CN109586384B - Optimal adjustment method and device for high renewable energy permeation in power grid - Google Patents
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J7/00—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
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- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The invention provides an optimal adjustment method and device for high renewable energy permeation in a power grid.
Description
Technical Field
The invention relates to the field of new energy power generation and power distribution network electric energy safety scheduling and optimization, in particular to an optimal adjustment method and device for high renewable energy penetration in a power grid.
Background
At present, most of power generation energy is from petrochemical fuel, the combustion of the petrochemical fuel brings serious pollution to the environment on which human beings live, and renewable energy sources such as wind energy, solar energy and the like are pollution-free and have huge reserves, so that the utilization of the renewable energy sources for power generation is generally regarded by all countries in the world. In recent years, wind power generation technology is rapidly developed, but wind power generation units are intermittent, and although the current unreasonable energy structure can be improved by accessing a large-scale power grid, the stability of the power grid can be seriously influenced by the characteristics of volatility, intermittence, randomness, inverse peak regulation and the like.
Therefore, it is a technical problem of those skilled in the art to provide a method for solving the problem of grid power fluctuation caused by the wind turbine generator incorporated into the interconnected grid.
Disclosure of Invention
The embodiment of the invention provides an optimal adjustment method and device for high renewable energy penetration in a power grid, which can reduce the influence of large-scale wind turbine generator access on the safety and power distribution quality of a power distribution network to the maximum extent.
According to one aspect of the invention, an optimal regulation method for high renewable energy penetration in a power grid is provided, which comprises the following steps:
determining a preset number of wind turbines and energy storage systems in a power grid system;
establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
and based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population and taking the comprehensive influence of feeder line energy loss, inverse flow numerical values, over/under utilization amount of energy of the battery energy storage system, conversion loss of the battery energy storage system and node voltage deviation as a target, and carrying out iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained.
Preferably, the first fitness function is:
in the formula (I), the compound is shown in the specification,is the generated power of the jth wind power generating set in the individuals of the first population, n is a preset number,the installed capacity of the jth wind turbine generator set,and the charge state variation of the jth energy storage system in the h hour is shown.
Preferably, the preset number is 3.
Preferably, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting losses for the battery energy storage system.
Preferably, the constraint condition corresponding to the second fitness function includes: the method comprises the following steps of wind turbine generator generating capacity limiting constraint, energy storage system energy distribution limiting constraint, energy storage system charging and discharging limiting constraint, energy storage system charge state limiting constraint, feeder line current limiting constraint, node power balance constraint and charge state balance constraint.
According to another aspect of the present invention, there is provided an optimal regulation device for high renewable energy penetration in an electrical grid, comprising:
the determining module is used for determining the preset number of wind turbines and energy storage systems in the power grid system;
the first calculation module is used for establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
and the second calculation module is used for establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, and taking the comprehensive influence of feeder energy loss, inverse power flow numerical values, over/under utilization amount of energy of the battery energy storage system, conversion loss of the battery energy storage system and node voltage deviation as a target, and performing iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained.
Preferably, the first fitness function is:
in the formula (I), the compound is shown in the specification,is the generated power of the jth wind power generating set in the individuals of the first population, n is a preset number,the installed capacity of the jth wind turbine generator set,and the charge state variation of the jth energy storage system in the h hour is shown.
Preferably, the preset number is 3.
Preferably, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting losses for the battery energy storage system.
Preferably, the constraint condition corresponding to the second fitness function includes: the method comprises the following steps of wind turbine generator generating capacity limiting constraint, energy storage system energy distribution limiting constraint, energy storage system charging and discharging limiting constraint, energy storage system charge state limiting constraint, feeder line current limiting constraint, node power balance constraint and charge state balance constraint.
