A photovoltaic power station output adaptive adjustment method based on PMU measurement data

By using a photovoltaic power plant output adaptive adjustment method based on PMU measurement data, the power generation of photovoltaic power plants can be monitored and adjusted in real time. This solves the grid stability problem caused by power fluctuations of photovoltaic power generation equipment, improves the grid access capacity and voltage deviation level, and promotes the development of clean energy.

CN119134522BActive Publication Date: 2025-12-16STATE GRID FUJIAN ELECTRIC POWER RES INST +2
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Patent Information

Application Number
CN202411185335.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-27
Publication Date
2025-12-16
Estimated Expiration
2044-08-27

AI Technical Summary

Technical Problem

Power fluctuations in photovoltaic power generation equipment lead to grid stability and voltage quality issues, and existing technologies struggle to achieve safe grid connection and efficient regulation between photovoltaic power plants and distribution networks.

Method used

An adaptive adjustment method for photovoltaic power plant output based on PMU measurement data is adopted. By monitoring the electrical quantities of photovoltaic power plants and distribution stations in real time, the impedance between the grid connection point and the secondary side is calculated, and the power generation of photovoltaic power plants is automatically adjusted to optimize grid load and voltage stability.

Benefits of technology

It achieves dynamic balance between photovoltaic power plants and distribution networks, reduces network transmission costs and operating computing power, improves the reliability and security of the power system, and promotes the utilization of clean energy.

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Abstract

The application provides a photovoltaic power station output adaptive adjustment method based on PMU measurement data, for each photovoltaic power station, a phasor measurement unit PMU is used to actively and timely manage the photovoltaic power station, the impedance between the grid-connected point of the photovoltaic power station and the secondary side of the distribution station is accurately measured, the optimal power generation of the photovoltaic power station is calculated by using the impedance, so that the power loss when the power grid load dynamically changes is minimized, and the photovoltaic access capacity of the distribution network and the voltage offset level of the distribution network are improved; the application has the characteristics of low calculation complexity, real-time and rapidness, by the method, the equivalent impedance of the distribution network can be measured in a simple method, and the calculated impedance is used for optimal scheduling of the photovoltaic power station.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent power distribution systems, and in particular to a photovoltaic power station output adaptive adjustment method based on PMU measurement data. BACKGROUND

[0002] As the last link of the power system structure, the power distribution system is responsible for receiving power from the high-voltage transmission system and delivering it to users at low voltage. When photovoltaic power stations are connected to the power distribution system, they may affect the steady-state and transient characteristics of the power grid, and appropriate control and adjustment measures need to be taken to ensure the safe grid connection of photovoltaic power stations and power distribution networks.

[0003] Power distribution system photovoltaic power station adaptive adjustment refers to the use of smart grid technology to accurately regulate photovoltaic power station power generation, keeping the supply and demand relationship with the grid in balance. This technology is mainly used in the field of distributed photovoltaic power generation, aiming to solve problems such as grid stability and voltage quality.

[0004] With the increasing number of photovoltaic power generation equipment, photovoltaic power generation power fluctuates under various weather conditions, leading to some safety hazards and voltage stability problems in the power grid. To solve these problems, power distribution system photovoltaic power station adaptive adjustment technology has emerged. This technology can automatically monitor grid voltage, frequency and load conditions, and adjust photovoltaic power station power generation based on real-time data. If the grid load is too heavy, the photovoltaic power station will automatically reduce power generation to ensure grid balance; if the grid load is light, the photovoltaic power station will automatically increase power generation to improve energy utilization efficiency.

[0005] In addition, power distribution system photovoltaic power station adaptive adjustment technology can also achieve remote monitoring and management through intelligent control systems, improving the reliability and safety of the power system, and reducing the maintenance and operating costs of the power grid.

[0006] Therefore, the application of power distribution system photovoltaic power station adaptive adjustment technology is of great significance, as it can effectively solve the problems existing in the field of photovoltaic power generation and promote the development and utilization of clean energy. SUMMARY

[0007] The present application proposes a photovoltaic power station output adaptive adjustment method based on PMU measurement data, which has low computational complexity, real-time and fast characteristics. By using this method, the equivalent impedance of the power distribution network can be measured simply, and the calculated impedance can be used for optimal scheduling of photovoltaic power stations.

