally, simulations are performed on a modified IEEE 39-bus example system to verify the effectiveness of the proposed method.

[0065] The technical effects of this invention are undeniable. This invention can further ensure the voltage quality of AC / DC systems with multiple wind power connections, reduce the voltage deviation between the central node and the converter station bus, improve the reactive power balance of the generator, reduce the number of DC equipment operations, and achieve outstanding overall control effects.

[0066] This invention proposes a coordinated two-stage voltage control method for AC / DC systems that considers the stochasticity of wind power. It clarifies the decision variable properties of the high-voltage bus of the power plant and the stochastic control variable properties of the generator terminal voltage. A probabilistic scenario method is used to represent the stochastic power deviation of wind power as typical scenarios, and a chance-constrained programming method is employed to solve the uncertainty optimization problem. This model shows significant advantages during periods of large wind power fluctuations, can adapt to various possible power output situations over a future period, significantly reduces the voltage deviation at the central point, and lowers the risk of exceeding limits at the central point and generator terminal voltage, thus possessing significant engineering value. Attached Figure Description

[0067] Figure 1 The probability distribution of wind power fluctuations during the characteristic period of 12:00–19:00 in spring;

[0068] Figure 2 The relationship between clustering effectiveness metrics and the number of clusters;

[0069] Figure 3This is a modified schematic diagram of the IEEE 39-node system with four partitions. Detailed Implementation

[0070] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0071] Example 1:

[0072] See Figure 1 , 2 3. A coordinated two-stage voltage control method for AC / DC systems considering the stochastic nature of wind power, including the following steps:

[0073] 1) Analyze the characteristics of random fluctuations in wind power.

[0074] This study analyzes the spatial correlation between wind power fluctuation characteristics and wind power output from three perspectives: single wind turbine, wind farm, and wind farm cluster.

[0075] Parameters describing the random fluctuation characteristics of wind power include relative power deviation.

[0076] The relative power deviation ρ% is shown below:

[0077]

[0078] In the formula, t0 is the initial time of the control period. t is the control period. P is the wind power, which is the sum of the measured wind power at the current moment and the random power deviation. ΔP is the fluctuating wind power during the control period. P(t0+t) is the wind power at time t0+t.

[0079] The wind power P(t0) at the initial moment of the control period and the fluctuating wind power ΔP during the control period are shown below:

[0080]

[0081] In the formula, This represents random power deviation.

[0082] 2) Select the characteristic time period of wind power fluctuation.

[0083] The characteristic period of wind power fluctuation includes the period in which the number of times of significant wind power fluctuation is greater than a set threshold t. max % of the time period.

[0084] The criteria for significant fluctuations in wind power are as follows:

[0085] ΔQ>D'Qc (37)

[0086] In the formula, ΔQ represents the reactive power deviation of wind power. D' is the dead zone coefficient of the compensation capacitor. c This refers to the capacitance of a group of capacitors.

[0087] 3) Use the k-means clustering method to compress the original wind power scenario into a typical scenario.

[0088] The steps to compress the original wind power scenario into a typical scenario using the k-means clustering method include:

[0089] 3.1) Let the sample size be N, the observation index of each sample be M, and the amount of data to be clustered be Z. N×M The number of clusters is k. At the initial time t=1, k samples are selected as the initial clustering points Z. j (t). j = 1, 2, ..., K.

[0090] 3.2) Calculate the Euclidean distance D(Z) from each sample to the initial cluster center. i Z j The data is then classified according to Euclidean distance. The classification criterion is to minimize the Euclidean distance from the sample to the initial cluster center. i = 1, 2, ..., N. Each sample is iterated over, and a clustering operation is performed on all samples. Each cluster contains n samples. j Samples. Minimum Euclidean distance D(Z) i Z m (t) is shown below:

[0091] D(Z i Z m (t))=min{D(Z i Z j (t),i=1,2,…,N)},m∈[1,L] (38)

[0092] 3.3) Update K new cluster centers Z j (t+1), that is:

[0093]

[0094] In the formula, Z i (j) This represents the cluster center of the j-th class. n is the number of spatial objects.

[0095] 3.4) Determine Z j (t+1)=Z j If (t) is true, then the clustering ends and a typical scenario is generated; otherwise, return to step 3.2.

[0096] The typical scenario probability P of the generated typical scenarioi As shown below:

[0097] P i =N i / N (40)

[0098] In the formula, N i Let be the number of samples included in the i-th typical scenario.

[0099] The metrics for evaluating the effectiveness of the optimal number of clusters are as follows:

[0100]

[0101] In the formula, F is the distance cost function, representing the sum of inter-class distance and intra-class distance. The distance cost function is negatively correlated with the effectiveness of the optimal number of clusters. L is the inter-class distance, representing the distance from all cluster centers to the spatial center. D is the intra-class distance, representing the sum of the distances from samples within each cluster to their cluster centers. m is the average of all samples. i For cluster C i The mean of the included samples. k is the number of clusters, and p is any sample in the space.

