CN104794541A - Simulated-annealing and conic optimization based power distribution network operation optimization method - Google Patents

Abstract

Disclosed is a simulated-annealing and conic optimization based power distribution network operation optimization method. The method includes: inputting basic parameters and information according to a selected power distribution system; according to the basic parameters and the information, establishing a mathematical model of power distribution network operation optimization problem concurrent with an interconnection switch and an intelligent soft switch and setting rotating cone constraints according to the network structure and scale to form a conic optimization model of the power distribution network operation optimization model concurrent with the interconnection switch and the intelligent soft switch; according to the basic principle of a simulated annealing method and network topological constraints, randomly generating a feasible switch-state combination, and performing calculation on the cone optimization model of the power distribution network operation optimization problem concurrent with the interconnection switch and the intelligent soft switch by adopting a cone optimization tool; outputting a calculation result and analyzing the optimal calculation condition by the aid of the simulated annealing principle. States of the interconnection switch in the power distribution system and transmission power of an SNOP (soft normally open point) are considered from the economic perspective of operation of the power distribution system, and the optimum switch combination of the interconnection switch in the power distribution network and the optimum transmission power of the SNOP are determined.

Description

A kind of power distribution network running optimizatin method optimized based on simulated annealing and cone

Technical field

The present invention relates to a kind of power distribution network running optimizatin algorithm.Particularly relate to a kind of power distribution network running optimizatin method optimized based on simulated annealing and cone.

Background technology

Along with the widespread use of the technology such as distributed power generation, energy storage, Demand Side Response, electric automobile, power distribution network changed into current collection can the various rolls such as production, transmission, storage and distribution in the novel energy system of one, be also the core that following intelligent power grid technology develops.Intelligent distribution network will be optimized and control the operation of distributed power source, energy storage, Demand Side Response resource, electric automobile, reactive-load compensation equipment, intelligent switch etc. on one's own initiative, the planning of conventional electrical distribution net, design and the method for operation will be changed up hill and dale, form new operational mode.Network reconfiguration, as the Main Means changing conventional electrical distribution network operation mode, under the condition ensureing the radial operation of power distribution network, realizes the conversion of network topology structure by interconnection switch (Tie Switch, TS) grid switching operation.But network reconfiguration mathematically belongs to large-scale nonlinear integer optimization problem, numerous research is devoted to improve the computing velocity and optimizing ability that solve, and but still the effective method of neither one solves this np hard problem.In actual application, also relate to the problems such as grid switching operation, Alloy White Iron impact, switch motion loss, the counting yield of network reconfiguration problem is difficult to the demand meeting real-time optimization.

Along with the development of Power Electronic Technique, various power electronic equipment is widely used in distribution system.Intelligence Sofe Switch (SoftNormally Open Point, SNOP) be the power electronic equipment being installed on traditional interconnection switch place, it can accurately control its institute connect both sides feeder line gain merit and reactive power.The introducing of SNOP revolutionizes the power supply mode of conventional electrical distribution net closed loop design, open loop operation, and the hybrid network of formation combines radial and advantage that is looped network shape power supply mode, brings many benefits to the operation of power distribution network.Consider that the investment operating cost of SNOP is higher, the interconnection switch that present stage SNOP can not be all in replacement system completely, thus cause the running optimizatin problem of distribution system to need overall thinking interconnection switch and SNOP and the situation of depositing.

From mathematics in essence, this problem belongs to mixed integer nonlinear optimization problem, and is also difficult to find one method for solving fast and effectively at present.Solving of this problem is proposed and developed multiple optimization method at present, has mainly contained following three aspects: 1) traditional mathematics optimisation technique, comprising analytical method, successive elimination method etc.; 2) heuritic approach, comprising Sensitivity Analysis Method, expert system etc.; 3) randomized optimization process, comprising genetic algorithm, particle cluster algorithm etc.

