CN117556969A - Flexible power distribution network distributed reactive power optimization method based on probability scene driving - Google Patents
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Abstract
The invention provides a distributed reactive power optimization method of a flexible power distribution network based on probabilistic scene driving, which comprises the steps of firstly, establishing a reactive power optimization model of the flexible power distribution network with the aim of minimizing system loss; secondly, comprehensively considering confidence constraints of 1-norm and ++norm, and constructing a flexible power distribution network distribution robust reactive power optimization model based on a probability scene fuzzy set; on the basis, a distributed optimization model is taken as an external framework, a consistent acceleration gradient Alternating Direction Multiplier Method (ADMM) is adopted to carry out overall coordination and updating iterative solution, and each sub-region distribution robust optimization model is taken as an internal framework, and a Column and Constraint Generation (CCG) algorithm is adopted to carry out solution; and finally, through system example simulation, the distributed reactive power optimization method for the flexible power distribution network has better convergence, and balance between economy and robustness is considered.
Description
Technical Field
The invention belongs to the technical field of reactive power optimization of a flexible power distribution network, and particularly relates to a distributed reactive power optimization method of the flexible power distribution network based on probabilistic scene driving.
Background
The intelligent soft switch is used as a novel power electronic device to replace a traditional interconnection switch to be widely interconnected in a traditional power distribution network, so that the intelligent soft switch gradually evolves into a flexible power distribution network. Compared with the traditional power distribution network, the flexible power distribution network can flexibly adjust the power flow distribution among the feed lines, improves the power supply reliability and reduces the operation loss. Meanwhile, as the distributed power supply (DG) is largely integrated into the flexible power distribution network, uncertainty of DG output and load demand makes reactive power optimization of the flexible power distribution network face a great challenge, so that how to coordinate the reactive power compensation device and SOP to improve reactive power distribution and power supply quality has very important significance.
According to the different uncertainty modeling forms of DG output and load, the uncertainty reactive power optimization method of the flexible power distribution network is mainly divided into a random optimization method and a robust optimization method. Random optimization models uncertainty of DG output force and load by adopting a discrete scene; and the robust optimization models the uncertainty of the DG output and the load by adopting a set, and the probability distribution of the DG output and the load does not need to be acquired, so that the method is easier to realize. The probability scene driving-based distributed robust optimization method combines a random optimization method and robust optimization, and searches for a solution under the most-averagely probability distribution under the fuzzy set of the probability scene, so that the accuracy of the solution can be ensured, and the robustness is good.
With the continuous development of the scale and the structure of the flexible power distribution network, the adoption of centralized optimization can lead to the problems of rapid expansion of the model solving scale, slow solving speed and the like. Thus, more and more students began to combine the alternating direction multiplier method and the DRO method to achieve distributed optimization.
Disclosure of Invention
The invention aims to solve the technical problems that: the distributed reactive power optimization method for the flexible power distribution network based on probability scene driving is used for reducing uncertainty introduced in reactive power optimization by accessing massive distributed resources into the flexible power distribution network in a layered distribution mode.
The technical scheme adopted by the invention for solving the technical problems is as follows: a distributed reactive power optimization method of a flexible power distribution network based on probability scene driving comprises the following steps:
s1: initializing, namely inputting active power distribution network line parameters, load prediction reference values, distributed photovoltaic parameters, energy storage system parameters, grouping switching capacitor parameters, static reactive power compensator parameters, on-load voltage regulating transformer parameters, intelligent soft switching parameters, ADMM algorithm parameters and CCG algorithm parameters;
s2: establishing a reactive power optimization model of the flexible power distribution network, wherein the reactive power optimization model comprises an objective function and operation constraint;
s3: clustering historical data of distributed photovoltaic output and load to obtain a typical scene set, comprehensively considering 1-norm and ++norm confidence constraint of probability distribution of each scene, and constructing a flexible distribution network distribution robust reactive power optimization model based on probability scene driving;
s4: introducing a gradient descent algorithm and a consistency theory improvement ADMM algorithm, and providing a distributed solving method of a flexible power distribution network distributed robust reactive power optimization model based on a consistency acceleration gradient ADMM algorithm;
s5: taking a flexible power distribution network distribution robust reactive power optimization model as an external frame, and adopting a consistency accelerating gradient ADMM algorithm to carry out global coordination and updating iterative solution; and taking each sub-region distribution robust model as an internal framework, solving by adopting a CCG algorithm, and outputting a result.
