CN115632404A - Distributed voltage control method and device based on digital twin power distribution system - Google Patents
Distributed voltage control method and device based on digital twin power distribution system Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J13/00—Circuit arrangements for providing remote indication of network conditions, e.g. an instantaneous record of the open or closed condition of each circuitbreaker in the network; Circuit arrangements for providing remote control of switching means in a power distribution network, e.g. switching in and out of current consumers by using a pulse code signal carried by the network
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
Abstract
A distributed voltage control method and apparatus based on a digital twin power distribution system is provided, wherein the method comprises: the method for voltage control of the subareas comprises the following steps: calculating to obtain a bus voltage value of the current area in a set period according to the bus voltage value of the previous area; initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period; dividing a set time interval into a plurality of iteration moments, and executing an iteration step at each iteration moment; taking an actual active voltage value and an actual reactive voltage value corresponding to the sub-region in the current region at the preferred iteration moment as a final active voltage value and a final reactive voltage value of the sub-region in the current region within a set time period; and adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value. This document enables voltage power cost reduction while meeting the actual voltage requirements of the user.
Description
Technical Field
The invention relates to the field of electric power, in particular to a distributed voltage control method and device based on a digital twin power distribution system.
Background
Generally, the entire power distribution system will be divided into several zones, with one general controller in each zone to control the voltage in the entire zone, and for one zone, the entire zone will be divided into several sub-zones, with one sub-controller in each sub-zone to control the voltage in the entire sub-zone.
In the prior art, the zone voltage is generally set to be a fixed voltage, so that the voltage of the sub-zone in the zone is also the fixed voltage. However, with the popularization of distributed energy in a power distribution system and the increase and decrease of electric appliances in areas and sub-areas, actual supply voltages in the areas and the sub-areas change, for example, if the electric appliances increase greatly, the supply voltages in the areas and the sub-areas are lower than a fixed voltage, and the actual voltage requirements of users cannot be met; if the electric appliances are greatly reduced, the power supply voltage of the area and the sub-area is higher than the fixed voltage, and the voltage power cost is improved. And the problem of communication delay between areas remains difficult to solve.
Therefore, a distributed voltage control method based on a digital twin power distribution system is needed, which can better adjust the voltage, so that the voltage in the region and the sub-region can meet the actual voltage requirement of the user, and the voltage and power costs can be reduced while the problem of communication delay is solved.
Disclosure of Invention
An object of the embodiments herein is to provide a distributed voltage control method and apparatus based on a digital twinborn power distribution system to better adjust the voltage so that the voltage in the region and sub-region meets the actual voltage demand of the user, and reduce the voltage power cost while solving the problem of communication delay.
In order to achieve the above object, in one aspect, an embodiment herein provides a distributed voltage control method based on a digital twin power distribution system, where the power distribution system is divided into a plurality of regions, the regions are connected by circuits, each region includes a plurality of independent sub-regions, and the regions are connected by circuits with the sub-regions included in the region, and the method for performing voltage control on the sub-regions includes:
calculating to obtain a bus voltage value of the current area within a set period of time according to the bus voltage value of the previous area;
initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period;
dividing a set time interval into a plurality of iteration moments, and executing the following iteration steps at each iteration moment:
obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment;
obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the previous iteration moment;
according to the communication condition in the process of transmitting voltage signals to the corresponding sub-area by the current area, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment to obtain the actual active voltage value and the actual reactive voltage value of the sub-area at the current iteration moment in the current area;
calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable;
updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the last iteration moment in a set time period, and executing the iteration steps;
taking the iteration time corresponding to the minimum bus power generation cost in all bus power generation costs in a set time period of the current region as the preferred iteration time;
taking an actual active voltage value and an actual reactive voltage value corresponding to the sub-region in the current region at the preferred iteration moment as a final active voltage value and a final reactive voltage value of the sub-region in the current region within a set time period;
and adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value.
Preferably, the calculating the bus voltage value of the current zone within the set period according to the bus voltage value of the previous zone further includes:
calculating the bus voltage value of the current area in the set period by the following formula:
wherein v is i Is the bus voltage value of the previous zone, v j Is the value of the bus voltage of the current region,the voltage values of the three phases a, b and c in the previous area are respectively,the current values of the three phases a, b and c in the previous area flowing to the three phases a, b and c in the current area respectively,to connect the circuit impedance of the previous and present regions,to communicate the complex power flow of the previous zone and the current zone circuits,meaning that the conjugate transpose operation is taken on the matrix,is the conjugate of the quantity.
Preferably, the obtaining an initial active voltage value of a sub-region in the current region at the current iteration time according to the voltage auxiliary variable at the current iteration time and the initial active voltage value at the previous iteration time further includes:
calculating the initial active voltage value of the sub-region in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial active voltage value of the sub-region k in the current region at the current iteration time,to communicate the active impedance of the circuit of the current region with sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the initial active voltage value of the sub-region k in the current region at the last iteration moment is obtained.
