CN104993525A - Active power distribution network coordination optimization control method considering ZIP loads - Google Patents

Abstract

The invention relates to an active power distribution network coordination optimization control method considering ZIP loads. The method comprises the following steps of inputting control variables in a network topology, determining object functions and constraining conditions, building an active power distribution network coordination optimization model considering the ZIP loads; and acquiring the optimal solution of the active power distribution network optimization model according to an optimization algorithm based on function transformation and generalized inverse. The method which provides a theory base for optimization control achieves simple operations. The coordination optimization control efficiency is improved. The power grid running quality and stability are further improved.

Description

A kind of active distribution network coordinating and optimizing control method taking into account ZIP load

Technical field

The present invention relates to a kind of optimal control method, be specifically related to a kind of active distribution network coordinating and optimizing control method taking into account ZIP load.

Background technology

For conventional electrical distribution net, because inside lacks meritorious power supply, when therefore studying its running optimizatin, can not active optimization be carried out, and only need carry out idle work optimization.Along with the continuous growth of electricity needs and the shortage of conventional energy resource, all kinds of distributed power source (DG, Distributed Generation) start to access power distribution network on a large scale, the thing followed is a large amount of energy storage and the extensive use of novel controllable device in power distribution network.The passive unidirectional supplying electricity and power distribution net of tradition just progressively changes to many power supplys bidirectional power supply power distribution network; in the face of distribution network voltage level, capacity of short circuit, relaying protection strategy, power supply reliability and the quality of power supply such as to highlight day by day at the series of problems; active distribution network (ADN, Active Distribution Network) as effective solution is arisen at the historic moment.In ADN, the power distribution network active optimization that exists for of meritorious power supply such as a large amount of DG and energy storage etc. provides hardware foundation.Consider meritorious in power distribution network and reactive power flow close-coupled, active optimization and idle work optimization separate carry out this traditional power transmission network Operation Mode Optimization directly apply to power distribution network will inevitably be unreasonable, therefore be necessary to include the adjustable meritorious and idle amount in ADN in control variables simultaneously, carry out active reactive coordination optimization.

Current about in ADN active reactive coordination optimization, load, according to constant power load model process, does not consider its Load static voltage characteristic.But strictly speaking, load is among constantly variation in optimizing process, and particularly evident for this characteristic of power distribution network, namely the application improves for this defect in current research always.

Summary of the invention

In order to make up the defect that prior art exists, the invention provides a kind of active distribution network coordinating and optimizing control method taking into account ZIP load, being applicable to the optimizing process considering Load static voltage characteristic.

The technical solution adopted in the present invention is:

Take into account an active distribution network coordinating and optimizing control method for ZIP load, described method comprises,

Control variables in input network topology, determines target function and constraints, builds the active distribution network Coordination and Optimization Model taking into account ZIP load; According to based on functional transformation and generalized inverse optimized algorithm, obtain described active distribution network Optimized model optimal solution.

Preferably, described control variables comprises: distributed power source is meritorious, idle exerts oneself, and Static Var Compensator is idle exerts oneself and switched shunts switching group number.

Preferably, describedly determine that target function comprises: be minimised as target function with active distribution network active power loss, its expression formula is:

$\min P_{loss}=\underset{i=1}{\overset{n}{\Σ}}{V}_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})---\left(1\right)$

In formula (1), P _lossfor active power loss, V _iand V _jfor the voltage magnitude of node i and j, G _ijand B _ijfor real part and the imaginary part of transadmittance between node i and j; θ _ijfor the phase difference of voltage of node i and j; N is nodes.

