CN106159955A - Based on the power system distributed optimal power flow method punishing Duality Decomposition continuously - Google Patents

Abstract

The invention discloses a kind of power system distributed optimal power flow method based on punishment Duality Decomposition continuously, comprise the following steps: first obtain power system network parameter, determine the mathematical model of optimal power flow problems；Next introduces auxiliary variable, obtains the equivalent problems of former optimal load flow control problem；Then this equivalent problems is solved by inside and outside two-layer iterative algorithm, wherein internal layer iteration utilizes that block coordinate descent algorithm is distributed in the case of fixing dual variable solves corresponding internal layer augmentation lagrange problem, each bus needs and adjacent bus interaction data before optimization often group variable, to realize the local optimization of local variable, external iteration then updates dual variable and penalty factor according to present confinement feasibility criterion；Optimal Power Flow Problems control is completed finally according to gained bus injecting power value.The present invention utilizes punishment Duality Decomposition technical point cloth design Optimal Power Flow Problems continuously, makes system performance loss minimum on the premise of ensureing power flow equation feasibility.

Description

Based on the power system distributed optimal power flow method punishing Duality Decomposition continuously

Technical field

The present invention relates to technical field of power systems, be specifically related to a kind of based on the power system punishing Duality Decomposition continuously Distributed optimal power flow method.

Background technology

Optimization Problems In Power Systems, including planning, dispatch, running on control, its target is security of system and economy Balance and compromise.As one of most important of which problem, optimal load flow (Optimal Power Flow, OPF) control is The structural parameters of finger power system and load condition have given timing the most, regulate available control variable (such as electromotor output work Rate, adjustable transformer tap etc.) find and can meet all operation constraints, and make system a certain performance indications (as Cost of electricity-generating or via net loss) power flowcontrol when minimizing value.In recent years, along with intelligent grid, distributed generation technology, The fast development of distribution type electric energy memory technology, on the premise of meeting power system security, improves economy as much as possible, Make rational use of resources configuration and existing equipment controls this classical problem with the optimal load flow reducing energy resource consumption and becomes again and grind Study carefully focus.

Since the sixties in 20th century, optimal load flow is as Operation of Electric Systems and the powerful tool of analysis, again always Concerned.Through the development of nearly 50 years, numerous optimization methods were introduced sequentially into this 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 The complexity of bundle makes it calculate complexity, and difficulty is bigger.On the other hand, in order to adapt to distributed nature and the calculation of power distribution network itself Method can be suitable for large-scale distribution network, it is desirable to optimal load flow control method can carry out distributed execution in power 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] propose in and utilize that convex relaxation method SOCP is lax solves optimal power flow problems.Although SOCP relaxation problem is permissible Utilize ADMM method to carry out distributed solving, but its to demonstrate this under certain condition lax be tight.For non-convex Excellent Power Flow Problem, convex relaxation method the most all cannot ensure to obtain the feasible solution of problem.Therefore, the present invention proposes based on punishing continuously Penalize the power system distributed optimal power flow control method of Duality Decomposition technology.

Summary of the invention

Present invention aims to the deficiencies in the prior art, it is provided that a kind of based on the electric power punishing Duality Decomposition continuously System distributed optimal power flow method, the inventive method considers the control problem of inverter in distributed power generation, passes through electric power In system, the local of each bus calculates mutual with the information between adjacent bus, completes power system distributed optimal power flow control System.Specifically include following steps:

Step 1: acquisition power system network parameter: bus setWith the set after the bus that goes to dig up the roots Grid branch set ε；The impedance z of branch road between bus_ij,Each bus nodes injecting power s_iConstraint set Square v of busbar voltage range value_iLower limitv _iAnd the upper limit

Step 2: by introducing auxiliary variableWithOptimal power flow problems is equivalent to following problem:

Wherein | a |, a^*The plural number amplitude of a, conjugation and real part is represented respectively with Re (a)；Represent and note at bus i Enter the system performance loss caused by power；l_ijRepresent from bus i to the current amplitude of bus j square；S_ijRepresent bus The trend of the line transmitting terminal between i to j；Bus i is responsible for variableRenewal, whereinWithPoint Not Biao Shi the current amplitude quadratic sum line transmitting terminal trend of bus h to the bus i local copy at bus i,Represent mother The local copy of line i voltage amplitude value square.

