CN102545252A - Voltage source commutation-high voltage direct current (VSC-HVDC) power flow computing method based on three-stage convergence Newton method - Google Patents

Abstract

The invention discloses a voltage source commutation-high voltage direct current (VSC-HVDC) power flow computing method based on a three-stage convergence Newton method, which includes first deducing a stable power flow model of the VSC-HVDC, deducing a multivariable matrix solving format of a Newton iteration method with the three-stage convergence rate, applying the format into the VSC-HVDC power flow computing, and conducting simulation tests on four computing examples of an IEEE5-57 nodal point test system. The result proves that the computing method has good convergence characteristics and requires few iteration times compared with the classic Newton method under the condition that identical accuracy requirements are met. Trend computing speed is improved due to the fact that a factor table of Jacobian matrix triangular factorization is completely utilized in each step of iteration.

Description

Based on three rank convergence Newton method VSC-HVDC tidal current computing method

Technical field

Invention relates to a kind of VSC-HVDC tidal current computing method based on three rank convergence Newton method, belongs to power system analysis and computing field.

Background technology

It is a kind of electric basically computing of research power system mesomeric state ruuning situation that electric power system tide calculates.Its task is to confirm the running status of whole system according to given service conditions and network topology structure; Like distribute power in the voltage on each bus (amplitude and phase angle), each generator output, the network and power loss etc., the electric power system tide result calculated is the basis of Model for Stability Calculation of Power System and accident analysis.

Along with the development of power grid construction, the application of direct current transportation in electrical network more and more widely increasing alternating current-direct current hybrid system will occur.With full-controlled switch device and voltage source converter (VoltageSource Converter; VSC) be high voltage direct current transmission of new generation (the High Voltage DirectCurrent on basis; HVDC); Than current source type direct current transportation, have directly to isolated distant loads power supply, more economical send advantages such as electricity, operation control method be flexible and changeable, so VSC-HVDC becomes hot research in recent years to load center based on thyristor.

Along with enlarging day by day and the proposition of online computational problem such as safety analysis of electric power system scale, the speed that makes trend calculate becomes a problem that presses for solution.Three rank convergence Newton method combines and simplification Newton method amount of calculation is little and the advantage of Newton method fast convergence rate, makes that VSC-HVDC trend computational speed is faster.

Summary of the invention

Technical problem to be solved by this invention is the defective that exists to existing tidal current computing method, and a kind of VSC-HVDC tidal current computing method based on three rank convergence Newton method is provided.

The present invention adopts following technical scheme for realizing above-mentioned purpose:

The present invention is based on the VSC-HVDC tidal current computing method of three rank convergence Newton method, it is characterized in that said method realizes according to the following steps:

(1) network parameter of acquisition electric power system; Comprise: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance;

(2) program initialization comprises: quantity of state is provided with initial value, the optimization of node order, forms node admittance matrix, step-up error precision ε;

(3) recover iteration count: k=1;

(4) rated output amount of unbalance f (x ^(k));

(5) the Jacobian matrix of computing system;

(6) separate following equation group, try to achieve

and obtain revised

Whether (7) judge

sets up; If; Stop to calculate, the output result, if not; Put k=k+0.5 (half iteration in the three rank Newton methods accomplished in 0.5 expression), return step (4);

(8) rated output amount of unbalance

(9) separate following equation group, try to achieve Δ x ^(k), and obtain revised x ^(k):

x ^(k+1)＝x ^(k)+Δx ^(k)

Whether (10) judge sets up; If; Stop to calculate, the output result, if not; Put k=k+0.5 (half iteration in the three rank Newton methods accomplished in 0.5 expression), return step (4).

The tidal current computing method of the unified solution by iterative method alternating current-direct current hybrid system that adopts at present is that expansion forms on the basis that the inferior method trend of traditional Newton-pressgang is calculated.This Algorithm Convergence is good, but need form new Jacobian matrix after the iteration each time, and amount of calculation is bigger, has had a strong impact on computational speed; The present invention and three rank convergence Newton method has not only been inherited and has been simplified the little advantage of Newton method amount of calculation, also has the advantage of Newton method fast convergence rate.

