A Voltage Control Method and System for Distribution Networks with High Photovoltaic Penetration

Abstract

The present invention discloses a method and system for voltage control of a distribution network with high photovoltaic penetration. The method includes: constructing a voltage control strategy for a distribution network with high photovoltaic penetration; constructing a dynamic degradation cost function of an energy storage system; constructing a calculation model for approximating the node voltage of the distribution network; constructing a CVaR function for evaluating the risk of voltage violation and the risk of inverter capacity violation; constructing a centralized optimization model for voltage control of a distribution network with high photovoltaic penetration considering photovoltaic uncertainty, calculating the weighted sum of the risk of node voltage exceeding the upper limit and the voltage control cost within a finite time domain, constructing an objective function with minimizing the weighted sum as the goal, and constructing a global optimal voltage control strategy; solving the centralized optimization model based on the distributed robust model predictive control algorithm to output a voltage-reactive power droop control curve; and adjusting the reactive power output of the photovoltaic inverter based on the voltage-reactive power droop control curve to achieve voltage control. The present invention can reduce voltage deviation in real time and lower the voltage control cost.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network voltage control, and particularly relates to a voltage control method and system for a distribution network with high photovoltaic penetration rate. Background Art

[0002] The installed capacity of distributed photovoltaics is increasing year by year, which has significantly changed the operating characteristics of active distribution networks. The uncertainty and volatility of photovoltaic power generation may cause the node voltage amplitude of the distribution network to exceed the safe range, thus increasing the cost and difficulty of distribution network voltage control. It is necessary to seek a balance between the two conflicting goals of economy and security.

[0003] In traditional distribution networks, voltage is often controlled by upgrading lines, installing power electronic reactive voltage regulation equipment, adjusting on-load tap-changing transformers and shunt capacitors, etc. However, limited by the installation cost, operation frequency and response speed of the equipment, the above methods cannot effectively address the voltage over-limit problem in distribution networks with high photovoltaic penetration rate. Photovoltaic inverters require no additional construction cost, have a fast response, and can adjust active power and reactive power frequently and independently; electrochemical energy storage systems can respond quickly and the construction cost is gradually decreasing, and are often connected as supporting facilities to power systems containing a high proportion of renewable energy. However, there are generally two limitations in existing distribution network voltage control strategies when considering energy storage scheduling: First, the battery degradation cost caused by the charge and discharge cycle of the battery energy storage system is not effectively considered; Second, the mathematical representation of the energy storage operation cost mostly uses a fixed cost coefficient. The above simplified model is likely to cause the energy storage unit to charge and discharge frequently, resulting in accelerated life decay, or cause unnecessary reduction of the renewable energy consumption capacity due to the deviation of the operation cost estimation, ultimately restricting the economic operation efficiency of the distribution network system and the grid connection and consumption capacity of high-penetration photovoltaics. Therefore, how to comprehensively consider the characteristics of photovoltaic inverters and energy storage, and reasonably dispatch photovoltaic inverters and energy storage systems to provide voltage control services for active distribution networks has become an issue worthy of attention. Summary of the Invention

[0004] To overcome the defects and deficiencies of the existing technologies, the present invention provides a method and system for voltage control of a distribution network with high photovoltaic (PV) penetration. The present invention is based on a centralized-local coordinated voltage control strategy for a distribution network with high PV penetration considering energy storage degradation, and takes into account the cyclic life degradation of the energy storage. In the centralized optimization stage of the control strategy, a distributionally robust model predictive control algorithm based on the Wasserstein distance is formulated to cope with the PV prediction error. Led by the distribution network operator, the risk of node voltage exceeding the upper limit is weighed against the distribution network voltage control cost including the dynamic degradation cost of the energy storage system, which can effectively control the risk of voltage over-limit, reduce the operation cost of the distribution network, extend the service life of the energy storage system, and improve the economic efficiency and safety of system operation. In the local control stage, the PV inverter adjusts the reactive power output according to the improved control curve in the centralized optimization stage to cope with the real-time fluctuations of PV. Based on the optimized voltage-reactive power droop control curve, the PV inverter can quickly provide reactive power to achieve real-time voltage control and reduce the voltage deviation. In addition, the dynamic degradation cost of the electrochemical energy storage system is incorporated into the distribution network voltage control cost to evaluate the impact of short-term scheduling on the long-term battery capacity.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for voltage control of a distribution network with high PV penetration, including the following steps:

[0007] Construct a voltage control strategy for a distribution network with high PV penetration;

[0008] Construct a dynamic degradation cost function of the energy storage system;

[0009] Construct a calculation model for the approximate value of the node voltage of the distribution network;

[0010] Construct a CVaR function for evaluating the risk of voltage over-limit and the risk of inverter capacity over-limit;

[0011] Construct a centralized optimization model for voltage control of a distribution network with high PV penetration considering PV uncertainty, calculate the weighted sum of the risk of node voltage exceeding the upper limit and the distribution network voltage control cost within a finite time domain, construct an objective function with minimizing the weighted sum as the goal, and construct a global optimal voltage control strategy;

[0012] Solve the centralized optimization model based on the distributionally robust model predictive control algorithm, and output a voltage-reactive power droop control curve;

[0013] Adjust the reactive power output of the PV inverter based on the voltage-reactive power droop control curve to achieve voltage control.

