CN105281327A - Optimal power flow calculation method considering discrete and sequential decision variables for large-scale power distribution network - Google Patents

Abstract

The invention relates to an optimal power flow calculation method considering discrete and sequential decision variables for a large-scale power distribution network. The optimal power flow calculation method is characterized by comprising the following steps of building a mathematical model of a complicated three-phase unbalanced power distribution network, carrying out complicated optimal power flow calculation decomposition, and carrying out a simplification process on network loss calculation of the three-phase unbalance power distribution network. By the optimal power flow calculation method, the complicated optimization problem can be decomposed into an integral linear programming primal problem and a non-linear feasible subproblem, decision making optimization and system security constraint are organically combined by using mutually-iterated calculation decisions, the optimal power flow is embedded to a decision process, and meanwhile, rapid calculation on asymmetric power flows at a large scale is achieved. The optimal power flow calculation method is suitably used for three-phase unbalance power flow calculation, looped network structure, bidirectional power flows, real-time decision of discrete and sequential decision and optimal power flow, and has the advantages of scientific reasonableness, high adaptability, operation accuracy, high speed and the like.

Description

Consider the large-scale distribution network optimal load flow computational methods of discrete and continuous decision variable

Technical field

The present invention relates to distribution network technology field, is a kind of large-scale distribution network optimal load flow computational methods considering discrete and continuous decision variable.

Background technology

Conventional electrical distribution network operation is static, passive.Along with regenerative resource access power distribution networks such as wind-driven generator, photo-voltaic power supply, energy storage, microgrids, power distribution network changes by radial, unidirectional trend, passive management to the operational mode of looped network, bi-directional current, active management.Current optimal load flow computational methods mainly concentrate on power transmission network, do not relate to three-phase imbalance power distribution network, cannot process the optimization problem containing discrete and continuous decision variable on a large scale, can not meet the requirement calculated in real time.Active distribution network technology is the key technology solving regenerative resource grid integration, and the startup stage that current active distribution network technology being in, Analysis of Policy Making and optimal load flow calculate respectively, cannot adapt to operation and the requirement of real-time control of active distribution network.

Summary of the invention

The object of the invention is, overcome the deficiencies in the prior art, using active distribution network technology as important support, a kind of large-scale distribution network optimal load flow computational methods considering discrete and continuous decision variable are provided, it is scientific and reasonable, adaptable, computing is accurate, speed is fast, is specially adapted to three-phase imbalance distribution system analysis and decision-making.

The technical scheme realizing goal of the invention employing is, a kind of large-scale distribution network optimal load flow computational methods considering discrete and continuous decision variable, and it is characterized in that, it comprises following content:

1) Mathematical Modeling relating to complicated three-phase imbalance power distribution network is set up

With minimum operating cost for target, foundation comprises: three-phase imbalance power distribution network, distributed rotary generator, distributed wind-power generator machine, photo-voltaic power supply, extensive energy storage, electric automobile energy storage, intelligent building, micro-grid system element, and consider the voltage of demand response, electrical network and the Mathematical Modeling of frequency adjustment and operation assistant service, discrete decision variable, continuously decision variable, discrete decision variable and the relation continuously between decision variable and decision-making time scope is comprised in model

Target function:

Minimizef(u _t,v _t)(1)

Constraints:

H _t(x _t,u _t,w _t)＝0(2)

J _t﹒u _t≥b(3)

K _t﹒v _t≥c(4)

L _t﹒w _t≥d(5)

G(x _t)≥0(6)

Wherein t ∈ T, and discrete decision variable and continuously decision variable have a lot of application, wherein load tap changer position, belong to discrete decision variable u _t; Unit Combination, belongs to discrete decision variable; Load switch, belongs to discrete decision variable; The unit dispatch of the distributed generation system of meritorious and reactive power, belongs to continuous decision variable v _t; Load side demand response, belongs to discrete decision variable; Home energy source management system, belongs to continuously and discrete decision variable; The microgrid energy and assistant service are additional continuous decision variable w _t, other is expressed as

Minimize: minimum value function;

F: objective cost function can be nonlinear cost curve;

X _t: the state vector of node voltage;

U _t: decision variable vector continuously;

V _t: discrete decision variable vector;

T ∈ T: the time interval t in period T;

W _t: additional continuous decision variable vector, as the idle of inverter control or Capacitor banks;

H _t(): the three-phase unbalanced load flow equation in the t of interval;

J _t: linear matrix, and formula (3) is continuity decision variable u _tupper and lower limit;

K _t: linear matrix, and formula (4) is discreteness decision variable v _tupper and lower limit;

L _t: linear matrix, and formula (5) is additional decision variable w _tupper and lower limit;

G (): the nonlinear function of power distribution system secure constraint.