Preferably, described constraints comprises: equality constraint and inequality constraints; Wherein,

The expression formula of described equality constraint is;

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{Gi}+P_{DGi}-P_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})=0,(i=1,...,n)\\ {\mathrm{\ΔQ}}_i=Q_{Gi}+Q_{DGi}+Q_{SVCi}-Q_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})=0,(i=1,...,n)\end{array}\right.---\left(2\right)$

In formula (2), Δ P _ifor the active power amount of unbalance of node i; Δ Q _ifor the reactive power amount of unbalance of node i; P _giand Q _gibe respectively the meritorious and reactive power that power transmission network is injected to power distribution network by root node i, non-root node place value is taken as 0; P _dGiand Q _dGibe respectively the meritorious and idle of node i place DG to exert oneself; Q _sVCibe respectively idle the exerting oneself of node i place SVC; P _liand Q _libe respectively the meritorious of node i and load or burden without work;

Described inequality constraints, comprise node voltage amplitude the constraint ,/idle units limits of gaining merit of distributed power source, the idle units limits of Static Var Compensator, the switching group number constraint of switched shunts, its expression formula is:

$\left\{\begin{array}{c}\underset{\‾}{V_i}\≤V_i\≤\stackrel{\‾}{V_i},\left(i=1,...,n\right)\\ \underset{\‾}{P_{DGi}}\≤P_{DGi}\≤\stackrel{\‾}{P_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{DGi}}\≤Q_{DGi}\≤\stackrel{\‾}{Q_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{SVCi}}\≤Q_{SVCi}\≤\stackrel{\‾}{Q_{SVCi}},\left(i=1,...,n\right)\\ \underset{\‾}{{\mathrm{KC}}_j}\≤{\mathrm{KC}}_j\≤\stackrel{\‾}{{\mathrm{KC}}_j},\left(i=1,...,n_C\right)\end{array}\right.---\left(3\right)$

In formula (3), with v _i be respectively the bound of node i voltage magnitude; with p _dGi be respectively the meritorious bound of exerting oneself of node i place DG; with q _dGi be respectively the idle bound of exerting oneself of node i place DG; with q _sVCi be respectively the idle bound of exerting oneself of node i place SVC; KC _jfor jth is connected to the switching group number of switched shunts node, with kC _j be respectively group number bound, n _cfor being connected to the nodes of switched shunts.

Further, the meritorious of ZIP load and load or burden without work P is connected in node i _liand Q _liexpression formula be:

$\left\{\begin{array}{c}{P}_{Li}=P_{LNi}\[a_{pi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{pi}\frac{V_i}{V_{Ni}}+c_{pi}\]\\ Q_{Li}=Q_{LNi}\[a_{qi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{qi}\frac{V_i}{V_{Ni}}+c_{qi}\]\end{array}\right.---\left(4\right)$

In formula (4), P _liand Q _libe respectively the actual burden with power and the load or burden without work that are connected to ZIP load in node i; P _lNiand Q _lNibe respectively the burden with power of node i under rated voltage and load or burden without work; V _iand V _nibe respectively the virtual voltage amplitude of node i and the rated voltage of ZIP load; a _pi, b _pi, c _pi, a _qi, b _qiand c _qibe all the proportionality coefficient of ZIP load, and meet $\left\{\begin{array}{c}{a}_{pi}+b_{pi}+c_{pi}=1\\ a_{qi}+b_{qi}+c_{qi}=1\end{array}\right..$

Preferably, the optimal solution of the described active distribution network Optimized model of described acquisition comprises the steps:

A) according to the actual requirements, contraction factor ds initial value, shrinkage ratio ns, convergence threshold d are set _minwith iterations N=0; Determine to optimize opening flag position flag;

If b) flag ≠ 0, then continue; If flag=0, then go to step and e) carry out constrained load flow calculating;

C) judge whether contraction factor ds is greater than convergence threshold d _minif be greater than, then preserve each variable currency, iterations N=0; Otherwise, go to step (l);

If d) convergence number of times reaches 5 times continuously, then first increase convergence factor ds=ds × ns, then shrink active power loss; Otherwise, directly shrink the active power loss of current contraction factor ds value;

E) substituted into by current voltage value in formula (4), export the actual negative charge values of ZIP load access node, all the other node loads are constant;

F) obtain each node power amount of unbalance, judge whether maximum power amount of unbalance DPQ is greater than convergence precision ite_jd, if be greater than, then continues; Otherwise, return step c);

