CN103066593A - Three-phase load flow calculation method of weak looped distribution network comprising multi-type distributed power sources - Google Patents

Abstract

The invention discloses a three-phase load flow calculation method of a weak looped distribution network comprising multi-type distributed power sources. Firstly, the effective three-phase load flow calculation method of a weak looped distribution network is put forward in a distribution sequencing network based on a sequence component calculation method and in combination with characteristics of the weak looped distribution network and a loop analysis of a road. Secondly, detailed formula derivation of iterative computation of distributed generation (DG) of a PQ node type, a PQ (V) node type, an OV node type and a PI node type is conducted and the easy formula is introduced into the load flow calculation method. The three-phase load flow calculation method of the weak looped distribution network comprising the multi-type distributed power sources can effectively process multi-type DG and the weak looped distribution network and is distinct in calculation procedure, simple in programming, and easy to achieve. In addition, the three-phase load flow calculation method of the weak looped distribution network comprising the multi-type distributed power sources retains strong points of rapid calculation and stable convergence of a forward-back substitution method catering to branch circuits. Finally, effectiveness and good convergence of the three-phase load flow calculation method of the weak looped distribution network comprising the multi-type distributed power sources is tested and verified by means of a IEEE (institute of electrical and electronic engineers)-37 generatrix test calculation case, and the three-phase load flow calculation method of the weak looped distribution network comprising the multi-type distributed power sources has good ability of processing the multi-type DG and the looped network.

Description

The weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source

Technical field

The present invention relates to a kind of weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source, belong to power system analysis and computing technique field.

Background technology

Distribution power system load flow calculation is the important content that distribution system is analyzed, and it is the important evidence of the reasonability of distribution system planning and designing and operational mode, reliability and economy being carried out quantitative analysis.On the one hand, power distribution network generally is annular design, the open loop operation, but when power distribution network is reconstructed and optimize analysis, the weak ring power distribution network Three-phase Power Flow when needing to calculate operation with closed ring; On the other hand, along with distributed generation technology develops rapidly, more and more distributed power source (distributed generation, DG) access power distribution networks have produced tremendous influence for network configuration, power loss, voltage distribution and the trend calculating of power distribution network; At first, power distribution network has become multi-power system from traditional single supply system, and the flow direction of trend is by the unidirectional non-directional that become; Secondly, generally only comprise 2 kinds of node types in traditional power distribution network: V θ node (balance node) and PQ node; And along with various distributed power source access power distribution networks, increased new node type: PQ (V) node, PV node and PI node in the system.Therefore, studying the weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source is very important.

Summary of the invention

Goal of the invention: the present invention is directed to the weak Three-phase Power Flow calculating that encircles power distribution network of three-phase imbalance that existing power distribution network Three Phase Power Flow can't be applicable to contain the polymorphic type distributed power source, proposed a kind of weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source.

Technical scheme: a kind of weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source comprises the steps:

A. set up the power flow algorithm of all types of distributed power sources (distributed generation, DG)

1) PQ node type DG

During conventional Load Flow calculated, the meritorious and reactive power of the injection of PQ node was set-point, but this processing mode can not simply be promoted and manages PQ type DG everywhere.Have the load that all PQ type DG simply is processed into system in the weak ring Power Flow Calculation Methods For Distribution Network that contains distributed power source now.But three-phase symmetrical DG encircles a little less than three-phase imbalance in the power distribution network, because three-phase voltage is asymmetric, the three phase power of output is also unequal.And, consider generator characteristic, negative phase-sequence and zero sequence active power can be thought and equal 0.Therefore, for the weak ring distribution system of three-phase imbalance, such processing mode is just reasonable not.Therefore it is considered herein that the constant meritorious and reactive power of PQ type DG output is the meritorious and positive sequence reactive power of the positive sequence of DG node, namely

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ Q_{}{}_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}\end{array}\right.$

In the formula: P _DGAnd Q _DGBe respectively the meritorious and idle output of PQ type DG.

2) PQ (V) node type DG

The processing method of the type DG is similar to PQ type DG, difference is, in the iterative process, need to constantly update DG node positive sequence reactive power according to up-to-date DG node positive sequence voltage iterative value, then obtain the new positive sequence Injection Current of DG node, the beginning next iteration.Its computation model is

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ Q_{}{}_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}=-f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)\end{array}\right.$

Value has following 2 kinds of situations in the formula:

When a. adopting without excitation regulation ability synchronous generator as interface, the reactive power that DG sends is

$Q_{\mathrm{DG}}=f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)=\sqrt{{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="E\; DGq\; U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{DGq}}{U}_{}{}_{1,\mathrm{DG},i}}{X_d}\right)}^2-P_{\mathrm{DG}}^2}-\frac{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2}{X_d}$

In the formula: P _DG, E _DGq, X _d, I _{1, DG, i}Be respectively meritorious output, no-load emf, synchronous reactance, the terminal voltage of DG unit.

B. the blower fan that adopts asynchronous generator is during as interface, and the reactive power that DG absorbs is

$Q_{\mathrm{DG}}=f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)=-\frac{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2}{x_p}+\frac{-{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2+\sqrt{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^4-4P_{\mathrm{DG}}^2{x}^2}}{2x}$

In the formula: P _DG, U _{1, DG, i}Be respectively meritorious output, the set end voltage of DG; X is asynchronous machine stator leakage reactance and rotor leakage reactance sum; x _pBe asynchronous machine excitation reactance and machine end shunt capacitance equivalent reactance.

3) PV node type DG

Consider that there are the asymmetric operation state status in generator characteristic and three-phase symmetrical DG, it is considered herein that it is that DG node positive sequence active power, output constant voltage amplitude are DG node positive sequence voltage amplitude that PV node type DG exports constant active power, but its output reactive power but is unknown.Therefore, the key of problem is exactly to obtain to satisfy the DG node positive sequence reactive power that DG node positive sequence voltage amplitude equates with PV type DG voltage rating.Then have

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ U_{}{}_{1,\mathrm{DG},i}=U_{\mathrm{DG}}\end{array}\right.$

For PV node type DG, can adopt open loop impedance matrix (Dai Weinan equivalent impedance matrix) to process PV type DG node, contain n at one _{DG, PV}In the positive sequence network of the weak ring of the three-phase of individual PV type DG power distribution network, if after each PV type DG Nodes open loop, n occurs _{DG, PV}Individual open loop point then exists

ΔU _1,DG=Z _1,DGΔI _1,DG

In the formula: Δ U _{1, DG}, Δ I _{1, DG}Positive sequence voltage, forward-order current matrix (n for the open loop point calibration _{DG, PV}* 1 rank); Z _{1, DG}Be the Dai Weinan equivalent impedance matrix (n that sees into from the open loop point _{DG, PV}* n _{DG, PV}Rank).