2) decomposition of complicated optimal load flow calculating

When formula (2) is as constraints a part of, formula (1) solves difficulty, and adopt Benders method, the complicated optimum problem of upper joint is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce,

(i) primal problem

Target function is formula (1), and constraints is formula (3), formula (4), because objective cost function f can carry out linearisation, and constraint equation (3), formula (4) are all linear, then primal problem is solved as MILP method by formula (1), formula (3) and formula (4), and the optimal solution solved is expressed as

(ii) feasible subproblem

Primal problem optimal solution when iterations is 0, crosses the border if there is state variable, then generate new constraints and be included in the statement of primal problem, then the new optimal solution of primal problem solve, then again forward feasible subproblem to and solve, the iteration occurred between primal problem and feasible subproblem continues to carry out, until no longer detect that in feasible subproblem state variable is crossed the border, feasible subproblem is expressed as

Target function:

Minimizef’＝1 ^T﹒s(7)

Constraints:

H _t(x _t,u _t,w _t)＝0(8)

$u_t={\hat{u}}_t^i---\left(9\right)$

L _t﹒w _t≥d(10)

G(x _t)+s≥0(11)

Because constraint equation (6) and formula (9) are all nonlinear, adopt solution by iterative method, its process is: first, setting w _tinitial value then, three-phase unbalanced load flow equation is solved must be done well x _tinitial value finally, exist carry out linearisation around,

Target function:

Minimizef’＝1 ^T﹒s(12)

Constraints:

$L_t\·(w_t^0+{\mathrm{\Δw}}_t)\≥d---\left(13\right)$

$u_t={\hat{u}}_t^i---\left(14\right)$

$w_t=w_t^0+{\mathrm{\Δw}}_t---\left(15\right)$

$G\left(x_t^0\right)+A\·{\mathrm{\Δw}}_t+s\≥0---\left(16\right)$

Wherein for partial differential operational factor, s is decision variable vector, and the element of matrix A is illustrate control variables w _tconstraints G (), the i.e. Jacobian matrix of G (x), by using uneven flow equation H _tnumerical computations is carried out in ()=0;

Optimization problem formula (12)-Shi (16) be one with decision variable Δ w _tlinear programming problem, simplex method can be adopted to solve, upgrade decision variable perform iterative solution, until the change f of target function is in predefined critical value, in iterative process, make objective cost function value s ^*>0 and the Lagrange's multiplier of constraint equation (14) is λ ^*, the new constraints of adding in primal problem is:

$S^{*}+{\left({\mathrm{\λ}}^{*}\right)}^T\·(u_t^i-u)\≥0---\left(17\right)$

The object of new constraints forces primal problem accept its decision-making to such an extent as to help elimination variable that identifies in feasible subproblem to cross the border;

3) the simplification process of three-phase imbalance distribution network loss calculating

In formula (16), the element of matrix A contains constraints, and node voltage and bypass flow are to the Sensitirity va1ue of node injecting power, and for three-phase imbalance power distribution system network, the derivation of analytic expression can become very difficult; In order to reduce the complexity of calculating, using approximate loss sensitivity analytic expression (18), considering two hypothesis: (1) this phase electrical network upstream branch and the impact of load on this phase loss large; (2) distribution possesses enough reactive power supports, the minor variations of load can not cause large voltage deviation, namely voltage is constant, these two hypothesis meet the requirement of power distribution network actual motion, after applying two hypothesis, loss sensitivity amount of calculation will simplify greatly, and for a given network node n in φ phase, loss sensitivity can approximate representation be:

$\∂P_{loss}/\∂D_{n-\mathrm{\φ}}\≅\frac{1}{\left|V_{n-\mathrm{\φ}}\right|}\{\underset{l\∈{\hat{L}}_n}{\Σ}(\∂P_{loss-l}/\∂|I_{n-\mathrm{\φ}}\left|\right)+\underset{tr\∈{\hat{X}}_n}{\Σ}(\∂P_{loss-tr}/\∂|I_{n-\mathrm{\φ}}\left|\right)\}---\left(18\right)$

Wherein

$\begin{array}{c}\∂P_{loss-l}/\∂\left|I_{n-\mathrm{\φ}}\right|\≅2\·K_{l-n}\·\left\{\right|I_{l-a}|\·R_{l-\mathrm{\φ}a}\·\cos ({\mathrm{\θ}}_{I-l-a}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})+\\ \left|I_{l-b}\right|\·R_{l-\mathrm{\φ}b}\·\cos ({\mathrm{\θ}}_{I-l-b}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})+\left|I_{l-c}\right|\·R_{l-\mathrm{\φ}c}\·\cos ({\mathrm{\θ}}_{I-l-c}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})\}\end{array}---\left(19\right)$

$\∂P_{loss-tr}/\∂\left|I_{n-\mathrm{\φ}}\right|\≅2\·K_{tr-n}\·\left|R_{tr-\mathrm{\φ}}\right|\·\left|I_{tr-\mathrm{\φ}}\right|\·\cos ({\mathrm{\θ}}_{I-tr-\mathrm{\φ}}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})---\left(20\right)$

$P_{loss-l}=\mathrm{Re}\left({\mathrm{\ΔV}}_l^T{I}_l^{*}\right)=\mathrm{Re}({\left(Z_l{I}_l\right)}^T\·I_l^{*})=\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(21\right)$

$P_{loss-tr}=\underset{\mathrm{\φ}\∈{\mathrm{\Φ}}_{tr}}{\Σ}{P}_{loss-tr}^{\mathrm{\φ}}=\underset{\mathrm{\φ}\∈{\mathrm{\Φ}}_{tr}}{\Σ}{\left|I_{tr}^{\mathrm{\φ}}\right|}^2{R}_{tr}^{\mathrm{\φ}}---\left(22\right)$

$P_{\mathrm{loss}-\mathrm{net}}=\underset{l\∈L}{\mathrm{\Σ}}{P}_{\mathrm{loss}-l}+\underset{\mathrm{tr}\∈X}{\mathrm{\Σ}}{P}_{\mathrm{loss}-\mathrm{tr}}---\left(23\right)$