Preferably, the obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration time according to the voltage auxiliary variable at the current iteration time and an initial reactive voltage value at the previous iteration time further includes:
calculating the initial reactive voltage value of the sub-region in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial reactive voltage value of the sub-region k in the current region at the current iteration time,to communicate the reactive impedance of the circuit of the current region with sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the voltage value of the reactive bus of the sub-region k in the current region at the last iteration moment is obtained.
Preferably, the adjusting the initial active voltage value and the initial reactive voltage value at the current iteration time according to the communication condition in the process of transmitting the voltage signal from the current region to the corresponding sub-region, and obtaining the actual active voltage value and the actual reactive voltage value corresponding to the current iteration time further includes:
if communication delay occurs in the process that the current region transmits voltage signals to the corresponding sub-region at the current iteration moment, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment according to the communication delay time to obtain an actual active voltage value and an actual reactive voltage value;
and if the communication channel is disconnected in the process of transmitting the voltage signal to the corresponding sub-region by the current region at the current iteration moment, taking the initial active voltage value and the initial reactive voltage value at the previous iteration moment as the actual active voltage value and the actual reactive voltage value at the current iteration moment.
Preferably, the adjusting the initial active voltage value and the initial reactive voltage value at the current iteration time according to the communication delay time to obtain the actual active voltage value and the actual reactive voltage value further includes:
calculating an actual active voltage value and an actual reactive voltage value by the following formulas:
wherein, the first and the second end of the pipe are connected with each other,being the actual active voltage value of the sub-region,communication delay time in the process of transmitting the voltage signal to the subarea for the current area,subtracting the communication delay time from the current iteration time to obtain an initial active voltage value corresponding to the time of the sub-region;is the actual reactive voltage value of the sub-area,and subtracting the communication delay time from the current iteration time to obtain an initial reactive voltage value corresponding to the time of the sub-region.
Preferably, the calculating the bus power generation cost of the current region at the current iteration time according to the active cost variable and the reactive cost variable further includes:
calculating to obtain an active power set value and a reactive power set value of each subregion in the current region at the current iteration moment according to the active cost variable and the reactive cost variable;
and integrating the active power set value and the reactive power set value of all the sub-areas in the current area at the current iteration moment, and calculating to obtain the bus power generation cost of the current area at the current iteration moment.
Preferably, the calculating to obtain the active power set value and the reactive power set value of each sub-region in the current region at the current iteration time according to the active cost variable and the reactive cost variable further includes:
and calculating an active power set value and a reactive power set value of any subregion in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time,the active power set point for a sub-area,as an active cost variable of the current region,being the cost factor of the active power of the sub-area,is an active parameter of a certain phase in the sub-region,the sum of all available phases in the sub-region, diag is the diagonal matrix function,for the reactive power set point of the sub-area,as a reactive cost variable for the current region,being the cost factor of the reactive power of the sub-area,is a reactive parameter of a certain phase in the sub-area,parameter factors of active power and reactive power of the sub-regions respectively.
Preferably, the step of calculating the bus power generation cost of the current area at the current iteration time by integrating the active power set values and the reactive power set values of all the sub-areas in the current area at the current iteration time further includes:
calculating the bus power generation cost of the current area at the current iteration moment by the following formula:
wherein, the first and the second end of the pipe are connected with each other,for the active power generation cost of the sub-area,cost of reactive power generation for sub-regionsIs the sum of the active parameters of all phases in the sub-region,is the sum of the reactive parameters of all phases in the sub-area,the active power set point for a sub-area,for the reactive power set point of the sub-area,being the cost factor of the active power of the sub-area,is the cost coefficient of the reactive power of the sub-area, s.t. is the constraint condition,andrespectively active in the sub-area power networkThe lower and upper limits of the cost of power generation,andthe lower limit and the upper limit of the reactive power generation cost in the sub-area power network are respectively, and N is the number of sub-areas in the current area.
On the other hand, embodiments herein provide a distributed voltage control apparatus based on a digital twin power distribution system, the power distribution system is divided into a plurality of regions, the plurality of regions are connected by a circuit, each region includes a plurality of independent sub-regions, the region is connected by a circuit with the sub-regions included therein, and the apparatus for performing voltage control on the sub-regions includes:
the analysis and calculation module is used for calculating to obtain a bus voltage value of the current area within a set period of time according to the bus voltage value of the previous area;
the initialization module is used for initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period;
the step-by-step iteration module is used for dividing the set time interval into a plurality of iteration moments, and the following iteration steps are executed at each iteration moment: obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment; obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the last iteration moment; adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment according to the communication condition of the current region in the process of transmitting voltage signals to the corresponding sub-region, so as to obtain the actual active voltage value and the actual reactive voltage value of the sub-region at the current iteration moment in the current region; calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable; updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the last iteration moment in a set time period, and executing the iteration steps;
the target optimization module is used for taking the iteration time corresponding to the minimum bus power generation cost in all the bus power generation costs in the current region within a set time period as the optimal iteration time;
the deduction determining module is used for taking an actual active voltage value and an actual reactive voltage value corresponding to the current sub-region at the optimal iteration moment as a final active voltage value and a final reactive voltage value of the current sub-region within a set time period;
and the adjusting control module is used for adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value.