In the positive sequence network for arbitrary weak ring power distribution network, from path matrix T ₁Middle each PV type DG node institute corresponding row vector is extracted forms a new matrix T _{1, DG}, then have

${\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{1,\mathrm{DG}}={\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="DG\; Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">DG</figure-callout>}}{Z}_{}{}_{1,\mathrm{<figure-callout\; id="1"\; label="b\; T"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">b</figure-callout>}}{T}_{}^{}{}_{1,\mathrm{DG}}^T$

Δ U _{1, DG}, Δ I _{1, DG}, Z _{1, DG}Be expressed as

ΔU _1,DG=Δe _1,DG+jΔf _1,DG

ΔI _1,DG=Δc _1,DG+jΔd _1,DG

Z _1,DG=R _1,DG+jX _1,DG

When the k time iteration, the open loop positive sequence voltage of i PV type DG node is

, suppose that open loop point both sides have identical phase angle, then the difference of the rated voltage of the actual positive sequence voltage of i PV type DG node and PV type DG is

$\mathrm{\&Delta;}{\stackrel{.}{U}}_{1,\mathrm{DG},i_k}=({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i})e^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}=\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}$

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i}$

In the formula: U _{DG, i}It is the rated voltage amplitude of i PV type DG; θ _{1, DG, i}For

Phase angle.

After the k time iteration, establish i PV type DG node forward-order current change amount and be , then the change amount of its positive sequence apparent power is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\mathrm{\&Delta;}{\stackrel{.}{I}}_{1,\mathrm{DG},i_k}^{*}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}-\mathrm{j\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})$

Then this PV type DG node positive sequence active power recruitment is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Re}\left(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}+\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}{\mathrm{\&Delta;<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})$

Because PV type DG node positive sequence active power is constant, so , can obtain according to following formula

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}=-\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}\tan {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}$

Because

It is smaller,

Much smaller than

, therefore Δ I is arranged _{1, DG}≈ j Δ d _{1, DG}, and Δ e _{1, DG}=Δ U _{1, DG}Cos θ _{1, DG}≈ Δ U _{1, DG}, then can draw

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,{\mathrm{DG}}_k}=-{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">X</figure-callout>}}_{1,\mathrm{DG}}^{-1}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,{\mathrm{DG}}_k}$

And this PV type DG node positive sequence reactive power increment is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Im}\left(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}-\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})$

Then can draw

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=-\frac{3U_{\mathrm{DG},i}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}}{\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\&ap;-3U_{\mathrm{DG},i}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}$

If U _{DG, i}Be 1.0pu, then

So, have

And during the k+1 time iteration, the positive sequence reactive power of i PV type DG node is

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}={\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_k}+\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}$

Then obtain the new injection forward-order current of DG node, the beginning next iteration.When | Δ U _{1, DG}| when satisfying convergence precision, stop iteration.

4) PI node type DG

Consider similar situation, it is considered herein that it is that DG node positive sequence active power, output constant current magnitude are DG node forward-order current amplitude that PI node type DG exports constant active power.Then have

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; I"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ I_{}{}_{1,\mathrm{DG},i}=I_{\mathrm{DG}}\end{array}\right.$

Corresponding DG output reactive power can be calculated as follows and draw:

$Q_{\mathrm{DG}}=\sqrt{{\left|I_{\mathrm{DG}}\right|}^2({\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">e</figure-callout>}}_{1,\mathrm{DG},i_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2+{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{1,\mathrm{DG},i_k}^2)-{\mathrm{<figure-callout\; id="2"\; label="P\; DG"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}^{}}$

In the formula: P _DGActive power for DG output; | I _DG| be the DG constant current magnitude;

With

Positive sequence voltage real part and the imaginary part of DG node i when being respectively the k time iteration.

Therefore, corresponding DG node positive sequence reactive power is during the k+1 time iteration

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=-Q_{\mathrm{DG}}$

Then obtain the new injection forward-order current of DG node, the beginning next iteration.

For i DG node, the forward-order current that its node injects can calculate with following formula:

${\stackrel{.}{I}}_{1,\mathrm{DG},i}={[({\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}+\mathrm{<figure-callout\; id="1"\; label="j\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">j</figure-callout>}{Q}_{}{}_{1,\mathrm{DG},i})/\left(3{\stackrel{.}{U}}_{1,\mathrm{DG},i}\right)]}^{*}$

In the formula:

Be this DG node positive sequence voltage phasor.

In the trend iterative process, if appearring in PQ (V), PV and PI type DG node, reactive power crosses the border, then convert thereof into PQ type DG node processing, and Q _DGGet the idle upper bound or the lower bound of each node type DG, then recomputate.

B. the weak ring Three-phase Power Flow Calculation Method for Distribution System flow process that contains the polymorphic type distributed power source is as follows

1) determine the tree of weak ring distribution network, give node serial number, the numbering of the root node in the regulation tree is minimum, is made as " 0 ", and all the other nodes are numbered by its distance from root node, and is larger from the node serial number of root node away from more.The numbering that tree props up then is defined as the large person who gets in the node serial number of two ends, adds 1 after the maximum that the numbering of chord is propped up from tree is successively numbered.

2) determine weak ring power distribution network topological structure parameter, comprise nodes, a way, feeder number.Might as well establish the weak ring of three-phase power distribution network has N node, b bar branch road and l independent loop, suppose first node (root node) be power supply and conduct with reference to node, then the isolated node number is n=N-1, separate branches number b=n+l.Wherein, a tree n bar, chord l bar.

3) determine DG access situation in the weak ring of the distributed power generation power distribution network, comprise node type and the corresponding position (node number) of DG access, the total quantity of access DG, all types of DG and network parameters, the separately quantity of all types of DG that are incorporated into the power networks.