[0102] 4) Establish a coordinated two-level voltage control model for AC / DC systems that takes into account the randomness of wind power.

[0103] The objective function of the AC / DC system coordinated two-stage voltage control model considering the stochasticity of wind power is shown below:

[0104]

[0105]

[0106] In the formula, s represents the scene, and ρ s Let W be the probability of scene s, N be the number of scenes, and W be the probability of scene s. a and W q Let W be the weights of the two objectives. a >W q . and V ref These are vectors representing the current and reference voltage values ​​of the central node, both with dimension n. p ×1. C p and C pw These are the sensitivity matrices of the central point voltage to the generator terminal voltage and the reactive power of wind power, respectively, with dimensions n. p ×n g and n p ×n w ΔQ w,s Let n be the wind power reactive power deviation vector in scenario s, with dimension n. w ×1. μ g,s and ΔVg,s Let n be the vector of generator reactive power output ratio and generator terminal voltage regulation under scenario s, with dimension n. g ×1. ||μ g,s || represents the generator reactive power balancing factor, where the i-th component is μ. gi,s . and These are the current value, lower limit, and upper limit vectors of the generator's reactive power output, each with dimension n. g ×1. They are respectively and The i-th line. C g and C gw These are the sensitivity matrices of generator reactive power output to generator terminal voltage and wind power reactive power, respectively, with dimensions n. p ×n g and n p ×n w C gi and C gwi C respectively g and C gw The i-th row. n p n g n w n d Does it indicate the number of central points, generators, wind turbines, and converters?

[0107] The constraints of the AC / DC system coordinated two-level voltage control model include generator control capability constraints, converter firing angle upper and lower limit constraints, central bus voltage upper and lower limit constraints, and converter station reactive power constraints. The generator control capability constraints include single-step adjustment constraints of the power plant bus, upper and lower limit constraints of the power plant high-voltage side bus voltage, upper and lower limit constraints of generator reactive power output, and upper and lower limit constraints of generator terminal voltage.

[0108] The single-step adjustment constraint for the power plant busbar is shown below:

[0109] ΔV h =C h ΔV g,s +C hw ΔQ w,s (44)

[0110]

[0111] In the formula, ΔV h and The single-step adjustment of the bus voltage on the high-voltage side of the power plant and its maximum allowable value, with a dimension of n. g ×1. C h and Chw These are the sensitivity matrices of the high-voltage bus voltage of the power plant to the generator terminal voltage and the reactive power output of wind power, respectively, with dimensions n. g ×n g and n g ×n w ΔV h These are decision variables.

[0112] The upper and lower limits of the high-voltage bus voltage at the power plant are constrained as follows:

[0113]

[0114] In the formula, and These represent the current, upper, and lower limits of the voltage on the high-voltage side bus of the power plant, respectively, each with dimension n. g ×1.

[0115] The upper and lower limits of the central bus voltage are constrained as follows:

[0116]

[0117] In the formula, and The upper and lower limits of the central point voltage are both n in dimension. p ×1. α p The confidence level of this constraint.

[0118] The upper and lower limits of generator reactive power output are constrained as follows:

[0119]

[0120] The upper and lower limits of the generator terminal voltage are constrained as follows:

[0121]

[0122] In the formula, and The generator terminal voltage has current, upper, and lower limits, each with dimension n. g ×1, α g The confidence level of this constraint.

[0123] The upper and lower limits of the converter firing angle are constrained as follows:

[0124]

[0125] In the formula, and Let n be the current value, upper limit, and lower limit of the cosine of the converter firing angle. d ×1. C d and C dwThese are the sensitivity matrices of the converter firing angle cosine to the generator terminal voltage and the wind power reactive power output, respectively, with dimensions n. d ×n g and n d ×n w .

[0126] The upper and lower limits of reactive power at the converter gate are constrained as follows:

[0127]

[0128] In the formula, and Let n be the current value, upper limit, and lower limit of reactive power at the converter station gateway, each with dimension n. d ×1. C n and C nw The sensitivity matrices for reactive power at the converter station gate to generator terminal voltage and reactive power output of wind power are given, with dimensions n respectively. d ×n g and n d ×n w .

[0129] 5) Solve the AC / DC system coordinated two-level voltage control model considering the randomness of wind power, and obtain the minimum expected value of the dual objectives of central point voltage deviation and generator reactive power balance.

[0130] Tools for solving coordinated two-stage voltage control models of AC / DC systems that take into account the stochasticity of wind power include the quadprog function on the Matlab software platform.