Although said method or technology have certain Application effect, but also all there is obvious deficiency, as although traditional mathematics optimization method can carry out global optimizing in theory, inevitably there is " dimension calamity " problem when practical application, often present explosion type computing time and increase sharply; Heuristic value requires a polynomial time in time complexity, and computing velocity is fast, but the optimum solution obtained or the optimality lacked in mathematical meaning or just locally optimal solution; Although the last solution that randomized optimization process is searched and initial solution have nothing to do, the power distribution network for different scales needs to reset its controling parameters, population quantity, iterations etc., thus ensures to find globally optimal solution with larger probability.Heuristic and random device is applicable to solve integer programming problem more, but for interconnection switch and SNOP and the power distribution network running optimizatin problem of depositing, mathematics is mixed integer nonlinear optimization problem in essence, so traditional mathematics optimization method, heuritic approach are for solving in this kind of problem, speed or precision is many can not meet the demands simultaneously.

Summary of the invention

Technical matters to be solved by this invention is, there is provided a kind of raising on computing time and precision to solve ability to mixed integer nonlinear optimization problem, the power distribution network running optimizatin method optimized based on simulated annealing and cone of prioritization scheme can be sought quickly and accurately.

The technical solution adopted in the present invention is: a kind of power distribution network running optimizatin method optimized based on simulated annealing and cone, comprises the steps:

1) according to selected distribution system input basic parameter and information, the initial value of system component parameter, load level, network topology annexation, intelligent Sofe Switch on-position and capacity, reference voltage and reference power is comprised;

2) according to step 1) basic parameter and information set up interconnection switch and intelligent Sofe Switch and the mathematical model of the power distribution network running optimizatin problem of depositing, comprise: choosing root node is balance node, the topological constraints of difference setting network, system load flow retrain, operation voltage level retrains, branch current retrains, the operation of intelligent Sofe Switch retrains and the power distribution network operation of capacity-constrained retrains;

3) rotating cone constraint is set according to network structure and scale

2R _iR _j≥S _ij ²+T _ij ²,i＝1,…,n,j∈N(i)

In formula, n is system node number; The set of the adjacent node that N (i) is node i; R _i, S _ij, T _ijbe respectively node voltage amplitude U _i, U _jand phase angle theta _ijfunction, $\left\{\begin{array}{c}{R}_i=U_i^2/\sqrt{2},i=1,...,n\\ S_{\mathrm{ij}}=U_i{U}_j\cos {\mathrm{\θ}}_{\mathrm{ij}},j\∈N\left(i\right)\\ T_{\mathrm{ij}}=U_i{U}_j\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.;$

Step 2) and step 3) together form interconnection switch and intelligent Sofe Switch and the cone Optimized model of the power distribution network running optimizatin problem of depositing;

4) retrain according to the ultimate principle of simulated annealing and network topology, the Switch State Combination in Power Systems that random generation is feasible, adopts cone optimization tool to described interconnection switch and intelligent Sofe Switch and the cone Optimized model of the power distribution network running optimizatin problem of depositing solves;

5) export step 4) solving result, comprise on off state, intelligent Sofe Switch optimal transmission performance number, network power flow solutions and target function value, utilize simulated annealing principle analysis optimum solution situation, namely the optimality of separating at Current Temperatures and all temperature is analyzed, if not optimum solution, then return step 4), if optimum solution, then terminate, and Output rusults.

Step 2) described in network topology constraint representation be:

$\underset{l=1}{\overset{L}{\mathrm{\Σ}}}[A_l(1-a_l)+(1-A_l)a_l]\≤W_{\max }$

In formula, L is system branch number; A _lfor the on off state of initial network branch road l, a _lfor the on off state of branch road l after network reconfiguration, being 0 when switch disconnects, is 1 when switch closes; W _maxfor the maximal value of network reconfiguration branch road.