4) establishing first node is power supply and as with reference to node, first node three-phase voltage phase moment matrix is U _{Abc, 0}(3 * 1 rank), each node three-phase voltage phase moment matrix is U _{Abc, n}(3n * 1 rank), in weak ring distribution system three sequence networks, three sequence voltage matrixes of the node of can informing against are U _012,0=AU _{Abc, 0}(3 * 1 rank), each node three sequence voltage matrix is U _{012, n}(3n * 1 rank).Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]$ ， $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right]$ 。

5) calculate each sequence network parameter Z _{S, b}Z _{S, b}Be the order impedance Z based on branch road i _{S, bi}The diagonal matrix (n * n rank) that forms, wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models; Three phase of impedance of branch road i are Z _{Abc, bi}, Z is then arranged _{012, bi}=AZ _{Abc, bi}A ^-1, wherein, $Z_{012,\mathrm{bi}}=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="bi"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">bi</figure-callout>}}& 0& 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{1,\mathrm{<figure-callout\; id="0"\; label="bi"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">bi</figure-callout>}}& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{2,\mathrm{bi}}\end{array}\right]$ ， $Z_{\mathrm{abc},\mathrm{bi}}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right]$ 。

6) calculate the path matrix T of each order net _sWith return-Zhi incidence matrices B _sWherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

7) calculate loop order impedance matrix in each order net , with and inverse matrix Y _{S, 1}=(Z _{S, 1}) ^-1Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

8) compose initial value for each node three-phase voltage of weak ring power distribution network

E wherein _n=[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs.

Each phase current that node i is injected when 9) calculating the k time iteration , wherein

Be each phase injecting power of node i,

Each phase node voltage of node i when being the k-1 time iteration, Y _{P, i}Be the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., n; K is the iterations variable.

Each order electric current that node i is injected when 10) calculating the k time iteration

, i=1,2 ..., n.

11) calculate respectively i DG node when the k time iteration for dissimilar DG according to power flow algorithm corresponding in the steps A With , the injection forward-order current of i DG node when then obtaining the k time iteration

, i=1,2 ..., n _DGWherein With

Be respectively active power and the reactive power of i DG node when the k time iteration,

Be the node voltage of i DG node when the k-1 time iteration, n _DGDG number for connecting system.

12) load bus is injected order electric current and DG node and inject the forward-order current stack, each node always injects the order electric current when obtaining the k time iteration

Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

When 13) calculating the k time iteration Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

When 14) calculating the k time iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, be n-dimensional vector; S=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

Node i three-phase voltage phasor when 15) calculating k iteration

, i=1,2 ..., n.

16) judge

With

Whether the difference of amplitude satisfies the convergence precision requirement.If satisfy, then finishing iteration; Otherwise turn step 9).

Beneficial effect: the weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source, at first based on the order component calculation method, in conjunction with the characteristics of weak ring power distribution network and the loop analysis of road, the ring power distribution network improves tidal current computing method propose a kind of effective three-phase imbalance in distribution order net a little less than, takes full advantage of the advantage of order component method when the processing three-phase unbalance system accesses symmetrical DG and PV node; Then the iterative computation model of PQ, PQ (V), PV and PI node type DG carried out the detailed derivation of equation, and can be incorporated into very simply institute and carry in the flow calculation program and realizing.The present invention can efficiently process polymorphic type DG and weak looped network, and its computational process is clear, and programming is simple, easily realizes, has kept before branch road pushing back the advantage fast for the method computational speed, that convergence is stable.At last, test sample calculation analysis and verified validity of the present invention and good convergence by the IEEE-37 bus, and have stronger processing polymorphic type DG and the ability of looped network.

Description of drawings

Fig. 1 is the flow chart of the embodiment of the invention;

Fig. 2 is the weak ring of the three-phase imbalance distribution network system schematic diagram that the IEEE-37 bus contains the polymorphic type distributed power source.

Embodiment

Below in conjunction with specific embodiment, further illustrate the present invention, should understand these embodiment only is used for explanation the present invention and is not used in and limits the scope of the invention, after having read the present invention, those skilled in the art all fall within the application's claims limited range to the modification of the various equivalent form of values of the present invention.

Contain the weak ring power distribution network Three Phase Power Flow of polymorphic type distributed power source, specifically comprise the steps:

1. set up the power flow algorithm of all types of distributed power sources (distributed generation, DG)

(1) PQ node type DG

During conventional Load Flow calculated, the meritorious and reactive power of the injection of PQ node was set-point, but this processing mode can not simply be promoted and manages PQ type DG everywhere.Have the load that all PQ type DG simply is processed into system in the weak ring Power Flow Calculation Methods For Distribution Network that contains distributed power source now.But three-phase symmetrical DG encircles a little less than three-phase imbalance in the power distribution network, because three-phase voltage is asymmetric, the three phase power of output is also unequal.And, consider generator characteristic, negative phase-sequence and zero sequence active power can be thought and equal 0.Therefore, for the weak ring distribution system of three-phase imbalance, such processing mode is just reasonable not.Therefore it is considered herein that the constant meritorious and reactive power of PQ type DG output is the meritorious and positive sequence reactive power of the positive sequence of DG node, namely

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ Q_{}{}_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}\end{array}\right.---\left(1\right)$

In the formula: P _DGAnd Q _DGBe respectively the meritorious and idle output of PQ type DG.

For i PQ type DG node, the forward-order current that node injects can calculate with following formula:

${\stackrel{.}{I}}_{1,\mathrm{DG},i}={[({\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}+\mathrm{<figure-callout\; id="1"\; label="j\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">j</figure-callout>}{Q}_{}{}_{1,\mathrm{DG},i})/\left(3{\stackrel{.}{U}}_{1,\mathrm{DG},i}\right)]}^{*}---\left(2\right)$

In the formula:

Be this DG node positive sequence voltage phasor.

(2) PQ (V) node type DG

The processing method of the type DG is similar to PQ type DG, difference is, in the iterative process, need to constantly update DG node positive sequence reactive power according to up-to-date DG node positive sequence voltage iterative value, then its substitution formula (2) is obtained the new positive sequence Injection Current of DG node, the beginning next iteration.Its computation model is

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i}=-{\mathrm{<figure-callout\; id="1"\; label="P\; DG\; Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{DG}}& \\ Q_{}{}_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}=-f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)\end{array}\right.---\left(3\right)$

Value has following 2 kinds of situations in the formula:

When a. adopting without excitation regulation ability synchronous generator as interface, the reactive power that DG sends is

$Q_{\mathrm{DG}}=f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)=\sqrt{{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="E\; DGq\; U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{DGq}}{U}_{}{}_{1,\mathrm{DG},i}}{X_d}\right)}^2-P_{\mathrm{DG}}^2}-\frac{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2}{X_d}---\left(4\right)$

In the formula: P _DG, E _DGq, X _d, U _{1, DG, i}Be respectively meritorious output, no-load emf, synchronous reactance, the terminal voltage of DG unit.

