Layered voltage control method and system for active power distribution network considering transmission and distribution cooperative scheduling

By adopting a layered voltage control method of coordinated scheduling of input and distribution in the active distribution network, the voltage fluctuation and instability problems caused by distributed power access are solved, and the coordinated control and stability of voltage are achieved.

CN119906038APending Publication Date: 2025-04-29STATE GRID ELECTRIC POWER RES INST
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Patent Information

Application Number
CN202510114127.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-01-24
Publication Date
2025-04-29

AI Technical Summary

Technical Problem

The prior art is difficult to effectively solve the voltage fluctuations, deviations and instability problems caused by large-scale access and application of distributed power supplies, especially in the case of high-permeability renewable energy power generation access.

Method used

The active distribution network layered voltage control method is adopted for the coordinated dispatch of transmission and distribution. By obtaining real-time voltage data of the distribution network and the transmission network, iteratively optimizes based on the pre-constructed optimization control model, and adjusts the voltages of the distribution network and the transmission network to achieve coordinated control of voltage.

Benefits of technology

It effectively reduces voltage fluctuations and deviations, improves the stability of the distribution network, and can keep the voltage within the normal range when the distributed power supply is connected, limiting the time when the voltage exceeds the limit.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses an active power distribution network layered voltage control method and system considering transmission and distribution cooperative scheduling in the technical field of power distribution network voltage optimization control. The method comprises the following steps: iteratively optimizing and solving a control measure quantity [mu] m, i which enables an optimization objective function in a region to correspond to an augmented Lagrange function to be minimum; iteratively optimizing and solving the voltage regulating variable VTR and the control measure quantity u of the high-voltage side bus connecting the power transmission network and the power distribution network transformer; iteratively optimizing and solving the voltage regulating variable VTC of the power transmission network; when the VTC is greater than or equal to the VTR or the number of iterations is greater than a preset number threshold, the power transmission network implements the VTC and controls the power distribution network global coordination center to issue a control measure quantity u to the power distribution network regional coordination control center; and when the power distribution network region coordination control center receives the control measure quantity u issued by the power distribution network global coordination control center, the voltage regulation quantity is regulated at the next sampling point according to a selective regulation principle. The problems of voltage fluctuation, deviation and instability caused by intermittency, volatility and uncertainty generated by large-scale access and application of the distributed power supply in the prior art can be solved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of distribution networks, and relates to a method and system for controlling hierarchical voltage of an active distribution network taking into account transmission and distribution coordinated scheduling. Background Art

[0002] The large-scale access and application of distributed generation (DG) will have a significant impact on the electrical characteristics of the distribution system, such as power flow distribution, voltage level, and short-circuit capacity. The traditional distribution network did not take the above factors into consideration during the design phase, and cannot meet the current requirements for high-penetration renewable energy generation access and efficient utilization. The voltage deviation and fluctuation problems of the distribution network are becoming increasingly prominent. In the context of the active distribution network (ADN), the inherent intermittent, volatile, and uncertain characteristics of high-penetration DG will cause voltage fluctuations, deviations, and even stability problems, requiring a higher level of control to comprehensively utilize the controllable elements of the distribution network to maintain the voltage within the normal range at all times, or to limit the voltage over-limit time to no more than the maximum action time of cutting off the distributed generation.

[0003] In existing research work, ADN voltage control structures can be mainly divided into four categories: decentralized, distributed, centralized, and hierarchical, among which the hierarchical type is a combination of the first three control structures.

[0004] ADN distributed control can respond based on locally collected information. Its advantage is that it does not require a communication system for data collection and centralized processing, and the controller can respond quickly to disturbances. However, its disadvantage is the lack of coordination between multiple distributed controllers. When simultaneous actions are taken on the same disturbance, it is easy to cause redundant control, over-control, and even control oscillation problems. ADN centralized control takes controller coordination issues into account and has good global control performance, but its global information collection and centralized optimization are relatively time-consuming. When the communication system fails, the entire control system will fail, and there will be reliability issues. ADN distributed control does not set up a coordination layer, and treats each controller or control area of ​​the distribution network as a different individual. In the distributed optimization process, individuals communicate and cooperate with each other to achieve the optimal global goal while meeting various system constraints. Under the premise of mastering accurate measurement data and precise optimization models, the global aspects of distributed optimization are far superior to distributed control, but inferior to centralized control. The ADN hierarchical voltage control structure adopts different control structures at each control level to achieve the purpose of complementary advantages of various control structures. However, existing research lacks consideration of information communication and coordination with external systems, and only considers the unidirectional obedience of the lower-level power grid to the upper-level power grid. The two-way interaction between the upper and lower power grids is not realized, and the communication and coordination mechanism between the control levels needs to be further optimized, so that the intermittent, volatile and uncertain characteristics inherent in high-penetration DG will cause voltage fluctuations, deviations, and even stability problems. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a method and system for hierarchical voltage control of an active distribution network taking into account coordinated transmission and distribution scheduling, which can solve the problems of voltage fluctuation, deviation and instability caused by the intermittent, volatility and uncertainty caused by large-scale access and application of distributed power sources in the prior art.

