CN106159955B - Electric system distributed optimal power flow method based on continuous punishment Duality Decomposition - Google Patents
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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
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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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
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Abstract
The invention discloses a kind of electric system distributed optimal power flow methods based on continuous punishment Duality Decomposition, include the following steps：Power system network parameter is obtained first, determines the mathematical model of optimal power flow problems；Secondly auxiliary variable is introduced, obtains the equivalent problems of former optimal load flow control problem；Then the equivalent problems are solved by inside and outside two layers of iterative algorithm, wherein internal layer iteration solves corresponding internal layer augmentation lagrange problem using block coordinate descent algorithm is distributed in the case of fixed dual variable, each busbar needs and adjacent busbar interaction data before every group of variable is optimized, to realize that the local of local variable optimizes, external iteration then updates dual variable and penalty factor according to present confinement feasibility criterion；Optimal Power Flow Problems control is finally completed according to gained busbar injecting power value.The present invention makes system performance loss minimum using continuous punishment Duality Decomposition technology distribution formula design Optimal Power Flow Problems under the premise of power flow equation feasibility is ensured.
Description
Technical field
The present invention relates to technical field of power systems, and in particular to a kind of electric system based on continuous punishment Duality Decomposition
Distributed optimal power flow method.
Background technology
Optimization Problems In Power Systems, including planning, dispatching, running on control, target is security of system and economy
Balance and compromise.As one of most important one problem, optimal load flow (Optimal Power Flow, OPF) control is
Refer to the structural parameters of electric system and load condition has all given timing, adjust available control variable (such as generator output work
Rate, adjustable transformer tap etc.) to find it can meet all operation constraintss, and make a certain performance indicator of system (such as
Cost of electricity-generating or via net loss) power flowcontrol when reaching minimum value.In recent years, with intelligent grid, distributed generation technology,
The fast development of distribution type electric energy memory technology under the premise of power system security is met, improves economy as much as possible,
Rationally this classical problem is controlled again to become to reduce the optimal load flow of energy consumption using resource distribution and existing equipment to grind
Study carefully hot spot.
Since the 1960s, optimal load flow is as Operation of Electric Systems and the powerful tool of analysis, always times
It is concerned.By the development of nearly 50 years, numerous optimal methods were introduced sequentially into the field, such as：Linear programming, quadratic programming,
Non-Linear Programming and Newton method and decoupling method etc..But optimal load flow is a typical nonlinear optimal problem, and due to about
It is complicated that the complexity of beam causes it to calculate, and difficulty is larger.On the other hand, in order to adapt to power distribution network distributed nature in itself and calculation
Method can be applicable in large-scale distribution network, it is desirable that optimal load flow control method can carry out distributed execution in electric system.When
Before, document [M.Farivar and S.H.Low, " Branch flow model：Relaxations and
Convexification (parts I, II), " IEEE Trans.Power Syst., vol.28, no.3, pp.2554-2572,
2013] being proposed in and utilize convex relaxation method --- SOCP relaxations solve optimal power flow problems.Although SOCP relaxation problems can be with
Distributed solution is carried out, but it is tight that it only demonstrates the relaxation under certain condition using ADMM methods.For it is non-convex most
Excellent Power Flow Problem, convex relaxation method even can not all ensure to obtain the feasible solution of problem.Therefore, the present invention proposes to be based on continuously punishing
Penalize the electric system distributed optimal power flow control method of Duality Decomposition technology.