B. the blower fan that adopts asynchronous generator is during as interface, and the reactive power that DG absorbs is

$Q_{\mathrm{DG}}=f\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}\right)=-\frac{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2}{x_p}+\frac{-{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^2+\sqrt{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i}^4-4P_{\mathrm{DG}}^2{x}^2}}{2x}---\left(5\right)$

In the formula: P _DG, U _{1, DG, i}Be respectively meritorious output, the set end voltage of DG; X is asynchronous machine stator leakage reactance and rotor leakage reactance sum; x _pBe asynchronous machine excitation reactance and machine end shunt capacitance equivalent reactance.

(3) PV node type DG

Consider that there are the asymmetric operation state status in generator characteristic and three-phase symmetrical DG, it is considered herein that it is that DG node positive sequence active power, output constant voltage amplitude are DG node positive sequence voltage amplitude that PV node type DG exports constant active power, but its output reactive power but is unknown.Therefore, the key of problem is exactly to obtain to satisfy the DG node positive sequence reactive power that DG node positive sequence voltage amplitude equates with PV type DG voltage rating.

For PV node type DG, can adopt open loop impedance matrix (Dai Weinan equivalent impedance matrix) to process PV type DG node, contain n at one _{DG, PV}In the positive sequence network of the weak ring of the three-phase of individual PV type DG power distribution network, if after each PV type DG Nodes open loop, n occurs _{DG, PV}Individual open loop point then exists

ΔU _1,DG=Z _1,DGΔI _1,DG (6)

In the formula: Δ U _{1, DG}, Δ I _{1, DG}Positive sequence voltage, forward-order current matrix (n for the open loop point calibration _{DG, PV}* 1 rank); Z _{1, DG}Be the Dai Weinan equivalent impedance matrix (n that sees into from the open loop point _{DG, PV}* n _{DG, PV}Rank).

In the positive sequence network for arbitrary weak ring power distribution network, from path matrix T ₁Middle each PV type DG node institute corresponding row vector is extracted forms a new matrix T _{1, DG}, then have

${\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{1,\mathrm{DG}}={\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="DG\; Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">DG</figure-callout>}}{Z}_{}{}_{1,\mathrm{<figure-callout\; id="1"\; label="b\; T"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">b</figure-callout>}}{T}_{}^{}{}_{1,\mathrm{DG}}^T---\left(7\right)$

Δ U _{1, DG}, Δ I _{1, DG}, Z _{1, DG}Be expressed as

ΔU _1,DG=Δe _1,DG+jΔf _1,DG (8)

ΔI _1,DG=Δc _1,DG+jΔd _1,DG (9)

Z _1,DG=R _1,DG+jX _1,DG (10)

When the k time iteration, the open loop positive sequence voltage of i PV type DG node is

, suppose that open loop point both sides have identical phase angle, then the difference of the rated voltage of the actual positive sequence voltage of i PV type DG node and PV type DG is

$\mathrm{\&Delta;}{\stackrel{.}{U}}_{1,\mathrm{DG},i_k}=({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i})e^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}=\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}---\left(11\right)$

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i}---\left(12\right)$

In the formula: U _{DG, i}It is the rated voltage amplitude of i PV type DG; θ _{1, DG, i}For

Phase angle.

After the k time iteration, establish i PV type DG node forward-order current change amount and be

, then the change amount of its positive sequence apparent power is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\mathrm{\&Delta;}{\stackrel{.}{I}}_{1,\mathrm{DG},i_k}^{*}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}-\mathrm{j\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})---\left(13\right)$

Then this PV type DG node positive sequence active power recruitment is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Re}\left(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}+\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})---\left(14\right)$

Because PV type DG node positive sequence active power is constant, so , substitution formula (14)

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,{\mathrm{DG},i}_k}=-\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}\tan {\mathrm{\&theta;}}_{1,{\mathrm{DG},i}_k}---\left(15\right)$

Because

It is smaller,

Much smaller than

, therefore Δ I is arranged _{1, DG}≈ j Δ d _{1, DG}, and Δ e _{1, DG}=Δ U _{1, DG}Cos θ _{1, DG}≈ then can get according to formula (6), (8) and (10)

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,{\mathrm{DG}}_k}=-{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">X</figure-callout>}}_{1,\mathrm{DG}}^{-1}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_{1,{\mathrm{DG}}_k}---\left(16\right)$

And this PV type DG node positive sequence reactive power increment is

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Im}\left(\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,\mathrm{DG},i_k}-\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k})---\left(17\right)$

Wushu (15) substitution formula (17) can get

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=-\frac{3U_{\mathrm{DG},i}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}}{\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\&ap;-3U_{\mathrm{DG},i}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{DG},i_k}---\left(18\right)$

If U _{DG, i}Be 1.0pu, then So, have

And during the k+1 time iteration, the positive sequence reactive power of i PV type DG node is

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}={\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_k}+\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}---\left(19\right)$

Then its substitution formula (2) is obtained the new injection forward-order current of DG node, the beginning next iteration.When | Δ U _{1, DG}| when satisfying convergence precision, stop iteration.

(4) PI node type DG

Consider similar situation, it is considered herein that it is that DG node positive sequence active power, output constant current magnitude are DG node forward-order current amplitude that PI node type DG exports constant active power.Corresponding DG output reactive power can be calculated as follows and draw:

$Q_{\mathrm{DG}}=\sqrt{{\left|I_{\mathrm{DG}}\right|}^2({\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">e</figure-callout>}}_{1,\mathrm{DG},i_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2+{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{1,\mathrm{DG},i_k}^2)-P_{\mathrm{DG}}^2}---\left(20\right)$

In the formula: P _DGActive power for DG output; | I _DG| be the DG constant current magnitude; With

Positive sequence voltage real part and the imaginary part of DG node i when being respectively the k time iteration.

Therefore, corresponding DG node positive sequence reactive power is during the k+1 time iteration

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1,\mathrm{DG},i_{(k+1)}}=-Q_{\mathrm{DG}}---\left(21\right)$

And its substitution formula (2) obtained the new injection forward-order current of DG node, the beginning next iteration.

In the trend iterative process, if appearring in PQ (V), PV and PI type DG node, reactive power crosses the border, then convert thereof into PQ type DG node processing, and Q _DGGet the idle upper bound or the lower bound of each node type DG, then recomputate.