${\mathrm{\λ}}_{n-\mathrm{\φ}}=\frac{{\mathrm{dP}}_{loss-net}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}=\underset{l\∈L}{\Σ}\left(\frac{{\mathrm{dP}}_{loss-l}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}\right)+\underset{tr\∈X}{\Σ}\left(\frac{{\mathrm{dP}}_{loss-tr}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}\right)---\left(24\right)$

${\mathrm{\ΔP}}_{loss-l}=\mathrm{Re}({\left(I_l+{\mathrm{\ΔI}}_l\right)}^T\·Z_l^T\·{\left(I_l+{\mathrm{\ΔI}}_l\right)}^{*})-\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(25\right)$

Wherein

D _n-φit is the φ phase load at network node n;

λ _n-φit is the φ phase loss sensitivity at network node n;

with flow to the circuit of node n and the set of transformer;

P _loss-land P _loss-trthe piecewise smooth loss function of load on circuit and transformer;

R and Z is line resistance and impedance respectively;

Re (), gets the real part of complex variable;

φ represents phase, and φ ∈ { a, b, c};

V and subscript represent: the node voltage of certain phase;

I and subscript represent: the electric current of certain phase circuit or transformer;

θ and subscript represent: the phase angle of curtage;

K and subscript represent: be a constant parameter relevant with transformer voltage ratio.

The large-scale distribution network optimal load flow computational methods of the discrete and continuous decision variable of consideration of the present invention, comprise the Mathematical Modeling set up and relate to complicated three-phase imbalance power distribution network, the contents such as the decomposition that complicated optimal load flow calculates and the simplification process that three-phase imbalance distribution network loss calculates, complicated optimum problem can be decomposed into MILP primal problem and non-linear feasible subproblem, adopt the calculative strategy of mutual iteration decision-making optimizing and system safety to be retrained to organically combine, optimal load flow is nested into decision process, utilize loss sensitivity to simplify process simultaneously, the quick calculating of extensive asymmetric optimal load flow can be realized.Be applicable to the three-phase unbalanced load flow calculating of power distribution network, ring network structure, bi-directional current, the Real-time Decision of discrete and continuous decision variable and optimal load flow, have scientific and reasonable, adaptable, the advantages such as computing is accurate, speed is fast.

Accompanying drawing explanation

Fig. 1 is active distribution network optimal load flow demonstration example;

Fig. 2 is the large-scale distribution network optimal load flow computational methods FB(flow block) considering discrete and continuous decision variable.

Embodiment

The invention will be further described to utilize accompanying drawing and example below.

Example shown in Fig. 1 is typical active distribution network structure, can verify the validity of the large-scale distribution network optimal load flow computational methods of the discrete and continuous decision variable of consideration of the present invention.Example is 21 node active distribution network test macros, and the distributed generation unit comprised and the total number of energy-storage units are 8, and its type, configuration parameter are as shown in table 1:

Table 1 distributed power source and energy-storage units configuration

Note: in table, the Parametric Representation of photovoltaic exports peak power

With reference to Fig. 2, the flow process of the large-scale distribution network optimal load flow computational methods of the discrete and continuous decision variable of consideration of the present invention is: start; Initialization three-phase imbalance power distribution network data; Solve MILP formula (1), formula (3), formula (4); Calculate linear sensitivity parameter; Solve linearisation subproblem formula (12)-Shi (16); Produce the new constraint equation (17) of primal problem; Judge whether convergence; Whether meet security constraint; Terminate.

The large-scale distribution network optimal load flow computational methods of the discrete and continuous decision variable of consideration of the present invention, it comprises following content:

1) Mathematical Modeling relating to complicated three-phase imbalance power distribution network is set up

With minimum operating cost for target, foundation comprises: three-phase imbalance power distribution network, distributed rotary generator, distributed wind-power generator machine, photo-voltaic power supply, extensive energy storage, electric automobile energy storage, intelligent building, micro-grid system element, and consider the voltage of demand response, electrical network and the Mathematical Modeling of frequency adjustment and operation assistant service, discrete decision variable, continuously decision variable, discrete decision variable and the relation continuously between decision variable and decision-making time scope is comprised in model

Target function:

Minimizef(u _t,v _t)(1)

Constraints:

H _t(x _t,u _t,w _t)＝0(2)

J _t﹒u _t≥b(3)

K _t﹒v _t≥c(4)

L _t﹒w _t≥d(5)

G(x _t)≥0(6)

Wherein t ∈ T, and discrete decision variable and continuously decision variable have a lot of application, wherein load tap changer position, belong to discrete decision variable u _t; Unit Combination, belongs to discrete decision variable; Load switch, belongs to discrete decision variable; The unit dispatch of the distributed generation system of meritorious and reactive power, belongs to continuous decision variable v _t; Load side demand response, belongs to discrete decision variable; Home energy source management system, belongs to continuously and discrete decision variable; The microgrid energy and assistant service are additional continuous decision variable w _t, other is expressed as

Minimize: minimum value function;

F: objective cost function can be nonlinear cost curve;

X _t: the state vector of node voltage;

U _t: decision variable vector continuously;

V _t: discrete decision variable vector;

T ∈ T: the time interval t in period T;

W _t: additional continuous decision variable vector, as the idle of inverter control or Capacitor banks;

H _t(): the three-phase unbalanced load flow equation in the t of interval;