According to the technical scheme provided by the embodiment, for any sub-area in the current area, the bus power generation cost needs to be calculated at each iteration time, the iteration time corresponding to the minimum bus power generation cost can be determined as the optimal iteration time after all the iteration times are executed, the actual active voltage value and the actual reactive voltage value at the optimal iteration time are used as the final active voltage value and the final reactive voltage value in the set time period, the sum of the final active voltage value and the final reactive voltage value is calculated to be the final voltage value, and the voltage of the sub-area is adjusted to be the final voltage value, so that the power generation cost of the sub-area can be controlled, and the power generation cost of the current area can be further controlled. Therefore, the voltage stability of the sub-region and the current region where the sub-region is located can be guaranteed, the user requirements are met, and the power generation cost can be reduced.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments or technical solutions in the prior art, the drawings used in the embodiments or technical solutions in the prior art are briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present disclosure, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 illustrates a schematic structural diagram of a power distribution system provided by embodiments herein;
fig. 2 illustrates a schematic flow diagram of a distributed voltage control provided by an embodiment herein;
fig. 3 shows a flow diagram of an iteration step provided by embodiments herein;
fig. 4 is a schematic flowchart illustrating a process of calculating a bus power generation cost of a current area at a current iteration time according to an active cost variable and a reactive cost variable, provided in an embodiment of the present disclosure;
fig. 5 shows a schematic block diagram of a distributed voltage control apparatus provided in an embodiment of the present disclosure;
fig. 6 shows a schematic structural diagram of a computer device provided in an embodiment herein.
Description of the symbols of the drawings:
100. an analysis calculation module;
200. initializing a module;
300. a step-by-step iteration module;
400. a target preference module;
500. a deduction determination module;
600. adjusting the control module;
602. a computer device;
604. a processor;
606. a memory;
608. a drive mechanism;
610. an input/output module;
612. an input device;
614. an output device;
616. a presentation device;
618. a graphical user interface;
620. a network interface;
622. a communication link;
624. a communication bus.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments 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 herein without making any creative effort, shall fall within the scope of protection.
In the prior art, the zone voltage is generally set to be a fixed voltage, so that the voltage of the sub-zone in the zone is also the fixed voltage. However, as the number of the electrical appliances in the area and the sub-area increases or decreases, the actual supply voltage in the area and the sub-area changes, for example, if the number of the electrical appliances increases, the supply voltage in the area and the sub-area is lower than a fixed voltage, and the actual voltage requirement of the user cannot be met; if the electric appliances are greatly reduced, the power supply voltage of the area and the sub-area is higher than the fixed voltage, and the voltage power cost is improved.
To solve the above problem, embodiments herein provide a digital twin-based voltage control method. Fig. 2 and 3 are schematic flow diagrams of a digital twin-based voltage control method provided in the embodiments herein, and the present specification provides the method operation steps as described in the embodiments or the flow diagrams, but may include more or less operation steps based on conventional or non-inventive labor. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. When an actual system or apparatus product executes, it can execute sequentially or in parallel according to the method shown in the embodiment or the figures.
It should be noted that the terms "first," "second," and the like in the description and claims herein and in the above-described drawings are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments herein described are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or device.
The distributed voltage control method based on the digital twin power distribution system is provided, referring to fig. 1, the power distribution system is divided into a plurality of areas, the areas are connected through circuits, each area comprises a plurality of independent sub-areas, and the areas are connected with the sub-areas.
Referring to fig. 2 and 3, the method of voltage control for the sub-region includes:
s101: calculating to obtain a bus voltage value of the current area in a set period according to the bus voltage value of the previous area;
s102: initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period;
s103: dividing the set time interval into a plurality of iteration moments, and executing the following iteration steps S104-S107 at each iteration moment:
s104: obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment;
s105: obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the last iteration moment;
s106: adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment according to the communication condition of the current region in the process of transmitting voltage signals to the corresponding sub-region, so as to obtain the actual active voltage value and the actual reactive voltage value of the sub-region at the current iteration moment in the current region;
s107: calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable;
s108: updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the current iteration moment in a set time period, and executing the iteration steps S104-S107;
s109: taking the iteration time corresponding to the minimum bus power generation cost in all bus power generation costs in a set time period of the current region as the preferred iteration time;
s110: taking an actual active voltage value and an actual reactive voltage value corresponding to the sub-region in the current region at the preferred iteration moment as a final active voltage value and a final reactive voltage value of the sub-region in the current region within a set time period;
s111: and adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value.