2. the weak ring Three-phase Power Flow Calculation Method for Distribution System that contains the polymorphic type distributed power source

For encircling power distribution network a little less than the three-phase with N node, b bar branch road and l independent loop, suppose that first node (root node) is power supply and as with reference to node, then the isolated node number is n=N-1, branch road number b=n+l.Wherein, a tree n bar, chord l bar.

For selected tree in the connected graph, owing to only comprising a chord in the fundamental circuit, the fundamental circuit number equals the chord number, and fundamental circuit-branch road (following abbreviation " return-Zhi ") incidence matrices B describes the contact between fundamental circuit, tree, the chord.Wherein return-Zhi incidence matrices B is a l * b rank matrix, and the positive direction of supposing the chord branch road all is to point to small size node from the large size node, and the positive direction of fundamental circuit is identical with the positive direction of chord branch road, if branch road j is in the j of loop, and the two direction is identical, then B (j, k)=1, if branch road k is in the j of loop, and the two opposite direction, then B (j, k)=-1, if branch road k not in the j of loop, B (j, k)=0 then.

The road of a node refer to node along tree to root the set of fingers on the path of process, the road of node is emphasized is branch road on the path, for a given tree, the road of node be unique, only by tree Zhi Zucheng, available road-branch road incidence matrices (abbreviation path matrix) T describes.Wherein path matrix T is a n * b rank matrix, and the positive direction of supposing road all is to point to each node from power supply point (being root node), and it is identical with the road positive direction that each sets the Zhi Zhilu positive direction, if branch road k on road i, T (i, k)=1 then, otherwise T (i, k)=0.Path matrix T is a sparse matrix, utilizes sparse technology can reduce memory requirements.

In weak ring distribution sequence network, it is I that defined node injects order current vector matrix _{S, n}(n * 1 rank), branch order current vector matrix is I _{S, b}(b * 1 rank), chord order electric current (also being loop order electric current) vector matrix is I _{S, l}(l * 1 rank).In each order pessimistic concurrency control circuit of decoupling zero, can obtain the path matrix of each sequence network and return-the Zhi incidence matrices is respectively T ₀, T ₁, T ₂And B ₀, B ₁, B ₂, and according to the KCL current law, the branch order electric current I _{S, b}Inject the order electric current I with node _{S, n}, loop order electric current I _{S, l}Satisfy following equation:

${I_{s,b}=T}_s^T{I}_{s,n}+B_s^T{I}_{s,l}---\left(22\right)$

Wherein, s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network in the sequence network model.

In arbitrary weak ring distribution system order component circuit model, based on Ohm's law, the branch road restrain condition is

U _s,b=Z _s,bI _s,b (23)

According to the KVL voltage law, fundamental circuit is constrained to

B _sU _s,b=0 (24)

Wherein, U _{S, b}Be power distribution network branch order voltage matrix (n * 1 rank); Z _{S, b}Be the order impedance Z based on branch road i _{S, bi}The diagonal matrix (n * n rank) that forms, s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the sequence network model.

Can be got by formula (22) and formula (23) substitution formula (24):

$B_s{Z}_{s,b}{B}_s^T{I}_{s,l}=B_s{Z}_{s,b}{T}_s^T{I}_{s,n}=0---\left(25\right)$

Order

, being the loop order impedance matrix, its inverse matrix is Y _{S, l}, then have

$I_{s,l}=-Y_{s,l}{B}_s{Z}_{s,b}{T}_s^T{I}_{s,n}---\left(26\right)$

$I_{s,b}=T_s^T{I}_{s,n}-B_s^T{Y}_{s,l}{B}_s{Z}_{s,b}{T}_s^T{I}_{s,n}---\left(27\right)$

$U_{s,b}=Z_{s,b}{I}_{s,b}=(Z_{s,b}-Z_{s,b}{B}_s^T{Y}_{s,l}{B}_s{Z}_{s,b})T_s^T{I}_{s,n}---\left(28\right)$

If power supply node three-phase voltage phase moment matrix is U _{Abc, 0}(3 * 1 rank), each node three-phase voltage phase moment matrix is U _{Abc, n}(3n * 1 rank), the three sequence voltage phase moment matrixs that then can draw power supply node are U _012,0=A U _{Abc, 0}(3 * 1 rank), each node three sequence voltage phase moment matrix is U _{012, n}(3n * 1 rank), so, in each sequence network model, as can be known the sequence voltage of arbitrary node and power supply node poor equal node from then on begin along the road of this node arrive power supply node through the branch order voltage sum of branch road, namely (establish 1 _n=[1,1 ..., 1] ^T, n individual 1 altogether; A=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]$ ， $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right]$ )：

$\mathrm{\&Delta;}{U}_{s,n}=1_n{U}_{s,0}-U_{s,n}=T_s{U}_{s,b}=T_s(Z_{s,b}-Z_{s,b}{B}_s^T{Y}_{s,l}{B}_s{Z}_{s,b})T_s^T{I}_{s,n}---\left(29\right)$

U _s,n=1 _nU _s,0-ΔU _s,n (30)

Formula (29) is the core that contains the weak ring Three-phase Power Flow Calculation Method for Distribution System calculating of polymorphic type distributed power source, as described in Figure 1, contains the weak ring power distribution network Three-phase Power Flow calculation process concrete steps following (k is iterations) of polymorphic type distributed power source:

1) determine the tree of weak ring distribution network, give node serial number, the numbering of the root node in the regulation tree is minimum, is made as " 0 ", and all the other nodes are numbered by its distance from root node, and is larger from the node serial number of root node away from more.The numbering that tree props up then is defined as the large person who gets in the node serial number of two ends, adds 1 after the maximum that the numbering of chord is propped up from tree is successively numbered.

2) determine weak ring power distribution network topological structure parameter, comprise nodes, a way, feeder number.Might as well establish the weak ring of three-phase power distribution network has N node, b bar branch road and l independent loop, suppose first node (root node) be power supply and conduct with reference to node, then the isolated node number is n=N-1, separate branches number b=n+l.Wherein, a tree n bar, chord l bar.

3) determine DG access situation in the weak ring of the distributed power generation power distribution network, comprise node type and the corresponding position (node number) of DG access, the total quantity of access DG, all types of DG and network parameters, the separately quantity of all types of DG that are incorporated into the power networks.

