CN103401234A - Load flow calculation method based on generator node type - Google Patents

Abstract

The invention relates to a load flow calculation method based on a generator node type. The method is characterized in that a load flow calculation model containing a P beta node is generated by defining the P beta node, a new Jacobian matrix equation is established by adopting a Newton-Raphson method and finally the equation is modified to realize load flow iterative solution. By using the method, different voltage regulation requirements can be met by adjusting beta under the condition of given upper and lower limits of generator reactive power according to different positions of a generator in a system, the reactive regulation capacity of the generator can be fully utilized by correctly selecting beta, the situation that the generator loses the regulation capacity and becomes a PQ node due to a reason that reactive power exceeds the limits is avoided, and the actual voltage-reactive power relationship during the voltage regulation of the generator can be reflected.

Description

A kind of tidal current computing method based on the generator node type

Technical field

The present invention relates to the trend computing technique field of generator, more particularly, is a kind of tidal current computing method of taking into account the generator node type of excitation system difference coefficient.

Background technology

It is the most basic calculating in the power system mesomeric state operating analysis that electric power system tide calculates, and conventional Load Flow calculates the known quantity according to node, and load bus is made as to the PQ node, and the generator node is made as PV node and balance node V θ.According to the node type of definition, generate the power equation of each node, with alternative manner, solve voltage and the phase angle of each node the unknown.

In fact, the voltage of generator-idle relation is to be determined by the difference coefficient β of its excitation system, namely in generator reactive bound restriction range, for different operational modes, the idle and node voltage that generator sends should change by the constraint of difference coefficient β.PV nodal analysis method during conventional Load Flow calculates is that generator voltage is made as to steady state value, a kind of extreme ruuning situation of generator just, that is: and β=0, thus be difficult to reflect generator real voltage power-less relation in the voltage-regulation process.

Summary of the invention

The objective of the invention is, provide a kind of based on generator nodal analysis method-P β node, by the different values to the excitation system difference coefficient, the continuous transition of P β node to PQ node or PV node can be realized, the tidal current computing method based on the generator node type of the voltage of generator-idle characteristic can be correctly truly reflected.

Realize that the technical scheme that purpose of the present invention adopts is: a kind of tidal current computing method based on the generator node type, it is characterized in that, it comprises following content:

1) definition of .P β node

The generator node is i, V _iFor the working voltage of node i, P _iQ _iFor active power and the reactive power of node i,

The difference coefficient of generator node i is:

${\mathrm{\β}}_i=-\frac{V_{\mathrm{iref}}-V_i}{Q_{\mathrm{iref}}-Q_i}={\mathrm{\β}}_i(V_i,Q_i)---\left(1\right)$

In formula (1), V _Iref, Q _IrefBe respectively reference voltage and the reactive power of node i, V _i, Q _iBe respectively working voltage and the reactive power of node i, the injection active-power P that so-called P β node is exactly known node i and the node of generator difference coefficient β;

According to generator residing diverse location in system, for given generator reactive power bound, can realize different pressure regulation requirements by regulating β, correctly select β, the idle regulating power of generator is fully used, and avoids idle transfiniting and make generator lose regulating power and become the PQ node, can reflect generator real voltage power-less relation in the voltage-regulation process, as two extreme cases

When β → 0, P β node becomes the PV node;

When β → ∞, P β node becomes the PQ node, normally works as Q _i=Q _IminOr Q _i=Q _ImaxThe time;

So P β node has reflected the various operation conditionss of generator node comprehensively;

2). contain the power flow algorithm of P β node

Set up departments the system in n node arranged, m generator node wherein arranged, and all the other are load bus or contact node, in the generator node, get a reference node, that is: V θ node, all the other m-1 node is made as P β node, when Q and V are all not out-of-limit, in order to narrate conveniently, m generator node come to back, wherein V θ node is the n node, polar form, order