Invention content
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of electric power based on continuous punishment Duality Decomposition
System distributed optimal power flow method, the method for the present invention consider the control problem of inverter in distributed power generation, pass through electric power
The local of each busbar calculates the information exchange between adjacent busbar in system, completes electric system distributed optimal power flow control
System.Specifically include following steps：
Step 1：Obtain power system network parameter：Busbar setWith the set after removal root busbar
Grid branch set ε；The impedance z of branch between busbarij,Each bus nodes injecting power siConstraint set
Square v of busbar voltage range valueiLower limitv iAnd the upper limit
Step 2：By introducing auxiliary variableWithOptimal power flow problems are equivalent to following problem：
Wherein | a |, a*Represent amplitude, conjugation and the real part of plural number a respectively with Re (a)；It represents to note at busbar i
Enter the system performance loss caused by power；lijIt represents from busbar i to square of the current amplitude of busbar j；SijRepresent busbar
The trend of line transmitting terminal between i to j；Busbar i is responsible for variableUpdate, whereinWithPoint
Not Biao Shi busbar h to busbar i local copy of the current amplitude quadratic sum line transmitting terminal trend at busbar i,Represent female
The local copy of line i voltage amplitude values square.
Step 3：Initialize external iteration number k=0, maximum external iteration number Kmax；It sets first at each busbar i
Initial pointAnd initial dual variableInitialize 1/ ρ of penalty coefficient0；If
Determine iteration control parameter c；
Step 4：Fixed current dual variableIt is solved using block coordinate descent algorithm distribution
The internal layer augmentation lagrange problem of OPF problems：
WhereinRepresent all variate-values that+1 external iteration of kth obtains after calculating；
Step 5：Judge whether to reach maximum iteration：K ＞ Kmax；If so, the injecting power of output busbar, calculates system
Performance of uniting loss, performs step 6；Otherwise, busbar i receives data from its father node WithParallel update as follows
Dual variable：
And update punishment parameter ρk+1=c ρk；Iterations k=k+1 is enabled, repeats step 4 and 5；
Step 6：Optimal load flow control is completed according to the busbar injecting power being calculated.
Wherein, the block coordinate descent algorithm in the step 4, specifically includes following steps：
Step 4.1：Set internal layer iterations m=0, maximum internal layer iterations Mmax；Each busbar is with the outer stacking of kth time
Result of calculation after generation is primary data, i.e.,HereTable
Show k-th of internal layer augmentation lagrange problem (ALk) the m times iterative calculation result；
Step 4.2：By internal layer augmentation lagrange problem (ALk) optimized variable be divided into { Sij, lij, vi,
{ siFour groups, this four groups of variables of each busbar i sequential updates, and concurrently calculated between busbar and respectively need the variable optimized.
First, each busbar i receives data from its father node jAnd problems with is solved with more new variables { Sij, lij, vi}：
s.t.lijvi=| Sij|2,
Secondly, each busbar i receives data from its child node hIt solves problems with and completes variable
Update：
Then, each busbar i receives data from its child node hIt solves problems with and completes variable's
Update：
Finally, each busbar i solves problems with and completes variable { siUpdate：
In above-mentioned each subproblem, other than optimized variable, remaining variables are all fixed as current iterative calculation result；
Sequence solves above three subproblem, obtains
Step 4.3：Enable iterations m=m+1；Judge whether to reach maximum iteration：M ＞ Mmax；If so, output meter
Calculate resultOtherwise, step 4.2 and 4.3 are repeated.
Advantageous effect of the present invention：The method of the present invention constructs optimal load flow and corresponds to planning problem first；Secondly auxiliary is introduced to become
Amount, obtains the equivalent problems of former optimal load flow control problem；The equivalent problems are solved by inside and outside two layers of iterative algorithm distribution,
Optimal Power Flow Problems control is finally completed according to gained busbar injecting power value.The present invention utilizes continuous punishment Duality Decomposition
Technology distribution formula designs Optimal Power Flow Problems, makes system performance loss most under the premise of power flow equation feasibility is ensured
It is small.
Description of the drawings
Fig. 1 is the system model figure that the embodiment of the present invention uses this method.
Fig. 2 is that the embodiment of the present invention updates optimized variable illustraton of model parallel.
Fig. 3 is the particular flow sheet that the embodiment of the present invention uses this method.
Fig. 4 is the desired value of the embodiment of the present invention and the relational graph of iterations.
Fig. 5 is system restriction of embodiment of the present invention feasibility criterion and iterations relational graph.