The method of the embodiment of the invention mainly performs voltage adjustment control on the sub-region, specifically, the voltage adjustment control is performed once every set time period, the set time period is divided into a plurality of iteration moments, the steps from S104 to S108 are performed at each iteration moment, until all the iteration moments in the set time period are performed, the preferred iteration moment is determined from all the iteration moments, the final active voltage value and the final reactive voltage value at the preferred iteration moment are summed, so that the final voltage value of the sub-region in the set time period can be obtained, and the voltage of the sub-region is adjusted to the final voltage value. For all the sub-regions in the region, each sub-region may be adjusted to the corresponding final voltage value within the set time period, and adjusting the voltage of each sub-region may adjust the bus voltage value of the region to which the sub-region belongs.
Specifically, when voltage control is performed on any sub-area in the current area, firstly, a bus voltage value of the current area in a set period needs to be calculated according to a bus voltage value of the previous area.
Specifically, the bus voltage value of the current region in the set period is calculated by the following formula:
wherein v is i Is the bus voltage value of the previous zone, v j Is the value of the bus voltage of the current region,the voltage values of the three phases a, b and c in the previous area are respectively,the current values of the three phases a, b and c in the previous area flowing to the three phases a, b and c in the current area respectively,to connect the circuit impedance of the previous and present regions,to communicate the complex power flow of the previous zone and the current zone circuits,meaning that the conjugate transpose operation is taken on the matrix,is the conjugate of the quantity.
And then, initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period, wherein in the subsequent iteration process, the active cost variable, the reactive cost variable and the voltage auxiliary variable which correspond to the iteration moment of 0 are all 0.
Therefore, the set time interval can be divided into a plurality of iteration moments, the iteration steps are executed, the initial active voltage value and the initial reactive voltage value of the sub-region in the current iteration moment are obtained through specific calculation according to the needs, and the initial active voltage value of the sub-region in the current iteration moment can be calculated through the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial active voltage value of the sub-region k in the current region at the current iteration time,to connect the active impedance of the circuit of the current region with the sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the initial active voltage value of the sub-region k in the current region at the last iteration moment is obtained.
Calculating the initial reactive voltage value of the sub-region in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial reactive voltage value of the sub-region k in the current region at the current iteration time,to communicate the reactive impedance of the circuit of the current region with sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the voltage value of the reactive bus of the sub-area k in the current area at the last iteration moment is obtained.
It should be noted that, since there is no previous iteration time when the iteration time is 0, both the initial active voltage value and the initial reactive voltage value of the previous iteration time corresponding to the current iteration time being 0 are set to 0.
Further, the adjusting the initial active voltage value and the initial reactive voltage value at the current iteration time according to the communication condition in the process of transmitting the voltage signal from the current area to the corresponding sub-area to obtain the actual active voltage value and the actual reactive voltage value corresponding to the current iteration time further includes:
if communication delay occurs in the process that the current region transmits voltage signals to the corresponding sub-region at the current iteration moment, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment according to the communication delay time to obtain an actual active voltage value and an actual reactive voltage value;
and if the communication channel is disconnected in the process of transmitting the voltage signal to the corresponding sub-region by the current region at the current iteration moment, taking the initial active voltage value and the initial reactive voltage value at the previous iteration moment as the actual active voltage value and the actual reactive voltage value at the current iteration moment.
Specifically, the adjusting the initial active voltage value and the initial reactive voltage value at the current iteration time according to the communication delay time to obtain the actual active voltage value and the actual reactive voltage value further includes:
calculating an actual active voltage value and an actual reactive voltage value by the following formulas:
wherein, the first and the second end of the pipe are connected with each other,for the actual active voltage value of the sub-region,communication delay time in the process of transmitting the voltage signal to the subarea for the current area,subtracting the communication delay time from the current iteration time to obtain an initial active voltage value corresponding to the time of the sub-region;is the actual reactive voltage value of the sub-area,and subtracting the communication delay time from the current iteration time to obtain an initial reactive voltage value corresponding to the time of the sub-region.
In this embodiment, referring to fig. 4, the calculating, according to the active cost variable and the reactive cost variable, a bus power generation cost of the current area at the current iteration time further includes:
s201: calculating to obtain an active power set value and a reactive power set value of each subregion in the current region at the current iteration moment according to the active cost variable and the reactive cost variable;
s202: and integrating the active power set values and the reactive power set values of all the sub-areas in the current area at the current iteration moment, and calculating to obtain the bus power generation cost of the current area at the current iteration moment.