According to the above scheme, in the step S2, the specific steps are as follows:
s21: is provided withIs thattTime branch->The magnitude of the current flowing upwards, +.>For branch->Resistance of->Is thattTime SOP at nodeiThe active power loss at the point(s),Tfor optimizing the total number of time periods of the scheduled operation +.>And->Respectively a load node set and an SOP node set; establishing a reactive power optimization objective function of the flexible power distribution network by taking minimum network loss and SOP loss as targetsfThe method comprises the following steps:
；
s22: reactive power optimization operation constraint of the flexible power distribution network comprises distributed photovoltaic output constraint, system power flow constraint, energy storage system constraint, on-load voltage regulating transformer constraint, grouping switching capacitor constraint, static reactive compensator constraint and intelligent soft switch constraint.
Further, in the step S22, it is set thatAnd->Respectively istTime nodejActive power and reactive power emitted by the PV, < >>Is thattTime nodejPredicted power of PV, +.>Is a nodejThe capacity of the PV; the distributed photovoltaic output constraint is:
，
；
is provided withAnd->Respectively istTime inflow nodejActive power and reactive power, +.>And->Respectively istTime slave nodeiInflow branch->Active power and reactive power, +.>For branch->Reactance of->And->Respectively istTime nodejActive power and reactive power required for the load, +.>Is thattTime nodeiSquare of voltage magnitude +.>Andrespectively->Upper and lower limits of>Is thattTime branch->Square of the magnitude of the current flowing upwards, +.>；/>Is->Upper limit of->And->Respectively istTime nodejActive power when charging ESS and ESS to nodejActive power during discharge, +.>Is thattTime CB to nodejReactive power of compensation->Is thattTime SVC nodejThe reactive power of the compensation is calculated,and->Respectively istTime-of-day SOP inflow nodeiActive power and reactive power of (a); the system power flow constraint is:
，
，
，
；
set 0-1 variableAnd->Respectively istTime nodejIn the charge-discharge state of the accessed ESS, +.>And->Respectively nodesjUpper and lower limits of ESS charging power at access, < ->And->Respectively nodesjUpper and lower limits of ESS discharge power at access, < ->Is thattTime nodejESS state of charge of access>And->Respectively nodesjCharging and discharging efficiency of ESS accessed at +.>For scheduling time intervals, +.>Is a nodejESS capacity size of access>And->Respectively nodesjThe upper and lower limits of the charge state of the ESS are accessed; the energy storage system constraints are:
，
，
，
；
by introducing auxiliary nodesoDividing on-load voltage regulating transformer branch into branchesAnd branch->Two parts are provided with，/>Is thattTime auxiliary nodeoSquare of the voltage amplitude>For branch->The number of gear positions of the upper transformer,for branch->Increment of each gear of upper transformer, +.>For branch->Upper transformer transformation ratio lower limit, +.>Is thattTime branch->The gear position of the upper transformer is changed,Mconstant introduced for Big-M method, < ->、/>And->Intermediate auxiliary variables introduced for linearization; the on-load tap changer constraint is:
，
，
；
is provided withIs thattTime nodejNumber of compensation groups at CB>Is a nodejSingle set of compensation powers at CB, +.>And->Respectively istTime nodejThe number of compensation groups where CB increases and decreases and are all non-negative, and +.>For a scheduled time periodTUpper limit of the number of actions of the inner CB>The maximum compensation group number of CB; the group switching capacitor constraint is:
，
；
is provided withAnd->Respectively nodesjAt the upper and lower limits of the SVC compensation power, the static var compensator is constrained as follows:
；
is provided withIs a nodeiLoss coefficient of SOP at->And->Is a nodeiAt the upper and lower limit of reactive power for SOP transmission, < ->Is a nodeiThe capacity of the SOP; the intelligent soft switch operation constraint is:
，
，
。
according to the above scheme, in the step S3, the specific steps are as follows:
s31: through K-means clustering pairsKScene clustering is carried out on the solar distributed photovoltaic output and load historical data to obtainA limited discrete typical scene and its initial scene probability distribution +.>The method comprises the steps of carrying out a first treatment on the surface of the Is provided with->For the actual typical scene probability distribution, +.>And->Maximum deviation value of probability of typical scene under 1-norm and + -norm limits, respectively, +.>Is a typical scenesIs a function of the probability of (1),for scenes obtained by K-means clusteringsIs>And->Confidence levels of 1-norm and + -norm respectively, 0-1 auxiliary variable->And->Respectively indicate->For->A positive offset state and a negative offset state of (a); building a distributed model based on 1-norms and ≡norms probability scene ambiguity set of photovoltaic and load +.>The method comprises the following steps:
，
；
s32: constructing a flexible power distribution network distribution robust reactive power optimization model based on probability scene driving;
according to the time scale of equipment regulation, setting the gear of the on-load voltage regulating transformer, the switching group number of the grouping switching capacitors and the charge and discharge state related discrete variables of the energy storage system as first-stage decision variablesOptimizing first, setting the rest continuous variable as the decision variable of the second stage +.>The following is shown:
，
；
is provided with、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>And->Respectively corresponding coefficient matrixes in constraint conditions, < ->Constraint set for decision variables of second stage, +.>Constraint set for decision variables of second stage, +.>Is a scenesThe magnitude of the lower distributed photovoltaic output and load; converting the deterministic reactive power optimization model of the flexible power distribution network established in the step S1 into a flexible power distribution network two-stage distribution robust reactive power optimization model based on probabilistic scene driving:
，
，
。
further, in the step S32, the two-stage robust problem is decomposed into a main problem and a sub-problem based on the CCG algorithm, and the distributed robust reactive power optimization model is solved through iteration.