Specific embodiment
In order to make the objects and effects of the present invention clearer, below in conjunction with the accompanying drawings to the specific embodiment party of the method for the present invention
Formula is described in detail.
As shown in Figure 1, considering radial power distribution network, it is made of the line of busbar and connection busbar.In the network
Root node is substation bus bar (for convenience of description, hereinafter referred to as root busbar), is connected with power transmission network.Root busbar uses fixation
Voltage, while will be from the electric power distribution received in transmission network to other busbares.The present invention defines the root busbar as mother
Line 0, other busbares are 1 ..., n；In addition, it enablesRepresent all busbares in power grid, definition
(i, j) represents that busbar i is connected with busbar j, and direction is i → j, and busbar j is on the exclusive path of busbar i and busbar 0.It enablesTable
Show the set of all branches in network, to arbitraryRepresent vector branch i → j.
For arbitrary busbarEnable viRepresent square of the voltage amplitude value at busbar i.As described above, substation is female
The voltage of line is fixed value v0.Define si=pi+iqiRepresent the injecting power at busbar i, wherein pi、qiInjection is represented respectively
Active power and reactive power.In addition, define PiFor busbar i to the exclusive path between busbar 0, for Radial network, Pi
It is unique.For arbitrary lineEnable lijIt represents from busbar i to square of the current amplitude of busbar j, zij=rij
+ixijRepresent the impedance of line between busbar i, j；Enable Sij=Pij+iQijRepresent the trend of the line transmitting terminal between busbar i to j
(or power flow), wherein PijAnd QijActive power stream and reactive power flow are represented respectively.In addition, for plural numberUse a*
Represent the conjugation of a.
Given network topologyImpedance z and substation bus bar voltage v0When, then other electrical network parameters (s, S,
V, l, s0) it can represent as follows by the branch flow model (branch flow model) of radial network：
Formula (1a) and (1b) are power balance equations, and formula (1c) and (1d) are the identical transformations of ohm formula.
The present invention considers following several power distribution network controllable devices：Distributed generator, inverter, controllable load, such as electricity
Motor-car, intelligent appliance, shunt capacitor.In practical applications, power grid is injected by controlling shunt capacitor and inverter
Reactive power adjusts voltage.After injecting power s is set, other electrical parameter (S, v, l, s can be determined by formula (1)0)。
According to the different type of controllable device, power grid median generatrixInjecting power siWith different constraint setI.e.：
According to device type definition setFor：
If 1. siRepresent a rated capacity asShunt capacitor, thenIf
siRepresent a maximum generating watt asSolar energy electroplax, be by a capacityInverter connect with power grid, then
If 2. siRepresent a power factor asActive power is consumed in sectionThe adjustable negative of consecutive variations
It carries, then
Note that siIt can represent the total injecting power of multiple above equipments.
In addition, it is necessary to square v by the voltage amplitude value of busbar iiControl is in preset voltage lower limit valuev iAnd voltage
Upper limit valueBetween, that is, it needs to meet
Under conditions of power flow constraint, voltage constraint, injecting power constraint, optimal power flow problems can be described as follows：
Wherein in object functionRepresent the system performance loss caused by busbar i injecting powers.If for appointing
MeaningThere is fi(x)=x, thenRepresent the total-power loss in power grid.
Due to existing such asNon-convex constraint, above-mentioned optimal power flow problems be non-convex optimization problem,
It is difficult to solve.Document [M.Farivar and S.H.Low, " Branch flow model：Relaxations and
Convexification (parts I, II), " IEEE Trans.Power Syst., vol.28, no.3, pp.2554-2572,
2013] it is proposed in and solves optimal power flow problems using SOCP relaxation methods.Although SOCP relaxation methods can utilize ADMM side
Method carries out distributed solution, however it is tight that it only demonstrates the relaxation under certain condition.General optimal load flow is asked
Topic, convex relaxation method even can not all ensure to obtain the feasible solution of problem.Therefore, the present invention is proposed based on continuous punishment antithesis point
The distributed optimal power flow control method of solution.