Step 2) described in intelligent Sofe Switch run constraint and be expressed as with capacity-constrained:

P _SNOPi+P _SNOPj＝0

$\sqrt{{P_{\mathrm{SNOPi}}}^2+{Q_{\mathrm{SNOPi}}}^2}\≤S_{\mathrm{SNOPi}}$

$\sqrt{{P_{\mathrm{SNOPj}}}^2+{Q_{\mathrm{SNOPj}}}^2}\≤S_{\mathrm{SNOPj}}$

In formula, P _sNOPi, Q _sNOPi, P _sNOPj, Q _sNOPjbe respectively active power and the reactive power of intelligent Sofe Switch connected node i and connected node j current transformer, and regulation is with the positive dirction of power direction for power delivery injecting intelligent Sofe Switch; S _sNOPi, S _sNOPjbe respectively the access capacity of intelligent Sofe Switch connected node i and connected node j current transformer.

A kind of power distribution network running optimizatin method optimized based on simulated annealing and cone of the present invention, the economy point run from distribution system considers the state of interconnection switch and the through-put power of SNOP distribution system, establishing to minimize whole network active loss is objective function, retrain with network topology, system load flow retrains, operation voltage level retrains, branch current retrains, SNOP runs constraint, SNOP capacity-constrained etc. is the power distribution network optimal operation model of constraint condition, the optimized switch combination of interconnection switch in power distribution network and the optimal transmission power of SNOP is determined by simulated annealing and cone optimized algorithm.When solving, be first optimize PROBLEM DECOMPOSITION to be asked the integer optimization problem of on off state and optimize the continuous optimization problems of SNOP through-put power.Integer optimization problem adopts simulated annealing to solve, and simulated annealing gives search procedure a kind of jumping characteristic according to probability, efficiently avoid search procedure and is absorbed in locally optimal solution, be beneficial to searching globally optimal solution.Continuous optimization problems adopts cone optimized algorithm to solve, and is replaced the linearization of problem of implementation, then introduce nonlinear rotating cone constraint condition by variable, this problem is converted into a cone optimization problem.

In counting yield, simulated annealing of the present invention is solving in integer optimization problem and interconnection switch state, and program realizes simple, has good convergence property, and as much as possible can find approximate optimal solution.Solving in continuous optimization problems, cone optimized algorithm can carry out Unify legislation to Load flow calculation problem and SNOP through-put power optimization problem, solve while realizing two problems, avoid loaded down with trivial details iteration and a large amount of tests, computing velocity has and promotes significantly; On the other hand, because bore the geometry of the grace had and special processing mode, solved optimality can be ensured, apply it in SNOP running optimizatin problem, the allocation plan after optimization can be obtained.

Accompanying drawing explanation

Fig. 1 is IEEE 33 node example structural drawing;

Fig. 2 is a kind of power distribution network running optimizatin method flow diagram optimized based on simulated annealing and cone of the present invention;

Fig. 3 is the structural drawing after IEEE 33 node example carries out network reconfiguration and SNOP optimization;

Fig. 4 is node voltage comparison diagram before and after IEEE 33 node example is optimized.

Embodiment

Below in conjunction with embodiment and accompanying drawing, a kind of power distribution network running optimizatin method optimized based on simulated annealing and cone of the present invention is described in detail.

A kind of power distribution network running optimizatin method optimized based on simulated annealing and cone of the present invention, in the research of distribution system running optimizatin, cone optimized algorithm can adopt the software simulating such as MOSEK, LINGO, CPLEX.The present invention adopts MOSEK software, with IEEE 33 bus test system shown in Fig. 1 for embodiment.

A kind of power distribution network running optimizatin method optimized based on simulated annealing and cone of the present invention, as shown in Figure 2, comprises the steps:

1) according to selected distribution system input basic parameter and information, the initial values such as system component parameter, load level, network topology annexation, SNOP on-position and capacity, reference voltage, reference power are comprised.