According to the above scheme, in the step S4, the specific steps are as follows:
s41: is provided withIs a regionaOptimized variable of->Coupling branch for region a->Related variable of->Is the area ofaAdjacent areasbCoupling branch->Related variable of->Penalty parameter for ADMM algorithm, +.>And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->Vector composed of global variables corresponding to related variables, +.>And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->A vector of dual variables; the traditional ADMM algorithm is improved by introducing the consistency theory, and the method is obtained:
；
s42: is provided withFor the acceleration step of the gradient descent method, +.>；/>And->The dual variables and the global variables after acceleration are respectively; nesterov-based gradient descent method for ∈K>And->And (5) performing acceleration update:
。
further, in the step S4, it is set thatFor the convergence accuracy based on the consistency acceleration gradient ADMM algorithm, the original residual error of the ADMM algorithm is used +.>And dual residual->The convergence criterion for the reference construction algorithm is as follows:
；
when (when)When in use, let->The method comprises the steps of carrying out a first treatment on the surface of the Acceleration step size by changing value of convergence accuracy in iterative process>Restarting to prevent the cause->Excessive large results in excessive oscillations of the objective function and convergence residual during algorithm convergence.
Further, in the step S5, the specific steps are as follows:
s51: initializing; in the subareaaIn which the iteration number is set，/>=0，/>，/>The method comprises the steps of carrying out a first treatment on the surface of the Given->Value of (2) and convergence accuracy->；
S52: solving the sub-problems of each region; solving the distribution robustness through each subarea to obtain the value of the related variable of each area coupling branch, providing an exchange variable for the next iteration of the external consistency acceleration gradient ADMM algorithm frame, and outputting the optimal solution of the objective function of each area;
constructing an augmented Lagrangian function of the objective function of each region and a sub-regionaThe objective function of (2) is:
；
s53: exchanging each area information and updating; each region receives the exchange variable of the adjacent region and updates the dual variable of each regionGlobal variable->And acceleration step +.>；
S54: judging whether convergence exists or not; computing the sum of the original residuals of the subareas in each sceneSum of sub-region dual residuals in each scene +.>Judging the maximum value of residual error in each scene +.>Whether or not to converge to +.>Outputting an optimal solution if convergence is achieved; otherwise, executing step S55;
s55: judgingWhether or not is greater than->If yes, restarting, and (E)>The method comprises the steps of carrying out a first treatment on the surface of the Whether or notThen it is not restarted; order thek=k+1, step S52 is performed.
A computer storage medium having stored therein a computer program executable by a computer processor for performing a probabilistic scene driven distributed reactive power optimization method for a flexible distribution network.
The beneficial effects of the invention are as follows:
1. according to the flexible power distribution network distributed reactive power optimization method based on probability scene driving, firstly, a flexible power distribution network reactive power optimization model is built with the aim of minimizing system loss, meanwhile, distributed photovoltaic output and load historical data are clustered to obtain a typical scene set, confidence constraints of 1-norm and ++norm are comprehensively considered, and a flexible power distribution network distribution robust DRO reactive power optimization model based on probability scene fuzzy set is built; then a distributed optimization framework is built according to the flexible power distribution network structure, a gradient descent algorithm and a consistency theory are introduced to improve the ADMM, and a distributed solving method of a flexible power distribution network DRO reactive power optimization model based on the consistency acceleration gradient ADMM is provided; finally, carrying out global coordination and updating iterative solution by taking a distributed optimization model as an external framework and adopting a consistent acceleration gradient Alternating Direction Multiplier Method (ADMM), solving each sub-region distribution robust DRO optimization model as an internal framework by adopting a Column and Constraint Generation (CCG) algorithm, and verifying the effectiveness of the provided flexible power distribution network distributed reactive power optimization method based on probability scene driving through system example simulation; the function of reducing uncertainty introduced to reactive power optimization by accessing the flexible power distribution network through layered distribution of mass distributed resources is realized, and the method has good convergence and balances economy and robustness.
2. According to the invention, information interaction between the subareas is carried out through the coupling branch and the SOP, so that the distributed optimization of the flexible power distribution network is realized, the data interaction burden is reduced, and the solving efficiency is accelerated.
3. The ADMM algorithm based on the consistency acceleration gradient can effectively solve the distributed robust reactive power optimization model, and has good convergence performance and stability.