[0006] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0007] In a first aspect, the present invention provides a method for controlling hierarchical voltage in an active distribution network taking into account transmission and distribution coordinated scheduling, comprising:

[0008] The voltage is obtained, and the voltage includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ;

[0009] When the distribution network system voltage V DT When the deviation exceeds the preset requirement range,

[0010] Based on the pre-built regional coordinated optimization control model of the distribution network, the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region is iteratively optimized and solved. m,i ;

[0011] Based on the pre-built global coordinated optimization control model of the distribution network, the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network is solved by iterative optimization. TR and the distribution network control measure quantity ∆u;

[0012] The high-voltage side bus voltage adjustment value ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC ;

[0013] When |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network;

[0014] When the distribution network regional coordination control center DAC receives the control measure quantity ∆u issued by the distribution network global coordination control center DCC, the distribution network regional coordination control center DAC calculates the control measure quantity ∆u according to the control measure quantity ∆u at this time. m,i The cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

[0015] Furthermore, the distribution network regional coordinated optimization control model includes an augmented Lagrangian function corresponding to the regional optimization objective function, and the expression of the augmented Lagrangian function includes:

[0016] ;

[0017] ;

[0018] in, is the number of iterations, For the The optimization objective function of the distribution network area is: For the The augmented Lagrangian function, For the The penalty function of the alternating direction multiplier method algorithm for each distribution network area is a constant set in advance. For the Next iteration In the distribution network area The voltage of the coupling node of the distribution network area, For the Distribution network area The fixed reference value of the iteration, For the distribution network area dual variable matrix, To control the number of sampling points in the time domain, is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures for distribution network areas, is a 2k*2k dimensional diagonal matrix set in advance, and The cost weight of implementing control in each distribution network area, is a 2*2 dimensional matrix set in advance, The penalty factor of the slack variable in the distribution network area is is a 1*2 dimensional matrix set in advance, The distribution network area slack variables, for The transposed matrix of

[0019] Considering the voltage support of the adjacent area to the local area, the expressions of the constraint conditions include:

[0020] ,

[0021]

[0022] ,

[0023] ,

[0024] ,

[0025] ,

[0026] in, For the Distribution network area sampling points The voltage matrix after optimizing the target node and implementing the optimized control at the moment is: For the Distribution network area sampling points Before implementing the optimization control of the optimized target node at the moment, based on the distribution network system voltage V DT The voltage matrix constructed, For the Sampling points in the distribution network area The optimized target node voltage at the time is relative to the and The sensitivity of the control measures in each distribution network area; is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures in each distribution network area; and For sampling point Time next The gradually tightening upper and lower limits of the voltage amplitude in each distribution network area; is a unit vector; =[ , ] is a 1*2 dimensional matrix set in advance, Distribution network area slack variables; For sampling point Time next and A matrix composed of the cumulative control measures of the distribution network regional control nodes; For the and A matrix composed of the minimum values ​​of the total control measures of the control nodes in the distribution network area; For the and A matrix composed of the maximum values ​​of the total control measures of the control nodes in the distribution network area; For sampling point Time next and The number of single-step control measures for each control node in the distribution network area; For the and The maximum value of the single-step control measure quantity of the distribution network regional control node; To control the number of sampling points in the time domain; It is a constant set in advance and is used to adjust the progressive tightening speed of the voltage constraint in the prediction time domain; , For the The upper and lower limits of the voltage amplitude in the distribution network area;

[0027] Iterate and optimize to find the voltage regulation value ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function in this area. m,i .

[0028] Furthermore, the fixed reference value for the next iteration is The distribution network area and The average voltage of the coupling node in the distribution network area is:

[0029] ,

[0030] in, For the Distribution network area Fixed reference value for iterations; For the Next iteration Distribution Network Regional Coordination and Control Center DAC m The calculated The distribution network area and The voltage of the coupling node of the distribution network area; For the Next iteration Distribution Network Regional Coordination and Control Center DAC n The calculated The distribution network area and The voltage of the coupling node of the distribution network area;

[0031] The regional dual variables are updated according to the fixed reference value of the next iteration, and the regional dual variables are:

[0032] ,

[0033] ,

[0034] in, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area The fixed reference value of the iteration, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area Fixed reference value for iterations;

[0035] The boundary residual is calculated according to the obtained coupling node voltage difference, and the boundary residual is limited to be less than a preset residual threshold:

[0036] ,

[0037] ,

[0038] in, is the boundary residual, is the residual threshold.

[0039] Furthermore, it also includes:

[0040] When the |∆V TC |<|∆V TR |, the transmission grid control center uses ∆V TC As the maximum value of the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network, the iterative optimization solution is obtained until the |∆V TC |≥|∆V TR |Or the number of iterations is greater than the preset threshold.