According to the technical scheme, the embodiment of the invention has the following advantages:
the invention provides an optimal adjustment method and device for high renewable energy penetration in a power grid, wherein the method comprises the following steps: determining a preset number of wind turbines and energy storage systems in a power grid system; establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained; and establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population and taking the comprehensive influence of the energy loss of the feeder line, the inverse flow numerical value, the over/under utilization amount of the energy of the battery energy storage system, the conversion loss of the battery energy storage system and the node voltage deviation as a target based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, and performing iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained. According to the method, the installed capacities of the wind turbine generator and the energy storage system are optimized to obtain the optimal installed capacity distribution of the wind turbine generator and the energy storage system, the positions of the wind turbine generator and the energy storage system in the power distribution network are optimized based on the first optimization result, the optimal installed capacities of the wind turbine generator and the battery energy storage system assembled in the power system are finally determined, in the optimization process, a plurality of factors influencing the wind turbine generator to be connected into the power grid are considered, and the influence of large-scale wind turbine generator connection on the safety and the power distribution quality of the power distribution network can be reduced to the maximum extent.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
Fig. 1 is a schematic flow chart of an embodiment of a method for optimally adjusting high renewable energy penetration in a power grid according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of the first optimization.
Fig. 3 is a schematic diagram of a second optimization.
Fig. 4 is a schematic structural diagram of an optimal regulating device for high renewable energy penetration provided by the invention.
Detailed Description
The embodiment of the invention provides an optimal adjustment method and device for high renewable energy penetration in a power grid, which can reduce the influence of large-scale wind turbine generator access on the safety and power distribution quality of a power distribution network to the maximum extent.
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the embodiments described below are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the method for optimally adjusting the high renewable energy penetration in the power grid according to the present invention includes:
101. determining a preset number of wind turbines and energy storage systems in a power grid system;
it should be noted that, in order to realize optimal adjustment, a certain number of wind turbines and energy storage systems are randomly selected to perform optimal adjustment, and the number of wind turbines and energy storage systems can be preset.
102. Establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
in this embodiment, in order to finally determine the optimal installed capacities of the three wind turbines and the three energy storage systems in the power grid system, the present invention separately performs optimization calculation, that is, the installed capacities of the wind turbines and the energy storage systems are optimized, and the optimization calculation method is a genetic algorithm, and the specific process is as follows: and establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained.
Specifically, the first fitness function is:
in the formula (I), the compound is shown in the specification,the generated power of the jth wind power unit in the first population of individuals,n is a preset number of the components,the installed capacity of the jth wind turbine generator set,and the charge state variation of the jth energy storage system in the h hour is shown. It is understood that, taking n-3 as an example, j represents any one of three wind turbines and three energy storage systems in an individual, regardless of the node position in the power distribution network system.
The specific process of step 102 is shown in fig. 2, before performing optimization calculation, the state of charge of the wind turbine generator and the energy storage system needs to be set to 50%, the initial management efficiency of the power grid system needs to be set to 0, and after initializing the individual value of the first population, optimization calculation of the genetic algorithm can be performed, the process of the genetic algorithm is the same as the process in the dashed frame in fig. 3, i.e., in the area a, it needs to be noted that the genetic algorithm is common knowledge of those skilled in the art, and is not specifically described here. After the optimization calculation is finished, the individual with the maximum management efficiency can be selected from all the iteration times, and at the moment, the individual is the installed capacity of the optimal wind turbine generator and the energy storage system.
103. And establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population and taking the comprehensive influence of the energy loss of the feeder line, the inverse flow numerical value, the over/under utilization amount of the energy of the battery energy storage system, the conversion loss of the battery energy storage system and the node voltage deviation as a target based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, and performing iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained.
After the optimal installed capacities of the wind turbine generator and the energy storage system are determined, the node positions of the wind turbine generator and the energy storage system in the power grid system need to be determined, based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, the positions of the wind turbine generator and the energy storage system are taken as individuals of a second population, a second fitness function is established by taking the comprehensive influence of feeder line energy loss, inverse current numerical values, over/under utilization amount of energy of the battery energy storage system, conversion loss of the battery energy storage system and node voltage deviation as a target, and iterative calculation of a genetic algorithm is carried out on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained.
Specifically, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting losses for the battery energy storage system.