[0008] The present application adopts the following technical solutions.

[0009] The application discloses a photovoltaic power station output adaptive regulation method based on PMU measurement data.

[0010] The method comprises the following steps;

[0011] Step S1: determining a PMU installation deployment position, using a PMU to monitor electrical quantities at two nodes of a photovoltaic power station and a distribution station in real time, and setting a threshold value of photovoltaic power station output fluctuation;

[0012] Step S2: regularly starting photovoltaic power station output adaptive regulation, judging whether photovoltaic power station output fluctuation exceeds the set threshold value, and when the output fluctuation is greater than the set threshold value, performing real-time regulation and control of the photovoltaic power station output;

[0013] Step S3: measuring impedance between a grid-connected point of the photovoltaic power station and a secondary side of the distribution station, then measuring optimal active and reactive power generation of the photovoltaic power station, and then adjusting the output;

[0014] Step S4: reading PMU measurement values again, judging whether a voltage variation amplitude exceeds the threshold value, when the threshold value is exceeded, updating optimal power generation of the photovoltaic power station, and re-measuring whether the voltage meets the threshold value requirement.

[0015] The specific implementation process of the PMU installation deployment position in step S1 is as follows: one PMU device is installed at a secondary side of a distribution station, and another PMU device is installed at a photovoltaic power station, high-time-resolution and time-tagged measurement data are provided; a GPS is configured at the whole station and is used for measuring time synchronization of the device, and then electrical quantities of two nodes of the photovoltaic power station and the secondary side of the distribution station are calculated and extracted.

[0016] In step S1, the calculation formula of the threshold value of photovoltaic power station output fluctuation is as follows:

[0017] S t -S t-1 |≥S N *α%

[0018] Wherein S t is a current photovoltaic power station output power, S t-1 is a photovoltaic power station output power at a previous moment, S N is a rated photovoltaic power station output power, and alpha is an adjustable variable.

[0019] The timing start photovoltaic power station output adaptive adjustment in step S2 is specifically: photovoltaic power station output monitoring is performed every t minutes, when the amplitude of the output fluctuation of the photovoltaic power station does not meet the threshold requirement, then according to the high sampling rate, high refresh rate photovoltaic power station real-time output data obtained by the PMU, the power adjustment of the photovoltaic power station is performed; if the requirement is met, the power adjustment is not performed.

[0020] The specific implementation steps of the step S3 of measuring and calculating the impedance between the photovoltaic power station grid-connected point and the secondary side of the distribution station are as follows:

[0021] S3A, re-read the measurement value of the PMU, based on the Thevenin equivalent theorem, ignore the specific situation of each branch, perform line equivalence and network simplification on the distribution system, define the distribution station secondary side node voltage as the reference voltage, and the system equivalent resistance and inductance are equal to the sum of the resistance and inductance between the distribution station secondary side and the photovoltaic power station;

[0022] S3B, the relationship between the actual active power and reactive power in the circuit at the current time is represented by a matrix as follows:

[0023] In the formula, V t ,δ t respectively represent the amplitude and phase angle of the photovoltaic power station node voltage at the current time, P t ,Q t respectively represent the active and reactive power output by the photovoltaic power station at the current time;

[0024] Similarly, the relationship between the actual active power and reactive power in the circuit at the previous time is represented by a matrix as follows:

[0025] In the formula, V t-1 ,δ t-1 respectively represent the amplitude and phase angle of the photovoltaic power station node voltage at the previous time, P t-1 ,Q t-1 respectively represent the active and reactive power output by the photovoltaic power station at the current time;

[0026] The actual active and reactive relationship in the circuit at the current time is compared with that at the previous time, and the system equivalent impedance is obtained, which is expressed by the formula as follows:

[0027]

[0028] In the formula: ΔP represents the difference between the active power of the photovoltaic power station at the current time and the previous time, and ΔQ represents the difference between the reactive power of the photovoltaic power station at the current time and the previous time.