J _t: linear matrix, and formula (3) is continuity decision variable u _tupper and lower limit;

K _t: linear matrix, and formula (4) is discreteness decision variable v _tupper and lower limit;

L _t: linear matrix, and formula (5) is additional decision variable w _tupper and lower limit;

G (): the nonlinear function of power distribution system secure constraint;

B, c, d are security constraint threshold value;

2) decomposition of complicated optimal load flow calculating

When formula (2) is as constraints a part of, formula (1) solves difficulty, and adopt Benders method, the complicated optimum problem of upper joint is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce,

(i) primal problem

Target function is formula (1), and constraints is formula (3), formula (4), because objective cost function f can carry out linearisation, and constraint equation (3), formula (4) are all linear, then primal problem is solved as MILP method by formula (1), formula (3) and formula (4), and the optimal solution solved is expressed as

(ii) feasible subproblem

Primal problem optimal solution when iterations is 0, crosses the border if there is state variable, then generate new constraints and be included in the statement of primal problem, then the new optimal solution of primal problem solve, then again forward feasible subproblem to and solve, the iteration occurred between primal problem and feasible subproblem continues to carry out, until no longer detect that in feasible subproblem state variable is crossed the border, feasible subproblem is expressed as

Target function:

Minimizef’＝1 ^T﹒s(7)

Constraints:

H _t(x _t,u _t,w _t)＝0(8)

$u_t={\hat{u}}_t^i---\left(9\right)$

L _t﹒w _t≥d(10)

G(x _t)+s≥0(11)

Because constraint equation (6) and formula (9) are all nonlinear, adopt solution by iterative method, its process is: first, setting w _tinitial value then, three-phase unbalanced load flow equation is solved must be done well x _tinitial value finally, exist carry out linearisation around,

Target function:

Minimizef’＝1 ^T﹒s(12)

Constraints:

$L_t\·(w_t^0+{\mathrm{\Δw}}_t)\≥d---\left(13\right)$

$u_t={\hat{u}}_t^i---\left(14\right)$

$w_t=w_t^0+{\mathrm{\Δw}}_t---\left(15\right)$

$G\left(x_t^0\right)+A\·{\mathrm{\Δw}}_t+s\≥0---\left(16\right)$

Wherein for partial differential operational factor, s is decision variable vector, and the element of matrix A is illustrate control variables w _tconstraints G (), the i.e. Jacobian matrix of G (x), by using uneven flow equation H _tnumerical computations is carried out in ()=0;

Optimization problem formula (12)-Shi (16) be one with decision variable Δ w _tlinear programming problem, simplex method can be adopted to solve, upgrade decision variable perform iterative solution, until the change f of target function is in predefined critical value, in iterative process, make objective cost function value s ^*>0 and the Lagrange's multiplier of constraint equation (14) is λ ^*, the new constraints of adding in primal problem is:

$S^{*}+{\left({\mathrm{\λ}}^{*}\right)}^T\·(u_t^i-u)\≥0---\left(17\right)$

The object of new constraints forces primal problem accept its decision-making to such an extent as to help elimination variable that identifies in feasible subproblem to cross the border;

3) the simplification process of three-phase imbalance distribution network loss calculating

In formula (16), the element of matrix A contains constraints, and node voltage and bypass flow are to the Sensitirity va1ue of node injecting power, and for three-phase imbalance power distribution system network, the derivation of analytic expression can become very difficult; In order to reduce the complexity of calculating, using approximate loss sensitivity analytic expression (18), considering two hypothesis: (1) this phase electrical network upstream branch and the impact of load on this phase loss large; (2) distribution possesses enough reactive power supports, the minor variations of load can not cause large voltage deviation, namely voltage is constant, these two hypothesis meet the requirement of power distribution network actual motion, after applying two hypothesis, loss sensitivity amount of calculation will simplify greatly, and for a given network node n in φ phase, loss sensitivity can approximate representation be:

$\∂P_{loss}/\∂D_{n-\mathrm{\φ}}\≅\frac{1}{\left|V_{n-\mathrm{\φ}}\right|}\{\underset{l\∈{\hat{L}}_n}{\Σ}(\∂P_{loss-l}/\∂|I_{n-\mathrm{\φ}}\left|\right)+\underset{tr\∈{\hat{X}}_n}{\Σ}(\∂P_{loss-tr}/\∂|I_{n-\mathrm{\φ}}\left|\right)\}---\left(18\right)$

Wherein

$\begin{array}{c}\∂P_{loss-l}/\∂\left|I_{n-\mathrm{\φ}}\right|\≅2\·K_{l-n}\·\left\{\right|I_{l-a}|\·R_{l-\mathrm{\φ}a}\·\cos ({\mathrm{\θ}}_{I-l-a}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})+\\ \left|I_{l-b}\right|\·R_{l-\mathrm{\φ}b}\·\cos ({\mathrm{\θ}}_{I-l-b}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})+\left|I_{l-c}\right|\·R_{l-\mathrm{\φ}c}\·\cos ({\mathrm{\θ}}_{I-l-c}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})\}\end{array}---\left(19\right)$

$\∂P_{loss-tr}/\∂\left|I_{n-\mathrm{\φ}}\right|\≅2\·K_{tr-n}\·\left|R_{tr-\mathrm{\φ}}\right|\·\left|I_{tr-\mathrm{\φ}}\right|\·\cos ({\mathrm{\θ}}_{I-tr-\mathrm{\φ}}-{\mathrm{\θ}}_{I-n-\mathrm{\φ}})---\left(20\right)$