[0041] Furthermore, the distribution network global coordinated optimization control model includes:

[0042] ,

[0043] in, The cost of controlling the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network is It is the voltage regulation of the high-voltage busbar connecting the transmission network and the distribution network transformer. is a 1*(M*k)-dimensional matrix, M is the total number of sub-areas of the distribution network system, k is the total number of distributed power sources and their compensation equipment in the mth distribution network area, is the control measure quantity of the distribution network control node, is a (M*k)*(M*k)-dimensional matrix, is the distribution network control cost weight diagonal matrix, is a 2*2 dimensional matrix set in advance, is the slack variable penalty factor, =[ , ] is a 1*2 dimensional matrix set in advance, which is the slack variable of the distribution network;

[0044] The expressions for the constraints include:

[0045]

[0046] in, After implementing the optimized control for the distribution network optimization target node, the voltage matrix is Before implementing optimization control for the distribution network optimization target node, based on the distribution network system voltage V DT The voltage matrix constructed, Optimizing the sensitivity of target node voltage with respect to reactive power for distribution networks; Optimizing the sensitivity of the target node voltage for the distribution network relative to the high-voltage side bus voltage connecting the transmission grid to the distribution grid transformer; and The progressive tightening of upper and lower limit constraints of voltage amplitude of target nodes for distribution network optimization; is a unit vector; It is a matrix composed of the minimum values ​​of control measures of distribution network control nodes; It is a matrix composed of the maximum values ​​of control measures of distribution network control nodes; It is the minimum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network; It is the maximum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network;

[0047] Iterative optimization solver Minimum high-voltage bus voltage regulation ∆V TR and the amount of control measures ∆u.

[0048] Furthermore, the transmission network coordinated optimization control model includes:

[0049] ,

[0050] in, The deviation weight of the voltage regulation amount of the high-voltage side busbar of the transformer connecting the transmission network and the distribution network; The voltage regulation value of the high-voltage busbar connecting the transmission network and the distribution network transformer is fed back by the global coordination control center of the distribution network; The voltage regulation of the high-voltage busbar on the transformer connecting the transmission network and the distribution network is solved for the transmission network; The amount of control measures for the control nodes of the transmission network; is the transmission network control cost weight diagonal matrix;

[0051] The expressions for the constraints include:

[0052] ,

[0053] ,

[0054] ,

[0055] in, is the total number of control nodes in the transmission network; The high-voltage bus voltage of the transformer connecting the transmission network and the distribution network The sensitivity of the control measure quantity relative to the t-th control node of the transmission network; is the control measure quantity of the tth control node in the transmission network; The amount of control measures for the control nodes of the transmission network; , is the minimum and maximum value of the control measure quantity of the transmission network control node; V is the voltage of the transmission network node; and are the minimum and maximum values ​​of the voltage at the transmission network nodes.

[0056] Furthermore, it is characterized in that the selective adjustment principle includes:

[0057] When ∆u m,i =∆u, the next sampling point controller is locked;

[0058] When ∆u m,i >∆u and ∑∆u m When ≥0, the control variable at the next sampling point approaches the reference value in steps with the set step size;

[0059] When ∆u m,i >∆u and ∑∆u m When <0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center;

[0060] When ∆u m,i <∆u and ∑∆u m When >0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center;

[0061] When ∆u m,i <∆u and ∑∆u m When ≤0, the control variable at the next sampling point approaches the reference value in steps with the set step size.

[0062] Furthermore, when the distribution network bus voltage deviation exceeds a preset required range, the method further includes:

[0063] Obtain distributed power supply and its compensation equipment LC m,k Real-time collected terminal voltage V LC ;

[0064] When the terminal voltage V LC In [V minth LC ,V maxth LC ] range, the reactive output of the distributed power source and its compensation equipment is controlled to be 0;

[0065] When the terminal voltage V LC In [V min LC ,V minth LC ] or [V maxth LC ,V max LC] range, the distributed power supply and its compensation equipment LC m,k The reactive power output is linearly related to the voltage;

[0066] When the terminal voltage V LC In [0,V min LC ] or higher than V max LC When the distributed power supply and its compensation equipment LC m,k The reactive power consumed and generated are constant values, Q min , Q max ;

[0067] Among them, the V min LC is the maximum terminal voltage when the reactive power is maximum, the V minth LC is the minimum terminal voltage when the reactive power is 0, the V maxth LC is the maximum terminal voltage when the reactive power is 0, the V max LC It is the minimum terminal voltage when the reactive power is the smallest.

[0068] In a second aspect, the present invention provides an active distribution network hierarchical voltage control system taking into account transmission and distribution coordinated scheduling, comprising:

[0069] The acquisition module is used to acquire the voltage, which includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC. DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ;

[0070] Iterative update module, used for when the distribution network system voltage V DT When the deviation exceeds the preset required range, based on the pre-built distribution network regional coordinated optimization control model, iterative optimization is performed to solve the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region. m,i Based on the pre-built global coordinated optimization control model of the distribution network, the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network is solved by iterative optimization. TR and the distribution network control measure ∆u; the high-voltage side bus voltage regulation ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC ;

[0071] Determination module for the |∆V TC |≥|∆VTR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network;

[0072] The adjustment module is used for when the distribution network regional coordination control center DAC receives the control measure quantity ∆u issued by the distribution network global coordination control center DCC, the distribution network regional coordination control center DAC adjusts the control measure quantity ∆u according to the control measure quantity ∆u at this time. m,i The cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

[0073] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] When the voltage deviation of the distribution network system exceeds the preset required range, the iterative optimization and solution are performed in turn to obtain the control measures that minimize the augmented Lagrangian function corresponding to the optimization objective function in this area and the high-voltage bus voltage regulation ∆V connecting the transmission network and the distribution network transformer. TR And the control measures, and then the high-voltage side bus voltage adjustment ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC , when the |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC When the distribution network regional coordination control center receives the control measure quantity ∆u issued by the distribution network global coordination control center, it adjusts the voltage regulation quantity at the next sampling point according to the selective adjustment principle to realize the voltage regulation of the transmission network and the distribution network, which solves the intermittent, volatility and uncertainty problems caused by the large-scale access and application of distributed power sources in the prior art, reduces voltage fluctuations and deviations, and improves stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The structure diagram of active distribution network hierarchical voltage control considering transmission and distribution coordinated dispatch; Figure 2 VQ characteristic curve diagram of local control of distributed power source and its compensation equipment; Figure 3 Optimization flow chart of the regional coordination control center of the distribution network; Figure 4 Optimization flow chart of the transmission network control center and the distribution network global coordination center. DETAILED DESCRIPTION

[0077] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0078] The term "and / or" is only a description of the association relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects are in an "or" relationship.