Specifically, the step of calculating to obtain the active power set value and the reactive power set value of each sub-area in the current iteration moment according to the active cost variable and the reactive cost variable further includes:
and calculating an active power set value and a reactive power set value of any subarea in the current area at the current iteration moment through the following formula:
wherein, t is the current iteration time,is the active power set point for the sub-area,as an active cost variable for the current region,being the cost factor of the active power of the sub-area,is an active parameter of a certain phase in the sub-region,the sum of all available phases in the sub-region, diag is the diagonal matrix function,for the reactive power set point of the sub-area,as a reactive cost variable for the current region,being the cost factor of the reactive power of the sub-area,is a reactive parameter of a certain phase in the sub-area,respectively, the parameter factors of the active power and the reactive power of the sub-area.
The step of calculating the bus power generation cost of the current area at the current iteration moment by integrating the active power set values and the reactive power set values of all the sub-areas in the current area at the current iteration moment further comprises the following steps:
calculating the bus power generation cost of the current area at the current iteration moment by the following formula:
wherein, the first and the second end of the pipe are connected with each other,for the active power generation cost of the sub-area,cost of reactive power generation for sub-regionsIs the sum of the active parameters of all phases in the sub-region,is the sum of the reactive parameters of all phases in the sub-area,is the active power set point for the sub-area,is the reactive power set point for the sub-area,being the cost factor of the active power of the sub-area,is the cost coefficient of the reactive power of the sub-area, s.t. is the constraint condition,andrespectively the lower limit and the upper limit of the active power generation cost in the sub-area power network,andthe lower limit and the upper limit of the reactive power generation cost in the sub-area power network are respectively, and N is the number of sub-areas in the current area.
Finally, the active cost variable, the reactive cost variable and the voltage auxiliary variable at the next iteration moment need to be updated, wherein the updating of the active cost variable, the reactive cost variable and the voltage auxiliary variable is not directed to a certain sub-region, but to all sub-regions in the current region.
Specifically, the voltage auxiliary variable at the next iteration time may be updated according to the bus voltage value (obtained through step S101) of the current region in the set time period and the voltage auxiliary variable at the current iteration time. It should be noted that, when the voltage auxiliary variable is updated, the voltage auxiliary variable upper limit value and the voltage auxiliary variable lower limit value need to be used, when the iteration time is 0, both the voltage auxiliary variable upper limit value and the voltage auxiliary variable lower limit value are 0, and when the voltage auxiliary variable is updated each time, the voltage auxiliary variable upper limit value and the voltage auxiliary variable lower limit value are updated accordingly.
The update formula of the voltage auxiliary variable is specifically as follows:
wherein the content of the first and second substances,for the voltage auxiliary variable of the current region at the current iteration time,the lower limit value of the voltage auxiliary variable of the current area at the current iteration moment,the upper limit value of the voltage auxiliary variable of the current area at the current iteration moment,is the lower limit value of the bus voltage of the current area,is the bus voltage upper limit value of the current area,is the value of the bus voltage of the current region,the lower limit value of the voltage auxiliary variable of the current area at the next iteration moment,for the upper value of the voltage auxiliary variable of the current region at the next iteration moment,for the voltage auxiliary variable of the current region at the next iteration instant,to set the step size.
Further, the active cost variable and the reactive cost variable are updated according to the updated voltage auxiliary variable at the next iteration time, and the specific formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,is the active cost variable of the current area at the next iteration moment, k is any sub-area in the current area,to connect the active impedance of the circuit of the current region with the sub-region k,for the voltage auxiliary variable of the current region at the next iteration instant,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,for the initial active voltage value of the sub-region k in the current region at the current iteration time,for the reactive cost variable of the current region at the next iteration time,to communicate the reactive impedance of the circuit of the current region with sub-region k,and the initial reactive voltage value of the sub-region k in the current region at the current iteration moment is obtained.
And updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment, and executing the steps from S104 to S108 until all the iteration moments are executed.
For any sub-area in the current area, because the bus power generation cost needs to be calculated at each iteration time, the iteration time corresponding to the minimum bus power generation cost can be determined as the optimal iteration time after all the iteration times are executed, the actual active voltage value and the actual reactive voltage value at the optimal iteration time are taken as the final active voltage value and the final reactive voltage value in the set time period, the sum of the final active voltage value and the final reactive voltage value is calculated to be the most final voltage value, the voltage of the sub-area is adjusted to be the final voltage value, the power generation cost of the sub-area can be controlled, and the power generation cost of the current area can be further controlled. Therefore, the voltage stability of the subareas and the current areas where the subareas are located can be ensured, the user requirements are met, and the power generation cost can be reduced.