$P_{loss-l}=\mathrm{Re}\left({\mathrm{\ΔV}}_l^T{I}_l^{*}\right)=\mathrm{Re}({\left(Z_l{I}_l\right)}^T\·I_l^{*})=\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(21\right)$

$P_{loss-tr}=\underset{\mathrm{\φ}\∈{\mathrm{\Φ}}_{tr}}{\Σ}{P}_{loss-tr}^{\mathrm{\φ}}=\underset{\mathrm{\φ}\∈{\mathrm{\Φ}}_{tr}}{\Σ}{\left|I_{tr}^{\mathrm{\φ}}\right|}^2{R}_{tr}^{\mathrm{\φ}}---\left(22\right)$

$P_{loss-net}=\underset{l\∈L}{\Σ}{P}_{loss-l}+\underset{tr\∈X}{\Σ}{P}_{loss-tr}---\left(23\right)$

${\mathrm{\λ}}_{n-\mathrm{\φ}}=\frac{{\mathrm{dP}}_{loss-net}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}=\underset{l\∈L}{\Σ}\left(\frac{{\mathrm{dP}}_{loss-l}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}\right)+\underset{tr\∈X}{\Σ}\left(\frac{{\mathrm{dP}}_{loss-tr}}{d{\left|D_{n-\mathrm{\φ}}\right|}^{+}}\right)---\left(24\right)$

${\mathrm{\ΔP}}_{loss-l}=\mathrm{Re}({\left(I_l+{\mathrm{\ΔI}}_l\right)}^T\·Z_l^T\·{\left(I_l+{\mathrm{\ΔI}}_l\right)}^{*})-\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(25\right)$

Wherein

D _n-φit is the φ phase load at network node n;

λ _n-φit is the φ phase loss sensitivity at network node n;

with flow to the circuit of node n and the set of transformer;

P _loss-land P _loss-trthe piecewise smooth loss function of load on circuit and transformer;

R, inputs other variable;

Re (), gets the real part of complex variable;

φ represents phase, and φ ∈ { a, b, c};

V and subscript represent: the node voltage of certain phase;

I and subscript represent: the electric current of certain phase circuit or transformer;

θ and subscript represent: the phase angle of curtage;

K and subscript represent: be a constant parameter relevant with transformer voltage ratio.

According to formula (1) ~ formula (6) in conjunction with embodiment, the large-scale distribution network optimal load flow computational methods of the discrete and continuous decision variable of consideration of the present invention, comprise following content:

1) Mathematical Modeling relating to Complicated Distribution Network is set up

Target function: formula (1) can be expressed as:

$\min imizef={\∫}_0^T\[(\underset{i=1}{\overset{N}{\Σ}}{P}_{PV-i}\left(t\right)+\underset{i=1}{\overset{N}{\Σ}}{P}_{E-i}\left(t\right))-\frac{R}{V_{A1}^2}{(\underset{i=1}{\overset{N}{\Σ}}{P}_{PV-i}\left(t\right)+\underset{i=1}{\overset{N}{\Σ}}{P}_{E-i}\left(t\right))}^2\]dt---\left(26\right)$

Constraints: can be expressed as by formula (2) ~ formula (6):

$\left\{\begin{array}{c}{P}_{PV-i}\left(t\right)+P_{E-i}\left(t\right)-P_{L-i}\left(t\right)-P_i\left(t\right)=0,P_i\left(t\right)=V_i\underset{j=1}{\overset{N}{\&Sigma;}}{Y}_{ij}{V}_j\cos ({\mathrm{\&delta;}}_i-{\mathrm{\&delta;}}_j-{\mathrm{\&theta;}}_{ij})\\ Q_{PV-i}\left(t\right)+Q_{E-i}\left(t\right)-Q_{L-i}\left(t\right)-Q_i\left(t\right)=0,Q_i\left(t\right)=V_i\underset{j=1}{\overset{N}{\&Sigma;}}{Y}_{ij}{V}_j\sin ({\mathrm{\&delta;}}_i-{\mathrm{\&delta;}}_j-{\mathrm{\&theta;}}_{ij})\\ n_{i,t}=\left\{\begin{array}{cc}{n}_{i,t-1}+\mathrm{\&Delta;}n(V_i-V_{ref}),& V_i>V_{ref}\\ n_{i,t-1}-\mathrm{\&Delta;}n(V_i-V_{ref}),& V_i<V_{ref}\end{array}\right.\\ E_i\left(t\right)=E_i(t-1)+R_{E-i}\left(t\right)\mathrm{\&Delta;}T\\ R_{E-i}\left(t\right)=\left\{\begin{array}{c}{P}_{E-i}\left(t\right)\&CenterDot;{\mathrm{\&eta;}}_{ch},P_{E-i}<0\\ P_{E-i}\left(t\right)/{\mathrm{\&eta;}}_{dis},P_{E-i}>0\end{array}\right.\end{array}\right.---\left(27\right)$

n _min≤n _i,t≤n _max(28)

${\underset{\&OverBar;}{P}}_{E.rated-i}\&le;P_{E-i}\left(t\right)\&le;{\stackrel{\&OverBar;}{P}}_{E.rated-i}---\left(29\right)$

$P_{E-i}^2+Q_{E-i}^2\&le;{\left(U_{E-i}{I}_{PCS-i}^{\max }\right)}^2,0\&le;E_i\left(t\right)\&le;E_{i.max}---\left(30\right)$