[0079] The iterative optimization mentioned in this application means that if each variable calculated according to the formula is within the range specified by the constraints, or meets the requirements of the objective function, or satisfies the conditions for the end of the iteration, then the calculation is completed, otherwise it enters the next round of calculation. This process is called iteration.

[0080] The Alternating Direction Method of Multipliers (ADMM) is a computational framework for solving separable convex optimization problems. It combines the advantages of the dual decomposition method and the augmented Lagrange multiplier method, making the algorithm have both good decomposition and good convergence. Embodiment 1:

[0081] The present invention provides a method for controlling voltage in a hierarchical manner in an active distribution network taking into account transmission and distribution coordinated dispatching. Figure 1 and attached Figure 2 As shown, including:

[0082] Step 1: Obtain voltage, which includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ;.

[0083] Step 2: When the distribution network system voltage V DT When the deviation exceeds the preset requirement range,

[0084] Each distribution network regional coordination control center DAC is based on the pre-built distribution network regional coordination optimization control model, combined with the control sensitivity information issued by the distribution network global coordination control center DCC at each sampling point, and uses the alternating direction multiplier method to iteratively optimize and solve the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region. m,i :

[0085] The distribution network regional coordinated optimization control model includes an augmented Lagrangian function corresponding to the regional optimization objective function, and the expression of the augmented Lagrangian function includes

[0086] ;

[0087] ;

[0088] in, is the number of iterations, For the The optimization objective function of the distribution network area is: For the The augmented Lagrangian function, For the The penalty function of the alternating direction multiplier method algorithm for each distribution network area is a constant set in advance. For the Next iteration In the distribution network area The voltage of the coupling node of the distribution network area, For the Distribution network area The fixed reference value of the iteration, For the distribution network area dual variable matrix, To control the number of sampling points in the time domain, is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures for distribution network areas, is a 2k*2k dimensional diagonal matrix set in advance, and The cost weight of implementing control in each distribution network area, is a 2*2 dimensional matrix set in advance, The penalty factor of the slack variable in the distribution network area is is a 1*2 dimensional matrix set in advance, The distribution network area slack variables, for The transposed matrix of

[0089] Considering the voltage support of the adjacent area to the local area, the expressions of the constraint conditions include:

[0090] ,

[0091]

[0092] ,

[0093] ,

[0094] ,

[0095] ,

[0096] in, For the Distribution network area sampling points The voltage matrix after optimizing the target node and implementing the optimized control at the moment is: For the Distribution network area sampling points Before implementing the optimization control of the optimized target node at the moment, based on the distribution network system voltage V DT The voltage matrix constructed, For the Sampling points in the distribution network area The optimized target node voltage at the time is relative to the and The sensitivity of the control measures in each distribution network area is the control sensitivity information issued by the distribution network global coordination control center DCC at each sampling point mentioned above; is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures in each distribution network area; and For sampling point Time next The gradually tightening upper and lower limits of the voltage amplitude in each distribution network area; is a unit vector; =[ , ] is a 1*2 dimensional matrix set in advance, Distribution network area slack variables; For sampling point Time next and A matrix composed of the cumulative control measures of the distribution network regional control nodes; For the and A matrix composed of the minimum values ​​of the total control measures of the control nodes in the distribution network area; For the and A matrix composed of the maximum values ​​of the total control measures of the control nodes in the distribution network area; For sampling point Time next and The number of single-step control measures for each control node in the distribution network area; For the and The maximum value of the single-step control measure quantity of the distribution network regional control node; To control the number of sampling points in the time domain; It is a constant set in advance and is used to adjust the progressive tightening speed of the voltage constraint in the prediction time domain; , For the The upper and lower limits of the voltage amplitude in the distribution network area;

[0097] Iterate and optimize to find the voltage regulation value ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function in this area. m,i For specific iterative optimization logic, please refer to the attached Figure 3 , for attachment Figure 3 The explanation is as follows:

[0098] The fixed reference value for the next iteration is the value of The distribution network area and The average voltage of the coupling node in the distribution network area is:

[0099] ,

[0100] in, For the Distribution network area Fixed reference value for iterations; For the Next iteration Distribution Network Regional Coordination and Control Center DAC m The calculated The distribution network area and The voltage of the coupling node of the distribution network area; For the Next iteration Distribution Network Regional Coordination and Control Center DAC n The calculated The distribution network area and The voltage of the coupling node of the distribution network area;

[0101] The regional dual variables are updated according to the fixed reference value of the next iteration, and the regional dual variables are:

[0102] ,

[0103] ,

[0104] in, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area The fixed reference value of the iteration, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area The fixed reference value of the iteration, the role of updating the regional dual variable is to keep the optimal solution unchanged while limiting the allowable range of changes in the constraints;

[0105] The boundary residual is calculated according to the obtained coupling node voltage difference, and the boundary residual is limited to be less than a preset residual threshold:

[0106] ,

[0107] ,

[0108] in, is the boundary residual, is the residual threshold. When the boundary residual is less than the preset residual threshold, the distribution network regional coordinated optimization control model converges and stops iteration.