G) iterations N=N+1, if N > 30, then goes to step j); Otherwise continue;

H) generate Expanded Jacobian matrix, by following formula, the meritorious of ZIP load and load or burden without work P are connected to node i _liand Q _lirevise;

$\left\{\begin{array}{c}\frac{{\mathrm{dP}}_{Li}}{{\mathrm{dV}}_i}=P_{LNi}(2a_{pi}\frac{V_i}{V_{Ni}^2}+\frac{b_{pi}}{V_{Ni}})\\ \frac{{\mathrm{dQ}}_{Li}}{{\mathrm{dV}}_i}=Q_{LNi}(2a_{qi}\frac{V_i}{V_{Ni}^2}+\frac{b_{qi}}{V_{Ni}})\end{array}\right.---\left(5\right)$

I) solve and obtain correction, each variable is revised, returns step e);

If j) flag ≠ 0, then each variable restore is last convergence result, and reduces convergence factor ds=ds/ns, returns step c); If flag=0, then continue;

K) constrained load flow is not restrained, and cannot be optimized, and optimizes and terminates;

L) export optimal solution, optimize and terminate.

Compared with immediate prior art, beneficial effect of the present invention is:

(1) by propose in power transmission network based on functional transformation and generalized inverse optimized algorithm be applied to ADN meritorious/idle coordination optimization, inequality constraints can be processed easily; And this algorithm is based on Newton-Raphson approach, simple to operate, be easy to programming realization.

(2) in optimizing process, ZIP load model is adopted to load, to take into account the impact of Load static voltage characteristic on coherent element in load value and expansion Jacobian matrix, make optimum results more accurately reliable.

Accompanying drawing explanation

Fig. 1 is a kind of active distribution network coordinating and optimizing control method flow chart taking into account ZIP load of the present invention.

Embodiment

Below in conjunction with accompanying drawing 1, the present invention is further described.

As shown in Figure 1, a kind of active distribution network coordinating and optimizing control method taking into account ZIP load, described method comprises,

Control variables in input network topology, determines target function and constraints, builds the active distribution network Coordination and Optimization Model taking into account ZIP load; According to based on functional transformation and generalized inverse optimized algorithm, obtain described active distribution network Optimized model optimal solution.

Described control variables comprises: distributed power source is meritorious, idle exerts oneself, and Static Var Compensator is idle exerts oneself and switched shunts switching group number.

Describedly determine that target function comprises: be minimised as target function with active distribution network active power loss, its expression formula is:

$\min P_{loss}=\underset{i=1}{\overset{n}{\Σ}}{V}_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})---\left(1\right)$

In formula (1), P _lossfor active power loss, V _iand V _jfor the voltage magnitude of two node i chosen arbitrarily and j, G _ijand B _ijfor real part and the imaginary part of transadmittance between node i and j; θ _ijfor the phase difference of voltage of node i and j; N is nodes.

Described constraints comprises: equality constraint and inequality constraints; Wherein,

The expression formula of described equality constraint is;

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{Gi}+P_{DGi}-P_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})=0,(i=1,...,n)\\ {\mathrm{\ΔQ}}_i=Q_{Gi}+Q_{DGi}+Q_{SVCi}-Q_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})=0,(i=1,...,n)\end{array}\right.---\left(2\right)$

In formula (2), Δ P _ifor the active power amount of unbalance of node i; Δ Q _ifor the reactive power amount of unbalance of node i; P _giand Q _gibe respectively the meritorious and reactive power that power transmission network is injected to power distribution network by root node i, non-root node place value is taken as 0; P _dGiand Q _dGibe respectively the meritorious and idle of node i place DG to exert oneself; Q _sVCibe respectively idle the exerting oneself of node i place SVC; P _liand Q _libe respectively the meritorious of node i and load or burden without work;

Described inequality constraints, comprise node voltage amplitude the constraint ,/idle units limits of gaining merit of distributed power source, the idle units limits of Static Var Compensator, the switching group number constraint of switched shunts, its expression formula is:

$\left\{\begin{array}{c}\underset{\‾}{V_i}\≤V_i\≤\stackrel{\‾}{V_i},\left(i=1,...,n\right)\\ \underset{\‾}{P_{DGi}}\≤P_{DGi}\≤\stackrel{\‾}{P_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{DGi}}\≤Q_{DGi}\≤\stackrel{\‾}{Q_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{SVCi}}\≤Q_{SVCi}\≤\stackrel{\‾}{Q_{SVCi}},\left(i=1,...,n\right)\\ \underset{\‾}{{\mathrm{KC}}_j}\≤{\mathrm{KC}}_j\≤\stackrel{\‾}{{\mathrm{KC}}_j},\left(i=1,...,n_C\right)\end{array}\right.---\left(3\right)$

In formula (3), with v _i be respectively the bound of node i voltage magnitude; with p _dGi be respectively the meritorious bound of exerting oneself of node i place DG; with q _dGi be respectively the idle bound of exerting oneself of node i place DG; with q _sVCi be respectively the idle bound of exerting oneself of node i place SVC; KC _jfor jth is connected to the switching group number of switched shunts node, with kC _j be respectively group number bound, n _cfor being connected to the nodes of switched shunts.

The meritorious of ZIP load and load or burden without work P is connected in node i _liand Q _liexpression formula be:

$\left\{\begin{array}{c}{P}_{Li}=P_{LNi}\[a_{pi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{pi}\frac{V_i}{V_{Ni}}+c_{pi}\]\\ Q_{Li}=Q_{LNi}\[a_{qi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{qi}\frac{V_i}{V_{Ni}}+c_{qi}\]\end{array}\right.---\left(4\right)$

In formula (4), P _liand Q _libe respectively the actual burden with power and the load or burden without work that are connected to ZIP load in node i; P _lNiand Q _lNibe respectively the burden with power of node i under rated voltage and load or burden without work; V _iand V _nibe respectively the virtual voltage amplitude of node i and the rated voltage of ZIP load; a _pi, b _pi, c _pi, a _qi, b _qiand c _qibe all the proportionality coefficient of ZIP load, and meet $\left\{\begin{array}{c}{a}_{pi}+b_{pi}+c_{pi}=1\\ a_{qi}+b_{qi}+c_{qi}=1\end{array}\right..$

The optimal solution of the described active distribution network Optimized model of described acquisition comprises the steps:

A) according to the actual requirements, contraction factor ds initial value, shrinkage ratio ns, convergence threshold d are set _minwith iterations N=0; Determine to optimize opening flag position flag; Make active distribution network operate in optimum state according to target setting, ensure the economical operation of system;

If b) flag ≠ 0, then continue; If flag=0, then go to step and e) carry out constrained load flow calculating;

C) judge whether contraction factor ds is greater than convergence threshold d _minif be greater than, then preserve each variable currency, iterations N=0; Otherwise, go to step (l);

If d) convergence number of times reaches 5 times continuously, then first increase convergence factor ds=ds × ns, then shrink active power loss; Otherwise, directly shrink the active power loss of current contraction factor ds value;

E) substituted into by current voltage value in formula (4), export the actual negative charge values of ZIP load access node, all the other node loads are constant;

F) obtain each node power amount of unbalance, judge whether maximum power amount of unbalance DPQ is greater than convergence precision ite_jd, if be greater than, then continues; Otherwise, return step c);

G) iterations N=N+1, if N > 30, then goes to step j); Otherwise continue;

H) generate Expanded Jacobian matrix, by following formula, the meritorious of ZIP load and load or burden without work P are connected to node i _liand Q _lirevise;

$\left\{\begin{array}{c}\frac{{\mathrm{dP}}_{Li}}{{\mathrm{dV}}_i}=P_{LNi}(2a_{pi}\frac{V_i}{V_{Ni}^2}+\frac{b_{pi}}{V_{Ni}})\\ \frac{{\mathrm{dQ}}_{Li}}{{\mathrm{dV}}_i}=Q_{LNi}(2a_{qi}\frac{V_i}{V_{Ni}^2}+\frac{b_{qi}}{V_{Ni}})\end{array}\right.---\left(5\right)$

I) solve and obtain correction, each variable is revised, returns step e);

If j) flag ≠ 0, then each variable restore is last convergence result, and reduces convergence factor ds=ds/ns, returns step c); If flag=0, then continue;

K) constrained load flow is not restrained, and cannot be optimized, and optimizes and terminates;

L) export optimal solution, optimize and terminate.