[0029] In step S3, the optimal active and reactive power generation of the photovoltaic power station is calculated, and the specific implementation process is as follows: in order to make the line power loss zero, the power injected into the photovoltaic power station node is all provided by the photovoltaic power station, and then the optimal active and reactive power output of the photovoltaic power station at the next moment is:

[0030]

[0031] In the formula, P ref.t+1 represents the active power output reference value of the photovoltaic power station at the next moment, Q ref.t+1 represents the reactive power output reference value of the photovoltaic power station at the next moment, V t+1 , and δ t+1 respectively represent the voltage amplitude and phase angle of the photovoltaic power station node at the next moment.

[0032] In step S4, the active and reactive power output of the photovoltaic power station is updated, and the specific implementation process is as follows: the measurement value of the PMU is read again, and when the node voltage of the photovoltaic power station changes, it is judged whether the power grid topology structure changes, if it changes, the equivalent impedance of the distribution network is updated, otherwise the active and reactive power output of the photovoltaic power station needs to be recalculated.

[0033] The specific steps of judging whether the distribution network topology structure changes are as follows:

[0034] S4A, define a threshold value of the change of the power ratio caused by the change of the topology structure as a switching change coefficient λ, and the selection of the coefficient is determined by the maximum load and the minimum load of the node;

[0035] S4B, it is considered that the change of the switching state of the branch will bring the fluctuation of the power ratio of the secondary side of the distribution station and the photovoltaic power station, therefore, the power ratio value η of the secondary side of the distribution station and the photovoltaic power station measured by the PMU is calculated:

[0036]

[0037] In the formula, P0 is the PMU measured power value at the secondary side of the distribution station, and P1 is the PMU measured power value at the node of the photovoltaic power station; when it is compared with the switching change coefficient λ, if the size relationship changes, it is determined that the topology structure of the distribution network changes; if the size relationship does not change, it is determined that the topology structure does not change.

[0038] In step S4, the photovoltaic power station node voltage is recalculated, and the specific implementation process is as follows: the corrected photovoltaic power station node voltage is recalculated, it is judged whether the node voltage of the photovoltaic power station meets the threshold condition, and the target node voltage deviation and the minimum active and reactive power adjustment are realized.

[0039] In the method, the photovoltaic power station reduces the network transmission cost and operation calculation power by self-executing adjustment operation.

[0040] The application is advantageous to improve the photovoltaic access capacity of the power distribution network and the voltage offset level of the power distribution network, can maximize the power generation benefit of the photovoltaic power station under the premise of ensuring the stable operation of the power grid, and meanwhile, the photovoltaic power station can be self-regulated to reduce the network transmission cost and operation computing power.

[0041] The method can automatically monitor the power grid voltage, frequency and load condition, and adjust the power generation power of the photovoltaic power station according to the real-time data. If the power grid load is too heavy, the photovoltaic power station will automatically reduce the power generation power to ensure the balance of the power grid; if the power grid load is light, the photovoltaic power station will automatically increase the power generation power to improve the energy utilization efficiency.

[0042] In the application, the photovoltaic power station adaptive adjustment technology of the power distribution system can also realize remote monitoring and management through the intelligent control system, improve the reliability and safety of the power system, and reduce the maintenance cost and operation cost of the power grid.

[0043] In the application, the application of the photovoltaic power station adaptive adjustment technology of the power distribution system has important significance, can effectively solve the problems existing in the photovoltaic power generation field, and promote the development and utilization of clean energy. BRIEF DESCRIPTION OF DRAWINGS

[0044] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0045] ATTACHED Figure 1 It is a method flow diagram of photovoltaic power station output adaptive adjustment based on PMU;

[0046] ATTACHED Figure 2 It is a schematic diagram of a power distribution system model and its simplified model. DETAILED DESCRIPTION

[0047] As shown in the figure, a photovoltaic power station output adaptive adjustment method based on PMU measurement data, the method uses a phasor measurement unit PMU to actively and real-time manage each photovoltaic power station, measures the impedance between the grid-connected point of the photovoltaic power station and the secondary side of the distribution station accurately, calculates the optimal power generation of the photovoltaic power station by using the impedance, so as to minimize the power loss when the power grid load dynamically changes, and improve the photovoltaic access capacity of the power distribution network and the voltage offset level of the power distribution network.