Step 3: initialize external iteration number of times k=0, maximum external iteration number of times K_max；Set at the beginning of at each bus i Initial pointAnd initial dual variableInitialize penalty coefficient 1/ ρ₀；If Determine iteration control parameter c；

Step 4: fixing current dual variableUtilize that block coordinate descent algorithm is distributed to be solved The internal layer augmentation lagrange problem of OPF problem:

WhereinRepresent all variate-values that+1 external iteration of kth obtains after calculating；

Step 5: judge whether to reach maximum iteration time: k ＞ K_max；If so, export the injecting power of bus, calculate system System performance loss, performs step 6；Otherwise, bus i receives data from its father node WithUpdate the most parallel Dual variable:

And update punishment parameter ρ_k+1=c ρ_k；Make iterations k=k+1, repeat step 4 and 5；

Step 6: complete optimal load flow control according to calculated bus injecting power.

Wherein, the block coordinate descent algorithm in described step 4, specifically include following steps:

Step 4.1: set internal layer iterations m=0, maximum internal layer iterations M_max；Each bus is with the outer stacking of kth time Result of calculation after Dai is primary data, i.e.HereTable Show kth internal layer augmentation lagrange problem (AL^k) the m time iterative computation result；

Step 4.2: by internal layer augmentation lagrange problem (AL^k) optimized variable be divided into { S_ij, l_ij, v_i, { s_iFour groups, each bus i sequential update these four groups calculates the variable each needing to optimize concurrently between variable, and bus.

First, each bus i receives data from its father node jAnd solve problems with more new variables { S_ij, l_ij, v_i}:

$\begin{array}{c}{\{S_{ij},l_{ij},v_i\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_j-2\left(z_{ij}^{*}{S}_{ij}\right)+|z_{ij}{|}^2{l}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-{\hat{S}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|l_{ij}-{\hat{l}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_i+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{3,k}^i{|}^2\end{array}---\left(P1\right)$

s.t.l_ijv_i=| S_ij|²,

Secondly, each bus i receives data from its child node hSolve problems with and complete variable Renewal:

$\begin{array}{c}{\{{\hat{S}}_{hi},{\hat{l}}_{hi}\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|0-s_0-\underset{h:h\→0}{\Σ}\left({\hat{S}}_{h0}-z_{h0}{\hat{l}}_{h0}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^0{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|S_{hi}-{\hat{S}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^h{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|l_{hi}-{\hat{l}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^h{|}^2\end{array},---\left(P2\right)$

Then, each bus i receives data from its child node hSolve problems with and complete variable's Update:

Finally, each bus i solves problems with and completes variable { s_iRenewal:

In above-mentioned each subproblem, in addition to optimized variable, remaining variables is all fixed as current iterative computation result； Order solves above three subproblem, obtains

Step 4.3: make iterations m=m+1；Judge whether to reach maximum iteration time: m ＞ M_max；If so, meter is exported Calculate resultOtherwise, repeated execution of steps 4.2 and 4.3.

The method have the benefit that first the inventive method constructs optimal load flow correspondence planning problem；Secondly introduce auxiliary to become Amount, obtains the equivalent problems of former optimal load flow control problem；This equivalent problems is solved by inside and outside two-layer iterative algorithm is distributed, Optimal Power Flow Problems control is completed finally according to gained bus injecting power value.The present invention utilizes and punishes Duality Decomposition continuously Technical point cloth design Optimal Power Flow Problems, is ensureing to make on the premise of power flow equation feasibility system performance loss Little.

Accompanying drawing explanation

Fig. 1 is the system model figure that the embodiment of the present invention uses the 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 the method.

Fig. 4 is the desired value graph of a relation with iterations of the embodiment of the present invention.

