General load flow calculation method for power systems with unified power flow controller

Abstract

A general load flow calculation method for power systems with unified power flow controller (UPFC). On the premise of satisfying the control objectives of UPFC, the calculation method combines the power injection model with the Newton-Raphson algorithm to solve the load flow of the power systems by iteration. It is applicable not only to a conventional UPFC structure, but also to a novel UPFC structure wherein the series and shunt transformers of a UPFC are connected to different AC buses or there are more than one series branch connected to a UPFC. The present invention provides the detailed process for performing a load flow evaluation, and it shows that it is unnecessary to add new state variables when solving the load flow by this method, the dimension of the Jacobian matrix will not increase during the iteration.

Claims

1. A general load flow calculation method for power systems with unified power flow controller (UPFC) comprising: replacing the UPFC by an equivalent power injection model; correcting a node power balance equation and a Jacobian matrix according to the equivalent power injection model of the UPFC:; and calculating a load flow distribution of the power system with the UPFC using a Newton-Raphson algorithm by an iteration according to a corrected node power balance equation and a corrected Jacobian matrix; wherein the step of replacing the UPFC by the equivalent power injection model comprises, replacing a shunt converter of the UPFC by a first equivalent voltage source, and connecting the first voltage source to an equivalent reactance of a shunt transformer in series then connecting a first alternating current (AC) bus at a shunt side; replacing a series transformer of the UPFC by a second equivalent voltage source, connecting one end of the second voltage source to a second AC bus at a series side, and replacing an AC transmission line between an other end of the second voltage source and a third AC bus at the series side by a -type equivalent circuit consisting of an impedance and two admittances; setting up a control objective of the load flow of the UPFC, replacing the series side of the UPFC by an equivalent power injection of the AC buses at two ends of the series side of the UPFC, wherein, an active injection power P.sub.ml and a reactive injection power Q.sub.ml of the third AC bus considered as a control end of the load flow are the control objectives of the load flow of the UPFC, and an active injection power P.sub.lm and a reactive injection power Q.sub.lm of the second AC bus at the other end are calculated according to a corresponding circuit parameter; calculating an active power P.sub.sm injected to a series connection node S of the second voltage source and the -type equivalent circuit by the UPFC according to a circuit parameter at the series side of the UPFC, and replacing the shunt side of the UPFC by the equivalent power injection of the first AC bus connected to the shunt side of the UPFC; wherein the UPFC does not consume the active power and due to the power balance, the active injection power of the first AC bus is P.sub.ne=P.sub.smP.sub.lm, and a voltage amplitude of the first AC bus is controlled by the UPFC, the reactive injection power Q.sub.ne is not considered in an iteration calculation of the load flow.