4) establishing first node is power supply and as with reference to node, first node three-phase voltage phase moment matrix is U _{Abc, 0}(3 * 1 rank), each node three-phase voltage phase moment matrix is U _{Abc, n}(3n * 1 rank), in weak ring distribution system three sequence networks, three sequence voltage matrixes of the node of can informing against are U _012,0=AU _{Abc, 0}(3 * 1 rank), each node three sequence voltage matrix is U _{012, n}(3n * 1 rank).Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]$ ， $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right]$ 。

5) calculate each sequence network parameter Z _{S, b}Z _{S, b}Be the order impedance Z based on branch road i _{S, bi}The diagonal matrix (n * n rank) that forms, wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models; Three phase of impedance of branch road i are Z _{Abc, bi}, then have, wherein, $Z_{012,\mathrm{bi}}=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="bi"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">bi</figure-callout>}}& 0& 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="HDA00002622341000011.png,HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{1,\mathrm{<figure-callout\; id="0"\; label="bi"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">bi</figure-callout>}}& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HDA00002622341000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{2,\mathrm{bi}}\end{array}\right]$ ， $Z_{\mathrm{abc},\mathrm{bi}}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right]$ 。

6) calculate the path matrix T of each order net _sWith return-Zhi incidence matrices B _sWherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

7) calculate loop order impedance matrix in each order net

, with and inverse matrix Y _{S, 1}=(Z _{S, 1}) ^-1Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

8) compose initial value for each node three-phase voltage of weak ring power distribution network E wherein _n[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs.

Each phase current that node i is injected when 9) calculating the k time iteration

, wherein

Be each phase injecting power of node i,

Each phase node voltage of node i when being the k-1 time iteration, Y _{P, i}Be the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., n.

Each order electric current that node i is injected when 10) calculating the k time iteration

, i=1,2 ..., n.

11) calculate respectively i DG node when the k time iteration for dissimilar DG according to power flow algorithm corresponding in the steps A

With

, the injection forward-order current of i DG node when then obtaining the k time iteration

, i=1,2 ..., n _DGWherein

With

Be respectively active power and the reactive power of i DG node when the k time iteration,

Be the node voltage of i DG node when the k-1 time iteration, n _DGDG number for connecting system.

12) load bus is injected order electric current and DG node and inject the forward-order current stack, each node always injects the order electric current when obtaining the k time iteration

Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

When 13) calculating the k time iteration

Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

When 14) calculating the k time iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, be n-dimensional vector; S=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models.

Node i three-phase voltage phasor when 15) calculating k iteration

, i=1,2 ..., n.

16) judge

With

Whether the difference of amplitude satisfies the convergence precision requirement.If satisfy, then finishing iteration; Otherwise turn step 9).

Sample calculation analysis

Fig. 2 is IEEE-37 bus three-phase imbalance power distribution network, and the transformer Δ-Δ mode of connection increases by 5 loops, is respectively DG-1, DG-2, DG-3, DG-4 and DG-5 in bus 12,25,29,5 DG systems of 30 and 35 accesses, and its line chart as shown in Figure 2.

Contain in the weak ring distribution system of polymorphic type DG at the IEEE-37 bus, 5 DG-1 of DG system, DG-2, DG-3, DG-4 and DG-5 access respectively PQ, PQ (V)-1, PQ (V)-2, PV and PI node type DG system successively, each node type DG and network parameters are as shown in table 1, with and idle boundary arrange as shown in table 2.

Each node type DG and network parameters in table 1 example

The idle boundary of each node type DG in table 2 example

Selected 7 kinds of operational modes shown in the table 3 to analyze discussion, trend convergence situation is as shown in table 3 under 7 kinds of operational modes, and under 7 kinds of operational modes access DG idle cross the border and idle output situation as shown in table 6.

7 kinds of operational modes of table 3 example and trend convergent iterations number of times

The idle of DG crosses the border and idle output situation in table 4 example

By as seen from Table 3, compare with other modes, occur iterations in mode 6 and the mode 7 and increased approximate one times, this be because: occur the idle output of access DG in mode 6 and the mode 7 and cross the border, Load Flow Program re-starts trend calculating after automatically the idle DG of crossing the border being converted to PQ type DG, therefore iterations can increase approximate one times.In addition, can find out also that from table 4 the PV type DG that accesses idle output occurs and crosses the border in mode 6 and mode 7.

From table 3 and table 4, as can be known, restrain number of times after the loop closure and reduce, and along with the increase Load Flow Program convergence of closed circuit is stable; System is when access DG and increase DG, and the convergence of trend changes very little, but when idle crossing the border appearred in DG, iterations can increase to some extent, but does not affect the trend convergence; Shown that the present invention has good convergence and processes DG and looped network ability.In the situation that mode 7 has all accessed 4 kinds of different node type DG simultaneously with mode 6, trend stable convergence has shown that the present invention has ability and the idle ability of crossing the border of processing DG that the multiple different node type DG of stronger processing are incorporated into the power networks simultaneously.

Claims (1)

1. a weak ring power distribution network Three Phase Power Flow that contains the polymorphic type distributed power source is characterized in that, comprises the steps:

Step 1 is set up the power flow algorithm of all types of distributed power sources

1) PQ node type DG

The constant meritorious and reactive power of PQ node type DG output is defined as the meritorious and positive sequence reactive power of the positive sequence of DG node, namely

$\left\{\begin{array}{c}{P}_{1,\mathrm{DG},i}=-P_{\mathrm{DG}}\\ Q_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}\end{array}\right.$

In the formula: P _DGAnd Q _DGBe respectively the meritorious and idle output of PQ node type DG;

2) PQ (V) node type DG

The processing method of PQ (V) node type DG is similar to PQ node type DG, difference is, in the iterative process, need to constantly update DG node positive sequence reactive power according to up-to-date DG node positive sequence voltage iterative value, then obtain the new positive sequence Injection Current of DG node, the beginning next iteration, its computation model is

$\left\{\begin{array}{c}{P}_{1,\mathrm{DG},i}=-P_{\mathrm{DG}}\\ Q_{1,\mathrm{DG},i}=-Q_{\mathrm{DG}}=-f\left(U_{1,\mathrm{DG},i}\right)\end{array}\right.$

Value has following 2 kinds of situations in the formula:

When a. adopting without excitation regulation ability synchronous generator as interface, the reactive power that DG sends is

$Q_{\mathrm{DG}}=f\left(U_{1,\mathrm{DG},i}\right)=\sqrt{{\left(\frac{E_{\mathrm{DGq}}{U}_{1,\mathrm{DG},i}}{X_d}\right)}^2-P_{\mathrm{DG}}^2}-\frac{U_{1,\mathrm{DG},i}^2}{X_d}$