4. The distributed photovoltaic and load uncertainty is considered, the flexible power distribution network distributed robust reactive power optimization model is established under the comprehensive constraint of the 1-norm and the infinity-norm, the problem that the robust optimization is too conservative is solved, and the balance of economy and robustness is realized to a certain extent.
Drawings
FIG. 1 is a schematic diagram of an OLTC branch model in accordance with an embodiment of the present invention.
Fig. 2 is a distributed reactive power optimization flow chart of the flexible power distribution network based on probabilistic scene driving in an embodiment of the invention.
Fig. 3 is a diagram of an improved 33 node test system in accordance with an embodiment of the present invention.
Fig. 4 is a graph of distributed photovoltaic output and load in a typical scenario of an embodiment of the present invention.
Fig. 5 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the drawings and the detailed description.
Referring to fig. 3, taking an improved 33-node system as an example, the embodiment of the invention adopts a flexible power distribution network distributed reactive power optimization method based on probability scene driving, which comprises the following steps of:
the first step: initializing, namely inputting active power distribution network line parameters, load prediction reference values, distributed Photovoltaic (PV) parameters, energy Storage System (ESS) parameters, grouping switching Capacitor (CB) parameters, static Var Compensator (SVC) parameters, on-load voltage regulating transformer (OLTC) parameters, intelligent soft Switching (SOP) parameters, ADMM algorithm parameters and CCG algorithm parameters.
In the embodiment, 33 node power distribution network line parameters are input; the access locations and parameter settings of the devices in the system are shown in table 1. The reference voltage of the flexible power distribution network is 12.66kV, and the reference capacity is 10MVA. The amplitude range of the node voltage is set to be 0.95 pu-1.05 pu, and the upper limit of the amplitude of the branch current is set to be 0.2pu; scheduling periodsT=24; the convergence accuracy of the ADMM algorithm was set to 10 -4 The convergence accuracy of the CCG algorithm was set to 10 -6 ；；/>. And clustering the distributed photovoltaic output and load historical data by adopting a K-means clustering algorithm to obtain a distributed photovoltaic output and load curve in a typical scene shown in figure 4.
Table 1 system parameter settings
And a second step of: and establishing a reactive power optimization model of the flexible power distribution network, wherein the reactive power optimization model comprises a reactive power optimization objective function of the flexible power distribution network and reactive power optimization operation constraint of the flexible power distribution network.
(1) And (3) establishing a reactive power optimization objective function of the flexible power distribution network by taking minimum network loss and SOP loss as targets:
in the method, in the process of the invention,is thattTime branch->The magnitude of the current flowing upwards; />For branch->Resistance of (2); />Is thattTime SOP at nodeiActive loss at the site;Tthe total time period number of the operation is optimized; />And->Respectively a load node set and an SOP node set.
(2) Reactive power optimization operation constraints of the flexible power distribution network include distributed Photovoltaic (PV) output constraints, system power flow constraints, energy Storage System (ESS) constraints, on-load voltage regulating transformer (OLTC) constraints, group switched Capacitor (CB) constraints, static Var Compensator (SVC) constraints, and intelligent soft Switching (SOP) constraints.
1) Distributed Photovoltaic (PV) output constraint
In the method, in the process of the invention,and->Respectively istTime nodejActive power and reactive power emitted by the PV; />Is thattTime nodejPredicted power at PV; />Is a nodejAt the capacity of the PV.
2) System power flow constraint
In the method, in the process of the invention,and->Respectively istTime inflow nodejActive power and reactive power of (a); />And->Respectively istTime slave nodeiInflow branch->Active power and reactive power of (a); />For branch->Is a reactance of (2); />And->Respectively istTime nodejActive power and reactive power required by the load; />Is thattTime nodeiSquare of the magnitude of the voltage;and->Respectively->Upper and lower limits of (2); />Is thattTime branch->Square of the magnitude of the current flowing upwards, +.>；/>Is->Upper limit of (2); />And->Respectively istTime nodejActive power when charging ESS and ESS to nodejActive power during discharge; />Is thattTime CB to nodejCompensating reactive power; />Is thattTime SVC nodejCompensating reactive power; />And->Respectively istTime-of-day SOP inflow nodeiActive power and reactive power of (a).
3) Energy Storage System (ESS) constraints
Wherein the variables 0-1And->Respectively istTime nodejThe ESS is in a charging and discharging state; />And->Respectively nodesjUpper and lower limits of the charging power of the ESS accessed; />And->Respectively nodesjUpper and lower limits of the discharge power of the ESS accessed. />Is thattTime nodejThe state of charge of the ESS accessed; />And->Respectively nodesjCharging and discharging efficiency of the ESS accessed at the position; />For a scheduling time interval; />Is a nodejThe capacity of the ESS accessed at the location; />And->Respectively nodesjAnd the upper and lower limits of the charge state of the ESS are accessed.