2. The general load flow calculation method according to claim 1, wherein expression of correction of the node power balance equation is $\{\begin{array}{c}{P}_{\mathrm{lo}}-P_{\mathrm{lm}}-V_l\underset{jL}{.Math.}{V}_j\left(G_{\mathrm{lj}}\cos {}_{\mathrm{lj}}+B_{\mathrm{lj}}\sin {}_{\mathrm{lj}}\right)=0\\ Q_{\mathrm{lo}}-Q_{\mathrm{lm}}-V_l\underset{jL}{.Math.}{V}_j\left(G_{\mathrm{lj}}\sin {}_{\mathrm{lj}}-B_{\mathrm{lj}}\cos {}_{\mathrm{lj}}\right)=0\\ P_{\mathrm{mo}}-P_{\mathrm{ml}}-V_m\underset{jM}{.Math.}{V}_j\left(G_{\mathrm{mj}}\cos {}_{\mathrm{mj}}+B_{\mathrm{mj}}\sin {}_{\mathrm{mj}}\right)=0\\ Q_{\mathrm{mo}}-Q_{\mathrm{ml}}-V_m\underset{jM}{.Math.}{V}_j\left(G_{\mathrm{mj}}\sin {}_{\mathrm{mj}}-B_{\mathrm{mj}}\cos {}_{\mathrm{mj}}\right)=0\\ P_{\mathrm{no}}-P_{\mathrm{ne}}-V_n\underset{jN}{.Math.}{V}_j\left(G_{\mathrm{nj}}\cos {}_{\mathrm{nj}}+B_{\mathrm{nj}}\sin {}_{\mathrm{nj}}\right)=0\end{array};$ wherein P.sub.lo is the active injection power of the second AC bus without considering the UPFC; Q.sub.lo is the reactive injection power of the second AC bus without considering the UPFC; P.sub.mo is the active injection power of the third AC bus without considering the UPFC; Q.sub.mo is the reactive injection power of the third AC bus without considering the UPFC; P.sub.no is the active injection power of the first AC bus without considering the UPFC; V.sub.l, V.sub.m and V.sub.n represent the voltage amplitude of the second AC bus l, the thrid AC bus m, the first AC bus n, respectively; V.sub.j represents the voltage amplitude of a fourth AC bus j; L represents a set of the second AC bus and all other AC buses that are directly connected to the second AC bus;.sub.lj represents a voltage phase angle difference between the second AC bus l and the fourth AC bus j; when jl, G.sub.lj and B.sub.lj respectively represent a real part and an imaginary part of a mutual admittance of the second AC bus and the fourth AC bus j; when j=l, G.sub.lj and B.sub.lj respectively represent a real part and an imaginary part of a self-admittance of the second AC bus and the fourth AC bus j; M represents a set of the third AC bus and all other AC buses that are directly connected to the third AC bus; .sub.mj represents a voltage phase angle difference between the third AC bus and the fourth AC bus j; when jm, G.sub.mj and B.sub.mj respectively represent a real part and an imaginary part of a mutual admittance of the third AC bus and the fourth AC bus j; when j=m, G.sub.mj and B.sub.mj respectively represent a real part and an imaginary part of a self-admittance of the third AC bus and the fourth AC bus j; N represents a set of the first AC bus and all other AC buses that are directly connected to the first AC bus; .sub.nj represents a voltage phase angle difference between the first AC bus n and the fourth AC bus j; when jn, G.sub.nj and B.sub.nj respectively represent a real part and an imaginary part of a mutual admittance of the first AC bus and the fourth AC bus j; when j=n, G.sub.nj and B.sub.nj respectively represent a real part and an imaginary part of a self-admittance of the first AC bus n and the fourth AC bus j.

3. The general load flow calculation method according to claim 1, wherein a correction of the Jacobian matrix includes first, calculating a partial derivative matrix Y of the equivalent injection power of the UPFC according to the expression $Y=\left[\begin{array}{cccc}\frac{P_{\mathrm{lm}}}{{}_l}& \frac{P_{\mathrm{lm}}}{{}_m}& \frac{P_{\mathrm{lm}}}{V_l}& \frac{P_{\mathrm{lm}}}{V_m}\\ \frac{Q_{\mathrm{lm}}}{{}_l}& \frac{Q_{\mathrm{lm}}}{{}_m}& \frac{Q_{\mathrm{lm}}}{V_l}& \frac{Q_{\mathrm{lm}}}{V_m}\\ \frac{P_{\mathrm{ne}}}{{}_l}& \frac{P_{\mathrm{ne}}}{{}_m}& \frac{P_{\mathrm{ne}}}{V_l}& \frac{P_{\mathrm{ne}}}{V_m}\end{array}\right];$ wherein V.sub.l and V.sub.m respectively represent the voltage amplitudes of the second AC bus l and the third AC bus, .sub.l and .sub.m respectively represent the phase angles of the second AC bus l and the third AC bus; and subsequently, subtracting the partial derivative matrix Y from the corresponding elements of the original Jacobian matrix Y to obtain the corrected Jacobian matrix.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1(a) and FIG. 1(b) are the structural schematic diagrams of two new UPFC topologies, respectively.

(2) FIG. 2 is a structural schematic diagram of the traditional UPFC topology.

(3) FIG. 3 is an equivalent circuit diagram of the new UPFC topology.

(4) FIG. 4 is a schematic diagram of an equivalent power injection model of the new UPFC topology.

(5) FIG. 5 is a schematic diagram of an equivalent power injection model of the traditional UPFC topology.

(6) FIG. 6 is a flow chart of the load flow calculation.

DETAILED DESCRIPTION OF THE INVENTION

(7) In order to describe the present invention concretely, the technical solutions of the present invention are described in detail with reference to the drawings and specific embodiments, hereinafter.