[0014] As a preferred technical solution, constructing a voltage control strategy for a distribution network with high PV penetration specifically includes:

[0015] Construct a voltage control strategy for a distribution network with a high photovoltaic penetration rate that coordinates the centralized and local phases. In the centralized optimization stage of the control strategy, make a decision once based on the electricity purchase and sale prices reported by the distribution network, photovoltaic power prediction information, load prediction information, and the state of charge of the energy storage system. Minimize the weighted sum of the risk of node voltage exceeding the upper limit and the distribution network voltage control cost within a finite time domain by controlling the electrical energy exchanged with the main grid, the active power output of the photovoltaic system, the active power output of the energy storage system, and the slope of the inverter voltage-reactive power droop control curve, and generate a global optimal strategy.

[0016] In the local control stage of the control strategy, based on the voltage-reactive power droop control curve, adjust the reactive power output of the photovoltaic inverter according to the node voltage of the distribution network.

[0017] As an optimal technical solution, construct a dynamic degradation cost function for the energy storage system, specifically including:

[0018] Taking the state of charge n of the energy storage system at node t at time as the input, construct a degradation cost density function of the energy storage system with respect to the state of charge , expressed as:

[0019] ;

[0020] Among them, is the cost per unit capacity of the energy storage system, is the total capacity of the energy storage system, is the charge-discharge efficiency of the energy storage system, and a and b are empirical parameters of battery degradation;

[0021] Based on the least squares method, simplify the degradation cost density function into a piecewise linear function, and construct a dynamic degradation cost function for the energy storage system, expressed as:

[0022] ;

[0023] Among them, is the output power of the energy storage system at node n at time t , is the decision time interval.

[0024] As an optimal technical solution, construct a calculation model for the approximate value of the node voltage of the distribution network, specifically including:

[0025] Based on the linear approximation method of the AC power flow equation, construct a calculation model for the approximate value t of the node voltage of the distribution network at time considering the influence of photovoltaic power prediction error, expressed as:

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] wherein, is the nodal admittance matrix without including the slack node, and are the corresponding resistance matrix and reactance matrix respectively, is the mutual admittance between the slack node and the PQ node, is the slack node voltage, is the prediction error of the photovoltaic at time , represents the active power prediction error vector affected by the uncertainty of photovoltaic output, represents the reactive power prediction error vector affected by the uncertainty of photovoltaic output, , and are the reactive power, active power and nodal voltage vector of the pre-determined photovoltaic output respectively, is the nodal voltage vector phase, and j represents the imaginary part of the complex number.

[0032] As a preferred technical solution, a CVaR function for evaluating the risk of voltage over-limit and the risk of inverter capacity over-limit is constructed, specifically including:

[0033] ;

[0034] ;

[0035] ;

[0036] wherein, represents the risk of voltage over-upper limit, represents the risk of voltage over-lower limit, represents the risk of inverter capacity over-limit, , and are all CVaR auxiliary variables, represents the reactive power injected by the photovoltaic at node n into the distribution network at time t , is the given confidence level, For the node n At the moment t In the photovoltaic prediction error dataset, the m th photovoltaic prediction error, M is the number of samples contained in the photovoltaic prediction error dataset, Is the probability density function, And Are respectively the node voltage amplitude and the maximum available active power of the photovoltaic when the photovoltaic prediction error is , V max Represents the upper limit allowed for the node voltage amplitude, V min Represents the lower limit allowed for the node voltage amplitude, Indicates that If the value inside is positive, take this value itself; if it is not positive, take 0, Is the proportion of the active power cut by the photovoltaic at node n at the moment t , Indicates the node n The square of the rated capacity of the photovoltaic at the location.

[0037] As a preferred technical solution, calculate the weighted sum of the risk of the node voltage exceeding the upper limit and the cost of distribution network voltage control within a finite time domain, and construct an objective function with minimizing the weighted sum as the goal, which is specifically expressed as:

[0038] ;

[0039] ;

[0040] Among them, Is the cost of distribution network voltage control at the prediction time , Is the risk coefficient, Indicates the finite time domain, Is the risk of the node voltage exceeding the upper limit, N is the total number of distribution network nodes, Represents the cost of the distribution network purchasing electricity from the public grid, Represents the cost of the reactive power output of the photovoltaic inverter in the distribution network, Represents the penalty for the change of the droop control curve of the photovoltaic inverter in the distribution network, Represents the penalty for curtailment of light in the distribution network affected by photovoltaic prediction uncertainty, Represents the total sum of the dynamic degradation costs of all distribution network energy storage systems.

[0041] As a preferred technical solution, the calculation formulas for each cost in the distribution network voltage control cost are expressed as:

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] Among them, is the set including all nodes of the distribution network, represents the power purchase cost of the distribution network from the public grid at the prediction time , is the time interval for decision-making, is the power purchase price, is the time the power purchase quantity of the distribution network from the public grid, is the reactive power output cost of the photovoltaic inverter of the distribution network at the prediction time , is the reactive power output cost price of the photovoltaic inverter, is the node n at the prediction time the reactive power output, is the time the penalty for the change of the photovoltaic inverter droop control curve of the distribution network, is the penalty cost coefficient for the change of the inverter voltage-reactive power droop curve, and are the positions of the 3rd and 4th nodes of the standard voltage-reactive power droop curve, and are the adjustable variables of the variable slope droop curve of the photovoltaic inverter at node n in the centralized control stage, represents the curtailment penalty of the distribution network affected by the uncertainty of photovoltaic prediction at the prediction time , is the curtailment penalty coefficient, is the node n at the photovoltaic at the prediction time the active power curtailment ratio, is the node n at the photovoltaic at the prediction time the maximum available active power considering the photovoltaic prediction error, is the prediction time the total dynamic degradation cost of all distribution network energy storage systems, is the node n at the prediction time the dynamic degradation cost of the energy storage system.