The penalty function of the node voltage deviation is as follows:
the penalty function of the over/under utilization amount of the energy of the battery energy storage system is as follows:
feeder energy loss:
the inverse power flow value is:
the conversion loss of the battery energy storage system is as follows:
wherein, the ith node in the power grid system, at the h hour, Vi hIs the magnitude of the voltage at the node,working angle, Pi hIn order to carry out the active injection,in order to realize the reactive power injection,is the state of charge of the battery energy storage system,and scheduling the charging and discharging of the battery energy storage system.
rijIs the resistance between the node I and the node j, eta is the charge-discharge efficiency of the battery energy storage system, phi is the day-to-year conversion coefficient, N is the total number of the system nodes, ISpc.Is the limit value of the reverse current of the power grid,Vis the lowest limit value of the node voltage,is the maximum limit value of the node voltage,SOCis the minimum limit value of the state of charge of the energy storage system,is the maximum limit value of the state of charge of the energy storage system, BPis the minimum charge-discharge capacity limit of the energy storage system,is the maximum charging and discharging amount limit value of the energy storage system,is the installed capacity of the energy storage system.
Specifically, the constraint condition corresponding to the second fitness function includes:
and (3) limiting and constraining the generated energy of the wind turbine generator:
energy distribution limit constraint of the energy storage system:
and (3) limiting and constraining the charge state of the energy storage system:
feeder current limit constraints:
node active/reactive power balance constraints:
state of charge balance constraint:
wherein the content of the first and second substances,WBi、andthe active power of the wind turbine generator, the energy distribution of the energy storage system, the maximum power limit of the wind turbine generator and the maximum energy limit of the energy storage system of the ith node are respectively. ThetaijIs the impedance angle, YijFor the elements of the Y-bus matrix,the current value at the h-th hour was,is the maximum current limit.
A wind turbine generator model:
whereinvcutin、vcutout、vr、Pr,iThe node i, the wind speed in the h hour, the wind cut-in speed, the wind cut-out speed, the rated wind speed of the wind turbine generator and the installed capacity of the wind turbine generator are respectively.
The optimization calculation process of step 103 is shown in fig. 3, after an initial second population is generated (at this time, installed capacity in an individual is determined in step 102, and node positions of the wind turbine generator and the energy storage system are to be determined for optimization), then, optimization iteration of the genetic algorithm can be performed, in all iterations, each individual is subjected to comprehensive influence f obtained through calculation of the second fitness function, and finally, the individual with the minimum comprehensive influence is determined to be the optimal position of the wind turbine generator and the energy storage system in the power grid system.
According to the method, the installed capacities of the wind turbine generator and the energy storage system are optimized to obtain the optimal installed capacity distribution of the wind turbine generator and the energy storage system, the positions of the wind turbine generator and the energy storage system in the power grid system are optimized based on the first optimization result, the optimal installed capacities of the wind turbine generator and the battery energy storage system assembled in the power system are finally determined, in addition, a plurality of factors influencing the wind turbine generator to be connected into the power grid are considered in the optimization process, and the influence of large-scale wind turbine generator connection on the safety and the power distribution quality of the power distribution network can be reduced to the maximum extent.
The above is a detailed description of the method for optimally adjusting high renewable energy penetration in a power grid provided by the present invention, and the following is a description of a structure of the apparatus for optimally adjusting high renewable energy penetration in a power grid provided by the present invention, referring to fig. 4, an embodiment of the apparatus for optimally adjusting high renewable energy penetration in a power grid provided by the present invention includes:
the determining module 401 is configured to determine a preset number of wind turbines and energy storage systems in a power grid system;
the first calculating module 402 is configured to establish a first fitness function with installed capacities of the wind turbine generator and the energy storage system as individuals of a first group and with management efficiency of the power grid system as a target, and perform iterative calculation of a genetic algorithm on the first group until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
and a second calculation module 403, configured to establish a second fitness function with the positions of the wind turbine generator and the energy storage system as individuals of a second group based on installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, and with a comprehensive influence of feeder energy loss, a reverse flow numerical value, an over/under utilization amount of energy of the battery energy storage system, a conversion loss of the battery energy storage system, and a node voltage deviation as a target, and perform iterative calculation of a genetic algorithm on the second group until positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained.
Optionally, the first fitness function is:
in the formula (I), the compound is shown in the specification,is the generated power of the jth wind power generating set in the individuals of the first population, n is a preset number,the installed capacity of the jth wind turbine generator set,and the charge state variation of the jth energy storage system in the h hour is shown.
Optionally, the preset number is 3.
Optionally, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting losses for the battery energy storage system.