V _i.min≤V _i(t)≤V _i.max(31)

P in formula _pV-iand Q _pV-iactive power and the reactive power at photovoltaic generating system node i place, i=1 ..., N, N are interstitial contents, N=21 in this example; P _e-iand Q _e-ienergy storage device in the active power of i-th node and reactive power; P _l-iand Q _l-iload in the active power of i-th node and reactive power; P _iand Q _iinjection active power and the reactive power of i-th node; R is the resistance that bus i place connects; V _i, V _jrepresent the voltage at node i, j place; δ _i, δ _jit is the phase angle of node i, j voltage; θ _ijnode i, admittance Y between j _ijphase angle; V _refbe on-load tap-changing transformer reference voltage, generally get 1.0p.u.; n _i,tit is node i place t period on-load transformer tap changer no-load voltage ratio; Δ n, n _minand n _maxthe rate of change of on-load transformer tap changer no-load voltage ratio respectively, no-load voltage ratio minimum value and no-load voltage ratio maximum; E _it () is the energy that node i place energy-storage travelling wave tube stores; E _i.maxit is the maximum of energy-storage travelling wave tube stored energy; R _e-it () is the Conversion of Energy speed of node i place energy-storage system t period; η _chand η _disbe respectively energy-storage system charging and discharging efficiency; P _e-i, Q _e-imutual the gaining merit and reactive power of node i place energy-storage system and electrical network respectively; p _e.rated-i, it is the bound of node i place energy-storage travelling wave tube power output; U _e-ifor node i place energy-storage system AC voltage effective value; for the higher limit that the energy-storage system discharge and recharge of node i place allows; V _i.min, V _i.maxbe respectively the minimum and maximum security constraint value of node i place voltage.Example to simplify the analysis, this example threephase load according to symmetrical treatment, computational process indifference.

2) decomposition of complicated optimal load flow calculating

When three-phase unbalanced load flow formula (2) is as constraints a part of, formula (1) solves difficulty, and adopt Benders method, the complicated optimum problem of upper joint is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce.

(i) primal problem

Target function is such as formula shown in (1), and constraints is such as formula shown in (3), formula (4).Because objective cost function f can carry out linearisation, and constraint equation (3) and formula (4) are all linear, then primal problem, formula (1), formula (3) and formula (4) can be used as MILP, namely MILP method solves, and the optimal solution solved is expressed as by simulation analysis, trying to achieve optimal value is 137.3940, u this moment _a6=0.997p.u., u _a10=1.001p.u., u _a19=1.003p.u., and this optimal solution is convergence.

(ii) feasible subproblem

Primal problem optimal solution when iterations is 0, crosses the border if there is state variable, then generate new constraints and be included in the statement of primal problem, then the new optimal solution of primal problem solve, such as, in network shown in Fig. 1, when subproblem is crossed the border, intermediate solution now comprises: network loss value is 27.4kW; And the voltage at bus subbus place is 1.052p.u., occur crossing the border, the voltage at bus A6 place is 1.049p.u., and the voltage of bus A17 is 1.036p.u. etc.And then forward feasible subproblem to and solve, the iteration occurred between primal problem and feasible subproblem continues to carry out, until no longer detect that in feasible subproblem state variable is crossed the border.The target function of feasible subproblem is such as formula shown in (7), and constraints is such as formula shown in (8) ~ formula (11).Because constraint equation (8) ~ formula (11) is all nonlinear, adopt solution by iterative method, its process is: first, setup control w _tinitial value then, three-phase unbalanced load flow equation is solved must do well finally, exist carry out linearisation around, obtain target function such as formula shown in (12), constraints is such as formula shown in (13) ~ formula (16).Wherein the element of matrix A is illustrate control variables w _tconstraints G (), the i.e. Jacobian matrix of G (x), by using uneven flow equation H _tnumerical computations is carried out in ()=0.

Optimization problem formula (12) ~ formula (16) be one with decision variable Δ w _tlinear programming problem, simplex method can be adopted to solve, upgrade decision variable perform iterative solution, until the change f of target function is in predefined critical value, in iterative process, make objective cost function value S ^*the > 0 and Lagrange's multiplier of constraint equation (16) is λ ^*, add new constraints in primal problem to such as formula shown in (17).The object of new constraints forces primal problem accept its decision-making to such an extent as to elimination variable that identifies in feasible subproblem can be helped to cross the border.

3) the simplification process of three-phase imbalance distribution network loss calculating

In formula (14), the element of matrix A contains constraints, and node voltage and bypass flow are to the Sensitirity va1ue of node injecting power, and for three-phase imbalance power distribution system network, the derivation of analytic expression can become very difficult; In order to reduce the complexity of calculating, use approximate loss sensitivity analytic expression (18).

As can be seen from the flow process of Fig. 2, solution iteration had both needed the iteration between primal problem and feasible subproblem, also needed the iteration of feasible subproblem self.Active distribution network according to Fig. 1, by calculating, can show that the network loss before optimization is 25.6kW, and the network loss after optimizing is 7.1kW, by optimizing the contrast of front and back network loss value, we can find, through optimizing, network loss value obviously reduces, and Utilities Electric Co. is by each component parameters of cooperation control, reduce cost, achieve energy-conservation.