[0048] As a preferred technical solution, a global optimal voltage control strategy is constructed, specifically including:

[0049] The global optimal voltage control strategy satisfies the power balance constraint:

[0050] ;

[0051] Among them, is the sum of the distribution network load powers at time t , is the sum of the powers absorbed by the energy storage system at time t , is the power transmitted from the public power grid to the distribution network at time t , is the sum of the active powers output by the photovoltaic at time t ;

[0052] The global optimal voltage control strategy satisfies the inverter voltage - reactive power droop control curve constraint:

[0053] ;

[0054] ;

[0055] Among them, is the upper limit of the reactive power output of the photovoltaic inverter, is the approximate value of the node voltage at node n at time t , is the position of the k th node of the standard voltage - reactive power droop curve, , respectively represent the adjustable variables of the variable - slope droop curve of the photovoltaic inverter at node n during the centralized control stage;

[0056] The global optimal voltage control strategy satisfies the energy storage system constraint:

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] Among them, the state of charge of the energy storage system at node n at time t , is the charge - discharge efficiency of the energy storage system at node n , is the set of distribution network nodes connected to energy storage, represents the capacity of the battery B at node n ; represents the absolute value of the power output by the energy storage at node n at time t ; is the energy input by the energy storage system at node n at time t ; is the energy output by the energy storage system at node n at time t ;

[0062] Using the direct sample average approximation method to handle the CVaR of node voltage below the lower limit and the CVaR of photovoltaic inverter capacity exceeding the limit, the global optimal voltage control strategy satisfies the following constraints:

[0063] ;

[0064] ;

[0065] ;

[0066] where M is the number of samples in the photovoltaic prediction error data set, V min represents the lower limit allowed for the node voltage amplitude, and are the node voltage amplitude and the maximum available active power of the photovoltaic respectively, , and are all CVaR auxiliary values, represents if the value within is positive, take the value itself, if not positive, take 0, is the given confidence level, is the proportion of the active power cut by the photovoltaic at node n at time t , represents the reactive power injected by the photovoltaic at node n at time t into the distribution network, represents the square of the rated capacity of the photovoltaic at node n ;

[0067] As a preferred technical solution, solving the centralized optimization model based on the distributionally robust model predictive control algorithm specifically includes:

[0068] Updating the photovoltaic prediction value and the load prediction value within the finite time domain;

[0069] Constructing a Wasserstein metric model based on the finite historical data set, expressed as:

[0070] ;

[0071] Among them, is the Wasserstein distance between the empirical probability distribution and the true probability distribution . and are respectively and random vectors in , represents the M-dimensional real space, the matrix and the vector are respectively the coefficient and vector in the uncertainty support set of the photovoltaic prediction error, represents the set of all values of the two-dimensional random vector ; is the joint probability distribution with and as the marginal probability distributions;

[0072] Establish a probability distribution fuzzy set based on the Wasserstein distance, denoted as:

[0073] ;

[0074] represents the probability distribution fuzzy set based on the Wasserstein distance, is the set of the true probability distribution , and this fuzzy set is centered on the empirical probability distribution and is the radius;

[0075] Establish a distributionally robust optimization model based on the probability distribution fuzzy set, denoted as:

[0076] ;

[0077] Among them, represents the expected value under the probability distribution ;

[0078] Reconstruct the distributionally robust optimization model based on a data-driven method. The reconstructed model is specifically:

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] Among them, and respectively represent the vectors formed by the th rows of the matrices n and , and are auxiliary variables for data-driven distributionally robust optimization, M represents the number of samples included in the photovoltaic prediction error dataset, T is the transpose symbol, n indicates the corresponding power grid node, represents the identity matrix of order N , represents the vector of the active power curtailment ratio of the photovoltaic inverter at time t , is an integer auxiliary variable, represents the zero matrix of order N , is an auxiliary variable in CVaR, is the given confidence level, , and respectively represent the vectors of the active power injected by photovoltaic at time t , the vectors of the active power absorbed by the energy storage system, and the vectors of the active power absorbed by the load, is the vector of the reactive power injected into the distribution network at time t ;

[0086] Solve the multi-stage distributionally robust optimization problem, and determine the amount of electric energy purchased from the main grid, the active power curtailment ratio of photovoltaic, the energy absorbed by the energy storage, and the voltage-reactive power droop control curve of the photovoltaic inverter in the control time domain according to the solution results.

[0087] The present invention also provides a voltage control system for a distribution network with high photovoltaic penetration rate, which is used to implement the above-mentioned voltage control method for a distribution network with high photovoltaic penetration rate. The system includes: a control strategy construction module, a dynamic degradation cost function construction module, a voltage calculation model construction module, a CVaR function construction module, a centralized optimization model construction module, a centralized optimization model solution module, and a voltage control module;

[0088] The control strategy construction module is used to construct a voltage control strategy for a distribution network with high photovoltaic penetration rate;

[0089] The dynamic degradation cost function construction module is used to construct the dynamic degradation cost function of the energy storage system;

[0090] The voltage calculation model construction module is used to construct a calculation model for the approximate value of the node voltage of the distribution network;

[0091] The CVaR function construction module is used to construct a CVaR function for evaluating the risk of voltage over-limit and the risk of inverter capacity over-limit;

[0092] The centralized optimization model construction module is used to construct a centralized optimization model for voltage control of a distribution network with a high photovoltaic penetration rate considering photovoltaic uncertainty, calculate the weighted sum of the risk of node voltage exceeding the upper limit and the distribution network voltage control cost within a finite time domain, construct an objective function with the goal of minimizing the weighted sum, and construct a global optimal voltage control strategy;

[0093] The centralized optimization model solving module is used to solve the centralized optimization model based on the distributionally robust model predictive control algorithm and output a voltage-reactive power droop control curve;

[0094] The voltage control module is used to adjust the reactive power output of the photovoltaic inverter based on the voltage-reactive power droop control curve to achieve voltage control.