For the present embodiment, first input the resistance value of circuit element in IEEE 33 node system, the active power of load cell, reactive power, network topology annexation; Then set two SNOP and access power distribution network, replace corresponding interconnection switch; The reference voltage finally arranging system is 12.66kV, reference power is 100MVA.

2) according to step 1) basic parameter and information set up interconnection switch and SNOP and the mathematical model of the power distribution network running optimizatin problem of depositing, comprise: choosing root node is balance node, the present embodiment is the node 1 chosen in Fig. 1 is balance node, the power distribution network operation that setting network topological constraints respectively, system load flow retrain, operation voltage level retrains, branch current retrains, SNOP runs constraint and capacity-constrained retrains, and the mathematical model of described optimization problem is set up based on boring optimized algorithm.Specific as follows:

(1) first setting minimizes the whole network active loss is objective function, can be expressed as:

$\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i---\left(1\right)$

In formula, n is system node number; P _ifor the active power sum that node i is injected, in available formula (3), the equality constraint of effective power flow represents;

(2) the network topology constraint representation described in is:

$\underset{l=1}{\overset{L}{\mathrm{\Σ}}}[A_l(1-a_l)+(1-A_l)a_l]\≤W_{\max }---\left(2\right)$

(3) the system load flow constraint representation described in is:

$\begin{array}{c}{P}_i=\sqrt{2}{G}_{\mathrm{ii}}{R}_i+\underset{j\∈N\left(i\right)}{\mathrm{\Σ}}(G_{\mathrm{ij}}{S}_{\mathrm{ij}}+B_{\mathrm{ij}}{T}_{\mathrm{ij}})\\ =P_{\mathrm{SNOPi}}-P_{\mathrm{LDi}},i=1,...,n\\ Q_i=-\sqrt{2}{B}_{\mathrm{ii}}{R}_i-\underset{j\∈N\left(i\right)}{\mathrm{\Σ}}(B_{\mathrm{ij}}{S}_{\mathrm{ij}}-G_{\mathrm{ij}}{T}_{\mathrm{ij}})\\ =Q_{\mathrm{SNOPi}}-Q_{\mathrm{LDi}},i=1,...,n\end{array}---\left(3\right)$

(4) the operation voltage level constraint representation described in is:

$\frac{U_{i,\min }^2}{\sqrt{2}}\≤R_i\≤\frac{U_{i,\max }^2}{\sqrt{2}},i=1,...,n---\left(4\right)$

(5) the branch current constraint representation described in is:

$I_{\mathrm{ij}}^2=({G_{\mathrm{ij}}}^2+{B_{\mathrm{ij}}}^2)(\sqrt{2}{R}_i+\sqrt{2}{R}_j-2S_{\mathrm{ij}})\≤I_{\mathrm{ij},\max }^2,---\left(5\right)$

i＝1,…,n,j∈N(i)

(6) SNOP described in runs constraint representation:

P _SNOPi+P _SNOPj＝0 (6)

(7) the SNOP capacity-constrained described in is expressed as:

$\begin{array}{c}\sqrt{{P_{\mathrm{SNOPi}}}^2+{Q_{\mathrm{SNOPi}}}^2}\≤S_{\mathrm{SNOPi}}\\ \sqrt{{P_{\mathrm{SNOPi}}}^2+{Q_{\mathrm{SNOPj}}}^2}\≤S_{\mathrm{SNOPj}}\end{array}---\left(7\right)$