The present invention relates to asymmetrical three-phase power distribution network optimal load flow computation model and solution strategies, it can be used for the planning of solution one class distribution system and Operation Decision problem.By adopting engineering approximation, sensitivity parameter matrix being revised, achieves the Efficient Solution of feasible subproblem.

Design conditions in the embodiment of the present invention, legend, table etc. are only for the present invention is further illustrated; and it is non exhaustive; do not form the restriction to claims; the enlightenment that those skilled in the art obtain according to the embodiment of the present invention; other equivalent in fact substituting, all in scope just can be expected without creative work.

Claims (1)

1. consider large-scale distribution network optimal load flow computational methods for discrete and continuous decision variable, it is characterized in that, it comprises following content:

1) Mathematical Modeling relating to complicated three-phase imbalance power distribution network is set up

With minimum operating cost for target, foundation comprises: three-phase imbalance power distribution network, distributed rotary generator, distributed wind-power generator machine, photo-voltaic power supply, extensive energy storage, electric automobile energy storage, intelligent building, micro-grid system element, and consider the voltage of demand response, electrical network and the Mathematical Modeling of frequency adjustment and operation assistant service, discrete decision variable, continuously decision variable, discrete decision variable and the relation continuously between decision variable and decision-making time scope is comprised in model

Target function:

Minimizef(u _t,v _t)(1)

Constraints:

H _t(x _t,u _t,w _t)＝0(2)

J _t﹒u _t≥b(3)

K _t﹒v _t≥c(4)

L _t﹒w _t≥d(5)

G(x _t)≥0(6)

Wherein t ∈ T, and discrete decision variable and continuously decision variable have a lot of application, wherein load tap changer position, belong to discrete decision variable u _t; Unit Combination, belongs to discrete decision variable; Load switch, belongs to discrete decision variable; The unit dispatch of the distributed generation system of meritorious and reactive power, belongs to continuous decision variable v _t; Load side demand response, belongs to discrete decision variable; Home energy source management system, belongs to continuously and discrete decision variable; The microgrid energy and assistant service, be additional continuous decision variable, other is expressed as

Minimize: minimum value function;

F: objective cost function can be nonlinear cost curve;

X _t: the state vector of node voltage;

U _t: decision variable vector continuously;

V _t: discrete decision variable vector;

T ∈ T: the time interval t in period T;

W _t: additional continuous decision variable vector, as the idle of inverter control or Capacitor banks;

H _t(): the three-phase unbalanced load flow equation in the t of interval;

J _t: linear matrix, and formula (3) is continuity decision variable u _tupper and lower limit;

K _t: linear matrix, and formula (4) is discreteness decision variable v _tupper and lower limit;

L _t: linear matrix, and formula (5) is additional decision variable w _tupper and lower limit;

G (): the nonlinear function of power distribution system secure constraint.

2) decomposition of complicated optimal load flow calculating

When formula (2) is as constraints a part of, formula (1) solves difficulty, and adopt Benders method, the complicated optimum problem of upper joint is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce,

(i) primal problem

Target function is formula (1), and constraints is formula (3), formula (4), because objective cost function f can carry out linearisation, and constraint equation (3), formula (4) are all linear, then primal problem is solved as MILP method by formula (1), formula (3) and formula (4), and the optimal solution solved is expressed as

(ii) feasible subproblem

Primal problem optimal solution when iterations is 0, crosses the border if there is state variable, then generate new constraints and be included in the statement of primal problem, then the new optimal solution of primal problem solve, then again forward feasible subproblem to and solve, the iteration occurred between primal problem and feasible subproblem continues to carry out, until no longer detect that in feasible subproblem state variable is crossed the border, feasible subproblem is expressed as

Target function:

Minimizef’＝1 ^T﹒s(7)

Constraints:

H _t(x _t,u _t,w _t)＝0(8)

$u_t={\hat{u}}_t^i---\left(9\right)$

L _t﹒w _t≥d(10)

G(x _t)+s≥0(11)

Because constraint equation (6) and formula (9) are all nonlinear, adopt solution by iterative method, its process is: first, setting w _tinitial value then, three-phase unbalanced load flow equation is solved must be done well x _tinitial value finally, exist carry out linearisation around,

Target function:

Minimizef’＝1 ^T﹒s(12)

Constraints:

$L_t\&CenterDot;(w_t^0+{\mathrm{\&Delta;w}}_t)\&GreaterEqual;d---\left(13\right)$

$u_t={\hat{u}}_t^i---\left(14\right)$

$w_t=w_t^0+{\mathrm{\&Delta;w}}_t---\left(15\right)$

$G\left(x_t^0\right)+A\&CenterDot;{\mathrm{\&Delta;w}}_t+s\&GreaterEqual;0---\left(16\right)$

Wherein for partial differential operational factor, s is decision variable vector, and the element of matrix A is illustrate control variables w _tconstraints G (), the i.e. Jacobian matrix of G (x), by using uneven flow equation H _tnumerical computations is carried out in ()=0;

Optimization problem formula (12)-Shi (16) be one with decision variable Δ w _tlinear programming problem, simplex method can be adopted to solve, upgrade decision variable perform iterative solution, until the change f of target function is in predefined critical value, in iterative process, make objective cost function value s ^*>0 and the Lagrange's multiplier of constraint equation (14) is λ ^*, the new constraints of adding in primal problem is:

$S^{*}+{\left({\mathrm{\&lambda;}}^{*}\right)}^T\&CenterDot;(u_t^i-u)\&GreaterEqual;0---\left(17\right)$