[0131] Example 2:

[0132] A coordinated two-stage voltage control method for AC / DC systems considering the stochastic nature of wind power includes the following steps:

[0133] 1) Analysis of the random fluctuation characteristics of wind power. This invention uses the active power data of a wind farm group A throughout 2019 with a sampling period of 1 minute as the basis to analyze and study the fluctuation characteristics of wind power. The wind farm group has a total of 552 wind turbines with an installed capacity of 752.4MW, which are connected to the grid through a 220kV substation. The time effect of wind power fluctuation is analyzed from the aspects of the fluctuation law, intraday characteristics and seasonal differences of wind power output at different time scales. The spatial correlation between wind power fluctuation characteristics and wind power is analyzed from three perspectives: single turbine, wind farm, and wind farm group, as shown in the table below:

[0134] Table 1. Overview of Wind Power Fluctuation Characteristics of Wind Farm Group A

[0135]

[0136] 2) Select the characteristic time period of wind power fluctuation.

[0137] Deterministic AC / DC system coordinated two-stage voltage control is based on the assumption that the power of random source loads remains constant during the control period. When the fluctuation of random source loads during the control period is small, this control strategy can basically meet the control requirements of important node voltages and the safety constraints of node voltages. However, when the fluctuation of random source loads during the control period is too large, on the one hand, it will cause the voltage of important nodes to deviate too much from the expected value, affecting the voltage quality in the converter station's vicinity and increasing the additional switching risk of discrete equipment in the converter station. On the other hand, it will affect the uneven distribution of reactive power flow in the near-field of the converter station under the existing control strategy, and cause problems such as uneven reactive power output from generators. Therefore, this invention defines the relative deviation of active power during the control period to describe the fluctuation characteristics of wind power and the degree of wind power fluctuation, as shown in the following expression:

[0138]

[0139] in,

[0140]

[0141] In the formula, t0 is the initial moment of the control cycle; t is the control cycle, which is 15 min; P is the wind power, which can be expressed as the sum of the measured wind power at the current moment and the random power deviation; ΔP is the fluctuating power of the wind power during the control cycle; and ρ% is the relative power deviation. In particular, the deviation at the initial moment of the control cycle is zero.

[0142] This invention considers large fluctuations to occur when wind power fluctuations within a control cycle cause capacitor switching actions in the substation's voltage reactive power control equipment; otherwise, they are considered small fluctuations. Therefore, within the coordinated secondary voltage control cycle, adjusting generator reactive power output is the primary means to balance large fluctuations in source load power as quickly and continuously as possible, avoiding additional switching actions on discrete equipment in the converter station and reducing voltage reactive power control costs. The definition of large wind power fluctuations is shown in the following formula:

[0143] ΔQ>DQ c (54)

[0144] In the formula, ΔQ is the reactive power deviation of wind power, D is the dead zone coefficient of the compensation capacitor, and Q c This refers to the capacitance of a group of capacitors.

[0145] The annual active and reactive power data are divided by season and time period. Based on experience, it is believed that wind power fluctuations are significant for more than 20% of the time within a given period, and these periods can be selected as characteristic periods. It is also believed that the randomness of wind power needs to be considered in the coordinated secondary voltage control during the characteristic periods, while the randomness of wind power does not need to be considered in the coordinated secondary voltage control during other periods.

[0146] 3) Use the K-means clustering method to compress the original wind power scenario into a small number of representative typical scenarios.

[0147] The original wind power scenario is large in scale, which can lead to slow computation speed during stochastic optimization. To improve computational efficiency, the original scenario can be compressed into a small number of representative typical scenarios to replace the large-scale original scenario. This invention adopts the K-means clustering method, which is widely used in traditional wind power scenario clustering, and uses Euclidean distance as the evaluation index. The K cluster centers after clustering are the retained scenarios. The specific steps are as follows:

[0148] 3.1) Let the sample size be N, the observation index of each sample be M, and the data to be clustered be Z. N×M Specify the number of clusters, k. At the initial time t=1, select k samples as the initial clustering points Z. j (t)(j=1,2,…K);

[0149] 3.2) Calculate the Euclidean distance D(Z) from each sample to the initial cluster center. i Z j (i = 1, 2, ..., N), find the minimum Euclidean distance for sample Z. i Belongs to C m Classification. Iterate through each sample, perform one clustering for all samples, and each class has n samples. j There are 10 samples. The minimum Euclidean distance is:

[0150] D(Z i Z m (t))=min{D(Z i Z j (t),i=1,2,…,N)},m∈[1,L] (55)

[0151] 3.3) Update K new cluster centers as the mean of each class, Z. i (j) Let the sample be of class j.

[0152]

[0153] 3.4) If the cluster centers no longer change, i.e., Z j (t+1)=Z j If (t) is true, the clustering process ends; otherwise, return to step 3.2.