Above-mentioned various in: L is system branch number; A _lfor the on off state of initial network branch road l, a _lfor the on off state of branch road l after network reconfiguration, being 0 when switch disconnects, is 1 when switch closes; W _maxfor the maximal value of network reconfiguration branch road; N is system node number; The set of the adjacent node that N (i) is node i; G _ii, B _ii, G _ij, B _ijbe respectively the self-conductance of node i, from susceptance, transconductance and mutual susceptance; P _ifor the active power sum that node i is injected, P _lDibe respectively the active power that in node i, load injects; Q _ifor the reactive power sum that node i is injected, Q _lDibe respectively the reactive power that in node i, load injects; U _{i, max}and U _{i, min}be respectively the bound of node i voltage magnitude; I _ijand I _{ij, max}be respectively the current amplitude and maximum permissible value thereof that flow through branch road ij; P _sNOPi, Q _sNOPi, P _sNOPj, Q _sNOPjbe respectively SNOP connected node i, the active power of j current transformer and reactive power, and regulation is with the positive dirction of power direction for power delivery injecting SNOP; S _sNOPi, S _sNOPjbe respectively SNOP connected node i, the access capacity of j current transformer; R _i, S _ij, T _ijbe respectively node voltage amplitude U _i, U _jand phase angle theta _ijfunction, $\left\{\begin{array}{c}{R}_i=U_i^2/\sqrt{2},i=1,...,n\\ S_{\mathrm{ij}}=U_i{U}_j\cos {\mathrm{\θ}}_{\mathrm{ij}},j\∈N\left(i\right)\\ T_{\mathrm{ij}}=U_i{U}_j\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right..$

3) rotating cone constraint is set according to network structure and scale:

2R _iR _j≥S _ij ²+T _ij ²,i＝1,…,n,j∈N(i) (8)

In formula, n is system node number; The set of the adjacent node that N (i) is node i.

Above-mentioned steps 2) and step 3) together form interconnection switch and SNOP and the cone Optimized model of the power distribution network running optimizatin problem of depositing.

4) retrain according to the ultimate principle of simulated annealing and network topology, the Switch State Combination in Power Systems that random generation is feasible, adopt cone optimized algorithm, adopt cone optimization tool (MOSEK software) to described interconnection switch and SNOP and the cone Optimized model of the power distribution network running optimizatin problem of depositing solve.

The present invention is based on while cone optimized algorithm achieves SNOP optimal transmission power and trend and solve, not only ensure that the computational accuracy of separating can also reduce computing time effectively.

5) export step 4) solving result, comprise on off state, SNOP optimal transmission performance number, network power flow solutions and target function value, utilize simulated annealing principle analysis optimum solution situation, namely the optimality of separating at Current Temperatures and all temperature is analyzed, if not optimum solution, then return step 4), if optimum solution, then terminate, and Output rusults.

For the present embodiment, choose two SNOP here and access power distribution network, interconnection switch TS1 and TS2 replaced in Fig. 1 analyzes, and Fig. 1 is IEEE 33 node example structural drawing, and the network loss of whole system when not being optimized is 202.67kW.Embodiment to interconnection switch and SNOP and the power distribution network deposited be optimized.

Performing the computer hardware environment optimizing calculating is Intel (R) Xeon (R) CPU E5-1620v2, and dominant frequency is 3.70GHz, inside saves as 32GB; Software environment is Windows 7 operating system.

Prioritization scheme changes system topology by network reconfiguration, as shown in Figure 3.The active power of network reconfiguration and SNOP and reactive power are optimized by prioritization scheme simultaneously, and after optimizing, system losses are 84.76kW, significantly reduce via net loss.On the other hand, network reconfiguration and SNOP running optimizatin can improve the operation voltage level of system to a certain extent, as shown in Figure 4, improve the quality of power supply further, improve power supply reliability.In order to verify the validity of optimized algorithm of the present invention, will the result obtained of embodiment be the present invention is directed to and solve the result that time and additive method obtain and compare.BONMIN is non-linear mixed-integer optimized algorithm bag, and pattern search method is the one of intelligent algorithm, and search for optimum solution by calling Load Flow Calculation Software OPENDSS calculating target function value, concrete data refer to table 1.By comparing, the on off state of three kinds of methods is consistent, and SNOP is meritorious substantially identical with idle work optimization result, different due to implementation method and computational accuracy, final solving result and real optimum solution all can have deviation slightly, but error all in allowed limits.Meanwhile, the method that the present invention proposes is solving on the time compared with additive method, has very large advantage.