Based on the above-mentioned distributed voltage control method based on the digital twin power distribution system, the embodiments herein also provide a distributed voltage control apparatus based on the digital twin power distribution system. The apparatus may include systems (including distributed systems), software (applications), modules, components, servers, clients, etc. that employ the methods described herein in embodiments, in conjunction with any necessary apparatus to implement the hardware. Based on the same innovative concept, the apparatus in one or more of the embodiments provided in the embodiments herein is described in the following embodiments. Since the implementation scheme of the apparatus for solving the problem is similar to that of the method, the specific apparatus implementation in the embodiment of the present disclosure may refer to the implementation of the foregoing method, and repeated details are not repeated. As used hereinafter, the term "unit" or "module" may be a combination of software and/or hardware that implements a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.
Specifically, fig. 5 is a schematic block structure diagram of an embodiment of a distributed voltage control apparatus based on a digital twin power distribution system provided in an embodiment of the present disclosure, the power distribution system is divided into a plurality of regions, the plurality of regions are connected by a circuit, each region includes a plurality of independent sub-regions, the region and the sub-regions included in the region are connected by a circuit, and the apparatus for performing voltage control on the sub-regions includes: the system comprises an analysis calculation module 100, an initialization module 200, a step-by-step iteration module 300, a target preference module 400, a deduction determination module 500 and an adjustment control module 600.
The analysis and calculation module 100 is configured to calculate a bus voltage value of a current area within a set time period according to a bus voltage value of a previous area;
an initialization module 200, configured to initialize an active cost variable, a reactive cost variable, and a voltage auxiliary variable within a set time period;
a step-by-step iteration module 300, configured to divide the set time period into a plurality of iteration moments, and execute the following iteration steps at each iteration moment: obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment; obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the last iteration moment; according to the communication condition in the process of transmitting voltage signals to the corresponding sub-area by the current area, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment to obtain the actual active voltage value and the actual reactive voltage value of the sub-area at the current iteration moment in the current area; calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable; updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the last iteration moment in a set time period, and executing the iteration steps;
the target optimization module 400 is configured to use an iteration time corresponding to the minimum bus power generation cost of all bus power generation costs in a set time period in a current region as an optimal iteration time;
the deduction determining module 500 is configured to use an actual active voltage value and an actual reactive voltage value corresponding to a sub-region in the current region at a preferred iteration time as a final active voltage value and a final reactive voltage value of the sub-region in the current region within a set time period;
and the adjusting control module 600 is configured to adjust and control the voltage value of the sub-region in the current region within the set time period according to the final active voltage value and the final reactive voltage value.
Referring to fig. 6, in an embodiment of the present disclosure, a computer device 602 is further provided based on the above-described distributed voltage control method based on the digital twin power distribution system, wherein the above-described method is executed on the computer device 602. The computer device 602 may include one or more processors 604, such as one or more Central Processing Units (CPUs) or Graphics Processors (GPUs), each of which may implement one or more hardware threads. The computer device 602 may also include any memory 606 for storing any kind of information, such as code, settings, data, etc., and in a particular embodiment a computer program running on the memory 606 and on the processor 604, which computer program, when executed by the processor 604, may perform the instructions according to the above-described method. For example, and without limitation, memory 606 may include any one or more of the following in combination: any type of RAM, any type of ROM, flash memory devices, hard disks, optical disks, etc. More generally, any memory may use any technology to store information. Further, any memory may provide volatile or non-volatile retention of information. Further, any memory may represent fixed or removable components of computer device 602. In one case, when the processor 604 executes the associated instructions, which are stored in any memory or combination of memories, the computer device 602 may perform any of the operations of the associated instructions. The computer device 602 also includes one or more drive mechanisms 608, such as a hard disk drive mechanism, an optical disk drive mechanism, or the like, for interacting with any of the memories.
The computer device 602 may also include an input/output module 610 (I/O) for receiving various inputs (via input devices 612) and for providing various outputs (via output devices 614). One particular output mechanism may include a presentation device 616 and an associated graphical user interface 618 (GUI). In other embodiments, input/output module 610 (I/O), input device 612, and output device 614 may also be excluded, as just one computer device in a network. Computer device 602 may also include one or more network interfaces 620 for exchanging data with other devices via one or more communication links 622. One or more communication buses 624 couple the above-described components together.
Communication link 622 may be implemented in any manner, such as over a local area network, a wide area network (e.g., the Internet), a point-to-point connection, etc., or any combination thereof. Communication link 622 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.
Corresponding to the methods in fig. 2-4, the embodiments herein also provide a computer-readable storage medium having stored thereon a computer program, which, when executed by a processor, performs the steps of the above-described method.
Embodiments herein also provide computer readable instructions, wherein when executed by a processor, a program thereof causes the processor to perform the method as shown in fig. 2-4.
It should be understood that, in various embodiments herein, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments herein.
It should also be understood that, in the embodiments herein, the term "and/or" is only one kind of association relation describing an associated object, and means that there may be three kinds of relations. For example, a and/or B, may represent: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps of the examples described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and that the components and steps of the examples have been described in a functional general in the foregoing description for the purpose of illustrating clearly the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
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 herein, it should be understood that the disclosed system, apparatus, and method may be implemented in other ways. 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 also be an electric, mechanical or other form of connection.