[0095] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0096] (1) The present invention adopts a technical solution of integrating the mathematical expression of the local control strategy into the centralized optimization model, solves the technical problem that the decisions at the centralized control level and the local control level are determined in isolation, and achieves the technical effects of global optimality and local fast response.

[0097] (2) The present invention adopts a technical solution of using the distributionally robust model predictive control algorithm based on the Wasserstein distance to solve the uncertainty problem brought by photovoltaic prediction errors, solves the technical problem that the existing hierarchical voltage control strategy does not fully exploit the information of photovoltaic prediction data, and achieves the technical effects of filtering abnormal data and rolling updating photovoltaic prediction data.

[0098] (3) The present invention adopts a technical solution of a calculation model for the dynamic degradation cost of energy storage considering charge and discharge cycles, solves the technical problem that the energy storage scheduling cost is not reasonably estimated, and achieves the effect of improving the overall performance of the strategy by reasonably balancing the energy storage degradation cost and the photovoltaic curtailment amount. Description of the Drawings

[0099] Figure 1 It is a schematic flowchart of the method for voltage control of a distribution network with a high photovoltaic penetration rate of the present invention;

[0100] Figure 2Schematic diagram of the voltage control strategy for a high PV penetration distribution network with coordinated central-local control in the present invention;

[0101] Figure 3 Schematic diagram of the voltage-reactive power droop control curve of the PV inverter with variable slope in the present invention;

[0102] Figure 4 Schematic diagram of the process for solving the optimal voltage control strategy for a high PV penetration distribution network in the present invention. Detailed implementation manners

[0103] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0104] Embodiment 1

[0105] As Figure 1 shown, this embodiment provides a voltage control method for a distribution network with high PV penetration, including the following steps:

[0106] S1: Determine the voltage control strategy for a high PV penetration distribution network with coordinated central-local control. Weigh the system voltage control cost including the dynamic degradation cost of the energy storage system and the voltage violation risk during the centralized optimization stage of the control strategy. In the local control stage, control the reactive power output of the PV inverter according to the local voltage-reactive power droop control curve adjusted in the centralized stage to cope with the rapid fluctuations of PV;

[0107] As Figure 2 shown, the voltage control strategy for a high PV penetration distribution network with coordinated central-local control in step S1 is specifically as follows:

[0108] In the centralized control layer, at each control time domain T e Make a decision once based on the power purchase and sale price, PV prediction information, load prediction information, and state of charge (SOC) of the energy storage system reported by the distribution network. In the centralized optimization stage, minimize the weighted sum of the node voltage over-limit risk and the distribution network voltage control cost within a finite time domain by controlling the electric energy exchanged with the main grid, the active power output of PV, the active power output of the energy storage, and the slope of the inverter voltage-reactive power droop control curve, and generate a global optimal strategy;

[0109] In the local control layer, each PV inverter determines the reactive power output of the PV inverter based on the voltage-reactive power droop control curve in the centralized optimization stage according to the node voltage of the distribution network, and finally realizes the real-time minimization of the node voltage deviation;

[0110] S2: Construct the dynamic degradation cost function of the energy storage system, specifically including:

[0111] Taking the state of charge (SOC) of the energy storage system at the node n at time t as the input, a deterioration cost density function of the energy storage system with respect to the state of charge is constructed (State of Charge, SOC), which is specifically expressed as: ;

[0112] ;

[0113] where is the cost per unit capacity of the energy storage system, is the total capacity of the energy storage system, is the charge-discharge efficiency of the energy storage system, the subscript B represents the battery, and a and b are empirical parameters of battery deterioration, which are generally determined according to the experimental data provided by the battery manufacturer.

[0114] Based on the least squares method, the deterioration cost density function is simplified to a piecewise linear function, and a dynamic deterioration cost function of the energy storage system applicable to complex problems is constructed:

[0115] ;

[0116] where is the output power of the energy storage system at the node n at time t , the subscript B represents the battery, is the decision time interval;

[0117] S3: Construct a calculation model for the approximate value of the distribution network node voltage;

[0118] The calculation model for the approximate value of the distribution network node voltage in step S3 is specifically as follows: Based on the linear approximation method of the AC power flow equation, a calculation model for the approximate value t of the distribution network node voltage at time considering the influence of photovoltaic prediction error is constructed, which is specifically expressed as:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] ;

[0124] where is the nodal admittance matrix excluding the slack node, and are the corresponding resistance matrix and reactance matrix respectively, is the mutual admittance between the slack node and the PQ node, is the slack node voltage, is the prediction error of the photovoltaic at time , which will cause the active power prediction error and reactive power prediction error of the photovoltaic, represents the active power prediction error vector affected by the uncertainty of photovoltaic output, represents the reactive power prediction error vector affected by the uncertainty of photovoltaic output, , and are the reactive power, active power and node voltage vectors of the pre-determined photovoltaic output respectively, is the node voltage vector phase of, j represents the imaginary part of the complex number.