4) On-load step-down transformer (OLTC) constraints
The schematic diagram of the branch model containing the OLTC is shown in figure 1, and the auxiliary node is introducedoDividing an OLTC branch into branchesAnd branch->Two parts, therefore OLTC operating constraints are:
in the method, in the process of the invention,；/>is thattTime auxiliary nodeoSquare of the magnitude of the voltage; />For branch->The number of gear positions of the upper transformer; />For branch->Incremental of each gear of the upper transformer; />For branch->The upper transformer ratio is lower. />Is thattTime branch->The gear position of the upper transformer is changed,Ma larger number; />、/>And->Intermediate auxiliary variables introduced for linearization.
5) Group switched Capacitor (CB) constraints
In the method, in the process of the invention,is thattTime nodejThe number of compensation groups of the CB; />Is a nodejSingle set of compensation powers at CB;and->Respectively istTime nodejThe number of compensation groups increased and decreased by CB is non-negative; />For a scheduled time periodTAn upper limit of the number of times of the inner CB actions; />The maximum compensation group number for CB.
6) Static Var Compensator (SVC) constraint
In the method, in the process of the invention,and->Respectively nodesjAt the upper and lower limits of the SVC compensation power.
7) Intelligent soft Switch (SOP) operational constraints
/>
In the method, in the process of the invention,is a nodeiA loss coefficient of the SOP; />And->Is a nodeiThe upper and lower limits of reactive power of SOP transmission are set; />Is a nodeiThe size of the SOP.
And a third step of: clustering the distributed photovoltaic output and load historical data to obtain a typical scene set, comprehensively considering the 1-norm and the infinity-norm confidence constraint of probability distribution of each scene, and constructing a flexible distribution network Distribution Robust (DRO) reactive power optimization model based on probability scene driving.
1) Probability scene ambiguity set for distributed photovoltaic output and load
Because the randomness of the distributed photovoltaic output and the load historical data is larger, it is difficult to obtain accurate scene probability distribution through a large amount of historical data, and the obtained scene probability distribution has a certain limitation; thus through K-means cluster pairsKScene clustering is carried out on the sky-distributed photovoltaic output and load history data curve to obtainA limited discrete typical scene and its initial scene probability distribution +.>. However, the actual scene probability distribution has an error with the initial scene probability obtained by the scene clustering. In contrast, the invention constructs the probability scene fuzzy set of distributed photovoltaic and load based on 1-norm and ++norm to restrict the error range of each typical scene probability to obtainProbability scene ambiguity set +.>：
Wherein, through K-means cluster pairsKScene clustering is carried out on the solar distributed photovoltaic output and load historical data to obtainA limited discrete typical scene and its initial scene probability distribution +.>；/>For the actual typical scene probability distribution, +.>And->Maximum deviation value of probability of typical scene under 1-norm and + -norm limits, respectively, +.>Is a typical scenesProbability of->For scenes obtained by K-means clusteringsIs>And->Confidence of 1-norm and + -norm respectivelyDegree, 0-1 auxiliary variable +.>And->Respectively indicate->For->A positive offset state and a negative offset state of (a); meanwhile, the fluctuation range of the probability of the typical scene is limited by adopting the 1-norm and the +_norm, so that the conservation of the probability distribution of the worst scene can be reduced by the distribution robustness searching.
2) Distributed robust reactive power optimization model solving method based on CCG algorithm
Setting the gear of the OLTC, the switching group number of the CB and the charge and discharge state related discrete variables of the ESS as first-stage decision variables according to the time scale of equipment adjustmentOptimizing first, setting the rest continuous variable as the decision variable of the second stage +.>The following is shown:
converting the established deterministic reactive power optimization model of the flexible power distribution network into a probability scene-driven flexible power distribution network two-stage distribution robust reactive power optimization model:
in the method, in the process of the invention,，/>，/>，/>，/>，/>，/>，/>，/>，/>，/>，/>，/>，/>the coefficient matrix is the corresponding coefficient matrix in the constraint condition; />Constraint sets for second-stage decision variables; />Constraint sets for second-stage decision variables; />Is a scenesLower distributed photovoltaic output and load size.
The flexible power distribution network distribution robust reactive power optimization model based on probability scene driving is a two-stage robust optimization problem, and iterative solution can be carried out through a CCG algorithm. The CCG algorithm decomposes the two-stage robust problem into a Main Problem (MP) and a sub-problem (SP) for iterative solution, when the optimal solution difference of the MP and the SP is smaller than a given convergence accuracyAnd then, the algorithm converges and an optimal solution is output.
Fourth step: and constructing a distributed optimization framework according to the flexible power distribution network structure, introducing a gradient descent algorithm and a consistency theory to improve the ADMM, and providing a DRO reactive power optimization model distributed solving method of the flexible power distribution network based on the consistency acceleration gradient ADMM.