Table 1 optimum results of the present invention and other optimization methods obtain Comparative result

Claims (3)

1., based on the power distribution network running optimizatin method that simulated annealing and cone are optimized, it is characterized in that, comprise the steps:

1) according to selected distribution system input basic parameter and information, the initial value of system component parameter, load level, network topology annexation, intelligent Sofe Switch on-position and capacity, reference voltage and reference power is comprised;

2) according to step 1) basic parameter and information set up interconnection switch and intelligent Sofe Switch and the mathematical model of the power distribution network running optimizatin problem of depositing, comprise: choosing root node is balance node, the topological constraints of difference setting network, system load flow retrain, operation voltage level retrains, branch current retrains, the operation of intelligent Sofe Switch retrains and the power distribution network operation of capacity-constrained retrains;

3) rotating cone constraint is set according to network structure and scale

2R _iR _j≥S _ij ²+T _ij ²,i＝1,…,n,j∈N(i)

In formula, n is system node number; The set of the adjacent node that N (i) is node i; R _i, S _ij, T _ijbe respectively node voltage amplitude U _i, U _jand phase angle theta _ijfunction, $\left\{\begin{array}{c}{R}_i=U_i^2/\sqrt{2},i=1,...,n\\ S_{\mathrm{ij}}=U_i{U}_j\cos {\mathrm{\θ}}_{\mathrm{ij}},j\∈N\left(i\right)\\ T_{\mathrm{ij}}=U_i{U}_j\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.;$

Step 2) and step 3) together form interconnection switch and intelligent Sofe Switch and the cone Optimized model of the power distribution network running optimizatin problem of depositing;

4) retrain according to the ultimate principle of simulated annealing and network topology, the Switch State Combination in Power Systems that random generation is feasible, adopts cone optimization tool to described interconnection switch and intelligent Sofe Switch and the cone Optimized model of the power distribution network running optimizatin problem of depositing solves;

5) export step 4) solving result, comprise on off state, intelligent Sofe Switch optimal transmission performance number, network power flow solutions and target function value, utilize simulated annealing principle analysis optimum solution situation, namely the optimality of separating at Current Temperatures and all temperature is analyzed, if not optimum solution, then return step 4), if optimum solution, then terminate, and Output rusults.

2. according to claim 1 a kind of based on simulated annealing and cone optimize power distribution network running optimizatin method, it is characterized in that, step 2) described in network topology constraint representation be:

$\underset{l=1}{\overset{L}{\mathrm{\Σ}}}[A_l(1-a_l)+(1-A_l)a_l]\≤W_{\max }$

In formula, L is system branch number; A _lfor the on off state of initial network branch road l, a _lfor the on off state of branch road l after network reconfiguration, being 0 when switch disconnects, is 1 when switch closes; W _maxfor the maximal value of network reconfiguration branch road.

3. a kind of power distribution network running optimizatin method optimized based on simulated annealing and cone according to claim 1, is characterized in that, step 2) described in intelligent Sofe Switch run constraint and be expressed as with capacity-constrained:

P _SNOPi+P _SNOPj＝0

$\sqrt{{P_{\mathrm{SNOPi}}}^2+{Q_{\mathrm{SNOPi}}}^2}\≤S_{\mathrm{SNOPi}}$

$\sqrt{{P_{\mathrm{SNOPj}}}^2+{Q_{\mathrm{SNOPj}}}^2}\≤S_{\mathrm{SNOPj}}$

In formula, P _sNOPi, Q _sNOPi, P _sNOPj, Q _sNOPjbe respectively active power and the reactive power of intelligent Sofe Switch connected node i and connected node j current transformer, and regulation is with the positive dirction of power direction for power delivery injecting intelligent Sofe Switch; S _sNOPi, S _sNOPjbe respectively the access capacity of intelligent Sofe Switch connected node i and connected node j current transformer.