First by introducing auxiliary variableOptimal power flow problems (3) are equivalent to following problem：
By introducing auxiliary variableWithOptimal power flow problems are equivalent to following problem：
WhereinWithRepresent the current amplitude quadratic sum line transmitting terminal trend of busbar h to busbar i in mother respectively
Local copy at line i,Represent the local copy of busbar i voltage amplitude values square.
Introduce dual variableWith punishment parameter ρk, above-mentioned optimal power flow problems can be obtained
(OPF) augmentation lagrange problem：
It can be proved that as punishment parameter ρkAnd dual variableIt is updated according to appropriate rule
When, problem (ALk) can be solved by inside and outside two layers of iteration.Specifically, k is enabled to represent external iteration index, m represents internal layer
Iteration index.So in interior stacking generation, fixed current dual variableWide lagrange problem
(ALk) optimized variable be divided into { Sij, lij, vi, { siFour groups, as shown in Fig. 2, each busbar i sequential updates this
Four groups of variables, and concurrently calculating respectively needs the variable optimized between busbar：
First, each busbar i receives data from its father node jAnd problems with is solved with more new variables { Sij, lij, vi}：
s.t.lijvi=| Sij|2,
Secondly, each busbar i receives data from its child node hIt solves problems with and completes variable
Update：
Then, each busbar i receives data from its child node hIt solves problems with and completes variable's
Update：
Finally, each busbar i solves problems with and completes variable { siUpdate：
Above-mentioned subproblem can be solved with enclosed.Using block coordinate descent algorithm, subproblem (P1), (P2) are iteratively solved,
(P3) and after (P4) can obtain internal layer iteration convergenceIt, can basis in external iteration
Following constraint feasibility criterion：K ＞ Kmax, corresponding dual variable, iteration control parameter and penalty factor are updated, and again
Into internal layer iteration.So and constantly internal layer and external iteration are carried out until convergence, it is possible to obtain optimal load flow control result.
Fig. 3 gives the above-mentioned electric system distributed optimal power flow control method based on continuous punishment Duality Decomposition technology
Flow chart.Specifically, it can be described as follows：
A kind of electric system distributed optimal power flow control method based on continuous punishment Duality Decomposition technology, this method packet
Include following steps：
Step 1：Obtain power system network parameter：Busbar setWith the set after removal root busbarGrid branch setThe impedance z of branch between busbarij,Each bus nodes injecting power si
Constraint setSquare v of busbar voltage range valueiLower limitv iAnd the upper limit
Step 2：By introducing auxiliary variableWithOptimal power flow problems are equivalent to following problem：
Wherein | a |, a*Represent amplitude, conjugation and the real part of plural number a respectively with Re (a)；It represents to note at busbar i
Enter the system performance loss caused by power；lijIt represents from busbar i to square of the current amplitude of busbar j；SijRepresent busbar
The trend of line transmitting terminal between i to j；Busbar i is responsible for variableUpdate, whereinWithPoint
Not Biao Shi busbar h to busbar i local copy of the current amplitude quadratic sum line transmitting terminal trend at busbar i,Represent female
The local copy of line i voltage amplitude values square.
Step 3：Initialize external iteration number k=0, maximum external iteration number Kmax；It sets first at each busbar i
Initial pointAnd initial dual variableInitialize 1/ ρ of penalty coefficient0；If
Determine iteration control parameter c；
Step 4：Fixed current dual variableIt is solved using block coordinate descent algorithm distribution
The internal layer augmentation lagrange problem of OPF problems：
WhereinRepresent all variate-values that+1 external iteration of kth obtains after calculating；
Step 5：Judge whether to reach maximum iteration：K ＞ Kmax；If so, the injecting power of output busbar, calculates system
Performance of uniting loss, performs step 6；Otherwise, busbar i receives data from its father node WithParallel update as follows
Dual variable：
And update punishment parameter ρk+1=c ρk；Iterations k=k+1 is enabled, repeats step 4 and 5；
Step 6：Optimal load flow control is completed according to the busbar injecting power being calculated.