[0048] The method comprises the following steps:

[0049] Step S1: determine the PMU installation and deployment position, use the PMU to real-time monitor the electrical quantity at the two nodes of the photovoltaic power station and the distribution station, and set the threshold value of the photovoltaic power station output fluctuation;

[0050] Step S2: Timing start photovoltaic power station output adaptive adjustment, determine whether the photovoltaic power station output fluctuation exceeds the set threshold, when the output fluctuation is greater than the set threshold, then the photovoltaic power station output real-time regulation is carried out;

[0051] Step S3: Measure the impedance between the photovoltaic power station and the secondary side of the distribution station, and then measure the optimal active and reactive power generation of the photovoltaic power station, and then adjust its output;

[0052] Step S4: Read the PMU measurement value again, determine whether the voltage variation amplitude exceeds the threshold, when exceeding the threshold, update the optimal power generation of the photovoltaic power station, and re-calculate whether the voltage meets the threshold requirement.

[0053] The specific implementation process of determining the PMU installation deployment position in step S1 is: installing a PMU device at the secondary side of the distribution station and another PMU device at the photovoltaic power station, providing high time resolution and time-stamped measurement data; A GPS is configured in the whole station for measuring the time synchronization of the device, and then the electrical quantities of the photovoltaic power station and the secondary side of the distribution station are calculated and extracted.

[0054] In step S1, the calculation formula of the threshold value of the photovoltaic power station output fluctuation is:

[0055] S t -S t-1 |≥S N *α%

[0056] Wherein S t is the current photovoltaic power station output power, S t-1 is the photovoltaic power station output power at the last time, S N is the rated output power of the photovoltaic power station, and α is an adjustable variable.

[0057] The timing start photovoltaic power station output adaptive adjustment in step S2 is: every t minutes, the photovoltaic power station output is monitored, when the amplitude of the photovoltaic power station output fluctuation does not meet the threshold requirement, then according to the high sampling rate and high refresh rate photovoltaic power station real-time output data obtained by PMU, the power adjustment of the photovoltaic power station is executed; If it meets the requirement, no power adjustment is performed.

[0058] The specific implementation steps of measuring the impedance between the photovoltaic power station and the secondary side of the distribution station in step S3 are:

[0059] S3A, re-read the PMU measurement value, based on Thevenin equivalent theorem, ignore the specific situation of each branch, carry out line equivalent and network simplification for the distribution system, define the node voltage of the secondary side of the distribution station as the reference voltage, and the equivalent resistance and inductance of the system are equal to the sum of the resistance and inductance between the secondary side of the distribution station and the photovoltaic power station;

[0060] S3B, the relationship between the actual active power and the reactive power in the circuit at the current time is represented by a matrix as follows:

[0061] wherein V t and δ t represent the voltage amplitude and the phase angle of the photovoltaic power station node at the current time, P t and Q t represent the active power and the reactive power output by the photovoltaic power station at the current time;

[0062] Similarly, the relationship between the actual active power and the reactive power in the circuit at the previous time is represented by a matrix as follows:

[0063] wherein V t-1 and δ t-1 represent the voltage amplitude and the phase angle of the photovoltaic power station node at the previous time, P t-1 and Q t-1 represent the active power and the reactive power output by the photovoltaic power station at the previous time;

[0064] The actual active power and the reactive power in the circuit at the current time are compared with those at the previous time, and the equivalent impedance of the system is obtained, which is expressed by a formula as follows:

[0065]

[0066] wherein ΔP represents the difference between the active power of the photovoltaic power station at the current time and that at the previous time, and ΔQ represents the difference between the reactive power of the photovoltaic power station at the current time and that at the previous time.

[0067] In step S3, the optimal active power and the optimal reactive power generated by the photovoltaic power station are calculated, and the specific implementation process is as follows: in order to make the line power loss zero, the power injected into the photovoltaic power station node is all provided by the photovoltaic power station, and the optimal active power and the optimal reactive power output by the photovoltaic power station at the next time are as follows:

[0068]

[0069] wherein P ref.t+1 represents the active power output reference value of the photovoltaic power station at the next time, Q ref.t+1 represents the reactive power output reference value of the photovoltaic power station at the next time, V t+1 and δ t+1 represent the voltage amplitude and the phase angle of the photovoltaic power station node at the next time.