The object of new constraints forces primal problem accept its decision-making to such an extent as to help elimination variable that identifies in feasible subproblem to cross the border;

3) the simplification process of three-phase imbalance distribution network loss calculating

In formula (16), the element of matrix A contains constraints, and node voltage and bypass flow are to the Sensitirity va1ue of node injecting power, and for three-phase imbalance power distribution system network, the derivation of analytic expression can become very difficult; In order to reduce the complexity of calculating, using approximate loss sensitivity analytic expression, considering two hypothesis: (1) this phase electrical network upstream branch and the impact of load on this phase loss large; (2) distribution possesses enough reactive power supports, the minor variations of load can not cause large voltage deviation, namely voltage is constant, these two hypothesis meet the requirement of power distribution network actual motion, after applying two hypothesis, loss sensitivity amount of calculation will simplify greatly, and for a given network node n in φ phase, loss sensitivity can approximate representation be:

$\&part;P_{loss}/\&part;D_{n-\mathrm{\&phi;}}\&cong;\frac{1}{\left|V_{n-\mathrm{\&phi;}}\right|}\left\{\underset{l\&Element;{\hat{L}}_n}{\&Sigma;}\left(\&part;P_{loss-l}/\&part;\left|I_{n-\mathrm{\&phi;}}\right|\right)+\underset{tr\&Element;{\hat{X}}_n}{\&Sigma;}\left(\&part;P_{loss-tr}/\&part;\left|I_{n-\mathrm{\&phi;}}\right|\right)\right\}---\left(18\right)$

Wherein

$\begin{array}{c}\&part;P_{loss-l}/\&part;\left|I_{n-\mathrm{\&phi;}}\right|\&cong;2\&CenterDot;K_{l-n}\&CenterDot;\left\{\right|I_{l-a}|\&CenterDot;R_{l-\mathrm{\&phi;}a}\&CenterDot;\cos \left({\mathrm{\&theta;}}_{I-l-a}-{\mathrm{\&theta;}}_{I-n-\mathrm{\&phi;}}\right)+\\ \left|I_{l-b}\right|\&CenterDot;R_{l-\mathrm{\&phi;}b}\&CenterDot;\cos \left({\mathrm{\&theta;}}_{I-l-b}-{\mathrm{\&theta;}}_{I-n-\mathrm{\&phi;}}\right)+\left|I_{l-c}\right|\&CenterDot;R_{l-\mathrm{\&phi;}c}\&CenterDot;cos\left({\mathrm{\&theta;}}_{I-l-c}-{\mathrm{\&theta;}}_{I-n-\mathrm{\&phi;}}\right)\}\end{array}---\left(19\right)$

$P_{loss-l}=\mathrm{Re}\left({{\mathrm{\&Delta;V}}_l}^T{I}_l^{*}\right)=\mathrm{Re}({\left(Z_l{I}_l\right)}^T\&CenterDot;I_l^{*})=\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(21\right)$

$P_{loss-tr}=\underset{\mathrm{\&phi;}\&Element;{\mathrm{\&Phi;}}_{tr}}{\&Sigma;}{P}_{loss-tr}^{\mathrm{\&phi;}}=\underset{\mathrm{\&phi;}\&Element;{\mathrm{\&Phi;}}_{tr}}{\&Sigma;}|I_{tr}^{\mathrm{\&phi;}}{|}^2{R}_{tr}^{\mathrm{\&phi;}}---\left(22\right)$

$P_{loss-net}=\underset{l\&Element;L}{\&Sigma;}{P}_{loss-l}+\underset{tr\&Element;X}{\&Sigma;}{P}_{loss-tr}---\left(23\right)$

${\mathrm{\&lambda;}}_{n-\mathrm{\&phi;}}=\frac{{\mathrm{dP}}_{loss-net}}{d|D_{n-\mathrm{\&phi;}}{|}^{+}}=\underset{l\&Element;L}{\&Sigma;}\left(\frac{{\mathrm{dP}}_{loss-l}}{d|D_{n-\mathrm{\&phi;}}{|}^{+}}\right)+\underset{tr\&Element;X}{\&Sigma;}\left(\frac{{\mathrm{dP}}_{loss-tr}}{d|D_{n-\mathrm{\&phi;}}{|}^{+}}\right)---\left(24\right)$

${\mathrm{\&Delta;P}}_{loss-l}=\mathrm{Re}({\left(I_l+{\mathrm{\&Delta;I}}_l\right)}^T\&CenterDot;Z_l^T\&CenterDot;{\left(I_l+{\mathrm{\&Delta;I}}_l\right)}^{*})-\mathrm{Re}\left(I_l^T{Z}_l^T{I}_l^{*}\right)---\left(25\right)$

Wherein

D _n-φit is the φ phase load at network node n;

λ _n-φit is the φ phase loss sensitivity at network node n;

with flow to the circuit of node n and the set of transformer;

P _loss-land P _loss-trthe piecewise smooth loss function of load on circuit and transformer;

R and Z represents resistance and impedance respectively;

Re (), gets the real part of complex variable;

φ represents phase, and φ ∈ { a, b, c};

V and subscript represent: the node voltage of certain phase;

I and subscript represent: the electric current of certain phase circuit or transformer;

θ and subscript represent: the phase angle of curtage;

K and subscript represent: be a constant parameter relevant with transformer voltage ratio.