Optionally, the constraint condition corresponding to the second fitness function includes: the method comprises the following steps of wind turbine generator generating capacity limiting constraint, energy storage system energy distribution limiting constraint, energy storage system charging and discharging limiting constraint, energy storage system charge state limiting constraint, feeder line current limiting constraint, node power balance constraint and charge state balance constraint.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (6)
1. An optimal regulation method for high renewable energy penetration in a power grid is characterized by comprising the following steps:
determining a preset number of wind turbines and energy storage systems in a power grid system;
establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
wherein the first fitness function is:
in the formula (I), the compound is shown in the specification,is the generated power of the jth wind power generating set in the individuals of the first population, n is a preset number,the installed capacity of the jth wind turbine generator set,the charge state variation of the jth energy storage system in the h hour;
based on the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population and taking the comprehensive influence of feeder line energy loss, inverse flow numerical values, over/under utilization amount of energy of the battery energy storage system, conversion loss of the battery energy storage system and node voltage deviation as a target, and carrying out iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained; specifically, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting loss of a battery energy storage system, and phi is a day-to-year conversion coefficient;
wherein, the over/under utilization amount of the energy of the battery energy storage system is Delta WBThe penalty function of (a) is:
in the formulaThe charging scheduling of the battery energy storage system is carried out for the ith node in the power grid system at the h hour,the discharging scheduling of the battery energy storage system is carried out for the ith node in the power grid system in the h hour;
in the formula Ispc.And the power grid inverse current limit value is obtained.
2. Method for optimal regulation of high renewable energy penetration in an electric network according to claim 1, characterized in that said preset number is 3.
3. The method for optimally adjusting the high renewable energy penetration in the power grid according to claim 2, wherein the constraint condition corresponding to the second fitness function comprises: the method comprises the following steps of wind turbine generator generating capacity limiting constraint, energy storage system energy distribution limiting constraint, energy storage system charging and discharging limiting constraint, energy storage system charge state limiting constraint, feeder line current limiting constraint, node power balance constraint and charge state balance constraint.
4. An optimal regulation device of high renewable energy penetration in an electric network, characterized in that it comprises:
the determining module is used for determining the preset number of wind turbines and energy storage systems in the power grid system;
the first calculation module is used for establishing a first fitness function by taking the installed capacities of the wind turbine generator and the energy storage system as individuals of a first population and taking the management efficiency of the power grid system as a target, and performing iterative calculation of a genetic algorithm on the first population until the installed capacities of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency are obtained;
wherein the first fitness function is:
in the formula (I), the compound is shown in the specification,in individuals of a first populationN is a preset number,the installed capacity of the jth wind turbine generator set,the charge state variation of the jth energy storage system in the h hour;
the second calculation module is used for establishing a second fitness function by taking the positions of the wind turbine generator and the energy storage system as individuals of a second population and taking the comprehensive influence of the energy loss of a feeder line, the inverse flow numerical value, the over/under utilization amount of the energy of the battery energy storage system, the conversion loss of the battery energy storage system and the node voltage deviation as a target based on the installed capacity of the wind turbine generator and the energy storage system corresponding to the maximum management efficiency, and performing iterative calculation of a genetic algorithm on the second population until the positions of the wind turbine generator and the energy storage system corresponding to the minimum comprehensive influence are obtained; specifically, the second fitness function is:
in the formula,. DELTA.VhFor node voltage deviation, Δ WBThe energy over/under utilization amount of the battery energy storage system,in order to provide for a loss of feeder energy,is a reverse trend value,Converting loss of a battery energy storage system, and phi is a day-to-year conversion coefficient;
wherein, the over/under utilization amount of the energy of the battery energy storage system is Delta WBThe penalty function of (a) is:
in the formulaThe charging scheduling of the battery energy storage system is carried out for the ith node in the power grid system at the h hour,the discharging scheduling of the battery energy storage system is carried out for the ith node in the power grid system in the h hour;
in the formula Ispc.And the power grid inverse current limit value is obtained.
5. Optimal regulation of high renewable energy penetration in an electric network according to claim 4, characterized in that said preset number is 3.
6. The optimal adjustment device for high renewable energy penetration in a power grid according to claim 5, wherein the constraint condition corresponding to the second fitness function comprises: the method comprises the following steps of wind turbine generator generating capacity limiting constraint, energy storage system energy distribution limiting constraint, energy storage system charging and discharging limiting constraint, energy storage system charge state limiting constraint, feeder line current limiting constraint, node power balance constraint and charge state balance constraint.
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