[0125] S4: Based on the constructed approximate calculation model of the node voltage of the distribution network, establish a CVaR function for evaluating the risk of voltage violation and the risk of inverter capacity violation;

[0126] In this embodiment, the CVaR function for evaluating the risk of voltage violation and the risk of inverter capacity violation is specifically:

[0127] ;

[0128] ;

[0129] ;

[0130] Among them, represents the risk of voltage exceeding the upper limit, represents the risk of voltage falling below the lower limit, represents the risk of inverter capacity violation, , and are all CVaR auxiliary variables, represents the node n the reactive power injected by the photovoltaic into the distribution network at time t , is the given confidence level, and the value range is between 0 and 1, is the node n at time t the m th photovoltaic prediction error in the photovoltaic prediction error dataset, M is the number of samples contained in the photovoltaic prediction error dataset, is the probability density function, and are the node voltage amplitude and the maximum available active power of the PV when the PV prediction error is respectively, and V max represents the upper limit allowed for the node voltage amplitude, in V min represents the lower limit allowed for the node voltage amplitude, denotes that if the value within is positive, take this value itself; if it is not positive, take 0, is the proportion of the active power curtailed by the PV at node n at time t , with a value range between 0 and 1, and is the n rated capacity of the PV at node denotes the n square of the rated capacity of the PV at node

[0131] S5: Establish a centralized optimization model for voltage control of a distribution network with high PV penetration considering PV uncertainty, specifically including:

[0132] (1) Based on the model predictive control algorithm, with the goal of minimizing the weighted sum of the risk of node voltage exceeding the upper limit within a finite time domain T p and the cost of distribution network voltage control, the determined objective function is:

[0133] ;

[0134] ;

[0135] where is the cost of distribution network voltage control at the prediction time , is the risk coefficient. The higher the risk coefficient, the more the distribution network operator attaches importance to the risk of the system voltage amplitude exceeding the upper limit, denotes the finite time domain, is the risk of node voltage exceeding the upper limit, N is the total number of distribution network nodes, with the superscript representing the quantity directly related to the PV prediction error dataset, and the cost of distribution network voltage control is composed of the cost of purchasing electricity from the public grid by the distribution network , the cost of reactive power output of the distribution network PV inverter , the penalty for the change of the droop control curve of the distribution network PV inverter , the penalty for curtailment of light in the distribution network affected by PV prediction uncertainty and the total dynamic degradation cost of all distribution network energy storage systems , and the specific calculation formula is as follows:

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] ;

[0141] Among them, is the set including all nodes of the distribution network, represents the power purchase cost of the distribution network from the public grid at the prediction time and is replaced by because there is a prediction time domain ( t to t to t +T p ), is the time interval for decision-making, is the power purchase price, is the time when the power purchase quantity of the distribution network from the public grid, is the prediction time of the reactive power output cost of the PV inverter in the distribution network, is the reactive power output cost price of the PV inverter, is the node n at the prediction time of the reactive power output. When there is no PV connected to the node n , it is constantly 0, and is the time of the droop control curve variation penalty of the PV inverter in the distribution network, is the droop curve variation penalty cost coefficient of the inverter voltage-reactive power, and are the 3rd and 4th node positions of the standard voltage-reactive power droop curve, and are the adjustable variables of the variable slope droop curve of the PV inverter at the node n in the centralized control stage, represents the prediction time of the curtailment penalty of the distribution network affected by PV prediction uncertainty, is the curtailment penalty coefficient, is the node n where the PV at the prediction time has the active power curtailment ratio, is the node n where the PV at the prediction time The maximum available active power considering the photovoltaic prediction error is the prediction time the total dynamic degradation cost of all distribution network energy storage systems is the node n at the prediction time the dynamic degradation cost of the energy storage system

[0142] (2)The formulated global optimal voltage control strategy should satisfy the following power balance constraints:

[0143] ;

[0144] where, is the sum of the distribution network load powers at time t , is the sum of the powers absorbed by the energy storage systems at time t , is the power transmitted from the public grid to the distribution network at time t , is the sum of the active powers output by the photovoltaics at time t ;

[0145] (3)The formulated global optimal voltage control strategy should satisfy the following inverter voltage - reactive power droop control curve constraints:

[0146] ;

[0147] ;

[0148] where, is the upper limit of the reactive power output of the photovoltaic inverter, is the approximate value of the node voltage at node n at time t , is the position of the k th node of the standard voltage - reactive power droop curve, , respectively represent the adjustable variables of the variable - slope droop curve of the photovoltaic inverter at node n in the centralized control stage. The proposed variable - slope photovoltaic inverter voltage - reactive power droop control curve is as Figure 3 shown.

[0149] (4)The formulated global optimal voltage control strategy should satisfy the following energy storage system constraints:

[0150] ;

[0151] ;

[0152] ;

[0153] ;

[0154] wherein, the state of charge of the energy storage system at node n at time t , is the charge-discharge efficiency of the energy storage system at node n , is the set of distribution network nodes with energy storage connected, represents the capacity of battery B at node n , represents the absolute value of the power output by the energy storage at node n at time t , is the energy input to the energy storage system at node n at time t , is the energy output by the energy storage system at node n at time t , and are both positive values.