[0109] Step 3:

[0110] The distribution network global coordination control center DCC is based on the pre-built distribution network global coordination optimization control model, combined with the high-voltage bus voltage V connecting the transmission network and the distribution network transformer calculated by the transmission network control center TC. TR Relative to the transmission network control node voltage u T Sensitivity , the voltage regulation range of the high-voltage busbar connecting the transmission network and the distribution network transformer [ΔV TRmin ,∆V TRmax ] and control cost S, where It is a value determined by the grid structure and determined by the transmission network control center. It is a constant matrix. The optimization algorithm is used to iteratively optimize the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network. TR and the control measure quantity ∆u of the distribution network. The optimization algorithm itself belongs to the prior art and will not be described here. For the specific iteration logic, please refer to the attached Figure 4 :

[0111] The distribution network global coordinated optimization control model includes

[0112] ,

[0113] in, The cost of controlling the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network is It is the voltage regulation of the high-voltage busbar connecting the transmission network and the distribution network transformer. is a 1*(M*k)-dimensional matrix, M is the total number of sub-areas of the distribution network system, k is the total number of distributed power sources and their compensation equipment in the mth distribution network area, is the control measure quantity of the distribution network control node, is a (M*k)*(M*k)-dimensional matrix, is the distribution network control cost weight diagonal matrix, is a 2*2 dimensional matrix set in advance, is the slack variable penalty factor, =[ , ] is a 1*2 dimensional matrix set in advance, which is the slack variable of the distribution network;

[0114] The expressions for the constraints include:

[0115] ,

[0116] in, After implementing the optimized control for the distribution network optimization target node, the voltage matrix is Before implementing optimization control for the distribution network optimization target node, based on the distribution network system voltage V DT The voltage matrix constructed, Optimize the sensitivity of the target node voltage to reactive power for the distribution network. If the control object is a reactive device such as a capacitor, That is, Q, that is, reactive power, Right now , is the reactive power change, i.e. the measure quantity; The sensitivity of the target node voltage for the distribution network optimization relative to the high-voltage bus voltage connecting the transmission network and the distribution network transformer is: and Based on Calculated sensitivity value; and The progressive tightening of upper and lower limit constraints of voltage amplitude of target nodes for distribution network optimization; is a unit vector; It is a matrix composed of the minimum values ​​of control measures of distribution network control nodes; It is a matrix composed of the maximum values ​​of control measures of distribution network control nodes; It is the minimum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network; It is the maximum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network;

[0117] Iterative optimization solver Minimum high-voltage bus voltage regulation ∆V TR and the amount of control measures ∆u.

[0118] Step 4:

[0119] The transmission network control center TC adjusts the high-voltage bus voltage adjustment value ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC :

[0120] The transmission network coordinated optimization control model includes:

[0121] ,

[0122] in, The deviation weight of the voltage regulation amount of the high-voltage side busbar of the transformer connecting the transmission network and the distribution network; The voltage regulation value of the high-voltage busbar connecting the transmission network and the distribution network transformer is fed back by the global coordination control center of the distribution network; The voltage regulation of the high-voltage busbar on the transformer connecting the transmission network and the distribution network is solved for the transmission network; The amount of control measures for the control nodes of the transmission network; is the transmission network control cost weight diagonal matrix;

[0123] The expressions for the constraints include:

[0124] ,

[0125] ,

[0126] ,

[0127] in, is the total number of control nodes in the transmission network; The high-voltage bus voltage of the transformer connecting the transmission network and the distribution network The sensitivity of the control measure quantity relative to the t-th control node of the transmission network; is the control measure quantity of the tth control node in the transmission network; The amount of control measures for the control nodes of the transmission network; , is the minimum and maximum value of the control measure quantity of the transmission network control node; V is the voltage of the transmission network node; and are the minimum and maximum values ​​of the voltage at the transmission network nodes.

[0128] Step 5:

[0129] When the |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network. When the |∆V TC |<|∆V TR |, the transmission grid control center uses ∆V TC As the maximum value of the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network, let ∆V TC replace , iterative optimization solution until the |∆V TC |≥|∆V TR |Or the number of iterations is greater than the preset threshold;

[0130] When the distribution network regional coordination control center receives the control measure quantity ∆u issued by the distribution network global coordination control center, the distribution network regional coordination control center calculates the control measure quantity ∆u based on the control measure quantity ∆u at this time. m,i The cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

[0131] Specifically, the selective adjustment principles include:

[0132] When ∆u m,i =∆u, the next sampling point controller is locked;

[0133] When ∆u m,i >∆u and ∑∆u m When ≥0, the control variable at the next sampling point approaches the reference value in steps with the set step size;

[0134] When ∆u m,i >∆u and ∑∆u m When <0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center;

[0135] When ∆u m,i <∆u and ∑∆u m When >0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center;

[0136] When ∆u m,i <∆u and ∑∆u m When ≤0, the control variable at the next sampling point approaches the reference value in steps with the set step size.