Fig. 5 is embodiment of the present invention system restriction feasibility criterion and iterations graph of a relation.

Detailed description of the invention

In order to make the purpose of the present invention and effect clearer, the specific embodiment party to the inventive method below in conjunction with the accompanying drawings Formula is described in detail.

As shown in Figure 1, it is considered to radial power distribution network, it is made up of the line of bus and connection bus.In this network Root node is substation bus bar (for convenience of describing, hereinafter referred to as root bus), and it is connected with power transmission network.Root bus uses fixing Voltage, the electric power received from transmission network is assigned to other buses simultaneously.The present invention defines this root bus for mother Line 0, other buses are 1 ..., n；It addition, orderRepresent all buses in electrical network, definition (i, j) represents that bus i is connected with bus j, and direction is i → j, and bus j is on the bus i exclusive path with bus 0.OrderTable Show the set of all branch roads in network, to arbitrarilyRepresent vector branch i → j.

For any busMake v_iRepresent voltage amplitude value at bus i square.As it has been described above, transformer station is female The voltage of line is fixed value v₀.Definition s_i=p_i+iq_iRepresent the injecting power at bus i, wherein p_i、q_iRepresent injection respectively Active power and reactive power.It addition, definition P_iFor the exclusive path between bus i to bus 0, for Radial network, P_i It is unique.For any lineMake l_ijRepresent from bus i to the current amplitude of bus j square, z_ij=r_ij +ix_ijRepresent bus i, the impedance of line between j；Make S_ij=P_ij+iQ_ijThe trend of the line transmitting terminal between expression bus i to j (or claiming power stream), wherein P_ijAnd Q_ijRepresent active power stream and reactive power flow respectively.It addition, for plural numberUse a^* Represent the conjugation of a.

Given network topologyImpedance z and substation bus bar voltage v₀Time, then other electrical network parameters (s, S, V, l, s₀) can be expressed as follows by a flow model (branch flow model) for radial network:

$S_{ij}=s_i+\underset{h:h\→i}{\Σ}(S_{hi}-z_{hi}{l}_{hi}),\∀(i,j)\∈\mathrm{\ϵ}---\left(1a\right)$

$0=s_0+\underset{h:h\→0}{\Σ}(S_{h0}-z_{h0}{l}_{h0})---\left(1b\right)$

$v_i-v_j=2\mathrm{Re}\left(z_{ij}^{*}{S}_{ij}\right)-|z_{ij}{|}^2{l}_{ij},\∀(i,j)\∈\mathrm{\ϵ}---\left(1c\right)$

$l_{ij}=\frac{|S_{ij}{|}^2}{v_i},\∀(i,j)\∈\mathrm{\ϵ}---\left(1d\right)$

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 device: distributed generator, inverter, controllable load, such as electricity Motor-car, intelligent appliance, shnt capacitor.In actual applications, electrical network is injected by control shnt capacitor and inverter Reactive power regulates voltage.After setting injecting power s, may determine that other electrical quantity (S, v, l, s by formula (1)₀)。

Dissimilar according to controllable device, electrical network median generatrixInjecting power s_iThere is different constraint setThat is:

According to device type definition setFor:

If 1. s_iRepresenting a rated capacity isShnt capacitor, then If s_iRepresenting a maximum generating watt isSolar energy electroplax, it by a capacity isInverter be connected with electrical network, that ?

If 2. s_iRepresenting a power factor isActive power consumes in intervalContinually varying adjustable negative Carry, then

Note, s_iThe injecting power that multiple the said equipment is total can be represented.