Further, the block coordinate descent algorithm in the step 4, specifically includes following steps：
Step 4.1：Set internal layer iterations m=0, maximum internal layer iterations Mmax；Each busbar is with the outer stacking of kth time
Result of calculation after generation is primary data, i.e.,HereTable
Show k-th of internal layer augmentation lagrange problem (ALk) the m times iterative calculation result；
Step 4.2：By internal layer augmentation lagrange problem (ALk) optimized variable be divided into { Sij, lij, vi,
{ siFour groups, this four groups of variables of each busbar i sequential updates, and concurrently calculated between busbar and respectively need the variable optimized.
First, each busbar i receives data from its father node jAnd problems with is solved with more new variables { Sij, lij, vi}：
s.t.lijvi=| Sij|2,
Secondly, each busbar i receives data from its child node hIt solves problems with and completes variable
Update：
Then, each busbar i receives data from its child node hIt solves problems with and completes variable's
Update：
Finally, each busbar i solves problems with and completes variable { siUpdate：
In above-mentioned each subproblem, other than optimized variable, remaining variables are all fixed as current iterative calculation result；
Sequence solves above three subproblem, obtains
Step 4.3：Enable iterations m=m+1；Judge whether to reach maximum iteration：M ＞ Mmax；If so, output meter
Calculate resultOtherwise, step 4.2 and 4.3 are repeated.
Technical scheme of the present invention is further elaborated below by specific example.In experiment, using IEEE-13 and
IEEE-34 network systems carry out proof of algorithm.Specifically, using following experiment parameter：
1. minimum power losses are set as target, and the voltage v of substation bus bar0Reference voltage for a unit
Value；
2. the setting for injecting power restrained boundary, the arbitrary busbar in power gridPlace is set there may be multiple
It is standby, such as shunt capacitance, tunable load, solar energy electroplax；Assuming that there are D in total in power gridiA equipment and to be numbered be 1,
2 ..., Di；
For d=1,2 ..., Di, sidRepresent the injecting power of equipment d.
If equipment d is a load, and known active power consumption p and reactive power consumption q, then s at this timeid=-p-
j·q；If the apparent energy peak value s of known load dpeak, then sid=-speakexp(jθ).Wherein, θ=arccos (0.9),
At this point, the injecting power s of loadidA namely constant；
If equipment d is a capacityCapacitance, then have
If equipment d is a capacityPhotovoltaic battery plate, then
According to above setting, injecting power total busbar i is at this time
Other parameter setting is as follows：Each reference capacity value, initialization busbar sum N, electricity are determined according to power grid actual conditions
Hinder rij, reactance xijAnd the capacity of relevant device type or active power consumption figures at busbar, concurrently set power transformation tiny node
Reference power value of the power for unit, enable external iteration total degree Kmax=1000, internal layer iteration total degree Mmax=
100, vmaxEqual to 1.1 cell voltage base values, vminEqual to 0.9 cell voltage base value, punishment parameter ρ0=10, iteration control parameter
C=0.996；Initialize bus voltage upper limitLower voltage limitIn addition, in the present embodiment, definition
To constrain feasibility criterion, value has arrived feasible close to explanation when 0.
Fig. 4,5 are simulation results figures by Matlab to designed method.
The result of calculation that the method for the present invention is applied in SCE-56 bus-bar systems is set forth in Fig. 4.In order to compare, in figure
Also give the centralization punishment obtained performance bound of Dual Decomposition Algorithm.It can be seen from the figure that the method for the present invention can be fast
Speed convergence makes system total power consumption with iteration time while meeting electric power system tide equation, power and voltage and constraining
It counts and constantly reduces until restraining, and the distributed optimal power flow control method based on Duality Decomposition technology has reached with centralization most
The almost the same desired value of excellent flow control method illustrates that technical solution of the present invention can realize distributed optimal power flow control.