Y _Ij=G _Ij+ jB _Ij(i, j=1,2 ..., n), V _i, θ _iFor amplitude and the angle of node voltage vector, G, B are that electricity is led and admittance, and the active power of given each PQ and P β node is

The reactive power of each PQ node is

The difference coefficient of each P β node is

Calculating the related active power balance equation of trend has n-1, as follows:

$\left\{\begin{array}{c}{{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}^{\mathrm{sp}}={\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\cos {\mathrm{\&theta;}}_{1j}+B_{1j}\sin {\mathrm{\&theta;}}_{1j})\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{sp}}={\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\cos {\mathrm{\&theta;}}_{2j}+B_{2j}\sin {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ P_{n-1}^{\mathrm{sp}}=V_{n-1}\underset{j\&Element;(n-1)}{\mathrm{\&Sigma;}}{V}_j(G_{n-1,j}\cos {\mathrm{\&theta;}}_{n-1,j}+B_{n-1,j}\sin {\mathrm{\&theta;}}_{n-1,j})\end{array}\right.---\left(2\right)$

And the related reactive power equilibrium equation of calculating has n-m individual, as follows:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1^{\mathrm{sp}}={\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\sin {\mathrm{\&theta;}}_{1j}-B_{1j}\cos {\mathrm{\&theta;}}_{1j})\\ {\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2^{\mathrm{sp}}={\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\sin {\mathrm{\&theta;}}_{2j}-B_{2j}\cos {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ Q_{n-m}^{\mathrm{sp}}=V_{(n-m)}\underset{j\&Element;(n-m)}{\mathrm{\&Sigma;}}{V}_j(G_{n-m,j}\sin {\mathrm{\&theta;}}_{n-m,j}-B_{n-m,j}\cos {\mathrm{\&theta;}}_{n-m,j})\end{array}\right.---\left(3\right)$

And the related difference coefficient equilibrium equation of calculating has m-1 individual, as follows:

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_{n-m+1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+1}(V_{n-m+1},Q_{n-m+1})\\ {\mathrm{\&beta;}}_{n-m+2}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+2}(V_{n-m+2},Q_{n-m+2})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&beta;}}_{n-1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-1}(V_{n-1},Q_{n-1})\end{array}\right.---\left(4\right)$

The amount to be asked of formula (2), (3), (4) equation is angle θ and the voltage magnitude V of each node, and wherein θ is total n-1, total n-1 of V, and unknown quantity is total 2n-2 like this, just can be obtained by an above 2n-2 equation;

3) inequality constraints equation

Node voltage is constrained to: V _min≤ V≤V _max

In formula, V is the node voltage size, V _min, V _maxFor node voltage lower limit and the upper limit;

Generator node reactive power is constrained to: Q _Gmin≤ Q _G≤ Q _Gmax

Q in formula _GFor the idle of generator exerted oneself; Q _GminAnd Q _GmaxBe respectively generator reactive exert oneself lower limit and the upper limit;

4) update equation formula

Adopt the Newton-Raphson method, the update equation formula of the trend of polar form is following form:

$\left[\begin{array}{c}\mathrm{\&Delta;P}\\ \mathrm{\&Delta;Q}\\ \mathrm{\&Delta;\&beta;}\end{array}\right]=K\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]=\left[\begin{array}{cc}H& N\\ J& L\\ R& S\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]---\left(5\right)$

K in formula (5) is Jacobian matrix; Element in H, N, J, L and conventional Load Flow calculate the Newton-Raphson method that adopts, element in the trend update equation formula of polar form is the same, repeated description no longer just here, wherein Δ P, Δ Q, Δ β are the active power balance equation, the reactive power equilibrium equation, the difference coefficient equilibrium equation, R, S element expression in formula (5) are as follows:

Wherein matrix R is:

$R_{\mathrm{ij}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}{V}_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})(j\&NotEqual;i)$ （6）

$R_{\mathrm{ii}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}({V_i}^2{G}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}))(j=i)$