In addition, it is necessary to by square v of the voltage amplitude value of bus i_iControl at voltage lower limit value set in advancev _iAnd voltage Higher limitBetween, i.e. need to meet

Under conditions of the constraint of power stream, voltage constraint, injecting power constraint, optimal power flow problems can be described as follows:

$s.t.S_{ij}=s_i+\underset{h:h\→i}{\Σ}(S_{hi}-z_{hi}{l}_{hi}),\∀(i,j)\∈\mathrm{\ϵ},---\left(3a\right)$

$0=s_0+\underset{h:h\→0}{\Σ}(S_{h0}-z_{h0}{l}_{h0}),---\left(3b\right)$

$v_i-v_j=2\mathrm{Re}\left(z_{ij}^{*}{S}_{ij}\right)-|z_{ij}{|}^2{l}_{ij},\∀(i,j)\∈\mathrm{\ϵ},---\left(3c\right)$

$l_{ij}{v}_i=|S_{ij}{|}^2,\∀(i,j)\∈\mathrm{\ϵ},---\left(3d\right)$

Wherein in object functionRepresent the system performance loss that bus i injecting power is caused.If for appointing MeaningThere is f_i(x)=x, thenI.e. represent the total-power loss in electrical network.

Owing to existing such asNon-convex constraint, above-mentioned optimal power flow problems is 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] propose in and utilize SOCP relaxation method to solve optimal power flow problems.Although SOCP relaxation method can utilize ADMM side Method carries out distributed solving, however it only to demonstrate this under certain condition lax be tight.General optimal load flow is asked Topic, convex relaxation method the most all cannot ensure to obtain the feasible solution of problem.Therefore, the present invention proposes to divide based on punishment antithesis continuously The distributed optimal power flow control method solved.

First pass through introducing auxiliary variableOptimal power flow problems (3) is equivalent to following problem:

By introducing auxiliary variableWithOptimal power flow problems is equivalent to following problem:

WhereinWithRepresent that the current amplitude quadratic sum line transmitting terminal trend of bus h to bus i is mother respectively Local copy at line i,Represent the local copy of bus i voltage amplitude value square.

Introduce dual variableWith punishment parameter ρ_k, above-mentioned optimal power flow problems can be obtained (OPF) augmentation lagrange problem:

May certify that, when punishment parameter ρ_kAnd dual variableIt is updated according to suitable rule Time, problem (AL^k) can be solved by inside and outside two-layer iteration.Specifically, making k represent external iteration index, m represents internal layer Iteration index.So in internal layer iteration, fixing current dual variableWide lagrange problem (AL^k) optimized variable be divided into { S_ij, l_ij, v_i, { s_iFour groups, as in figure 2 it is shown, each bus i sequential update this Four groups of variablees calculating each needs optimization between variable, and bus concurrently:

First, each bus i receives data from its father node jAnd solve problems with more new variables { S_ij, l_ij, v_i}:

$\begin{array}{c}{\{S_{ij},l_{ij},v_i\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_j-2\left(z_{ij}^{*}{S}_{ij}\right)+|z_{ij}{|}^2{l}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-{\hat{S}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|l_{ij}-{\hat{l}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_i+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{3,k}^i{|}^2\end{array}---\left(P1\right)$

s.t.l_ijv_i=| S_ij|²,

Secondly, each bus i receives data from its child node hSolve problems with and complete variable Renewal:

$\begin{array}{c}{\{{\hat{S}}_{hi},{\hat{l}}_{hi}\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|0-s_0-\underset{h:h\→0}{\Σ}\left({\hat{S}}_{h0}-z_{h0}{\hat{l}}_{h0}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^0{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|S_{hi}-{\hat{S}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^h{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|l_{hi}-{\hat{l}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^h{|}^2\end{array},---\left(P2\right)$

Then, each bus i receives data from its child node hSolve problems with and complete variable's Update:

Finally, each bus i solves problems with and completes variable { s_iRenewal:

Above-mentioned subproblem all can solve with enclosed.Employing block coordinate descent algorithm, iterative subproblem (P1), (P2), (P3) and after (P4) can obtain internal layer iteration convergenceIn external iteration, can basis Retrain feasibility criterion as follows: k ＞ K_max, update corresponding dual variable, iteration control parameter and penalty factor, and again Enter internal layer iteration.So and constantly carry out internal layer and external iteration until restraining, it is possible to obtain optimal load flow and control result.