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 purposes of the embodiments herein.
In addition, functional units in the embodiments herein 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 may be implemented in the form of hardware, or may also be implemented in the 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 solutions in the present invention substantially or partially contribute to the prior art, or all or part of the technical solutions may be embodied in the form of a software product, which is stored in a storage medium and includes several 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 methods described in the embodiments herein. 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 various media capable of storing program codes.
The principles and embodiments of this document are explained herein using specific examples, which are presented only to aid in understanding the methods and their core concepts; meanwhile, for the general technical personnel in the field, according to the idea of this document, there may be changes in the concrete implementation and the application scope, in summary, this description should not be understood as the limitation of this document.
Claims (10)
1. A distributed voltage control method based on a digital twin power distribution system is characterized in that the power distribution system is divided into a plurality of areas, the areas are connected through circuits, each area comprises a plurality of independent sub-areas, the areas are connected with the sub-areas included in the areas through circuits, and the method for performing voltage control on the sub-areas comprises the following steps:
calculating to obtain a bus voltage value of the current area within a set period of time according to the bus voltage value of the previous area;
initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period;
dividing a set time interval into a plurality of iteration moments, and executing the following iteration steps at each iteration moment:
obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment;
obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the last iteration moment;
according to the communication condition in the process of transmitting voltage signals to the corresponding sub-area by the current area, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment to obtain the actual active voltage value and the actual reactive voltage value of the sub-area at the current iteration moment in the current area;
calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable;
updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the last iteration moment in a set time period, and executing the iteration steps;
taking the iteration time corresponding to the minimum bus power generation cost in all bus power generation costs in a set time period of the current region as the preferred iteration time;
taking an actual active voltage value and an actual reactive voltage value corresponding to the sub-region in the current region at the preferred iteration moment as a final active voltage value and a final reactive voltage value of the sub-region in the current region within a set time period;
and adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value.
2. The distributed voltage control method according to claim 1, wherein the calculating the bus voltage value of the current zone within the set period according to the bus voltage value of the previous zone further comprises:
calculating the bus voltage value of the current area in the set period by the following formula:
wherein v is i Is the bus voltage value of the previous zone, v j Is the value of the bus voltage of the current region,the voltage values of the three phases a, b and c in the previous area are respectively,the current values of the three phases a, b and c in the previous area flowing to the three phases a, b and c in the current area respectively,to connect the circuit impedance of the previous and present regions,to communicate the complex power flow of the previous zone and the current zone circuits,representing the conjugate transpose operation on the matrix,is the conjugate of the quantity.
3. The distributed voltage control method according to claim 1, wherein obtaining an initial active voltage value of a sub-region in a current region at a current iteration time according to the voltage auxiliary variable at the current iteration time and an initial active voltage value at a previous iteration time further comprises:
calculating the initial active voltage value of the sub-region in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial active voltage value of the sub-region k in the current region at the current iteration time,to connect the active impedance of the circuit of the current region with the sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the initial active voltage value of the sub-region k in the current region at the last iteration moment is obtained.
4. The distributed voltage control method according to claim 1, wherein obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration time according to the voltage auxiliary variable at the current iteration time and an initial reactive voltage value at a previous iteration time further comprises:
calculating the initial reactive voltage value of the sub-region in the current region at the current iteration moment by the following formula:
wherein t is the current iteration time, k is any sub-region in the current region,for the initial reactive voltage value of the sub-region k in the current region at the current iteration time,to communicate the reactive impedance of the circuit of the current region with sub-region k,is the voltage auxiliary variable of the current region,the delay value in the transmission of the voltage auxiliary variable to the sub-area for the current area,and the voltage value of the reactive bus of the sub-area k in the current area at the last iteration moment is obtained.
5. The distributed voltage control method according to claim 1, wherein the adjusting an initial active voltage value and an initial reactive voltage value at a current iteration time according to a communication condition in a process of transmitting a voltage signal from a current region to a corresponding sub-region to obtain an actual active voltage value and an actual reactive voltage value corresponding to the current iteration time further comprises:
if communication delay occurs in the process that the current area transmits the voltage signals to the corresponding sub-area at the current iteration moment, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment according to the communication delay time to obtain an actual active voltage value and an actual reactive voltage value;
and if the communication channel is disconnected in the process of transmitting the voltage signal to the corresponding sub-region by the current region at the current iteration moment, taking the initial active voltage value and the initial reactive voltage value at the previous iteration moment as the actual active voltage value and the actual reactive voltage value at the current iteration moment.