Is provided withIs a regionaOptimized variable of->Coupling branch for region a->Related variable of->Is the area ofaAdjacent areasbCoupling branch->Related variable of->Penalty parameter for ADMM algorithm, +.>And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->A vector composed of global variables corresponding to the related variables; />And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->A vector of dual variables; the traditional ADMM algorithm is improved by introducing the consistency theory, and the method is obtained:
；
the ADMM algorithm based on the consistency theory realizes the synchronous ADMM algorithm by solving the problems of all the subareas in parallel and then carrying out coordinated updating through coupling branches among the areas to finally obtain the global solution of the original problem. In order to further improve the convergence of the ADMM algorithm, the gradient descent method pair based on NesterovAnd->And (5) performing acceleration update:
in the method, in the process of the invention,for the acceleration step of the gradient descent method, +.>；/>And->The dual variables and the global variables after acceleration are respectively.
The invention uses the original residual error of ADMM algorithmAnd dual residual->For reference, an algorithm convergence criterion is constructed as follows:
in the method, in the process of the invention,is the convergence accuracy of the gradient ADMM algorithm based on consistency acceleration.
In order to improve the stability of ADMM algorithm in the convergence process, the invention accelerates the step length by the change value of convergence precision in the iteration processRestarting to prevent the cause->Excessive size results in excessive target function and convergence residual during algorithm convergenceOscillation, i.e. when->When in use, let->。
Fifth step: and carrying out global coordination and updating iterative solution by taking the distributed optimization model as an external framework and adopting a consistency accelerating gradient ADMM, and carrying out CCG algorithm solution by taking each subregion DRO model as an internal framework to output a result.
The distributed reactive power optimization of the flexible power distribution network based on probability scene driving is established by taking the distributed optimization of a consistency accelerating gradient ADMM algorithm as an external framework, coordinating all subareas to update global optimal solutions, taking the distributed robust optimization of all areas as an internal framework, and providing the value of a coupling branch related variable for the external distributed optimization. Fig. 2 is a distributed reactive power optimization flow chart of a flexible power distribution network based on probabilistic scene driving, which comprises the following specific steps:
(1) initializing. Setting the iteration times；/>=0，/>；/>The method comprises the steps of carrying out a first treatment on the surface of the Given->Value of (2) and convergence accuracy。
(2) Solving the sub-problems of each region. Constructing an augmented Lagrangian function of the objective function of each region to obtain the regionaFor example, the sub-region objective function is:
，
in the method, in the process of the invention,iandjrepresenting a regionaAnd coupling leg nodes of adjacent regions. And solving the distribution robustness through each subarea to obtain the value of the related variable of each area coupling branch, providing the exchange variable for the next iteration of the external consistency accelerating gradient ADMM algorithm frame, and outputting the optimal solution of the objective function of each area.
(3) Exchanging the area information and updates. Each region receives the exchange variable of the adjacent region and updates the dual variable of each regionGlobal variable->And acceleration step +.>。
(4) And judging whether convergence is achieved. Computing the sum of the original residuals of the subareas in each sceneSum of sub-region dual residuals in each scene +.>Judging the maximum value of residual error in each scene +.>Whether or not to converge to +.>If the convergence is carried out, outputting an optimal solution; otherwise, continuing to step (5).
(5) JudgingWhether or not is greater than->If yes, restarting, and (E)>The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, not restarting. Order thek=k+1 returns to step (2).
Table 2 gives the optimization results for the 3 ADMM algorithms at different initial penalty parameters. It can be seen from table 2 that the algorithm 3 proposed by the present invention converges most rapidly, least time-consuming and better under different initial penalty parameters.
Table 2 results data of each algorithm
The above embodiments are merely for illustrating the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, the scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present invention are within the scope of the present invention.
Claims (9)
1. A distributed reactive power optimization method of a flexible power distribution network based on probability scene driving is characterized by comprising the following steps of: the method comprises the following steps:
s1: initializing, namely inputting active power distribution network line parameters, load prediction reference values, distributed photovoltaic parameters, energy storage system parameters, grouping switching capacitor parameters, static reactive power compensator parameters, on-load voltage regulating transformer parameters, intelligent soft switching parameters, ADMM algorithm parameters and CCG algorithm parameters;
s2: establishing a reactive power optimization model of the flexible power distribution network, wherein the reactive power optimization model comprises an objective function and operation constraint;
s3: clustering historical data of distributed photovoltaic output and load to obtain a typical scene set, comprehensively considering 1-norm and ++norm confidence constraint of probability distribution of each scene, and constructing a flexible distribution network distribution robust reactive power optimization model based on probability scene driving;
s4: introducing a gradient descent algorithm and a consistency theory improvement ADMM algorithm, and providing a distributed solving method of a flexible power distribution network distributed robust reactive power optimization model based on a consistency acceleration gradient ADMM algorithm;
s5: taking a flexible power distribution network distribution robust reactive power optimization model as an external frame, and adopting a consistency accelerating gradient ADMM algorithm to carry out global coordination and updating iterative solution; and taking each sub-region distribution robust model as an internal framework, solving by adopting a CCG algorithm, and outputting a result.