Finally should be noted that: above embodiment is only in order to illustrate the technical scheme of the application but not the restriction to its protection range; although with reference to above-described embodiment to present application has been detailed description; those of ordinary skill in the field are to be understood that: those skilled in the art still can carry out all changes, amendment or equivalent replacement to the embodiment of application after reading the application; these change, amendment or equivalent to replace, and it is all within it applies for the right that awaits the reply.

Claims (6)

1. take into account an active distribution network coordinating and optimizing control method for ZIP load, it is characterized in that, described method comprises,

Control variables in input network topology, determines target function and constraints, builds the active distribution network Coordination and Optimization Model taking into account ZIP load; According to based on functional transformation and generalized inverse optimized algorithm, obtain described active distribution network Optimized model optimal solution.

2. the method for claim 1, is characterized in that, described control variables comprises: distributed power source is meritorious, idle exerts oneself, and Static Var Compensator is idle exerts oneself and switched shunts switching group number.

3. the method for claim 1, is characterized in that, describedly determines that target function comprises: be minimised as target function with active distribution network active power loss, its expression formula is:

$\min P_{loss}=\underset{i=1}{\overset{n}{\Σ}}{V}_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})---\left(1\right)$

In formula (1), P _lossfor active power loss, V _iand V _jfor the voltage magnitude of node i and j, G _ijand B _ijfor real part and the imaginary part of transadmittance between node i and j; θ _ijfor the phase difference of voltage of node i and j; N is nodes.

4. method according to claim 1, is characterized in that, described constraints comprises: equality constraint and inequality constraints; Wherein,

The expression formula of described equality constraint is;

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{Gi}+P_{DGi}-P_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{cos\θ}}_{ij}+B_{ij}{\mathrm{sin\θ}}_{ij})=0,(i=1,...,n)\\ {\mathrm{\ΔQ}}_i=Q_{Gi}+Q_{DGi}+Q_{SVCi}-Q_{Li}-V_i\underset{j=1}{\overset{n}{\Σ}}{V}_j(G_{ij}{\mathrm{sin\θ}}_{ij}-B_{ij}{\mathrm{cos\θ}}_{ij})=0,(i=1,...,n)\end{array}\right.---\left(2\right)$

In formula (2), Δ P _ifor the active power amount of unbalance of node i; Δ Q _ifor the reactive power amount of unbalance of node i; P _giand Q _gibe respectively the meritorious and reactive power that power transmission network is injected to power distribution network by root node i, non-root node place value is taken as 0; P _dGiand Q _dGibe respectively the meritorious and idle of node i place DG to exert oneself; Q _sVCibe respectively idle the exerting oneself of node i place SVC; P _liand Q _libe respectively the meritorious of node i and load or burden without work;

Described inequality constraints, comprise node voltage amplitude the constraint ,/idle units limits of gaining merit of distributed power source, the idle units limits of Static Var Compensator, the switching group number constraint of switched shunts, its expression formula is:

$\left\{\begin{array}{c}\underset{\‾}{V_i}\≤V_i\≤\stackrel{\‾}{V_i},\left(i=1,...,n\right)\\ \underset{\‾}{P_{DGi}}\≤P_{DGi}\≤\stackrel{\‾}{P_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{DGi}}\≤Q_{DGi}\≤\stackrel{\‾}{Q_{DGi}},\left(i=1,...,n\right)\\ \underset{\‾}{Q_{SVCi}}\≤Q_{SVCi}\≤\stackrel{\‾}{Q_{SVCi}},\left(i=1,...,n\right)\\ \underset{\‾}{{\mathrm{KC}}_j}\≤{\mathrm{KC}}_j\≤\stackrel{\‾}{{\mathrm{KC}}_j},\left(i=1,...,n_C\right)\end{array}\right.---\left(3\right)$