Description of drawings

Fig. 1: the inventive method flow chart.

Fig. 2: the alternating current-direct current hybrid system model that the present invention adopts.

Fig. 3: the VSC-HVDC trend of the three rank convergence Newton method that the present invention proposes is calculated applied four example systems; Wherein: figure (a) is the IEEE-5 node system; Figure (b) is the IEEE-14 node system, and figure (c) is the IEEE-30 node system, and figure (d) is the IEEE-57 node system.

Embodiment

Fig. 1 is the inventive method flow chart.The alternating current-direct current hybrid system model that Fig. 2 adopts for the present invention.I representes to insert i VSC of DC network among Fig. 2.The fundamental voltage phasor of supposing i VSC output does

With the voltage phasor of AC system junction do

The converter transformer impedance is jX _Li, R _iBe the equivalent resistance of i inverter inside loss and converter transformer loss, active power and reactive power that AC system flows into converter transformer are respectively P _SiAnd Q _Si, the active power and the reactive power that flow into converter bridge are respectively P _CiAnd Q _Ci, the electric current that wherein flows through converter transformer does

Suppose that direction is as shown in Figure 1, then

The complex power

that AC system flows into converter transformer satisfies following relational expression:

In order to discuss conveniently, make δ _i=θ _Si-θ _Ci,

α _i=arctan (X _Li/ R _i), with formula (1) substitution formula (2), further derivation can get

$P_{\mathrm{si}}=-\left|Y_i\right|U_{\mathrm{si}}{U}_{\mathrm{ci}}\cos ({\mathrm{\δ}}_i+{\mathrm{\α}}_i)+\left|Y_i\right|U_{\mathrm{si}}^2\cos {\mathrm{\α}}_i$

$Q_{\mathrm{si}}=-\left|Y_i\right|U_{\mathrm{si}}{U}_{\mathrm{ci}}\sin ({\mathrm{\δ}}_i+{\mathrm{\α}}_i)+\left|Y_i\right|U_{\mathrm{si}}^2\sin {\mathrm{\α}}_i$

In like manner can derive and obtain:

$P_{\mathrm{ci}}=\left|Y_i\right|U_{\mathrm{si}}{U}_{\mathrm{ci}}\cos ({\mathrm{\δ}}_i-{\mathrm{\α}}_i)-\left|Y_i\right|U_{\mathrm{ci}}^2\cos {\mathrm{\α}}_i$

$Q_{\mathrm{ci}}=-\left|Y_i\right|U_{\mathrm{si}}{U}_{\mathrm{ci}}\sin ({\mathrm{\δ}}_i-{\mathrm{\α}}_i)-\left|Y_i\right|U_{\mathrm{ci}}^2\sin {\mathrm{\α}}_i$

Because the loss of the change of current brachium pontis of VSC is by R _iSo equivalence is direct current power P _DiShould with the P that injects converter bridge _CiEquate, therefore can get

$P_{\mathrm{di}}=U_{\mathrm{di}}{I}_{\mathrm{di}}=\left|Y_i\right|U_{\mathrm{si}}{U}_{\mathrm{ci}}\cos ({\mathrm{\δ}}_i-{\mathrm{\α}}_i)-\left|Y_i\right|U_{\mathrm{ci}}^2\cos {\mathrm{\α}}_i$

U wherein _Di, I _DiBe respectively the direct voltage and the electric current of direct current node.In addition, voltage equation is:

$U_{\mathrm{ci}}=\frac{\sqrt{6}}{4}{M}_i{U}_{\mathrm{di}}$

M wherein _iIt is the modulation degree of i VSC.

Above-mentioned 8 equations have constituted mark one system steady-state model of VSC-HVDC down.