Fig. 5 is set forth in SCE-56 bus-bar systems using after the method for the present invention, and feasibility criterion is constrained in model
With iterations relational graph.It can be seen from the figure that with the increase of iterations, constraints is gradually met, and
After external iteration the 1000th time, the method for the present invention can meet constraint feasibility criterion.Although the convergence rate of the method for the present invention
Centralized algorithm is slightly slower than, but in final convergence, the performance of the two is comparable.
The present invention is not only limited to above-mentioned specific embodiment, and persons skilled in the art are according to disclosed by the invention interior
Hold, other a variety of specific embodiments may be used and implement the present invention.Therefore, every design structure using the present invention and think of
Road does some simple designs changed or change, both falls within the scope of the present invention.
Claims (2)
- A kind of 1. electric system distributed optimal power flow method based on continuous punishment Duality Decomposition, which is characterized in that this method Include the following steps：Step 1：Obtain power system network parameter：Busbar setWith the set after removal root busbarPower grid Set of fingers ε；The impedance z of branch between busbarij,Each bus nodes injecting power siConstraint setBusbar Square v of voltage amplitude valueiLower limit viAnd the upper limitStep 2：By introducing auxiliary variableWithOptimal power flow problems are equivalent to following problem：Wherein | a |, a*Represent amplitude, conjugation and the real part of plural number a respectively with Re (a)；fi:It represents to inject work(at busbar i System performance loss caused by rate；lijIt represents from busbar i to square of the current amplitude of busbar j；SijRepresent busbar i to j Between line transmitting terminal trend；Busbar i is responsible for variableUpdate, whereinWithTable respectively Show local copy of the current amplitude quadratic sum line transmitting terminal trend of busbar h to busbar i at busbar i,Represent busbar i The local copy of voltage amplitude value square；Step 3：Initialize external iteration number k=0, maximum external iteration number Kmax；Set the initial point at each busbar iAnd initial dual variableInitialize 1/ ρ of penalty coefficient0；Setting changes For control parameter c；Step 4：Fixed current dual variableOPF is solved using block coordinate descent algorithm distribution The internal layer augmentation lagrange problem of problem：WhereinRepresent all variate-values that+1 external iteration of kth obtains after calculating；Step 5：Judge whether to reach maximum iteration：k>Kmax；If so, the injecting power of output busbar, computing system performance Loss performs step 6；Otherwise, busbar i receives data from its father nodeWithParallel update is to mutation as follows Amount：And update punishment parameter ρk+1=c ρk；Iterations k=k+1 is enabled, repeats step 4 and 5；Step 6：Optimal load flow control is completed according to the busbar injecting power being calculated.
- 2. a kind of electric system distributed optimal power flow side based on continuous punishment Duality Decomposition according to claim 1 Method, which is characterized in that the block coordinate descent algorithm in the step 4 specifically includes following steps：Step 4.1：Set internal layer iterations m=0, maximum internal layer iterations Mmax；After each busbar is with kth time external iteration Result of calculation for primary data, i.e.,HereRepresent the K internal layer augmentation lagrange problem (ALk) the m times iterative calculation result；Step 4.2：By internal layer augmentation lagrange problem (ALk) optimized variable be divided into { Sij,lij,vi,With {siFour groups, this four groups of variables of each busbar i sequential updates, and concurrently calculated between busbar and respectively need the variable optimized；First, each busbar i receives data from its father node jAnd problems with is solved with more new variables { Sij,lij,vi}：Secondly, each busbar i receives data from its child node hIt solves problems with and completes variableMore Newly：Then, each busbar i receives data from its child node hIt solves problems with and completes variableUpdate：Finally, each busbar i solves problems with and completes variable { siUpdate：In above-mentioned each subproblem, other than optimized variable, remaining variables are all fixed as current iterative calculation result；Sequentially Above three subproblem is solved, is obtainedStep 4.3：Enable iterations m=m+1；Judge whether to reach maximum iteration：m>Mmax；If so, output result of calculationOtherwise, step 4.2 and 4.3 are repeated.
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