[0137] When the distribution network bus voltage deviation exceeds a preset required range, the method further includes:

[0138] Obtain distributed power supply and its compensation equipment LC m,k Real-time collected terminal voltage V LC ;

[0139] When the terminal voltage V LC In [V minth LC ,V maxth LC ] range, the reactive output of the distributed power source and its compensation equipment is controlled to be 0;

[0140] When the terminal voltage V LC In [V min LC ,V minth LC ] or [V maxth LC ,V max LC ] range, the distributed power supply and its compensation equipment LC m,k The reactive power output is linearly related to the voltage;

[0141] When the terminal voltage V LC In [0,V min LC ] or higher than V max LC When the distributed power supply and its compensation equipment LC m,k The reactive power consumed and generated are constant values, Q min , Q max ;

[0142] Among them, the V min LC is the maximum terminal voltage when the reactive power is maximum, the V minthLC is the minimum terminal voltage when the reactive power is 0, the V maxth LC is the maximum terminal voltage when the reactive power is 0, the V max LC It is the minimum terminal voltage when the reactive power is the smallest.

[0143] Embodiment 2:

[0144] This embodiment provides an active distribution network hierarchical voltage control system taking into account transmission and distribution coordinated scheduling, which can be used to execute the active distribution network hierarchical voltage control method taking into account transmission and distribution coordinated scheduling described in Example 1, and has the beneficial effects of the active distribution network hierarchical voltage control method taking into account transmission and distribution coordinated scheduling described in Example 1, including:

[0145] The acquisition module is used to acquire the voltage, which includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC. DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ;

[0146] Iterative update module, used for when the distribution network system voltage V DT When the deviation exceeds the preset required range, based on the pre-built distribution network regional coordinated optimization control model, iterative optimization is performed to solve the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region. m,i Based on the pre-built global coordinated optimization control model of the distribution network, the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network is solved by iterative optimization. TR and the distribution network control measure ∆u; the high-voltage side bus voltage regulation ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC ;

[0147] Determination module for the |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network;

[0148] The adjustment module is used for when the distribution network regional coordination control center DAC receives the control measure quantity ∆u issued by the distribution network global coordination control center DCC, the distribution network regional coordination control center DAC adjusts the control measure quantity ∆u according to the control measure quantity ∆u at this time. m,iThe cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

[0149] According to the attached Figure 1 , the distribution network global coordination control center DCC and distribution network regional coordination control center DAC mentioned above m (where m=1,2…M, M is the total number of sub-areas of the distribution network system), the transmission network control center TC, and the distributed generation and its compensation equipment LC m , k (k=1,2…K, K is the total number of distributed power sources and their compensation equipment in the mth distribution network area) are explained: two-way information interaction between the transmission network control layer and the global coordination control layer of the distribution network, two-way information interaction between the global coordination control layer DCC of the distribution network and the regional coordination control layer of the distribution network, two-way information interaction between adjacent distribution network regional coordination control centers within the regional coordination control layer of the distribution network, setting the nodes shared by adjacent areas as coupling nodes, and two-way information interaction between the regional coordination control layer of the distribution network and the local control layer.

[0150] Regarding the above, the active distribution network hierarchical voltage control system provided in this embodiment taking into account the coordinated dispatch of transmission and distribution can be summarized as a hierarchical coordinated optimization structure including three control levels: local control, regional coordinated control of distribution network and global coordinated control of distribution network, and considers the two-way information interaction between the global coordinated control center of the distribution network and the external transmission network system. By setting the high-voltage side bus voltage connecting the transmission network and the distribution network transformer as the coupling boundary variable of the transmission and distribution network, the coordinated control of the transmission and distribution network is realized in an iterative optimization manner. The transmission network sends its adjustment capability of the boundary variable to each global coordination center of the distribution network. When the distribution network is optimized, the coupling boundary variable is used as an alternative control measure. After optimization, the expected adjustment value of the coupling boundary variable is returned to the transmission network control center, and the transmission network performs control verification until the centralized optimization strategy is generated by iteration, and the control measure quantity is sent to each regional coordination center of the distribution network; each regional coordination center of the distribution network negotiates to realize distributed voltage optimization control through information interaction between regions, and selectively corrects the control trajectory according to the control measure quantity sent by the global coordinated control center of the distribution network; local control makes decisions based on local voltage measurement information to achieve rapid adjustment of voltage deviation. Each control layer makes decisions in parallel and serves as a backup for each other. It can take into account the uncertainty of distribution network operation and the impact on the external transmission network system, give full play to the dispatching capabilities of all levels, and achieve temporal and spatial coordination of voltage regulation control measures for the transmission and distribution grids.

[0151] Embodiment three:

[0152] Embodiment 5 of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in Embodiment 1 or Embodiment 2 are implemented, and the computer program has the corresponding functional modules and beneficial effects of the execution method.