Wherein matrix S is:

$S_{\mathrm{ij}}=\frac{(V_{\mathrm{iref}}-V_i)*\left(V_i{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\right)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(i\&NotEqual;j)$

$S_{\mathrm{ii}}=\frac{-V_i*(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\left)\right)-(V_{\mathrm{iref}}-V_i)*({V_i}^2{B}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(j=i)---7.$

The accompanying drawing explanation

Fig. 1 generator node schematic diagram;

Fig. 2 difference coefficient and V, the graph of a relation between Q;

Fig. 3 is 5 machine 19 node system wiring schematic diagrams.

Embodiment

The invention will be further described below to utilize drawings and Examples.

With reference to Fig. 1, a kind of tidal current computing method based on the generator node type of the present invention, it comprises following content:

1) definition of .P β node

The generator node is i, V _iFor the working voltage of node i, P _iQ _iFor active power and the reactive power of node i,

The difference coefficient of generator node i is:

${\mathrm{\&beta;}}_i=-\frac{V_{\mathrm{iref}}-V_i}{Q_{\mathrm{iref}}-Q_i}={\mathrm{\&beta;}}_i(V_i,Q_i)---\left(1\right)$

In formula (1), V _Iref, Q _IrefBe respectively reference voltage and the reactive power of node i, V _i, Q _iBe respectively working voltage and the reactive power of node i, the injection active-power P that so-called P β node is exactly known node i and the node of generator difference coefficient β;

According to generator residing diverse location in system, for given generator reactive power bound, can realize different pressure regulation requirements by regulating β, as shown in Figure 2, according to difference coefficient and V, relation between Q is correctly selected β, the idle regulating power of generator is fully used, and avoid idle transfiniting and make generator lose regulating power and become the PQ node, can reflect generator real voltage power-less relation in the voltage-regulation process, as two extreme cases

When β → 0, P β node becomes the PV node;

When β → ∞, P β node becomes the PQ node, normally works as Q _i=Q _IminOr Q _i=Q _ImaxThe time;

So P β node has reflected the various operation conditionss of generator node comprehensively;

2). contain the power flow algorithm of P β node

Set up departments the system in n node arranged, m generator node wherein arranged, and all the other are load bus or contact node, in the generator node, get a reference node, that is: V θ node, all the other m-1 node is made as P β node, when Q and V are all not out-of-limit, in order to narrate conveniently, m generator node come to back, wherein V θ node is the n node, polar form, order

Y _Ij=G _Ij+ jB _Ij(i, j=1,2 ..., n), V _i, θ _iFor amplitude and the angle of node voltage vector, G, B are that electricity is led and admittance, and the active power of given each PQ and P β node is

The reactive power of each PQ node is

The difference coefficient of each P β node is

Calculating the related active power balance equation of trend has n-1, as follows:

$\left\{\begin{array}{c}{{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}^{\mathrm{sp}}={\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\cos {\mathrm{\&theta;}}_{1j}+B_{1j}\sin {\mathrm{\&theta;}}_{1j})\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{sp}}={\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\cos {\mathrm{\&theta;}}_{2j}+B_{2j}\sin {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ P_{n-1}^{\mathrm{sp}}=V_{n-1}\underset{j\&Element;(n-1)}{\mathrm{\&Sigma;}}{V}_j(G_{n-1,j}\cos {\mathrm{\&theta;}}_{n-1,j}+B_{n-1,j}\sin {\mathrm{\&theta;}}_{n-1,j})\end{array}\right.---\left(2\right)$