[0154] Let N be the number of samples contained in the i-th typical scenario. i If there are 1, then the probability of this typical scenario is:

[0155] P i =Ni / N (57)

[0156] The probabilities of each typical scenario can be calculated sequentially using formula (57). Typical scenarios reflect the overall random state of the initial sample, and the sum of their probabilities is 1. In K-means clustering, the number of scenarios after clustering should be predetermined, and the key to selecting the number of scenarios is to establish a clustering effectiveness index for evaluation. This invention uses a distance cost function as an index to evaluate the effectiveness of the optimal number of clusters, as shown in the following expression:

[0157]

[0158] In the formula, F is the distance cost function, representing the sum of inter-class distance and intra-class distance; L is the inter-class distance, representing the distance from all cluster centers to the spatial center; D is the intra-class distance, representing the sum of distances from samples within each cluster to their cluster centers; and m is the average of all samples. i For cluster C i The mean of the included samples; k is the number of clusters, and p is any sample in the space.

[0159] Different numbers of clusters result in different distance cost functions; the smaller the distance cost function F, the better the clustering effect. Generally, the optimal number of clusters...

[0160] 4) Establish a coordinated two-stage voltage control model for AC / DC systems that takes into account the randomness of wind power.

[0161] The objective function of the AC / DC system coordinated two-level voltage control model considering the stochasticity of wind power, taking into account the central point voltage deviation and generator reactive power balance, is as follows:

[0162]

[0163]

[0164] In the formula, s represents the scene, and ρ s Let W be the probability of scene s, N be the number of scenes, and W be the probability of scene s. a and W q The weights of the two objectives; and V pref These are vectors representing the current and reference voltage values ​​of the central node, both with dimension n. p ×1;C p and C pw These are the sensitivity matrices of the central point voltage to the generator terminal voltage and the reactive power of wind power, respectively, with dimensions n. p ×n g and n p ×n w ;ΔQ w,sLet n be the wind power reactive power deviation vector in scenario s, with dimension n. w ×1;μ g,s and ΔV g,s Let n be the vector of generator reactive power output ratio and generator terminal voltage regulation under scenario s, with dimension n. g ×1;||μ g,s || represents the generator reactive power balancing factor, where the i-th component is μ. gi,s ; and These are vectors representing the current value, upper limit, and lower limit of the generator's reactive power output, each with dimension n. g ×1;C g and C gw These are the sensitivity matrices of generator reactive power output to generator terminal voltage and wind power reactive power, respectively, with dimensions n. p ×n g and n p ×n w C gi and C gwi C respectively g and C gw The i-th row.

[0165] The objective function contains two terms. The first term is the objective of minimizing the voltage deviation between the central point and the converter bus node, which means minimizing the sum of the squares of the differences between the current voltage values ​​and their reference values ​​for all central points and converter bus nodes. The second term is the objective of generator reactive power output balance, which means minimizing the sum of the squares of the reactive power output ratios of all generators within the zone. This invention assumes that the objective of minimizing the voltage deviation at the central point has a higher priority than the objective of generator reactive power output balance, i.e., the objective weight W. a Greater than W q The scenario with a bi-objective objective function has the minimum expectation.

[0166] The constraints of the AC / DC system coordinated two-level voltage control model considering the stochasticity of wind power include generator control capability constraints, converter control capability constraints, central point voltage safety constraints, and converter station reactive power constraints. When using chance-constrained programming to handle stochastic constraints, the high-voltage bus voltage constraint of the power plant is considered a decision variable constraint; the generator reactive power output constraint and the single-step adjustment constraint of the high-voltage bus voltage of the power plant are rigid physical constraints; the converter firing angle constraint and the converter station reactive power constraint are to prevent the converter transformer tap changers and reactive power compensation equipment from operating, requiring these constraints to be 100% satisfied; while the generator terminal voltage control variable constraint and the remaining power flow inequality constraints are allowed a certain probability of not being satisfied. Based on the above constraint handling approach, the constraint equations of the established model are specifically expressed as follows:

[0167] Among them, the single-step adjustment constraints of the power plant bus are shown in (61) and (62):

[0168] ΔV h =C h ΔV g,s +C hw ΔQ w,s (61)

[0169] |ΔV h |≤ΔV h max (62)

[0170] In the formula, ΔV h and The single-step adjustment of the bus voltage on the high-voltage side of the power plant and its maximum allowable value, with a dimension of n. g ×1;C h and C hw These are the sensitivity matrices of the high-voltage bus voltage of the power plant to the generator terminal voltage and the reactive power output of wind power, respectively, with dimensions n. g ×n g and n g ×n w ΔV h As a decision variable, its value does not change with the wind power scenario, therefore it has no subscript S.