[0155] (5) To improve the calculation efficiency, the direct sample average approximation method is further used to process the CVaR of the node voltage below the lower limit and the CVaR of the photovoltaic inverter capacity exceeding the limit. Therefore, the globally optimal voltage control strategy formulated should satisfy the following constraints:

[0156] ;

[0157] ;

[0158] ;

[0159] where M is the number of samples included in the photovoltaic prediction error data set;

[0160] S6: Use the data-driven distributionally robust model predictive control algorithm to solve the centralized optimization model of the voltage control of the high photovoltaic penetration distribution network considering photovoltaic uncertainty established in step S5, as Figure 4 shown. The specific process is as follows:

[0161] S61: Update the photovoltaic prediction value and the load prediction value within the finite time horizon ;

[0162] S62: Establish a Wasserstein metric model based on the finite historical data set, specifically expressed as:

[0163] ;

[0164] Among them, is the Wasserstein distance between the empirical probability distribution and the true probability distribution . and are respectively and random vectors, and their value sets are both . represents the M-dimensional real space. The matrix and the vector are respectively the coefficients and vectors in the uncertainty support set of the photovoltaic prediction error. represents the set of all values of the two-dimensional random vector . is the joint probability distribution with and as the marginal probability distributions.

[0165] S63: Establish a probability distribution fuzzy set based on the Wasserstein distance , specifically expressed as:

[0166] ;

[0167] Among them, represents the probability distribution fuzzy set based on the Wasserstein distance. is the set of the true probability distribution . This fuzzy set is centered on the empirical probability distribution , and is the radius. The distribution network operator can control the confidence level of the probability distribution fuzzy set containing the true probability distribution of the random variable and the conservativeness of the decision by adjusting as the radius.

[0168] S64: Establish a distributionally robust optimization model based on the probability distribution fuzzy set. The model is specifically:

[0169] ;

[0170] Among them, represents the expected value under the probability distribution ;

[0171] The distributionally robust optimization model makes an optimization decision for the probability distribution that maximizes the voltage violation risk in the fuzzy set established in step S63 to consider the impact of photovoltaic prediction error uncertainty on the CVaR of voltage over-limit.

[0172] S65: Reconstruct the distributionally robust optimization model based on a data-driven approach. The reconstructed model is specifically as follows:

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] ;

[0178] ;

[0179] and respectively represent the vectors formed by the and th rows of the matrices n . , and are auxiliary variables for data-driven distributionally robust optimization. M represents the number of samples in the photovoltaic prediction error dataset, T is the transpose symbol, n indicates the corresponding power grid node, represents the identity matrix of order N , represents the vector of active power curtailment ratios of the photovoltaic inverter at time t , is an integer auxiliary variable, represents the zero matrix of order N , is an auxiliary variable in CVaR, is the given confidence level, , and respectively represent the vectors of active power injected by photovoltaic, the vectors of active power absorbed by the energy storage system, and the vectors of active power absorbed by the load in the distribution network at time t , is the vector of reactive power injected into the distribution network at time t , and together define the uncertainty set .

[0180] S66: Solve the multi-stage distributionally robust optimization problem and determine the control horizon based on the solution results T eThe quantity of electric energy purchased from the main grid inward, the reduction ratio of PV active power, the energy absorbed by the energy storage, and the voltage-reactive power droop control curve of the PV inverter. These controls are at the minute level. After the control instructions are issued, while the centralized controller advances the solution time by one control time domain and then returns to step S61 to continue rolling solution, the PV inverter, based on the voltage-reactive power droop control curve, controls its own reactive power output according to the locally measurable voltage amplitude to cope with the second-level fluctuations of the PV.

[0181] Embodiment 2

[0182] This embodiment provides a voltage control system for a distribution network with high PV penetration rate to implement the voltage control method for a distribution network with high PV penetration rate in the above Embodiment 1. The system includes: a control strategy construction module, a dynamic degradation cost function construction module, a voltage calculation model construction module, a CVaR function construction module, a centralized optimization model construction module, a centralized optimization model solution module, and a voltage control module;

[0183] In this embodiment, the control strategy construction module is used to construct a voltage control strategy for a distribution network with high PV penetration rate;

[0184] In this embodiment, the dynamic degradation cost function construction module is used to construct a dynamic degradation cost function of the energy storage system;

[0185] In this embodiment, the voltage calculation model construction module is used to construct a calculation model for the approximate value of the distribution network node voltage;

[0186] In this embodiment, the CVaR function construction module is used to construct a CVaR function for evaluating the risk of voltage over-limit and the risk of inverter capacity over-limit;

[0187] In this embodiment, the centralized optimization model construction module is used to construct a centralized optimization model for voltage control of a distribution network with high PV penetration rate considering PV uncertainty, calculate the weighted sum of the risk of node voltage exceeding the upper limit and the distribution network voltage control cost within a finite time domain, construct an objective function with minimizing the weighted sum as the goal, and construct a global optimal voltage control strategy;

[0188] In this embodiment, the centralized optimization model solution module is used to solve the centralized optimization model based on the distributionally robust model predictive control algorithm and output a voltage-reactive power droop control curve;

[0189] In this embodiment, the voltage control module is used to adjust the reactive power output of the PV inverter based on the voltage-reactive power droop control curve to achieve voltage control.