And the related reactive power equilibrium equation of calculating has n-m individual, as follows:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1^{\mathrm{sp}}={\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\sin {\mathrm{\&theta;}}_{1j}-B_{1j}\cos {\mathrm{\&theta;}}_{1j})\\ {\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2^{\mathrm{sp}}={\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\sin {\mathrm{\&theta;}}_{2j}-B_{2j}\cos {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ Q_{n-m}^{\mathrm{sp}}=V_{(n-m)}\underset{j\&Element;(n-m)}{\mathrm{\&Sigma;}}{V}_j(G_{n-m,j}\sin {\mathrm{\&theta;}}_{n-m,j}-B_{n-m,j}\cos {\mathrm{\&theta;}}_{n-m,j})\end{array}\right.---\left(3\right)$

And the related difference coefficient equilibrium equation of calculating has m-1 individual, as follows:

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_{n-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">m</figure-callout>}+1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+1}(V_{n-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">m</figure-callout>}+1},Q_{n-m+1})\\ {\mathrm{\&beta;}}_{n-\mathrm{<figure-callout\; id="2"\; label="m\; +"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">m</figure-callout>}+2}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+2}(V_{n-\mathrm{<figure-callout\; id="2"\; label="m\; +"\; filenames="HDA00003549842800021.png"\; state="\{\{state\}\}">m</figure-callout>}+2},Q_{n-m+2})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&beta;}}_{n-1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-1}(V_{n-1},Q_{n-1})\end{array}\right.---\left(4\right)$

The amount to be asked of formula (2), (3), (4) equation is angle θ and the voltage magnitude V of each node, and wherein θ is total n-1, total n-1 of V, and unknown quantity is total 2n-2 like this, just can be obtained by an above 2n-2 equation;

3) inequality constraints equation

Node voltage is constrained to: V _min≤ V≤V _max

In formula, V is the node voltage size, V _min, V _maxFor node voltage lower limit and the upper limit;

Generator node reactive power is constrained to: Q _Gmin≤ Q _G≤ Q _Gmax

Q in formula _GFor the idle of generator exerted oneself; Q _GminAnd Q _GmaxBe respectively generator reactive exert oneself lower limit and the upper limit;

4) update equation formula

Adopt the Newton-Raphson method, the update equation formula of the trend of polar form is following form:

$\left[\begin{array}{c}\mathrm{\&Delta;P}\\ \mathrm{\&Delta;Q}\\ \mathrm{\&Delta;\&beta;}\end{array}\right]=K\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]=\left[\begin{array}{cc}H& N\\ J& L\\ R& S\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]---\left(5\right)$

K in formula (5) is Jacobian matrix; Element in H, N, J, L and conventional Load Flow calculate the Newton-Raphson method that adopts, element in the trend update equation formula of polar form is the same, repeated description no longer just here, wherein Δ P, Δ Q, Δ β are the active power balance equation, the reactive power equilibrium equation, the difference coefficient equilibrium equation, R, S element expression in formula (5) are as follows:

Wherein matrix R is:

$R_{\mathrm{ij}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}{V}_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})(j\&NotEqual;i)$ （6）

$R_{\mathrm{ii}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}({V_i}^2{G}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}))(j=i)$

Wherein matrix S is:

$S_{\mathrm{ij}}=\frac{(V_{\mathrm{iref}}-V_i)*\left(V_i{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\right)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(i\&NotEqual;j)$

$S_{\mathrm{ii}}=\frac{-V_i*(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\left)\right)-(V_{\mathrm{iref}}-V_i)*({V_i}^2{B}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(j=i)---\left(7\right).$

With reference to Fig. 3, specifically take into account excitation system difference coefficient node trend calculation procedure

(1) form node admittance matrix Y

(2) initial value of establishing each node voltage is V _i ⁽⁰⁾, θ _i ⁽⁰⁾

(3) initial value of each node voltage is brought into to formula (1)-(4), asked the amount of unbalance Δ P in the update equation formula _i ⁽⁰⁾, Δ Q _i ⁽⁰⁾And Δ β _i ⁽⁰⁾

(4) initial value substitution formula (5)-(7) of each node voltage are asked to each element value of Jacobian matrix.