Among the VSC-HVDC, the direct relation of whether stablizing of direct voltage that can system normally move and the stability of AC side output voltage.If the active power that the VSC of meritorious transmitting terminal absorbs from this end AC system sends to the active power of corresponding end AC system greater than receiving terminal VSC, direct voltage raises, otherwise direct voltage reduces.Therefore in order to realize this power-balance, wherein an end VSC must adopt and decide direct voltage control.In addition, if direct voltage is constant, then the variable quantity of direct current is proportional to the amount of unbalance of active power, and it is equivalent then deciding direct current control and deciding active power control.Comprehensive above the analysis, the control mode that VSC can select among the VSC-HVDC has following several kinds:

1.. decide direct voltage, decide Reactive Power Control;

2.. decide direct voltage, decide alternating voltage control;

3.. decide active power, decide Reactive Power Control;

4.. decide active power, decide alternating voltage control.

The present invention adopts following four kinds of control modes combination to the VSC-HVDC at direct current branch two ends:

(1).①+③；(2).①+④；

(3).③+②；(4).④+②。

Whether be connected to converter transformer according to node, node is divided into direct current node and the pure node that exchanges.The direct current node is meant the node that primary side connected of converter transformer, node as shown in Figure 1, owing to connected converter exchanging on the node, its corresponding control and state variable are at the former exchange status variable U that exchanges node _i, θ _iIncreased direct current variable U on the basis _Di, I _Di, δ _i, M _i, P _Si, Q _Si, δ wherein _i, M _iPhase angle and modulation degree for converter; Pure interchange node is meant the node that does not link to each other with converter transformer.The node of uniting of setting up departments adds up to n, and wherein the number of VSC is n _c, then direct current node number is n _c, pure interchange node number is n _a=n-n _cIn order to compose a piece of writing conveniently, suppose that the node serial number of alternating current-direct current hybrid system is in proper order: 1～n below _aNode is pure interchange node; n _a+ 1～n node is the direct current node.

For the direct current node, its trend accounting equation is:

$\left\{\begin{array}{c}\mathrm{\Δ}{P}_{\mathrm{ti}}=P_{\mathrm{ti}}^s-U_{\mathrm{ti}}\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})-P_{\mathrm{si}}\\ \mathrm{\Δ}{Q}_{\mathrm{ti}}=Q_{\mathrm{ti}}^s-U_{\mathrm{ti}}\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})-Q_{\mathrm{si}}\end{array}\right.$

Wherein: subscript t representes that this interchange node is connected with VSC.Δ P _Ti, Δ Q _TiBe direct current node power amount of unbalance;

For the node behind the deduction load sends power; U _TiFor being connected to the interchange node voltage amplitude of VSC, subscript j is all nodes (representing with j ∈ i in the formula) that directly link to each other with node i; U _jFor exchanging node voltage amplitude, θ _IjBe node i, phase angle difference between j; G _Ij, B _IjBe node i, the real part of admittance and imaginary part between j.P _Si, Q _SiFlow into the meritorious and reactive power of converter transformer for AC system.

According to the steady-state model of VSC-HVDC, the trend accounting equation that can obtain direct current system is:

$\mathrm{\Δ}{d}_{i1}=P_{\mathrm{si}}+(\sqrt{6}/4)M_i{U}_{\mathrm{si}}{U}_{\mathrm{di}}\left|Y_i\right|\cos ({\mathrm{\δ}}_i+{\mathrm{\α}}_i)-U_{\mathrm{si}}^2\left|Y_i\right|\cos {\mathrm{\α}}_i$

$\mathrm{\Δ}{d}_{i2}=Q_{\mathrm{si}}+(\sqrt{6}/4)M_i{U}_{\mathrm{si}}{U}_{\mathrm{di}}\left|Y_i\right|\sin ({\mathrm{\δ}}_i+{\mathrm{\α}}_i)-U_{\mathrm{si}}^2\left|Y_i\right|\sin {\mathrm{\α}}_i-U_{\mathrm{si}}^2/X_{\mathrm{fi}}$

$\mathrm{\Δ}{d}_{i3}=U_{\mathrm{di}}{I}_{\mathrm{di}}-(\sqrt{6}/4)M_i{U}_{\mathrm{si}}{U}_{\mathrm{di}}\left|Y_i\right|\cos ({\mathrm{\δ}}_i-{\mathrm{\α}}_i)+(3/8){(M_i/U_{\mathrm{di}})}^2\left|Y_i\right|\cos {\mathrm{\α}}_i$

In the formula, subscript i representes i VSC.