[0070] The active and reactive power output of the photovoltaic power station is updated in step S4. The implementation process is: the measurement value of the PMU is read again. When the node voltage of the photovoltaic power station changes, it is judged whether the power grid topology structure changes. If the power grid topology structure changes, the equivalent impedance of the distribution network is updated. Otherwise, the active and reactive power output of the photovoltaic power station needs to be recalculated.

[0071] The specific steps for judging whether the distribution network topology structure changes are:

[0072] S4A, a threshold value of the change of the ratio of the two sides caused by the change of the topology structure is defined as a switching change coefficient λ. The selection of the coefficient is determined by the maximum load and the minimum load of the node.

[0073] S4B, the change of the switching state of the branch will cause the fluctuation of the power ratio of the secondary side of the distribution station and the photovoltaic power station. Therefore, the power ratio value η of the secondary side of the distribution station and the photovoltaic power station measured by the PMU is calculated.

[0074]

[0075] In the formula, P0 is the PMU measured power value at the secondary side of the distribution station, and P1 is the PMU measured power value at the node of the photovoltaic power station. When it is compared with the switching change coefficient λ, if the size relationship changes, it is determined that the topology structure of the distribution network changes. If the size relationship does not change, it is determined that the topology structure does not change.

[0076] The node voltage of the photovoltaic power station is recalculated in step S4. The implementation process is: the corrected node voltage of the photovoltaic power station is recalculated. It is judged whether the node voltage of the photovoltaic power station meets the threshold condition, so as to realize the minimization of the target node voltage deviation and the active and reactive power regulation.

[0077] In the method, the photovoltaic power station reduces the network transmission cost and operation computing power by performing the adjustment operation by itself.

Claims

1. A method for adaptive adjustment of photovoltaic power plant output based on PMU measurement data, characterized in that: The method uses a phasor measurement unit (PMU) to manage each photovoltaic power station. By accurately measuring the impedance between the grid connection point of the photovoltaic power station and the secondary side of the distribution station, the optimal power generation of the photovoltaic power station is calculated using this impedance. This minimizes power loss when the grid load changes dynamically, thereby improving the photovoltaic access capacity of the distribution network and the voltage deviation level of the distribution network. The method includes the following steps; Step S1: Determine the installation and deployment location of the PMU, use the PMU to monitor the electrical quantities at the two nodes of the photovoltaic power station and the distribution substation in real time, and set the threshold for the output fluctuation of the photovoltaic power station. Step S2: Periodically start the adaptive adjustment of photovoltaic power station output, determine whether the output fluctuation of photovoltaic power station exceeds the set threshold, and when the output fluctuation is greater than the set threshold, perform real-time control of photovoltaic power station output; Step S3: Calculate the impedance between the grid connection point of the photovoltaic power station and the secondary side of the distribution station, then calculate the optimal active and reactive power generation of the photovoltaic power station, and then adjust its output. Step S4: Read the PMU measurement value again to determine whether the voltage change exceeds the threshold. If it exceeds the threshold, update the optimal power generation of the photovoltaic power station and recalculate whether the voltage meets the threshold requirement. The specific implementation steps for calculating the impedance between the grid connection point of the photovoltaic power station and the secondary side of the distribution substation, as described in step S3, are as follows: S3A, reread the PMU measurement value, based on Thevenin's equivalent theorem, ignore the specific situation of each branch, perform line equivalence and network simplification on the power distribution system, define the secondary side node voltage of the power distribution station as the reference voltage, and the system equivalent resistance and inductance are equal to the sum of the resistance and inductance between the secondary side of the power distribution station and the photovoltaic power station. S3B, The relationship between the actual active power and reactive power in the circuit at the current moment can be represented by a matrix as follows: In the formula V t ,δ t P represents the voltage amplitude and phase angle of the photovoltaic power station node at the current moment, respectively. t Q t These represent the active and reactive power outputs of the photovoltaic power station at the current moment, respectively. Similarly, the relationship between the actual active power and reactive power in the circuit at the previous moment can be represented by a matrix as follows: In the formula V t-1 ,δ t-1 P represents the node voltage amplitude and phase angle of the photovoltaic power station at the previous moment, respectively. t-1 Q t-1 These represent the active and reactive power outputs of the photovoltaic power station at the current moment, respectively. By comparing the actual active and reactive power relationship in the circuit at the current moment with that at the previous moment, the equivalent impedance of the system is obtained, which can be expressed by the formula: In the formula: ΔP represents the difference between the active power of the photovoltaic power station at the current time and the previous time, and ΔQ represents the difference between the reactive power of the photovoltaic power station at the current time and the previous time.

2. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: The specific implementation process of determining the PMU installation and deployment location in step S1 is as follows: install one PMU device on the secondary side of the substation and another PMU device at the photovoltaic power station to provide high time resolution and time-stamped measurement data; configure a GPS for the entire station for time synchronization of the measurement devices, and then calculate and extract the electrical quantities of the two nodes, the photovoltaic power station and the secondary side of the substation.

3. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: In step S1, the calculation formula for the threshold of photovoltaic power plant output fluctuation is set as follows: |S t -S t-1 |≥S N *a% Where S t S represents the current output power of the photovoltaic power station. t-1 S represents the output power of the photovoltaic power station at the previous moment. N Let α be the rated output power of the photovoltaic power station, and α be an adjustable variable.

4. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: The timed start of adaptive adjustment of photovoltaic power station output mentioned in step S2 is as follows: the output of photovoltaic power station is monitored every t minutes. When the output fluctuation of photovoltaic power station does not meet the threshold requirement, the power of photovoltaic power station is adjusted according to the real-time output data of photovoltaic power station with high sampling rate and high refresh rate obtained by PMU. If the requirement is met, the power adjustment is not performed.

5. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: In step S3, the specific process for calculating the optimal active and reactive power generation of the photovoltaic power station is as follows: Assuming that in order to achieve zero line power loss, all power injected into the photovoltaic power station nodes is provided by the photovoltaic power station, then the optimal active and reactive power output of the photovoltaic power station at the next moment is: In the formula, P ref.t+1 Q represents the reference value of the active power output of the photovoltaic power station at the next moment. ref.t+1 V represents the reference value of reactive power output of the photovoltaic power station at the next moment. t+1 ,δ t+1 These represent the voltage amplitude and phase angle of the photovoltaic power station node at the next moment, respectively.

6. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: The specific implementation process of updating the active and reactive power output of the photovoltaic power station in step S4 is as follows: read the measurement value of PMU again. If the node voltage of the photovoltaic power station changes, determine whether the grid topology has changed. If it has changed, update the equivalent impedance of the distribution network. Otherwise, the active and reactive power output of the photovoltaic power station needs to be recalculated.

7. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 6, characterized in that: The specific steps to determine whether the distribution network topology has changed are as follows: S4A. Define a threshold for the change in the power ratio on both sides caused by the change in topology as the switching change coefficient λ. The selection of this coefficient is determined by the maximum and minimum loads carried by the node. S4B. Suppose that changes in the switching state of a branch circuit will cause fluctuations in the power ratio between the secondary side of the distribution station and the photovoltaic power station. Therefore, calculate the power ratio η between the secondary side of the distribution station and the photovoltaic power station as measured by the PMU: In the formula, P0 is the power measured by the PMU at the secondary side of the substation, and P1 is the power measured by the PMU at the photovoltaic power station node. When compared with the switching change coefficient λ, if the magnitude relationship changes, it is determined that the distribution network topology has changed; if the magnitude relationship remains unchanged, it is determined that the topology has not changed.

8. The photovoltaic power plant output adaptive adjustment method based on PMU measurement data according to claim 1, characterized in that: Step S4 also includes recalculating the node voltage of the photovoltaic power station. The specific implementation process is as follows: recalculate the corrected node voltage of the photovoltaic power station, determine whether the node voltage at the photovoltaic power station meets the threshold condition, and minimize the target node voltage deviation and active and reactive power regulation. In the method described, the photovoltaic power station reduces network transmission costs and operating computing power by spontaneously performing adjustment operations.

Citation Information

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