(5) separate the update equation formula, ask the variable quantity of each node voltage, i.e. correction amount V _i ⁽⁰⁾, Δ θ _i ⁽⁰⁾

(6) calculate the new value of each node voltage, value after namely revising

V _i ⁽¹⁾=V _i ⁽¹⁾+ΔV _i ⁽⁰⁾；θ _i ⁽¹⁾=θ _i ⁽⁰⁾+Δθ _i ⁽⁰⁾

(7) by the new value of each node voltage, from the 3rd step, start to enter next iteration, until Δ P, Δ Q, Δ β meet required precision, stop iteration.

Referring to 5 machine 19 nodes shown in accompanying drawing 3, wherein the 1-14 node is the PQ node, the 15-18 node is P β node, to be balance node V θ node form node admittance matrix Y by given power system network structural parameters to 19 nodes, and the self-admittance that in its matrix Y, each diagonal entry equals each node equals the admittance sum on respective nodes institute's chord road; The admittance value of the respective branch that its matrix Y off diagonal element equals to bear; Then use Matlab, apply 7 formula, tide model in this paper is carried out to simulation calculation, the result of calculation that obtains, generator reactive meets its bound constraint requirements, and the idle and node voltage that sends of generator meets the constraint of the difference coefficient β of formula (1).

Claims (1)

1. the tidal current computing method based on the generator node type, is characterized in that, it comprises following content:

1) definition of .P β node

The generator node is i, V _iFor the working voltage of node i, P _iQ _iFor active power and the reactive power of node i,

The difference coefficient of generator node i is:

${\mathrm{\&beta;}}_i=-\frac{V_{\mathrm{iref}}-V_i}{Q_{\mathrm{iref}}-Q_i}={\mathrm{\&beta;}}_i(V_i,Q_i)---\left(1\right)$

In formula (1), V _Iref, Q _IrefBe respectively reference voltage and the reactive power of node i, V _i, Q _iBe respectively working voltage and the reactive power of node i, the injection active-power P that so-called P β node is exactly known node i and the node of generator difference coefficient β;

According to generator residing diverse location in system, for given generator reactive power bound, can realize different pressure regulation requirements by regulating β, correctly select β, the idle regulating power of generator is fully used, and avoids idle transfiniting and make generator lose regulating power and become the PQ node, can reflect generator real voltage power-less relation in the voltage-regulation process, as two extreme cases

When β → 0, P β node becomes the PV node;

When β → ∞, P β node becomes the PQ node, normally works as Q _i=Q _IminOr Q _i=Q _ImaxThe time;

So P β node has reflected the various operation conditionss of generator node comprehensively;

2). contain the power flow algorithm of P β node

Set up departments the system in n node arranged, m generator node wherein arranged, and all the other are load bus or contact node, in the generator node, get a reference node, that is: V θ node, all the other m-1 node is made as P β node, when Q and V are all not out-of-limit, in order to narrate conveniently, m generator node come to back, wherein V θ node is the n node, polar form, order

Y _Ij=G _Ij+ jB _Ij(i, j=1,2 ..., n), V _i, θ _iFor amplitude and the angle of node voltage vector, G, B are that electricity is led and admittance, and the active power of given each PQ and P β node is

The reactive power of each PQ node is

The difference coefficient of each P β node is

Calculating the related active power balance equation of trend has n-1, as follows:

$\left\{\begin{array}{c}{P_1}^{\mathrm{sp}}=V_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\cos {\mathrm{\&theta;}}_{1j}+B_{1j}\sin {\mathrm{\&theta;}}_{1j})\\ P_2^{\mathrm{sp}}=V_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\cos {\mathrm{\&theta;}}_{2j}+B_{2j}\sin {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ P_{n-1}^{\mathrm{sp}}=V_{n-1}\underset{j\&Element;(n-1)}{\mathrm{\&Sigma;}}{V}_j(G_{n-1,j}\cos {\mathrm{\&theta;}}_{n-1,j}+B_{n-1,j}\sin {\mathrm{\&theta;}}_{n-1,j})\end{array}\right.---\left(2\right)$