Add the current deviation amount equation of DC network:

$\mathrm{\Δ}{d}_{i4}=I_{\mathrm{di}}-\underset{j=1}{\overset{n_c}{\mathrm{\Σ}}}{g}_{\mathrm{dij}}{U}_{\mathrm{dj}}$

G wherein _DijBe the electric conductivity value between direct current node i, the j.

It is following to have the constringent Newton method expression formula in three rank:

$x_{k+1}=x_k-\frac{f(x_k-f\left(x_k\right)/f^{\′}\left(x_k\right))+f\left(x_k\right)}{f^{\′}\left(x_k\right)}$

X wherein _k, x _K+1For k time with k+1 iteration after variate-value, f (x _k) be x _kCorresponding functional value, f ' (x _k) be that f (x) is at x _kThe slope at place.

It is a Newton method and simplify combining of Newton method, is equivalent on original Newton method iteration basis each time, once simplify the Newton method iteration:

Wherein is the value of xk after three rank Newton method first step iteration, and

is

corresponding power amount of unbalance.

It is good and simplify the little advantage of amount of calculation of Newton method that this algorithm has been drawn the convergence of Newton method, and its multi-variable matrix form is following:

$\left\{\begin{array}{c}{y}^{\left(k\right)}=x^{\left(k\right)}-J{\left(x^{\left(k\right)}\right)}^{-1}f\left(x^{\left(k\right)}\right)\\ x^{(k+1)}=x^{\left(k\right)}-J{\left(x^{\left(k\right)}\right)}^{-1}(f\left(x^{\left(k\right)}\right)+f\left(y^{\left(k\right)}\right))\end{array}\right.$

X wherein ^(k)Be the system variable after k iteration, y ^(k)Be x ^(k)System variable after three rank Newton method first step iteration, J (x ^(k)), f (x ^(k)) be x ^(k)Corresponding Jacobian matrix and power amount of unbalance, f (y ^(k)) be y ^(k)Corresponding power amount of unbalance.

The Jacobian matrix is constant in twice calculating, has reduced to form Jacobian matrix and the amount of calculation of carrying out triangle decomposition, has saved certain amount of calculation.

Fig. 3 calculates applied four example systems for the VSC-HVDC trend of the three rank convergence Newton method that the present invention proposes.Figure (a) is IEEE-5 node system, wherein VSC ₁, VSC ₂Be connected on the node 2,3; Figure (b) is IEEE-14 node system, wherein VSC ₁, VSC ₂Be connected on the node 13,14; Figure (c) is IEEE-30 node system, wherein VSC ₁, VSC ₂Be connected on the node 29,30; Figure (d) is IEEE-57 node system, wherein VSC ₁, VSC ₂Be connected on the node 54,55 VSC ₃, VSC ₄Be connected on the node 56,57;

Introduce three embodiment of the present invention below:

Example one:

The present invention adopts the modified IEEE-5 node standard example shown in Fig. 3 (a), and the direct current branch parameter is seen table 1.

Each variable initial value of table 1VSC

N	R	X L	P 1	Q 1	U	θ	P s	Q s	U d
										2	0.006	0.150	2.000	1.000	1.078	0.000	1.416	-0.244	2.000
3	0.006	0.150	3.700	1.300	1.036	0.000	-1.277	0.203	2.000

Wherein N representes female wire size at VSC place, P ₁, Q ₁Meritorious, idle for the load that VSC place ac bus connects, U, θ represent alternating voltage amplitude, the phase angle of VSC place bus, P _s, Q _sFor the injection of direct current system meritorious, idle, U _dBe direct voltage.R is the equivalent resistance of inverter inside loss and converter transformer loss, R, X _L, P ₁, Q ₁Given by system; P _s, Q _sInitial value be made as with revise before system branch power equate, calculate by the trend of original system.I _d, δ, M obtain by following:

I _di＝(P _gi-P _1i)/U _di

${\mathrm{\&delta;}}_i=\arctan (P_{\mathrm{ti}}/({\mathrm{<figure-callout\; id="2"\; label="U\; ti"\; filenames="HDA0000123419260000022.png,HDA0000123419260000023.png"\; state="\{\{state\}\}">U</figure-callout>}}_{\mathrm{ti}}^{}/X_{\mathrm{Li}}-Q_{\mathrm{ti}}))$

$M_i=\sqrt{6}{P}_{\mathrm{ti}}{X}_{\mathrm{Li}}/\left({4U}_{\mathrm{ti}}{U}_{\mathrm{di}}\sin {\mathrm{\&delta;}}_i\right)$

P wherein _GiMeritorious for the node generating, if this node is not the generator node, then be 0.

Convergences Newton method in three rank is calculated (direct current branch two ends VSC control mode be combined as 1.+3.) in the alternating current-direct current trend that contains VSC-HVDC, and simulation result is shown in table 2, table 3.

Table 2 AC system result

N	U	θ	P g	Q g
					1	0.972	-3.202°	0.000	0.000
2	1.085	19.176°	0.000	0.000
					3	1.046	-4.018°	0.000	0.000
4	1.050	23.141°	5.000	1.361
					5	1.050	0.000°	2.442	1.986

Table 3 direct current system result

The direct current variable	U d	I d	δ	M	P s	Q s
							VSC 1	2.000	0.650	9.315	0.919	1.308	-0.244
VSC 2	1.981	-0.650	-10.214	0.858	-1277	0.203

P wherein _g, Q _gFor generator is meritorious, idle exerting oneself.Numerical results shows the feasibility that three rank convergence Newton method VSC-HVDC trend is calculated.

Example two:

In actual motion, in order to realize functions such as stable operation, minimizing loss, VSC-HVDC need move under the various control pattern.Make up with different control modes at the DC line two ends of example, and shown in gained node voltage and the phase angle table 4, the VSC variable at DC line two ends is as shown in table 5 under each control mode.

Each busbar voltage under table 4 different control modes

Each VSC variable under table 5 different control modes

Numerical results has been verified the validity of this algorithm under different control modes in the table.

Example three:

The present invention adopts the standard example of IEEE-5 node shown in Figure 3, IEEE-14 node, IEEE-30 node, IEEE-57 node; Three rank convergence Newton method is used to contain the alternating current-direct current trend calculating of VSC-HVDC; And calculate with unified iterative method trend and to contrast, simulation result is as shown in table 6.

The alternating current-direct current trend based on three rank convergence Newton method that this invention of numerical results proof proposes in the table is calculated iterations and is less than unified iterative method, and significantly reduce computing time.Reason is three rank convergence ox

Unified iterative method of table 6 and three rank convergence Newton method simulation result are relatively

The Jacobian matrix is constant in twice calculating of method, has reduced to form Jacobian matrix and the amount of calculation of carrying out triangle decomposition, has saved certain amount of calculation.This shows that it is feasible calculating based on the alternating current-direct current trend of three rank convergence Newton method, and on computational speed and convergence, its superior part is arranged.

Claims (1)

1. VSC-HVDC tidal current computing method based on three rank convergences Newton method is characterized in that may further comprise the steps:

(1) network parameter of acquisition electric power system; Comprise: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance;

(2) program initialization comprises: quantity of state is provided with initial value, the optimization of node order, forms node admittance matrix, step-up error precision ε;

(3) recover iteration count: k=1;

(4) rated output amount of unbalance f (x ^(k));

(5) the Jacobian matrix of computing system;

(6) separate following equation group, try to achieve

and obtain revised

Whether (7) judge sets up; If; Stop to calculate, the output result, if not; Put k=k+0.5 (half iteration in the three rank Newton methods accomplished in 0.5 expression), return step (4);

(8) rated output amount of unbalance

(9) separate following equation group, try to achieve Δ x ^(k), and obtain revised x ^(k):

x ^(k+1)＝x ^(k)+Δx ^(k)

Whether (10) judge

sets up; If; Stop to calculate, the output result, if not; Put k=k+0.5 (half iteration in the three rank Newton methods accomplished in 0.5 expression), return step (4).

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