[0153] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An active distribution network hierarchical voltage control method taking into account transmission and distribution coordinated scheduling, characterized in that: include: The voltage is obtained, and the voltage includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ; When the distribution network system voltage V DT When the deviation exceeds the preset required range, based on the pre-built distribution network regional coordinated optimization control model, iterative optimization is performed to solve the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region. m,i ; Based on the pre-built global coordinated optimization control model of the distribution network, the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network is solved by iterative optimization. TR and the distribution network control measure quantity ∆u; The high-voltage side bus voltage adjustment value ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC ; When |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network; When the distribution network regional coordination control center DAC receives the control measure quantity ∆u issued by the distribution network global coordination control center DCC, the distribution network regional coordination control center DAC calculates the control measure quantity ∆u according to the control measure quantity ∆u at this time. m,i The cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

2. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated scheduling according to claim 1 is characterized in that: The distribution network regional coordinated optimization control model includes an augmented Lagrangian function corresponding to the regional optimization objective function, and the expression of the augmented Lagrangian function includes: ; ; in, is the number of iterations, For the The optimization objective function of the distribution network area is: For the The augmented Lagrangian function, For the The penalty function of the alternating direction multiplier method algorithm for each distribution network area is a constant set in advance. For the Next iteration In the distribution network area The voltage of the coupling node of the distribution network area, For the Distribution network area The fixed reference value of the iteration, For the distribution network area dual variable matrix, To control the number of sampling points in the time domain, is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures for distribution network areas, is a 2k*2k dimensional diagonal matrix set in advance, and The cost weight of implementing control in each distribution network area, is a 2*2 dimensional matrix set in advance, The penalty factor of the slack variable in the distribution network area is is a 1*2 dimensional matrix set in advance, The distribution network area slack variables, for The transposed matrix of Considering the voltage support of the adjacent area to the local area, the expressions of the constraint conditions include: , , , , , in, For the Distribution network area sampling points The voltage matrix after optimizing the target node and implementing the optimized control at the time is: For the Distribution network area sampling points Before implementing the optimization control of the optimized target node at the moment, based on the distribution network system voltage V DT The voltage matrix constructed, For the Sampling points in the distribution network area The optimized target node voltage at the time is relative to the and The sensitivity of the control measures in each distribution network area; is a 1*2k dimensional matrix, which is the sampling point Time next and The number of control measures in each distribution network area; and For sampling point Time next The gradually tightening upper and lower limits of the voltage amplitude in each distribution network area; is a unit vector; =[ , ] is a 1*2 dimensional matrix set in advance, Distribution network area slack variables; For sampling point Time next and A matrix composed of the cumulative control measures of the distribution network regional control nodes; For the and A matrix composed of the minimum values ​​of the total control measures of the control nodes in the distribution network area; For the and A matrix composed of the maximum values ​​of the total control measures of the control nodes in the distribution network area; For sampling point Time next and The number of single-step control measures for each control node in the distribution network area; For the and The maximum value of the single-step control measure quantity of the distribution network regional control node; To control the number of sampling points in the time domain; It is a constant set in advance and is used to adjust the progressive tightening speed of the voltage constraint in the prediction time domain; , For the The upper and lower limits of the voltage amplitude in the distribution network area; Iterate and optimize to find the voltage regulation value ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function in this area. m,i .

3. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated dispatching according to claim 2 is characterized in that: The fixed reference value for the next iteration is the value of The distribution network area and The average voltage of the coupling node in the distribution network area is: , in, For the Distribution network area Fixed reference value for iterations; For the Next iteration Distribution Network Regional Coordination and Control Center DAC m The calculated The distribution network area and The voltage of the coupling node of the distribution network area; For the Next iteration Distribution Network Regional Coordination and Control Center DAC n The calculated The distribution network area and The voltage of the coupling node of the distribution network area; The regional dual variables are updated according to the fixed reference value of the next iteration, and the regional dual variables are: , , in, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area The fixed reference value of the iteration, For the Distribution network area The dual variable matrix of the iteration; For the Distribution network area The dual variable matrix of the iteration, For the Distribution network area Fixed reference value for iterations; The boundary residual is calculated according to the obtained coupling node voltage difference, and the boundary residual is limited to be less than a preset residual threshold: , , in, is the boundary residual, is the residual threshold.

4. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated dispatching according to claim 1 is characterized in that: Also includes: When the |∆V TC |<|∆V TR |, the transmission grid control center uses ∆V TC As the maximum value of the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network, the iterative optimization solution is obtained until the |∆V TC |≥|∆V TR |Or the number of iterations is greater than the preset threshold.

5. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated dispatching according to claim 4 is characterized in that: The distribution network global coordinated optimization control model includes: , in, The cost of controlling the high-voltage bus voltage of the transformer connecting the transmission network and the distribution network is It is the voltage regulation of the high-voltage busbar connecting the transmission network and the distribution network transformer. is a 1*(M*k)-dimensional matrix, M is the total number of sub-areas of the distribution network system, k is the total number of distributed power sources and their compensation equipment in the mth distribution network area, is the control measure quantity of the distribution network control node, is a (M*k)*(M*k)-dimensional matrix, is the distribution network control cost weight diagonal matrix, is a 2*2 dimensional matrix set in advance, is the slack variable penalty factor, =[ , ] is a 1*2 dimensional matrix set in advance, which is the slack variable of the distribution network; The expressions for the constraints include: in, After implementing the optimized control for the distribution network optimization target node, the voltage matrix is Before implementing optimization control for the distribution network optimization target node, based on the distribution network system voltage V DT The voltage matrix constructed, Optimizing the sensitivity of target node voltage with respect to reactive power for distribution networks; Optimize the sensitivity of the target node voltage for the distribution network with respect to the high voltage side bus voltage connecting the transmission grid to the distribution grid transformer; and The progressive tightening of upper and lower limit constraints for the voltage amplitude of the target node in the distribution network optimization; is a unit vector; It is a matrix composed of the minimum values ​​of control measures of distribution network control nodes; It is a matrix composed of the maximum values ​​of control measures of distribution network control nodes; It is the minimum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network; It is the maximum value of the bus voltage on the high-voltage side of the transformer connecting the transmission network and the distribution network; Iterative optimization solver Minimum high voltage side bus voltage regulation ∆V TR and the amount of control measures ∆u.