Fig. 3 gives above-mentioned based on the power system distributed optimal power flow control method punishing Duality Decomposition technology continuously Flow chart.Specifically, can be described as follows:

A kind of power system distributed optimal power flow control method based on punishment Duality Decomposition technology continuously, the method bag Include following steps:

Step 1: acquisition power system network parameter: bus setWith the set after the bus that goes to dig up the rootsGrid branch setThe impedance z of branch road between bus_ij,Each bus nodes injecting power s_i Constraint setSquare v of busbar voltage range value_iLower limitv _iAnd the upper limit

Step 2: by introducing auxiliary variableWithOptimal power flow problems is equivalent to following problem:

Wherein | a |, a^*The plural number amplitude of a, conjugation and real part is represented respectively with Re (a)；Represent and note at bus i Enter the system performance loss caused by power；l_ijRepresent from bus i to the current amplitude of bus j square；S_ijRepresent bus The trend of the line transmitting terminal between i to j；Bus i is responsible for variableRenewal, whereinWithPoint Not Biao Shi the current amplitude quadratic sum line transmitting terminal trend of bus h to the bus i local copy at bus i,Represent mother The local copy of line i voltage amplitude value square.

Step 3: initialize external iteration number of times k=0, maximum external iteration number of times K_max；Set at the beginning of at each bus i Initial pointAnd initial dual variableInitialize penalty coefficient 1/ ρ₀；If Determine iteration control parameter c；

Step 4: fixing current dual variableUtilize that block coordinate descent algorithm is distributed to be solved The internal layer augmentation lagrange problem of OPF problem:

WhereinRepresent all variate-values that+1 external iteration of kth obtains after calculating；

Step 5: judge whether to reach maximum iteration time: k ＞ K_max；If so, export the injecting power of bus, calculate system System performance loss, performs step 6；Otherwise, bus i receives data from its father node WithUpdate the most parallel Dual variable:

And update punishment parameter ρ_k+1=c ρ_k；Make iterations k=k+1, repeat step 4 and 5；

Step 6: complete optimal load flow control according to calculated bus injecting power.

Further, the block coordinate descent algorithm in described step 4, specifically include following steps:

Step 4.1: set internal layer iterations m=0, maximum internal layer iterations M_max；Each bus is with the outer stacking of kth time Result of calculation after Dai is primary data, i.e.HereTable Show kth internal layer augmentation lagrange problem (AL^k) the m time iterative computation result；

Step 4.2: by internal layer augmentation lagrange problem (AL^k) optimized variable be divided into { S_ij, l_ij, v_i, { s_iFour groups, each bus i sequential update these four groups calculates the variable each needing to optimize concurrently between variable, and bus.

First, each bus i receives data from its father node jAnd solve problems with more new variables { S_ij, l_ij, v_i}:

$\begin{array}{c}{\{S_{ij},l_{ij},v_i\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_j-2\left(z_{ij}^{*}{S}_{ij}\right)+|z_{ij}{|}^2{l}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-{\hat{S}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|l_{ij}-{\hat{l}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_i+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{3,k}^i{|}^2\end{array}---\left(P1\right)$

s.t.l_ijv_i=| S_ij|²,

Secondly, each bus i receives data from its child node hSolve problems with and complete variable Renewal:

$\begin{array}{c}{\{{\hat{S}}_{hi},{\hat{l}}_{hi}\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}\left({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|0-s_0-\underset{h:h\→0}{\Σ}\left({\hat{S}}_{h0}-z_{h0}{\hat{l}}_{h0}\right)+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^0{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|S_{hi}-{\hat{S}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^h{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|l_{hi}-{\hat{l}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^h{|}^2\end{array},---\left(P2\right)$

Then, each bus i receives data from its child node hSolve problems with and complete variable's Update:

Finally, each bus i solves problems with and completes variable { s_iRenewal:

In above-mentioned each subproblem, in addition to optimized variable, remaining variables is all fixed as current iterative computation result； Order solves above three subproblem, obtains

Step 4.3: make iterations m=m+1；Judge whether to reach maximum iteration time: m ＞ M_max；If so, meter is exported Calculate resultOtherwise, repeated execution of steps 4.2 and 4.3.