[0171] Among them, the upper and lower limits of the voltage of the high-voltage side bus of the power plant are constrained as shown in (63):

[0172]

[0173] In the formula, and These represent the current, upper, and lower limits of the voltage on the high-voltage side bus of the power plant, respectively, each with dimension n. g ×1.

[0174] Among them, the upper and lower limits of the central bus voltage are constrained as shown in (64):

[0175]

[0176] In the formula, and The upper and lower limits of the central point voltage are both n in dimension. p ×1.

[0177] α p The confidence level of this constraint.

[0178] Among them, the upper and lower limits of the generator reactive power output are constrained as shown in (65):

[0179]

[0180] The upper and lower limits of the generator terminal voltage are constrained as shown in (66):

[0181]

[0182] In the formula, and The generator terminal voltage has current, upper, and lower limits, each with dimension n. g ×1, α g The confidence level of this constraint.

[0183] The upper and lower limits of the converter firing angle are constrained as shown in (67):

[0184]

[0185] In the formula, and Let n be the current value, upper limit, and lower limit of the cosine of the converter firing angle. d ×1. C d and C dw These are the sensitivity matrices of the converter firing angle cosine to the generator terminal voltage and the wind power reactive power output, respectively, with dimensions n. d ×n g and n d ×n w .

[0186] Among them, the upper and lower limits of reactive power at the converter gate are constrained as shown in (68):

[0187]

[0188] In the formula, and Let n be the current value, upper limit, and lower limit of reactive power at the converter station gateway, each with dimension n. d ×1. C n and C nw The sensitivity matrices for reactive power at the converter station gate to generator terminal voltage and reactive power output of wind power are given, with dimensions n respectively. d ×n g and n d ×n w The upper and lower limits of reactive power at the converter station threshold are determined by the dead zone of the reactive power compensation equipment.

[0189] 5) Solve uncertain quadratic programming problems using the quadprog function.

[0190] The objective function of the coordinated two-stage voltage control model for AC / DC systems considering the stochasticity of wind power established in this invention is a quadratic function, and the constraint equations are linear functions, constituting an uncertain quadratic programming problem. This invention solves the problem by calling the quadprog function on the Matlab software platform.

[0191] Example 3:

[0192] See Figures 1 to 3 A coordinated two-stage voltage control method for AC / DC systems considering the stochastic nature of wind power includes the following steps:

[0193] 1) Wind power scenario processing

[0194] The 220kV substation of wind farm group A selected in this invention is equipped with a capacitor bank with a capacity of 8Mvar. Assuming the dead zone of the capacitor is 80%, the power deviation ΔQ converted to capacitor operation is 6.4Mvar. Statistical analysis of the active and reactive power data of wind farm group A on a typical day yields the function shown in equation (69). The fitting parameters are: variance 337.8, coefficient of determination 0.996, and root mean square 0.4354.

[0195] Q = -1.007 × 10 8 +1.007×10 8 ×cos(1.333×10 -5 P)+1617×sin(1.333×10 -5 P)(69)

[0196] Based on the characteristic period selection method for wind power fluctuations proposed earlier, this paper iterates through the original data and selects seven time periods from 12:00 to 19:00 in spring that meet the criteria as characteristic periods. The probability density curve of their power deviation is shown in the figure. Figure 1 As shown.

[0197] The power deviation probability density curves for the seven characteristic periods are symmetrically distributed, with a relatively concentrated distribution in the range of [-10 MW, 10 MW]. The maximum power deviations for the seven characteristic periods are 44.44 MW, 37.39 MW, 42.61 MW, 53.44 MW, 56.17 MW, 64.85 MW, and 126.01 MW, respectively, which are much higher than the deviation values ​​for summer, autumn, and winter.

[0198] This invention adds wind farm cluster B, which is geographically close to wind farm cluster A within the same county, during scene compression, assuming its characteristic time period is the same as A. Both wind farms are connected to a 220kV substation. Wind farm cluster A has an installed capacity of 752.4MW, and wind farm cluster B has an installed capacity of 1233MW. The data for both wind farm clusters A and B are measured wind power data from 2019 with a sampling interval of 1 minute, and there is no correlation issue. Scene compression is then performed on the data from the two wind farm clusters during a characteristic time period of spring (17:00-18:00) with a sampling period of 1 minute for a specific time period. Based on the wind power data, distance cost function curves are generated for different k values, as shown below. Figure 2 As shown.

[0199] according to Figure 2 It can be seen that the distance cost function first decreases rapidly and then oscillates in the interval [0.5,1]. When the number of clusters K = 20, the distance cost function is minimized. Therefore, for the wind power scenario in this characteristic period, the number of clusters is selected as 20.

[0200] Using MATLAB R2014 software, the wind power deviation data was compressed using the k-means clustering method. The compressed scenarios and their probabilities are shown in the table below. The compressed 20 typical wind power scenarios have an intra-class distance of 1292.5 and an inter-class distance of 528.6.