In formula (3), with v _i be respectively the bound of node i voltage magnitude; with p _dGi be respectively the meritorious bound of exerting oneself of node i place DG; with q _dGi be respectively the idle bound of exerting oneself of node i place DG; with q _sVCi be respectively the idle bound of exerting oneself of node i place SVC; KC _jfor jth is connected to the switching group number of switched shunts node, with kC _j be respectively group number bound, n _cfor being connected to the nodes of switched shunts.

5. method as claimed in claim 4, is characterized in that, is connected to the meritorious of ZIP load and load or burden without work P in node i _liand Q _liexpression formula be:

$\left\{\begin{array}{c}{P}_{Li}=P_{LNi}\[a_{pi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{pi}\frac{V_i}{V_{Ni}}+c_{pi}\]\\ Q_{Li}=Q_{LNi}\[a_{qi}{\left(\frac{V_i}{V_{Ni}}\right)}^2+b_{qi}\frac{V_i}{V_{Ni}}+c_{qi}\]\end{array}\right.---\left(4\right)$

In formula (4), P _liand Q _libe respectively the actual burden with power and the load or burden without work that are connected to ZIP load in node i; P _lNiand Q _lNibe respectively the burden with power of node i under rated voltage and load or burden without work; V _iand V _nibe respectively the virtual voltage amplitude of node i and the rated voltage of ZIP load; a _pi, b _pi, c _pi, a _qi, b _qiand c _qibe all the proportionality coefficient of ZIP load, and meet $\left\{\begin{array}{c}{a}_{pi}+b_{pi}+c_{pi}=1\\ a_{qi}+b_{qi}+c_{qi}=1\end{array}\right..$

6. method according to claim 1, is characterized in that, the optimal solution of the described active distribution network Optimized model of described acquisition comprises the steps:

A) according to the actual requirements, contraction factor ds initial value, shrinkage ratio ns, convergence threshold d are set _minwith iterations N=0; Determine to optimize opening flag position flag;

If b) flag ≠ 0, then continue; If flag=0, then go to step and e) carry out constrained load flow calculating;

C) judge whether contraction factor ds is greater than convergence threshold d _minif be greater than, then preserve each variable currency, iterations N=0; Otherwise, go to step (l);

If d) convergence number of times reaches 5 times continuously, then first increase convergence factor ds=ds × ns, then shrink active power loss; Otherwise, directly shrink the active power loss of current contraction factor ds value;

E) substituted into by current voltage value in formula (4), export the actual negative charge values of ZIP load access node, all the other node loads are constant;

F) obtain each node power amount of unbalance, judge whether maximum power amount of unbalance DPQ is greater than convergence precision ite_jd, if be greater than, then continues; Otherwise, return step c);

G) iterations N=N+1, if N > 30, then goes to step j); Otherwise continue;

H) generate Expanded Jacobian matrix, by following formula, the meritorious of ZIP load and load or burden without work P are connected to node i _liand Q _lirevise;

$\left\{\begin{array}{c}\frac{{\mathrm{dP}}_{Li}}{{\mathrm{dV}}_i}=P_{LNi}(2a_{pi}\frac{V_i}{V_{Ni}^2}+\frac{b_{pi}}{V_{Ni}})\\ \frac{{\mathrm{dQ}}_{Li}}{{\mathrm{dV}}_i}=Q_{LNi}(2a_{qi}\frac{V_i}{V_{Ni}^2}+\frac{b_{qi}}{V_{Ni}})\end{array}\right.---\left(5\right)$

I) solve and obtain correction, each variable is revised, returns step e);

If j) flag ≠ 0, then each variable restore is last convergence result, and reduces convergence factor ds=ds/ns, returns step c); If flag=0, then continue;

K) constrained load flow is not restrained, and cannot be optimized, and optimizes and terminates;

L) export optimal solution, optimize and terminate.