6. The distributed voltage control method of claim 5, wherein the adjusting the initial active voltage value and the initial reactive voltage value at the current iteration time according to the communication delay time to obtain the actual active voltage value and the actual reactive voltage value further comprises:
calculating the actual active voltage value and the actual reactive voltage value by the following formulas:
wherein the content of the first and second substances,for the actual active voltage value of the sub-region,communication delay time in the process of transmitting the voltage signal to the sub-area for the current area,subtracting the communication delay time from the current iteration time of the sub-region to obtain an initial active voltage value corresponding to the time;is the actual reactive voltage value of the sub-area,subtracting the communication delay for the sub-region at the current iteration timeAnd obtaining an initial reactive voltage value corresponding to the time.
7. The distributed voltage control method according to claim 1, wherein the calculating a bus power generation cost of the current region at the current iteration time according to the active cost variable and the reactive cost variable further comprises:
calculating to obtain an active power set value and a reactive power set value of each subarea in the current area at the current iteration moment according to the active cost variable and the reactive cost variable;
and integrating the active power set value and the reactive power set value of all the sub-areas in the current area at the current iteration moment, and calculating to obtain the bus power generation cost of the current area at the current iteration moment.
8. The distributed voltage control method of claim 7, wherein calculating an active power setpoint and a reactive power setpoint for each sub-region in the current region at the current iteration time based on the active cost variable and the reactive cost variable further comprises:
and calculating an active power set value and a reactive power set value of any subarea in the current area at the current iteration moment through the following formula:
wherein t is the current iteration time,is the active power set point for the sub-area,as an active cost variable of the current region,being the cost factor of the active power of the sub-area,is an active parameter of a certain phase in the sub-region,is the sum of all available phases in the sub-region, diag is a diagonal matrix function,for the reactive power set point of the sub-area,as a reactive cost variable for the current region,being the cost factor of the reactive power of the sub-area,is a reactive parameter for a certain phase in the sub-area,respectively, the parameter factors of the active power and the reactive power of the sub-area.
9. The distributed voltage control method of claim 8, wherein the integrating the active power set value and the reactive power set value of all sub-areas in the current area at the current iteration time, and calculating the bus power generation cost of the current area at the current iteration time further comprises:
calculating the bus power generation cost of the current area at the current iteration moment by the following formula:
wherein, the first and the second end of the pipe are connected with each other,for the active power generation cost of the sub-area,cost of reactive power generation for sub-areasIs the sum of the active parameters of all phases in the sub-area,is the sum of the reactive parameters of all phases in the sub-area,the active power set point for a sub-area,is the reactive power set point for the sub-area,being the cost factor of the active power of the sub-area,is the cost coefficient of the reactive power of the subarea, s.t. is the constraint condition,andrespectively the lower limit and the upper limit of the active power generation cost in the sub-area power network,andthe lower limit and the upper limit of the reactive power generation cost in the sub-area power network are respectively set, and N is the number of sub-areas in the current area.
10. The utility model provides a distributed voltage control device based on digital twin distribution system which characterized in that, distribution system divides and forms a plurality of regions, passes through circuit connection between a plurality of regions, includes a plurality of independent subregions in each region, passes through circuit connection between the subregion that region and its include, and the device that carries out voltage control to the subregion includes:
the analysis and calculation module is used for calculating to obtain a bus voltage value of the current area within a set period of time according to the bus voltage value of the previous area;
the initialization module is used for initializing an active cost variable, a reactive cost variable and a voltage auxiliary variable in a set time period;
the step-by-step iteration module is used for dividing the set time interval into a plurality of iteration moments, and the following iteration steps are executed at each iteration moment: obtaining an initial active voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial active voltage value at the last iteration moment; obtaining an initial reactive voltage value of a sub-region in the current region at the current iteration moment according to the voltage auxiliary variable at the current iteration moment and the initial reactive voltage value at the previous iteration moment; according to the communication condition in the process of transmitting voltage signals to the corresponding sub-area by the current area, adjusting the initial active voltage value and the initial reactive voltage value at the current iteration moment to obtain the actual active voltage value and the actual reactive voltage value of the sub-area at the current iteration moment in the current area; calculating to obtain the bus power generation cost of the current region at the current iteration moment according to the active cost variable and the reactive cost variable; updating to obtain an active cost variable, a reactive cost variable and a voltage auxiliary variable at the next iteration moment according to the bus voltage value of the current region and the voltage auxiliary variable at the last iteration moment in a set time period, and executing the iteration steps;
the target optimization module is used for taking the iteration time corresponding to the minimum bus power generation cost in all the bus power generation costs in the current region within a set time period as the optimal iteration time;
the deduction determining module is used for taking an actual active voltage value and an actual reactive voltage value corresponding to the current sub-region at the optimal iteration moment as a final active voltage value and a final reactive voltage value of the current sub-region within a set time period;
and the adjusting control module is used for adjusting and controlling the voltage value of the sub-region in the current region within a set time period according to the final active voltage value and the final reactive voltage value.
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