[0201] Table 2 Compressed Scene

[0202]

[0203] 2) Simulation of coordinated two-stage voltage control for AC / DC systems considering the randomness of wind power

[0204] This invention is based on a modified IEEE 39-node simulation system, adding nodes 40 and 41 next to generator nodes 31 and 32 to simulate the high-voltage side busbar of a power plant. The partitioning and central point information of the modified IEEE 39-node system are shown in Table 3. The wiring diagram and partitioning scheme are as follows: Figure 3 As shown. Based on the background of an asynchronous power grid, a sending-end DC converter station is connected at node 4, and the DC line is connected to the remote asynchronous power grid. The sending-end converter station adopts constant power and constant converter transformer ratio control, while the receiving-end converter station adopts constant voltage and constant arc extinction angle control. The DC power of the sending-end converter station is 1.086 pu, and the receiving-end converter station maintains the sending-end DC voltage at 0.92 pu by controlling the DC voltage. The current ratio of the converter transformer is 1.09, with an adjustment range of 1 ± 15 × 0.01. The equivalent reactance of the converter transformer is 0.1 Ω, and the commutation effect coefficient is 0.995. Parallel capacitors are connected within the converter station as reactive power compensation devices, with a rated capacity of 80 Mvar per group, and a total of 6 groups. The converter firing angle range is 8°-18°.

[0205] The system is divided into 4 reactive power zones. The red circle in the figure shows the central point, and the blue circle shows the converter bus node. The parameters of the 4 new branches after the addition of the high-voltage side bus of the power plant are shown in Table 4.

[0206] Table 3 shows the modified IEEE 39-node system partition and hub information.

[0207]

[0208] Table 4 Parameters of Newly Added Branch Roads

[0209]

[0210] The wind power grid connection points are nodes 5 and 14. Node 5 connects to wind farm cluster A, and node 14 connects to wind farm cluster B. The initial active power of wind farm nodes 5 and 14 is 5MW and 8MW, respectively, and the initial reactive power is 10Mvar and 6Mvar, respectively. Taking data from 17:00-18:00 in spring for wind farm clusters A and B as samples, the installed capacities of wind farm clusters A and B are 752.4MW and 1233MW, respectively. Statistical analysis yields 20 typical power deviation scenarios based on the initial wind power and their probabilities, as shown in Table 1. All wind power connection points are located in reactive power zone 2. The voltage sensitivity of the central point 7 to the active power of the wind farm nodes is 5.10 × 10⁻⁶. -4 and 1.21×10 -3 The voltage sensitivity of central point 7 to reactive power at wind power nodes is 1.01 × 10⁻⁶. -2 and 1.27×10 -2 The sensitivity of the central point voltage to the reactive power of wind power nodes is more than 10 times that to the active power of wind power nodes. Therefore, the coordinated two-level voltage control model proposed in this invention can ignore the impact of wind power active power fluctuations on node voltage.

[0211] Simulations of coordinated two-level voltage control were performed on reactive power zone 2, while generator and load parameters for other zones remained unchanged. The safe range for node voltages was set as follows: central point voltage 0.95–1.05 pu, generator terminal voltage and power plant high-voltage bus voltage 0.9–1.1 pu, and the maximum single-step adjustment of generator terminal voltage 0.01 pu. The confidence levels for central point voltage constraints and generator terminal voltage constraints were set to 90%.

[0212] To verify the effectiveness of the method proposed in this invention, under the same network parameters and operating conditions, the following two control schemes were adopted for reactive power zone 2:

[0213] Option 1: Coordinated two-stage voltage control of AC / DC systems without considering the randomness of wind power.

[0214] Option 2: The coordinated two-stage voltage control proposed in this invention.

[0215] Table 4 presents the voltage control strategies for the high-voltage side bus of the power plant under two different schemes. In the table, ΔV h40 and ΔV h41 These represent the voltage regulation values ​​for nodes 40 and 41 on the high-voltage side of the power plant, respectively. Applying these values ​​to all wind power scenarios, the control effects under the two schemes are shown in Table 5.

[0216] Table 5. Voltage control strategies for the high-voltage side bus of the power plant under the two schemes.