6. The active distribution network hierarchical voltage control method taking into account transmission and distribution coordinated scheduling according to claim 4 or 5, characterized in that: The transmission network coordinated optimization control model includes: , in, The deviation weight of the voltage regulation amount of the high-voltage side busbar of the transformer connecting the transmission network and the distribution network; The voltage regulation value of the high-voltage busbar connecting the transmission network and the distribution network transformer is fed back by the global coordination control center of the distribution network; The voltage regulation of the high-voltage busbar on the transformer connecting the transmission network and the distribution network is solved for the transmission network; The amount of control measures for the control nodes of the transmission network; is the transmission network control cost weight diagonal matrix; The expressions for the constraints include: , , , in, is the total number of control nodes in the transmission network; The high-voltage bus voltage of the transformer connecting the transmission network and the distribution network The sensitivity of the control measure quantity relative to the t-th control node of the transmission network; is the control measure quantity of the tth control node in the transmission network; The amount of control measures for the control nodes of the transmission network; , is the minimum and maximum value of the control measure quantity of the transmission network control node; V is the voltage of the transmission network node; and are the minimum and maximum values ​​of the voltage at the transmission network nodes.

7. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated dispatching according to claim 1 is characterized in that: The selective adjustment principles include: When ∆u m,i =, the next sampling point controller is locked; When ∆u m,i > and∑∆u m When ≥0, the control variable at the next sampling point approaches the reference value in steps with the set step size; When ∆u m,i > and∑∆u m When <0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center; When ∆u m,i < and ∑∆u m When >0, the next sampling point is still executed according to the optimization result of the distribution network regional coordination center; When ∆u m,i < and ∑∆u m When ≤0, the control variable at the next sampling point approaches the reference value in steps with the set step size.

8. The active distribution network hierarchical voltage control method considering transmission and distribution coordinated dispatching according to claim 1 is characterized in that: When the distribution network bus voltage deviation exceeds a preset required range, the method further includes: Obtain distributed power supply and its compensation equipment LC m,k Real-time collected terminal voltage V LC ; When the terminal voltage V LC In [V minth LC ,V maxth LC ] range, the reactive output of the distributed power source and its compensation equipment is controlled to be 0; When the terminal voltage V LC In [V min LC ,V minth LC ] or [V maxth LC ,V max LC ] range, the distributed power supply and its compensation equipment LC m,k Reactive power output is linearly related to voltage; When the terminal voltage V LC In [0,V min LC ] or higher than V max LC When the distributed power supply and its compensation equipment LC m,k The reactive power consumed and generated are constant values, Q min , Q max ; Among them, the V min LC is the maximum terminal voltage when the reactive power is maximum, the V minth LC is the minimum terminal voltage when the reactive power is 0, the V maxth LC is the maximum terminal voltage when the reactive power is 0, the V max LC It is the minimum terminal voltage when the reactive power is the smallest.

9. An active distribution network hierarchical voltage control system taking into account transmission and distribution coordinated dispatching, characterized in that: include: The acquisition module is used to acquire the voltage, which includes the distribution network system voltage V collected in real time by the distribution network global coordination control center DCC and the distribution network regional coordination control center DAC. DT And the transmission network system voltage V collected in real time by the transmission network control center TC TR ; Iterative update module, used for when the distribution network system voltage V DT When the deviation exceeds the preset required range, based on the pre-built distribution network regional coordinated optimization control model, iterative optimization is performed to solve the control measure quantity ∆u that minimizes the augmented Lagrangian function corresponding to the optimization objective function of this region. m,i Based on the pre-built global coordinated optimization control model of the distribution network, the high-voltage bus voltage regulation value ∆V of the transformer connecting the transmission network and the distribution network is solved by iterative optimization. TR and the distribution network control measure ∆u; the high-voltage side bus voltage regulation ∆V TR Input the pre-built transmission network coordinated optimization control model, and iteratively optimize and solve the transmission network voltage regulation ∆V TC ; Determination module for the |∆V TC |≥|∆V TR | or the number of iterations is greater than the preset threshold, the transmission network implements ∆V TC , and control the global coordination center of the distribution network to send the control measure quantity ∆u to the regional coordination control center of the distribution network; The adjustment module is used for when the distribution network regional coordination control center DAC receives the control measure quantity ∆u issued by the distribution network global coordination control center DCC, the distribution network regional coordination control center DAC adjusts the control measure quantity ∆u according to the control measure quantity ∆u at this time. m,i The cumulative control measures of distributed power sources and their compensation equipment ∑△u m , at the next sampling point, the voltage regulation amount is adjusted according to the selective adjustment principle.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.