2. The flexible power distribution network distributed reactive power optimization method based on probabilistic scene driving as claimed in claim 1, wherein the method comprises the following steps: in the step S2, the specific steps are as follows:
s21: is provided withIs thattTime branch->The magnitude of the current flowing upwards, +.>For branch->Resistance of->Is thattTime SOP at nodeiThe active power loss at the point(s),Tfor optimizing the total number of time periods of the scheduled operation +.>And->Respectively a load node set and an SOP node set; establishing a reactive power optimization objective function of the flexible power distribution network by taking minimum network loss and SOP loss as targetsfThe method comprises the following steps:
；
s22: reactive power optimization operation constraint of the flexible power distribution network comprises distributed photovoltaic output constraint, system power flow constraint, energy storage system constraint, on-load voltage regulating transformer constraint, grouping switching capacitor constraint, static reactive compensator constraint and intelligent soft switch constraint.
3. The flexible power distribution network distributed reactive power optimization method based on probabilistic scene driving as claimed in claim 2, wherein the method comprises the following steps: in the step S22, set upAnd->Respectively istTime nodejActive power and reactive power emitted by the PV, < >>Is thattTime nodejPredicted power of PV, +.>Is a nodejThe capacity of the PV; the distributed photovoltaic output constraint is:
，
；
is provided withAnd->Respectively istTime inflow nodejIs provided withActive and reactive power, +.>And->Respectively istTime slave nodeiInflow branch->Active power and reactive power, +.>For branch->Reactance of->And->Respectively istTime nodejActive power and reactive power required for the load, +.>Is thattTime nodeiSquare of voltage magnitude +.>And->Respectively->Upper and lower limits of>Is thattTime branch->Square of the magnitude of the current flowing upwards, +.>；/>Is->Is set at the upper limit of (c),and->Respectively istTime nodejActive power when charging ESS and ESS to nodejThe active power at the time of the discharge,is thattTime CB to nodejReactive power of compensation->Is thattTime SVC nodejReactive power of compensation->Andrespectively istTime-of-day SOP inflow nodeiActive power and reactive power of (a); the system power flow constraint is:
，
，
，
；
set 0-1 variableAnd->Respectively istTime nodejIn the charge-discharge state of the accessed ESS, +.>And->Respectively nodesjUpper and lower limits of ESS charging power at access, < ->And->Respectively nodesjUpper and lower limits of ESS discharge power at access, < ->Is thattTime nodejESS state of charge of access>And->Respectively nodesjCharging and discharging efficiency of ESS accessed at +.>For scheduling time intervals, +.>Is a nodejESS capacity size of access>And->Respectively nodesjThe upper and lower limits of the charge state of the ESS are accessed; the energy storage system constraints are:
，
，
，
；
by introducing auxiliary nodesoDividing on-load voltage regulating transformer branch into branchesAnd branch->Two parts are provided with，/>Is thattTime auxiliary nodeoSquare of the voltage amplitude>For branch->The number of gear positions of the upper transformer,for branch->Increment of each gear of upper transformer, +.>For branch->Upper transformer transformation ratio lower limit, +.>Is thattTime branch->The gear position of the upper transformer is changed,Mconstant introduced for Big-M method, < ->、/>And->Intermediate auxiliary variables introduced for linearization; the on-load tap changer constraint is:
，
，
；
is provided withIs thattTime nodejNumber of compensation groups at CB>Is a nodejSingle set of compensation powers at CB, +.>And->Respectively istTime nodejThe number of compensation groups where CB increases and decreases and are all non-negative, and +.>For a scheduled time periodTUpper limit of the number of actions of the inner CB>The maximum compensation group number of CB; the group switching capacitor constraint is:
，
；
is provided withAnd->Respectively nodesjAt the upper and lower limits of the SVC compensation power, the static var compensator is constrained as follows:
；
is provided withIs a nodeiLoss coefficient of SOP at->And->Is a nodeiAt the upper and lower limit of reactive power for SOP transmission, < ->Is a nodeiThe capacity of the SOP; the intelligent soft switch operation constraint is:
，
，
。
4. the flexible power distribution network distributed reactive power optimization method based on probabilistic scene driving as claimed in claim 1, wherein the method comprises the following steps: in the step S3, the specific steps are as follows:
s31: through K-means clustering pairsKScene clustering is carried out on the solar distributed photovoltaic output and load historical data to obtainA limited discrete typical scene and its initial scene probability distribution +.>The method comprises the steps of carrying out a first treatment on the surface of the Is provided with->For the actual typical scene probability distribution, +.>And->Maximum deviation value of probability of typical scene under 1-norm and + -norm limits, respectively, +.>Is a typical scenesProbability of->For scenes obtained by K-means clusteringsIs>And->Confidence levels of 1-norm and + -norm respectively, 0-1 auxiliary variable->And->Respectively indicate->For->Is of positive offset form (1)A state and a negative offset state; building a distributed model based on 1-norms and ≡norms probability scene ambiguity set of photovoltaic and load +.>The method comprises the following steps:
，
；
s32: constructing a flexible power distribution network distribution robust reactive power optimization model based on probability scene driving;
according to the time scale of equipment regulation, setting the gear of the on-load voltage regulating transformer, the switching group number of the grouping switching capacitors and the charge and discharge state related discrete variables of the energy storage system as first-stage decision variablesOptimizing first, setting the rest continuous variable as the decision variable of the second stage +.>The following is shown:
，
；
is provided with、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>、/>And->Respectively corresponding coefficient matrixes in the constraint conditions,constraint set for decision variables of second stage, +.>Constraint set for decision variables of second stage, +.>Is a scenesThe magnitude of the lower distributed photovoltaic output and load; converting the deterministic reactive power optimization model of the flexible power distribution network established in the step S1 into a flexible power distribution network two-stage distribution robust reactive power optimization model based on probabilistic scene driving:
，
，
。
5. the flexible power distribution network distributed reactive power optimization method based on probabilistic scene driving as claimed in claim 4, wherein the method comprises the following steps: in the step S32, the two-stage robust problem is decomposed into a main problem and a sub-problem based on the CCG algorithm, and the distributed robust reactive power optimization model is solved through iteration.
6. The flexible power distribution network distributed reactive power optimization method based on probabilistic scene driving as claimed in claim 1, wherein the method comprises the following steps: in the step S4, the specific steps are as follows:
s41: is provided withIs a regionaOptimized variable of->Coupling branch for region a->Related variable of->Is the area ofaAdjacent areasbCoupling branch->Related variable of->Penalty parameter for ADMM algorithm, +.>And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->Vector composed of global variables corresponding to related variables, +.>And->Respectively the firstkRegion at time of iterationaSum regionbMiddle coupling branch->A vector of dual variables; the traditional ADMM algorithm is improved by introducing the consistency theory, and the method is obtained:
；
s42: is provided withFor the acceleration step of the gradient descent method, +.>；/>And->The dual variables and the global variables after acceleration are respectively; nesterov-based gradient descent method for ∈K>And->And (5) performing acceleration update:
。
7. the probability scene driving-based distributed reactive power optimization method for the flexible power distribution network, as claimed in claim 6, is characterized by comprising the following steps: in the step S4, set upFor the convergence accuracy based on the consistency acceleration gradient ADMM algorithm, the original residual error of the ADMM algorithm is used +.>And dual residual->The convergence criterion for the reference construction algorithm is as follows:
；
when (when)When in use, let->The method comprises the steps of carrying out a first treatment on the surface of the Acceleration step size by changing value of convergence accuracy in iterative process>Restarting to prevent the cause->Excessive large results in excessive oscillations of the objective function and convergence residual during algorithm convergence.
8. The probability scene driving-based distributed reactive power optimization method for the flexible power distribution network, as claimed in claim 7, is characterized by comprising the following steps: in the step S5, the specific steps are as follows:
s51: initializing; in the subareaaIn which the iteration number is set，/>=0，/>，/>The method comprises the steps of carrying out a first treatment on the surface of the Given->Value of (2) and convergence accuracy->；
S52: solving the sub-problems of each region; solving the distribution robustness through each subarea to obtain the value of the related variable of each area coupling branch, providing an exchange variable for the next iteration of the external consistency acceleration gradient ADMM algorithm frame, and outputting the optimal solution of the objective function of each area;
constructing an augmented Lagrangian function of the objective function of each region and a sub-regionaThe objective function of (2) is:
；
s53: exchanging each area information and updating; each region receives the exchange variable of the adjacent region and updates the dual variable of each regionGlobal variable->And acceleration step +.>；
S54: judging whether convergence exists or not; computing the sum of the original residuals of the subareas in each sceneSum of sub-region dual residuals in each scene +.>Judging the maximum value of residual error in each scene +.>Whether or not to converge to +.>Outputting an optimal solution if convergence is achieved; otherwise, executing step S55;
s55: judgingWhether or not is greater than->If yes, restarting, and (E)>The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, not restarting; order thek=k+1, step S52 is performed.
9. A computer storage medium, characterized by: a computer program executable by a computer processor is stored therein, the computer program executing a probability scene driven based distributed reactive power optimization method of a flexible power distribution network as claimed in any one of claims 1 to 8.
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