Below by instantiation, technical scheme is further elaborated.In experiment, use IEEE-13 and IEEE-34 network system carries out proof of algorithm.Specifically, following experiment parameter is used:

1. setting power loss is minimised as target, and the voltage v of substation bus bar₀It it is the reference voltage of a unit Value；

2. for the setting of injecting power restrained boundary, any bus in electrical networkPlace there may be multiple setting Standby, such as shunt capacitance, tunable load, solar energy electroplax etc.；Assume electrical network always co-exists in D_iIndividual equipment and by its numbered 1, 2 ..., D_i；

For d=1,2 ..., D_i, s_idThe injecting power of expression equipment d.

If equipment d is a load, and known active power consumes p and reactive power consumption q, then now s_id=-p- j·q；If the apparent energy peak value s of known load d_peak, then s_id=-s_peakexp(jθ).Wherein, θ=arccos (0.9), Now, the injecting power s of load_idNamely a constant；

If equipment d is a capacityElectric capacity, then have

If equipment d is a capacityPhotovoltaic electroplax, then

Setting according to above, now total for bus i injecting power is

Other parameters set as follows: determine each reference capacity value according to electrical network practical situation, initialize bus sum N, electricity Resistance r_ij, reactance x_ijAnd at bus the capacity of relevant device type or active power consumption figures, concurrently set transformer station's node The reference power value that power is a unit, make external iteration total degree K_max=1000, internal layer iteration total degree M_max= 100, v_maxEqual to 1.1 cell voltage base values, v_minEqual to 0.9 cell voltage base value, punish parameter ρ₀=10, iteration control parameter C=0.996；Initialize bus voltage upper limitLower voltage limitIt addition, in the present embodiment, definition

For constraint feasibility criterion, its value has arrived feasible close to explanation when 0.

Fig. 4,5 it is by the Matlab simulation results figure to designed method.

Fig. 4 sets forth the result of calculation applying the inventive method in SCE-56 bus-bar system.In order to compare, in figure Give also the performance bound obtained by centralized punishment Dual Decomposition Algorithm.It can be seen that the inventive method can be fast Speed convergence, makes system total power consumption along with iteration time while meeting electric power system tide equation, power and voltage constraint Number constantly reduces until convergence, and distributed optimal power flow control method based on Duality Decomposition technology has reached and centralized The desired value that excellent flow control method is almost identical, illustrates that technical solution of the present invention is capable of distributed optimal power flow control.

Fig. 5 sets forth after applying the inventive method in SCE-56 bus-bar system, retrains feasibility criterion in model With iterations graph of a relation.It can be seen that along with the increase of iterations, constraints is gradually met, and After external iteration the 1000th time, the inventive method can meet constraint feasibility criterion.Although the convergence rate of the inventive method It is slightly slower than centralized algorithm, but when finally restraining, both performances are comparable.

The present invention is not only limited to above-mentioned detailed description of the invention, and persons skilled in the art are according to disclosed by the invention interior Hold, other multiple specific embodiments can be used to implement the present invention.Therefore, the design structure of every employing present invention and think of Road, does some simply change or designs of change, both falls within scope.

Claims (2)

1. a power system distributed optimal power flow method based on punishment Duality Decomposition continuously, it is characterised in that the method Comprise the steps:

Step 1: acquisition power system network parameter: bus setWith the set after the bus that goes to dig up the rootsElectrical network Set of fingers ε；The impedance z of branch road between bus_ij,Each bus nodes injecting power s_iConstraint setBus Square v of voltage amplitude value_iLower limitv _iAnd the upper limit

Step 2: by introducing auxiliary variableWithOptimal power flow problems is equivalent to following problem:

Wherein | a |, a^*The plural number amplitude of a, conjugation and real part is represented respectively with Re (a)；Represent and at bus i, inject merit System performance loss caused by rate；l_ijRepresent from bus i to the current amplitude of bus j square；S_ijRepresent bus i to j Between the trend of line transmitting terminal；Bus i is responsible for variableRenewal, whereinWithTable respectively Show the current amplitude quadratic sum line transmitting terminal trend of bus h to the bus i local copy at bus i,Represent bus i The local copy of voltage amplitude value square.