In the formula: P _DG, E _DGq, X _d, U _{1, DG, i}Be respectively meritorious output, no-load emf, synchronous reactance, the terminal voltage of DG unit;

B. the blower fan that adopts asynchronous generator is during as interface, and the reactive power that DG absorbs is

$Q_{\mathrm{DG}}=f\left(U_{1,\mathrm{DG},i}\right)=-\frac{U_{1,\mathrm{DG},i}^2}{x_p}+\frac{-U_{1,\mathrm{DG},i}^2+\sqrt{U_{1,\mathrm{DG},i}^4-4P_{\mathrm{DG}}^2{x}^2}}{2x}$

In the formula: P _DG, U _{1, DG, i}Be respectively meritorious output, the set end voltage of DG; X is asynchronous machine stator leakage reactance and rotor leakage reactance sum; x _pBe asynchronous machine excitation reactance and machine end shunt capacitance equivalent reactance;

3) PV node type DG

Consider that there are the asymmetric operation state status in generator characteristic and three-phase symmetrical DG, PV node type DG is exported constant active power be defined as DG node positive sequence active power, to export the constant voltage amplitude and be defined as DG node positive sequence voltage amplitude, and obtain and satisfy the DG node positive sequence reactive power that DG node positive sequence voltage amplitude equates with PV type DG voltage rating; Then have

$\left\{\begin{array}{c}{P}_{1,\mathrm{DG},i}=-P_{\mathrm{DG}}\\ U_{1,\mathrm{DG},i}=U_{\mathrm{DG}}\end{array}\right.$

For PV node type DG, adopt the open loop impedance matrix to process PV type DG node, contain n at one _{DG, PV}In the positive sequence network of the three-phase distribution net of individual PV type DG, if after each PV type DG Nodes open loop, n occurs _{DG, PV}Individual open loop point then exists

ΔU _1,DG=Z _1,DGΔI _1,DG

In the formula: Δ U _{1, DG}, Δ I _{1, DG}Positive sequence voltage, forward-order current matrix for the open loop point calibration; Z _{1, DG}Be the Dai Weinan equivalent impedance matrix of seeing into from the open loop point;

In the positive sequence network for arbitrary weak ring power distribution network, from path matrix T ₁Middle each PV type DG node institute corresponding row vector is extracted forms a new matrix T _{1, DG}, then have

$Z_{1,\mathrm{DG}}=T_{1,\mathrm{DG}}{Z}_{1,b}{T}_{1,\mathrm{DG}}^T$

Δ U _{1, DG}, Δ I _{1, DG}, Z _{1, DG}Be expressed as

ΔU _1,DG=Δe _1,DGjΔf _1,DG

ΔI _1,DG=Δc _1,DGjΔd _1,DG

Z _1,DG=R _1,DGjX _1,DG

In the formula: Δ e _{1, DG}With Δ f _{1, DG}Represent respectively Δ U _{1, DG}Real part and imaginary-part matrix; Δ c _{1, DG}With Δ d _{1, DG}Represent respectively Δ I _{1, DG}Real part and imaginary-part matrix; R _{1, DG}And X _{1, DG}Represent respectively Z _{1, DG}Real part and imaginary-part matrix;

When the k time iteration, the open loop positive sequence voltage of i PV type DG node is

, suppose that open loop point both sides have identical phase angle, then the difference of the rated voltage of the actual positive sequence voltage of i PV type DG node and PV type DG is

$\mathrm{\&Delta;}{\stackrel{.}{U}}_{1,\mathrm{DG},i_k}=(U_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i})e^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}=\mathrm{\&Delta;}{U}_{1,\mathrm{DG},i_k}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}$

$\mathrm{\&Delta;}{U}_{1,\mathrm{DG},i_k}=U_{1,\mathrm{DG},i_k}-U_{\mathrm{DG},i}$

In the formula: U _{DG, i}It is the rated voltage amplitude of i PV type DG; θ _{1, DG, i}For

Phase angle;

After the k time iteration, establish i PV type DG node forward-order current change amount and be , then the change amount of its positive sequence apparent power is

$\mathrm{\&Delta;}{S}_{1,\mathrm{DG},i_{(k+1)}}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\mathrm{\&Delta;}{\stackrel{.}{I}}_{1,\mathrm{DG},i_k}^{*}=3U_{\mathrm{DG},i}{e}^{j{\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}(\mathrm{\&Delta;}{c}_{1,\mathrm{DG},i_k}-\mathrm{j\&Delta;}{d}_{1,\mathrm{DG},i_k})$

Then this PV type DG node positive sequence active power recruitment is

$\mathrm{\&Delta;}{P}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Re}\left(\mathrm{\&Delta;}{S}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{c}_{1,\mathrm{DG},i_k}+\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}{\mathrm{\&Delta;d}}_{1,\mathrm{DG},i_k})$

Because PV type DG node positive sequence active power is constant, so , can obtain according to following formula

$\mathrm{\&Delta;}{c}_{1,\mathrm{DG},i_k}=-\mathrm{\&Delta;}{d}_{1,\mathrm{DG},i_k}\tan {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}$

Because It is smaller,

Much smaller than

, therefore Δ I is arranged _{1, DG}≈ j Δ d _{1, DG}, and Δ e _{1, DG}=Δ U _{1, DG}Cos θ _{1, DG}≈ Δ U _{1, DG}, then can draw

$\mathrm{\&Delta;}{d}_{1,{\mathrm{DG}}_k}=-X_{1,\mathrm{DG}}^{-1}\mathrm{\&Delta;}{U}_{1,{\mathrm{DG}}_k}$

And this PV type DG node positive sequence reactive power increment is

$\mathrm{\&Delta;}{Q}_{1,\mathrm{DG},i_{(k+1)}}=\mathrm{Im}\left(\mathrm{\&Delta;}{S}_{1,\mathrm{DG},i_{(k+1)}}\right)=3U_{\mathrm{DG},i}(\sin {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{c}_{1,\mathrm{DG},i_k}-\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}\mathrm{\&Delta;}{d}_{1,\mathrm{DG},i_k})$