And the related reactive power equilibrium equation of calculating has n-m individual, as follows:

$\left\{\begin{array}{c}{Q}_1^{\mathrm{sp}}=V_1\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{1j}\sin {\mathrm{\&theta;}}_{1j}-B_{1j}\cos {\mathrm{\&theta;}}_{1j})\\ Q_2^{\mathrm{sp}}=V_2\underset{j\&Element;2}{\mathrm{\&Sigma;}}{V}_j(G_{2j}\sin {\mathrm{\&theta;}}_{2j}-B_{2j}\cos {\mathrm{\&theta;}}_{2j})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ Q_{n-m}^{\mathrm{sp}}=V_{(n-m)}\underset{j\&Element;(n-m)}{\mathrm{\&Sigma;}}{V}_j(G_{n-m,j}\sin {\mathrm{\&theta;}}_{n-m,j}-B_{n-m,j}\cos {\mathrm{\&theta;}}_{n-m,j})\end{array}\right.---\left(3\right)$

And the related difference coefficient equilibrium equation of calculating has m-1 individual, as follows:

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_{n-m+1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+1}(V_{n-m+1},Q_{n-m+1})\\ {\mathrm{\&beta;}}_{n-m+2}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-m+2}(V_{n-m+2},Q_{n-m+2})\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&beta;}}_{n-1}^{\mathrm{sp}}={\mathrm{\&beta;}}_{n-1}(V_{n-1},Q_{n-1})\end{array}\right.---\left(4\right)$

The amount to be asked of formula (2), (3), (4) equation is angle θ and the voltage magnitude V of each node, and wherein θ is total n-1, total n-1 of V, and unknown quantity is total 2n-2 like this, just can be obtained by an above 2n-2 equation;

3) inequality constraints equation

Node voltage is constrained to: V _min≤ V≤V _max

In formula, V is the node voltage size, V _min, V _maxFor node voltage lower limit and the upper limit;

Generator node reactive power is constrained to: Q _Gmin≤ Q _G≤ Q _Gmax

Q in formula _GFor the idle of generator exerted oneself; Q _GminAnd Q _GmaxBe respectively generator reactive exert oneself lower limit and the upper limit;

4) update equation formula

Adopt the Newton-Raphson method, the update equation formula of the trend of polar form is following form:

$\left[\begin{array}{c}\mathrm{\&Delta;P}\\ \mathrm{\&Delta;Q}\\ \mathrm{\&Delta;\&beta;}\end{array}\right]=K\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]=\left[\begin{array}{cc}H& N\\ J& L\\ R& S\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;V}/V\end{array}\right]---\left(5\right)$

K in formula (5) is Jacobian matrix; Element in H, N, J, L and conventional Load Flow calculate the Newton-Raphson method that adopts, element in the trend update equation formula of polar form is the same, repeated description no longer just here, wherein Δ P, Δ Q, Δ β are the active power balance equation, the reactive power equilibrium equation, the difference coefficient equilibrium equation, R, S element expression in formula (5) are as follows:

Wherein matrix R is:

$R_{\mathrm{ij}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}{V}_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})(j\&NotEqual;i)$ （6）

$R_{\mathrm{ii}}=\frac{-(V_{\mathrm{iref}}-V_i)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;1}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}({V_i}^2{G}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}))(j=i)$

Wherein matrix S is:

$S_{\mathrm{ij}}=\frac{(V_{\mathrm{iref}}-V_i)*\left(V_i{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\right)}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(i\&NotEqual;j)$

$S_{\mathrm{ii}}=\frac{-V_i*(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\left)\right)-(V_{\mathrm{iref}}-V_i)*({V_i}^2{B}_{\mathrm{ii}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}{{(Q_{\mathrm{iref}}-V_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}))}^2}(j=i)---\left(7\right).$

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