Step 3: initialize external iteration number of times k=0, maximum external iteration number of times K_max；Set initially accounting at each bus iAnd initial dual variableInitialize penalty coefficient 1/ ρ₀；Set repeatedly In generation, controls parameter c；

Step 4: fixing current dual variableUtilize that block coordinate descent algorithm is distributed solves OPF 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 time: k ＞ K_max；If so, export the injecting power of bus, calculate systematicness Can be lost, perform step 6；Otherwise, bus i receives data from its father nodeWithUpdate antithesis the most parallel Variable:

And update punishment parameter ρ_k+1=c ρ_k；Make iterations k=k+1, repeat step 4 and 5；

Step 6: complete optimal load flow control according to calculated bus injecting power.

The most according to claim 1 a kind of based on the power system distributed optimal power flow side punishing Duality Decomposition continuously Method, it is characterised in that the block coordinate descent algorithm in described step 4, specifically includes following steps:

Step 4.1: set internal layer iterations m=0, maximum internal layer iterations M_max；After each bus is with kth time external iteration Result of calculation be primary data, i.e.HereRepresent the K internal layer augmentation lagrange problem (AL^k) the m time iterative computation result；

Step 4.2: by internal layer augmentation lagrange problem (AL^k) optimized variable be divided into { S_ij, l_ij, v_i,With {s_iFour groups, each bus i sequential update these four groups calculates the variable each needing to optimize concurrently between variable, and bus.

First, each bus i receives data from its father node jAnd solve problems with more new variables { S_ij, l_ij, v_i}:

$\begin{array}{c}{\{S_{ij},l_{ij},v_i\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi})+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_j-2\left(z_{ij}^{*}{S}_{ij}\right)+{\left|z_{ij}\right|}^2{l}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-{\hat{S}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|l_{ij}-{\hat{l}}_{ij}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^i{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|v_i-{\hat{v}}_i+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{3,k}^i{|}^2\end{array}---\left(P1\right)$

s.t.l_ijv_i=| S_ij|²,

Secondly, each bus i receives data from its child node hSolve problems with and complete variableMore New:

$\begin{array}{c}{\{{\hat{S}}_{hi},{\hat{l}}_{hi}\}}^{k,m+1}=\arg \min \frac{1}{2{\mathrm{\ρ}}_k}|S_{ij}-s_i-\underset{h:h\→i}{\Σ}({\hat{S}}_{hi}-z_{hi}{\hat{l}}_{hi})+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^i{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}|0-s_0-\underset{h:h\→0}{\Σ}({\hat{S}}_{h0}-z_{h0}{\hat{l}}_{h0})+{\mathrm{\ρ}}_k{\mathrm{\λ}}_{1,k}^0{|}^2\\ +\frac{1}{2{\mathrm{\ρ}}_k}\underset{h:h\→i}{\Σ}|S_{hi}-{\hat{S}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{1,k}^h{|}^2+\frac{1}{2{\mathrm{\ρ}}_k}|l_{hi}-{\hat{l}}_{hi}+{\mathrm{\ρ}}_k{\mathrm{\μ}}_{2,k}^h{|}^2,\end{array}---\left(P2\right)$

Then, each bus i receives data from its child node hSolve problems with and complete variableRenewal:

Finally, each bus i solves problems with and completes variable { s_iRenewal:

In above-mentioned each subproblem, in addition to optimized variable, remaining variables is all fixed as current iterative computation result；Sequentially Solve above three subproblem, obtain

Step 4.3: make iterations m=m+1；Judge whether to reach maximum iteration time: m ＞ M_max；If so, output calculates knot ReallyOtherwise, repeated execution of steps 4.2 and 4.3.