[0190] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A voltage control method for a distribution network with high photovoltaic penetration, characterized in that: The steps include: Construct a voltage control strategy for distribution networks with high photovoltaic penetration, including: Construct a centralized-local coordinated voltage control strategy for high photovoltaic penetration distribution networks. In the centralized optimization stage of the control strategy, a decision is made once based on the purchase and sale prices of electricity reported by the distribution network, photovoltaic forecast information, load forecast information, and the state of charge of the energy storage system. By controlling the electric energy exchanged with the main grid, the photovoltaic active output, the active power output of the energy storage, and the slope of the inverter voltage-reactive droop control curve, the risk of node voltage exceeding the upper limit in a limited time domain and the weighted sum of the distribution network voltage control cost are minimized to generate a global optimal strategy. In the local control stage of the control strategy, the reactive power output of the PV inverter is adjusted according to the voltage of the distribution network node based on the voltage-reactive power droop control curve; Construct the dynamic degradation cost function of the energy storage system, including: Node n Energy storage system in time t State of charge As input, construct the degradation cost density function of the energy storage system with respect to the state of charge , expressed as: ； in, is the cost per unit capacity of the energy storage system, is the total capacity of the energy storage system, is the charge and discharge efficiency of the energy storage system, a and b are the empirical parameters of battery degradation; Based on the least squares method, the degradation cost density function is simplified into a piecewise linear function, and the dynamic degradation cost function of the energy storage system is constructed, which is expressed as: ； in, For Node n Energy storage system in time t The output power, The time interval for decision making; Construct a distribution network node voltage approximation calculation model; Construct a CVaR function for assessing voltage over-limit risk and inverter capacity over-limit risk; A centralized optimization model for voltage control of distribution networks with high photovoltaic penetration rates considering photovoltaic uncertainty is constructed. The weighted sum of the risk of node voltage exceeding the upper limit and the voltage control cost of the distribution network in a limited time domain is calculated. The objective function is constructed with the goal of minimizing the weighted sum, and the global optimal voltage control strategy is constructed. Solve the centralized optimization model based on the distributed blue stick model predictive control algorithm and output voltage-reactive power droop control curve; The reactive power output of the photovoltaic inverter is adjusted based on the voltage-reactive power droop control curve to achieve voltage control.

2. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 1, characterized in that: Construct a distribution network node voltage approximate value calculation model, including: Based on the linear approximation method of the AC power flow equation, the moment considering the influence of photovoltaic prediction error is constructed. t Approximate voltage value of distribution network node The calculation model is expressed as: ； ； ； ； ； in, is the node admittance matrix excluding the equilibrium node, and are the corresponding resistance matrix and reactance matrix respectively, To balance the mutual admittance between the node and the PQ node, To balance the node voltage, For photovoltaic at all times The prediction error, represents the active power prediction error vector affected by the uncertainty of photovoltaic output, represents the reactive power prediction error vector affected by the uncertainty of PV output, , and are the reactive power, active power and node voltage vector of the predetermined photovoltaic output, is the node voltage vector The phase of , j represents the complex imaginary part.

3. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 1, characterized in that: Construct a CVaR function for assessing voltage over-limit risk and inverter capacity over-limit risk, including: ； ； ； in, Indicates the risk of voltage exceeding the upper limit. Indicates the risk of voltage exceeding the lower limit. Indicates the risk of inverter capacity exceeding the limit. , and are all CVaR auxiliary variables, Representation Node n Photovoltaic at the moment t The reactive power injected into the distribution network, For a given confidence level, For Node n At the moment t The first m PV prediction errors, M is the number of samples contained in the PV prediction error dataset, is the probability density function, and The photovoltaic prediction errors are The node voltage amplitude and the maximum available active power of photovoltaic power, V max Represents the upper limit of the node voltage amplitude, V min Represents the lower limit of the node voltage amplitude allowed, express If the value is positive, it takes the value itself; if it is not positive, it takes 0. is the photovoltaic power generation at node n at time t The proportion of active power cut, Representation Node n The square of the rated capacity of the photovoltaic power plant.

4. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 1, characterized in that: The weighted sum of the node voltage exceeding the upper limit risk and the distribution network voltage control cost in the finite time domain is calculated, and the objective function is constructed with the goal of minimizing the weighted sum, which is specifically expressed as: ； ； in, For prediction time The voltage control cost of the distribution network is is the risk factor, represents a finite time domain, t Indicates time t , is the risk of node voltage exceeding the upper limit, N is the total number of distribution network nodes, It represents the cost of power purchased by the distribution network from the public grid. Represents the reactive power output cost of photovoltaic inverters in distribution network, It represents the penalty of the droop control curve change of the photovoltaic inverter in the distribution network. represents the distribution network curtailment penalty affected by PV forecast uncertainty, Represents the sum of the dynamic degradation costs of all distribution network energy storage systems.

5. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 4, characterized in that: The calculation formula of each cost in the distribution network voltage control cost is expressed as: ； ； ； ； ； in, is the set of all nodes in the distribution network. Indicates the prediction time The cost of purchasing electricity from the public grid for the distribution network is is the time interval for decision making, is the electricity purchase price, For time The distribution network purchases electricity from the public grid. For prediction time The reactive power output cost of photovoltaic inverters in the distribution network, is the reactive power output cost price of the photovoltaic inverter, For Node n At prediction time The reactive power output, For time The penalty for the change of the droop control curve of the photovoltaic inverter in the distribution network, is the penalty cost coefficient for the inverter voltage-reactive power droop curve change, and It is the third and fourth node positions of the standard voltage-reactive power droop curve. and For Node n The adjustable variables of the variable slope droop curve of the photovoltaic inverter at the centralized control stage are: Indicates the prediction time The distribution network curtailment penalty affected by PV forecast uncertainty, is the light abandonment penalty coefficient, For Node n Photovoltaic in the forecast time The active power reduction ratio is For Node n Photovoltaic in the forecast time The maximum available active power taking into account the PV prediction error, For prediction time The sum of the dynamic degradation costs of all distribution network energy storage systems, For Node n At prediction time Dynamic degradation cost of energy storage system.

6. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 1, characterized in that: Construct a global optimal voltage control strategy, including: The global optimal voltage control strategy satisfies the power balance constraint: ； in, For the moment t The sum of the distribution network load power, For the moment t The sum of the powers absorbed by the energy storage system, For the moment t The power delivered from the public grid to the distribution grid, For the moment t The sum of active power output from photovoltaics; The global optimal voltage control strategy satisfies the inverter voltage-reactive power droop control curve constraint: ； ； in, Representation Node n Photovoltaic at the moment t The reactive power injected into the distribution network, is the upper limit of reactive power output of the PV inverter, For Node n In time t The node voltage approximation is The standard voltage-reactive power droop curve k The location of the nodes, , Respectively represent nodes n The adjustable variables of the variable slope droop curve of the photovoltaic inverter at the centralized control stage; The global optimal voltage control strategy satisfies the energy storage system constraints: ； ； ； ； in, is the time interval for decision making, node n Energy storage system in time t The state of charge, For Node n The charging and discharging efficiency of the energy storage system, is the collection of distribution network nodes connected to energy storage, Representation Node n The capacity of battery B at Representation Node n Energy storage in time t The absolute value of the output power, For Node n Energy storage system in time t The input energy, For Node n Energy storage system in time t Output energy; The direct sample average approximation method is used to deal with the node voltage exceeding the lower limit CVaR and the photovoltaic inverter capacity exceeding the limit CVaR. The global optimal voltage control strategy satisfies the following constraints: ； ； ； Where M is the number of samples contained in the photovoltaic prediction error dataset, V min Represents the lower limit of the node voltage amplitude allowed, and are the node voltage amplitude and the maximum available active power of photovoltaic, , and All are CVaR auxiliary values, express If the value is positive, it takes the value itself; if it is not positive, it takes 0. For a given confidence level, is the photovoltaic power generation at node n at time t The proportion of active power cut, Representation Node n Photovoltaic at the moment t The reactive power injected into the distribution network, Representation Node n The square of the rated capacity of the photovoltaic power plant.

7. The method for controlling voltage of a distribution network with high photovoltaic penetration according to claim 1, characterized in that: The centralized optimization model is solved based on the distributed robust model predictive control algorithm, including: Update the photovoltaic prediction value and load prediction value within a limited time domain; Construct a Wasserstein metric model based on a limited historical data set, expressed as: ； in, is the empirical probability distribution and the true probability distribution The Wasserstein distance between and They are and The random vectors in the set of values ​​are , Represents an M-dimensional real space, the matrix and vector are the coefficients and vectors of the uncertainty support set of the PV prediction error, Represents a two-dimensional random vector All value sets, For and is the joint probability distribution of the marginal probability distribution; The probability distribution fuzzy set based on Wasserstein distance is established and expressed as: ； represents the probability distribution fuzzy set based on Wasserstein distance, is the true probability distribution The fuzzy set is distributed in empirical probability As the center, is the radius; Based on the probability distribution fuzzy set, a distributed robust optimization model is established, which is expressed as: ； in, Represents probability distribution The expected value under Indicates the risk of voltage exceeding the upper limit; The distributed robust optimization model is reconstructed based on the data-driven method. The reconstructed model is as follows: ； ； ； ； ； ； in, and Respectively represent matrices and No. n A vector of rows, , and is the auxiliary variable of data-driven distributed robust optimization, M represents the number of samples contained in the photovoltaic prediction error dataset, T is the transposed sign, n Indicates the corresponding grid node, The order is N The identity matrix of Indicates at time t The active power reduction ratio vector of the PV inverter is: is an integer auxiliary variable, The order is N The zero matrix of is the auxiliary variable in CVaR, For a given confidence level, , and Represent the distribution network at time t The active power vector injected by photovoltaic, the active power vector absorbed by energy storage system, and the active power vector absorbed by load, For at the moment t The reactive power vector injected into the distribution network is V max Represents the upper limit of the node voltage amplitude allowed, The photovoltaic prediction error is The node voltage amplitude at represents the photovoltaic prediction error; Solve the multi-stage distributed blue stick optimization problem, and determine the amount of electricity purchased from the main grid, the proportion of photovoltaic active power reduction, the energy absorbed by the energy storage, and the voltage-reactive power droop control curve of the photovoltaic inverter within the control time domain according to the solution results.

8. A distribution network voltage control system with high photovoltaic penetration, characterized in that: A distribution network voltage control method for achieving high photovoltaic penetration as described in any one of claims 1 to 7, the system comprising: a control strategy building module, a dynamic degradation cost function building module, a voltage calculation model building module, a CVaR function building module, a centralized optimization model building module, a centralized optimization model solving module, and a voltage control module; The control strategy building module is used to build a voltage control strategy for a high photovoltaic penetration distribution network; The dynamic degradation cost function construction module is used to construct a dynamic degradation cost function of the energy storage system; The voltage calculation model building module is used to build a distribution network node voltage approximate value calculation model; The CVaR function building module is used to build a CVaR function for evaluating voltage over-limit risk and inverter capacity over-limit risk; The centralized optimization model building module is used to build a centralized optimization model for voltage control of a high photovoltaic penetration distribution network taking into account photovoltaic uncertainty, calculate the weighted sum of the node voltage exceeding the upper limit risk and the distribution network voltage control cost in a limited time domain, build an objective function with the goal of minimizing the weighted sum, and build a global optimal voltage control strategy; The centralized optimization model solving module is used to solve the centralized optimization model based on the distributed robust model predictive control algorithm and output the voltage-reactive power droop control curve; The voltage control module is used to adjust the reactive power output of the photovoltaic inverter based on the voltage-reactive power droop control curve to achieve voltage control.

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