Then can draw

$\mathrm{\&Delta;}{Q}_{1,\mathrm{DG},i_{(k+1)}}=-\frac{3U_{\mathrm{DG},i}\mathrm{\&Delta;}{d}_{1,\mathrm{DG},i_k}}{\cos {\mathrm{\&theta;}}_{1,\mathrm{DG},i_k}}\&ap;-3U_{\mathrm{DG},i}\mathrm{\&Delta;}{d}_{1,\mathrm{DG},i_k}$

If U _{DG, i}Be 1.0pu, then

So, have

And during the k+1 time iteration, the positive sequence reactive power of i PV type DG node is

$Q_{1,\mathrm{DG},i_{(k+1)}}=Q_{1,\mathrm{DG},i_k}+\mathrm{\&Delta;}{Q}_{1,\mathrm{DG},i_{(k+1)}}$

Then obtain the new injection forward-order current of DG node, the beginning next iteration; When | Δ U _{1, DG}| when satisfying convergence precision, stop iteration;

4) PI node type DG

Consider similar situation, it is considered herein that it is that DG node positive sequence active power, output constant current magnitude are DG node forward-order current amplitude that PI node type DG exports constant active power; Then have

$\left\{\begin{array}{c}{P}_{1,\mathrm{DG},i}=-P_{\mathrm{DG}}\\ I_{1,\mathrm{DG},i}=I_{\mathrm{DG}}\end{array}\right.$

Corresponding DG output reactive power can be calculated as follows and draw:

$Q_{\mathrm{DG}}=\sqrt{{\left|I_{\mathrm{DG}}\right|}^2(e_{1,\mathrm{DG},i_k}^2+f_{1,\mathrm{DG},i_k}^2)-P_{\mathrm{DG}}^2}$

In the formula: P _DGActive power for DG output; | I _DG| be the DG constant current magnitude;

With

Positive sequence voltage real part and the imaginary part of DG node i when being respectively the k time iteration;

Therefore, corresponding DG node positive sequence reactive power is during the k+1 time iteration

$Q_{1,\mathrm{DG},i_{(k+1)}}=-Q_{\mathrm{DG}}$

Then obtain the new injection forward-order current of DG node, the beginning next iteration;

For i DG node, the forward-order current that its node injects can calculate with following formula:

${\stackrel{.}{I}}_{1,\mathrm{DG},i}={[(P_{1,\mathrm{DG},i}+j{Q}_{1,\mathrm{DG},i})/\left(3{\stackrel{.}{U}}_{1,\mathrm{DG},i}\right)]}^{*}$

In the formula:

Be this DG node positive sequence voltage phasor;

In the trend iterative process, if appearring in PQ (V), PV and PI type DG node, reactive power crosses the border, then convert thereof into PQ type DG node processing, and Q _DGGet the idle upper bound or the lower bound of each node type DG, then recomputate;

Step 2, the weak ring Three-phase Power Flow Calculation Method for Distribution System flow process that contains the polymorphic type distributed power source is as follows

1) determine the tree of weak ring distribution network, give node serial number, the numbering of the root node in the regulation tree is minimum, is made as " 0 ", and all the other nodes are numbered by its distance from root node, and is larger from the node serial number of root node away from more; The numbering that tree props up then is defined as the large person who gets in the node serial number of two ends, adds 1 after the maximum that the numbering of chord is propped up from tree is successively numbered;

2) determine weak ring power distribution network topological structure parameter, comprise nodes, a way, feeder number; Might as well establish the weak ring of three-phase power distribution network has N node, b bar branch road and l independent loop, suppose first node be power supply and conduct with reference to node, then the isolated node number is n=N-1, separate branches number b=n+l; Wherein, a tree n bar, chord l bar;

3) determine DG access situation in the weak ring of the distributed power generation power distribution network, comprise node type and the corresponding position of DG access, the total quantity of access DG, all types of DG and network parameters, the separately quantity of all types of DG that are incorporated into the power networks;

4) establishing first node is power supply and as with reference to node, first node three-phase voltage phase moment matrix is

, each node three-phase voltage phase moment matrix is U _{Abc, n}, in weak ring distribution system three sequence networks, three sequence voltage matrixes of the node of can informing against are U _012,0=AU _{Abc, 0}, each node three sequence voltage matrix is U _{012, n}Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]$ ， $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right]$ ；

5) calculate each sequence network parameter Z _{S, b}Z _{S, b}Be the order impedance Z based on branch road i _{S, bi}The diagonal matrix (n * n rank) that forms, wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models, three phase of impedance of branch road i are Z _{Abc, bi}, Z is then arranged _{012, bi}=AZ _{Abc, bi}A ^-1, wherein, $Z_{012,\mathrm{bi}}=\left[\begin{array}{ccc}{Z}_{0,\mathrm{bi}}& 0& 0\\ 0& Z_{1,\mathrm{bi}}& 0\\ 0& 0& Z_{2,\mathrm{bi}}\end{array}\right]$ ， $Z_{\mathrm{abc},\mathrm{bi}}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right]$ ；

6) calculate the path matrix T of each order net _sWith return-Zhi incidence matrices B _sWherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models;

7) calculate loop order impedance matrix in each order net

, with and inverse matrix Y _{S, 1}=(Z _{S, 1}) ^-1Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models;

8) compose initial value for each node three-phase voltage of weak ring power distribution network

E wherein _n=[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs;

Each phase current that node i is injected when 9) calculating the k time iteration

, wherein

Be each phase injecting power of node i, Each phase node voltage of node i when being the k-1 time iteration, Y _{P, i}Be the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., n; K is the iterations variable;

Each order electric current that node i is injected when 10) calculating the k time iteration

, i=1,2 ..., n;

11) calculate respectively i DG node when the k time iteration for dissimilar DG according to power flow algorithm corresponding in the steps A

With

, the injection forward-order current of i DG node when then obtaining the k time iteration

, i=1,2 ..., n _DGWherein

With

Be respectively active power and the reactive power of i DG node when the k time iteration,

Be the node voltage of i DG node when the k-1 time iteration, n _DGDG number for connecting system;

12) load bus is injected order electric current and DG node and inject the forward-order current stack, each node always injects the order electric current when obtaining the k time iteration

Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models;

When 13) calculating the k time iteration

Wherein, subscript s=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models;

When 14) calculating the k time iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, be n-dimensional vector; S=0,1,2, represent respectively zero sequence, positive sequence and negative sequence network model in the three sequence network models;

Node i three-phase voltage phasor when 15) calculating k iteration , i=1,2 ..., n;

16) judge

With Whether the difference of amplitude satisfies the convergence precision requirement; If satisfy, then finishing iteration; Otherwise turn step 9).

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