[0217]

[0218] Table 6. Control effects under the two schemes

[0219]

[0220] From the perspective of AC system indicators, after considering the randomness of wind power, the average voltage deviation at the central point of Scheme 2 is 0.0176, which is 0.0113 lower than that of Scheme 1, representing a decrease of 39.10%. The average voltage deviation at the converter station bus of Scheme 2 is 0.0118, which is 0.0025 lower than that of Scheme 1, representing a decrease of 17.48%. The reactive power balance factor of Scheme 1 is 1.4110, while that of Scheme 2 is 1.4032, a decrease of 0.0078 compared to Scheme 1, representing a decrease of 0.56%, indicating that the reactive power output of the generators in Scheme 2 is more balanced. This demonstrates that the AC / DC system coordinated two-stage voltage control considering the randomness of wind power proposed in this invention can adapt to various possible wind power outputs within the control cycle, reduce voltage deviations at the central point and converter station nodes in all scenarios, improve voltage quality, and enhance the balance of reactive power output of the generators, which is beneficial to the stable operation of the AC / DC system.

[0221] From the perspective of DC system indicators, the reactive power absorption of the converter station in Scheme 2 is slightly lower than that in Scheme 1 by 0.011. The number of converter firing angle overruns in Scheme 1 is 32, while the number in Scheme 2 is reduced to 0. This is because the converter firing angle constraint and the reactive power cutoff constraint of the converter station must be fully satisfied, thus reducing unnecessary actions of the converter transformer tap changers and reactive power compensation devices. Correspondingly, to increase control flexibility, the generator control variable constraints and network constraints are allowed to be satisfied with a certain probability. The model proposed in this invention takes into account the impact of wind power fluctuations on the converter firing angle, fully utilizes the voltage and reactive power regulation capabilities of the AC-side generators, significantly reduces converter firing angle overruns caused by random disturbances on the AC side, and reduces the number of converter transformer tap changer actions. In summary, under the condition of large fluctuations in wind power, the AC / DC system coordinated two-level voltage control method that takes into account the randomness of wind power can further ensure the voltage quality of AC / DC systems with multiple wind power connections, reduce the voltage deviation between the central node and the converter station bus, improve the reactive power balance of the generator, reduce the number of DC equipment operations, and achieve outstanding overall control effect.

Claims

1. A coordinated two-stage voltage control method for AC / DC systems considering the randomness of wind power, characterized in that, Includes the following steps: 1) Analyze the characteristics of random fluctuations in wind power; 2) Select the characteristic time period of wind power fluctuation; 3) The original wind power scenario is compressed into a typical scenario using the k-means clustering method; 4) Establish a coordinated two-stage voltage control model for AC / DC systems that considers the randomness of wind power; 5) Solve the AC / DC system coordinated two-level voltage control model considering the randomness of wind power, and obtain the minimum expected value of the dual objectives of central point voltage deviation and generator reactive power balance. The objective function of the AC / DC system coordinated two-stage voltage control model considering the stochasticity of wind power is shown below: In the formula, s represents the scene, and ρ s Let W be the probability of scene s, N be the number of scenes, and W be the probability of scene s. a and W q Let W be the weights of the two objectives. a >W q ; and V ref These are vectors representing the current and reference voltage values ​​of the central node, both with dimension n. p ×1;C p and C pw These are the sensitivity matrices of the central point voltage to the generator terminal voltage and the reactive power of wind power, respectively, with dimensions n. p ×n g and n p ×n w ;ΔQ w,s Let n be the wind power reactive power deviation vector in scenario s, with dimension n. w ×1;μ g,s and ΔV g,s Let n be the vector of generator reactive power output ratio and generator terminal voltage regulation under scenario s, with dimension n. g ×1;||μ g,s || represents the generator reactive power balancing factor, where the i-th component is μ. gi,s ; and These are the current value, lower limit, and upper limit vectors of the generator's reactive power output, each with dimension n. g ×1; They are respectively and The i-th line; C g and C gw These are the sensitivity matrices of generator reactive power output to generator terminal voltage and wind power reactive power, respectively, with dimensions n. p ×n g and n p ×n w C gi and C gwi C respectively g and C gw The i-th row; n p n g n w n d Does it indicate the number of central points, generators, wind turbines, and converters? The constraints of the AC / DC system coordinated two-level voltage control model considering the stochasticity of wind power include generator control capability constraints, converter firing angle upper and lower limit constraints, central bus voltage upper and lower limit constraints, and converter station shut-off reactive power constraints. The control capability constraints of the generator include single-step adjustment constraints of the power plant bus, upper and lower limit constraints of the voltage of the high-voltage side bus of the power plant, upper and lower limit constraints of the generator reactive power output, and upper and lower limit constraints of the generator terminal voltage.

2. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 1, characterized in that: This study analyzes the spatial correlation between wind power fluctuation characteristics and wind power output from three perspectives: single wind turbine, wind farm, and wind farm cluster.

3. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 2, characterized in that: Parameters describing the random fluctuation characteristics of wind power include relative power deviation; The relative power deviation ρ% is shown below: In the formula, t0 is the initial moment of the control period; t is the control period; P is the wind power, which is the sum of the measured wind power value at the current moment and the random power deviation; ΔP is the fluctuating power value of wind power during the control period. The wind power P(t0) at the initial moment of the control period and the fluctuating wind power ΔP during the control period are shown below: In the formula, This represents random power deviation.

4. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 1, characterized in that: The characteristic period of wind power fluctuation includes the period in which the number of times of significant wind power fluctuation is greater than a set threshold t. max % of the time period; The criteria for significant fluctuations in wind power are as follows: ΔQ>D'Q c (5) In the formula, ΔQ is the reactive power deviation of wind power; D' is the dead zone coefficient of the compensation capacitor; Q c This refers to the capacitance of a group of capacitors.

5. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 1, characterized in that, The steps to compress the original wind power scenario into a typical scenario using the k-means clustering method include: 1) Let the sample size be N, the observation index of each sample be M, and the amount of data to be clustered be Z. N×M The number of clusters is k; at the initial time t=1, k samples are selected as the initial agglomeration points Z. j (t); j = 1, 2, ..., K; 2) Calculate the Euclidean distance D(Z) from each sample to the initial cluster center. i Z j The algorithm iterates through each sample and performs a clustering operation on all samples, with n samples in each cluster. The classification criterion is minimizing the Euclidean distance from the sample to the initial cluster center. The values ​​i = 1, 2, ..., N are used to identify the clustering groups. j 1 sample; minimum Euclidean distance D(Z) i Z m (t) is shown below: D(Z i ,Z m (t))=min{D(Z i ,Z j (t),i=1,2,…,N)},m∈[1,L] (6) In the formula, L is the inter-class distance, representing the distance from all cluster centers to the spatial center; 3) Update K new cluster centers Z j (t+1), that is: In the formula, Z i (j) Let represent the cluster center of the j-th class, and n be the number of spatial objects; 4) Determine Z j (t+1)=Z j (t) If true, clustering ends and typical scenarios are generated; otherwise, return to step 2.

6. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 5, characterized in that, The typical scenario probability P of the generated typical scenario i As shown below: P i =N i / N (8) In the formula, N i Let be the number of samples included in the i-th typical scenario.

7. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 5, characterized in that, The metrics for evaluating the effectiveness of the optimal number of clusters are as follows: In the formula, F is the distance cost function, which represents the sum of inter-class distance and intra-class distance. The distance cost function is negatively correlated with the effectiveness of the optimal number of clusters; L is the inter-class distance, which represents the distance from all cluster centers to the spatial center; D is the intra-class distance, which represents the sum of the distances from the samples within each cluster to their cluster centers. m is the mean of all samples, m i For cluster C i The mean of the included samples; k is the number of clusters, and p is any sample in the space.

8. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 1, characterized in that, The single-step adjustment constraint for the power plant busbar is shown below: ΔV h =C h ΔV g,s +C hw ΔQ w,s (10) In the formula, ΔV h and The single-step adjustment of the bus voltage on the high-voltage side of the power plant and its maximum allowable value, with dimension n. g ×1;C h and C hw These are the sensitivity matrices of the high-voltage bus voltage of the power plant to the generator terminal voltage and the reactive power output of wind power, respectively, with dimensions n. g ×n g and n g ×n w ;ΔV h For decision variables; The upper and lower limits of the high-voltage bus voltage at the power plant are constrained as follows: In the formula, and These represent the current, upper, and lower limits of the voltage on the high-voltage side bus of the power plant, respectively, each with dimension n. g ×1; The upper and lower limits of the central bus voltage are constrained as follows: In the formula, and The upper and lower limits of the central point voltage are both n in dimension. p ×1;α p The confidence level of this constraint; The upper and lower limits of generator reactive power output are constrained as follows: The upper and lower limits of the generator terminal voltage are constrained as follows: In the formula, and The generator terminal voltage has current, upper, and lower limits, each with dimension n. g ×1, α g The confidence level of this constraint; The upper and lower limits of the converter firing angle are constrained as follows: In the formula, and Let n be the current value, upper limit, and lower limit of the cosine of the converter firing angle. d ×1;C d and C dw These are the sensitivity matrices of the converter firing angle cosine to the generator terminal voltage and the wind power reactive power output, respectively, with dimensions n. d ×n g and n d ×n w ; The upper and lower limits of reactive power at the converter gate are constrained as follows: In the formula, and Let n be the current value, upper limit, and lower limit of reactive power at the converter station gateway, each with dimension n. d ×1;C n and C nw The sensitivity matrices for reactive power at the converter station gate to generator terminal voltage and reactive power output of wind power are given, with dimensions n respectively. d ×n g and n d ×n w .

9. The AC / DC system coordinated two-stage voltage control method considering the randomness of wind power according to claim 1, characterized in that, Tools for solving coordinated two-stage voltage control models of AC / DC systems that take into account the stochasticity of wind power include the quadprog function on the Matlab software platform.

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