(8) As shown in FIG. 1 and FIG. 2, the main difference between the traditional topology and the new topology is that the AC bus to which the shunt converter of the UPFC with the traditional topology is connected via, the shunt transformer is exactly one end of the line to which the series side of the UPFC is connected. However, the new topology does not have this limitation. FIG. 1(a) and FIG. 1(b) both show a new topology, while the main difference being that in FIG. 1(a), the UPFC only contains a series converter which is connected to one series branch, and in FIG. 1(b), there are two series converters which are connected to two series branches, respectively. The general load flow calculation method of the present invention is not only applicable to the traditional UPFC topology shown in FIG. 2, but also applicable to both cases shown in FIG. 1. In fact, the method is also applicable to a UPFC topology that includes more series converters and more series branches.

(9) The steps of the load flow calculation for the power systems with UPFC using the present invention are described in detail hereinafter.

(10) (1) The equivalence using power injection model.

(11) Hereinafter, taking FIG. 1(a) as an example, the additional injection power of the nodes of the UPFC is calculated and the method by which the UPFC is considered in equivalent to the power injection model is introduced.

(12) In the UPFC with new topology shown in FIG. 1(a), one end of the series transformer is connected to the AC bus l, the other end thereof is connected to the bus m via the AC transmission lines, and the shunt transformer is connected to the bus n. The series transformer is replaced by an equivalent voltage source V.sub.E.sub.E and the shunt converter is replaced by an equivalent voltage source V.sub.E.sub.E to obtain the equivalent circuit shown in FIG. 3. In FIG. 3, r.sub.ml+jx.sub.ml represents the line impedance jb.sub.ml0 represents the line-to-ground admittance, jx.sub.E represents the equivalent reactance of the shunt transformer. P.sub.lm, Q.sub.lm, P.sub.ml, Q.sub.ml, P.sub.no and Q.sub.no represent the active power and the reactive power injected from the three points of l, m, n, respectively. P.sub.sm, Q.sub.sm represent the active power and the reactive power injected into the series converter, respectively V.sub.l.sub.l, V.sub.m.sub.m, V.sub.n.sub.n represent the voltages of the three points of l, m, n, V.sub.S.sub.S represents the voltage of point S.

(13) When the load flow drawn from the point by the UPFC is selected to be P.sub.c+jQ.sub.c, and the voltage amplitude of the point n is selected to be V.sub.set (P.sub.c+jQ.sub.c and V,.sub.set are the controlled variables of the UPFC), the following equations are satisfied under the steady state:
P.sub.ml=P.sub.c Q.sub.ml=Q.sub.c V.sub.n=V.sub.set

(14) The powers at the series side can be calculated according to the equivalent circuit:

(15) $\begin{array}{cc}{P}_{\mathrm{lm}}=\frac{V_l}{V_m}\left(S_2-b_{\mathrm{lm}0}\left(\begin{array}{c}-V_m^2\sin \left({}_l-{}_m\right)+\\ S_1{r}_{\mathrm{lm}}+S_2{x}_{\mathrm{lm}}\end{array}\right)\right)& \left(1\right)\\ Q_{\mathrm{lm}}=\frac{V_l}{V_m}\left(-S_1+b_{\mathrm{lm}0}\left(\begin{array}{c}-V_m^2\cos \left({}_l-{}_m\right)-\\ S_2{r}_{\mathrm{lm}}+S_1{x}_{\mathrm{lm}}\end{array}\right)\right)& \left(2\right)\\ \begin{array}{c}{P}_{\mathrm{sm}}=-P_c+\frac{\left(P_c^2+Q_c^2+2Q_c{V}_m^2{b}_{\mathrm{lm}0}+V_m^4{b}_{\mathrm{lm}0}\right)r_{lm}}{V_m^2}\\ =-P_c+\frac{\left(S_1^2+S_2^2\right)r_{\mathrm{lm}}}{V_m^2}\end{array}& \left(3\right)\end{array}$
where:
S.sub.1=Q.sub.ccos(.sub.l.sub.m)+P.sub.csin(.sub.l.sub.m)+V.sub.m.sup.2cos(.sub.l.sub.m)b.sub.lm0
S.sub.2=Q.sub.csin(.sub.l.sub.m)P.sub.ccos(.sub.l.sub.m)+V.sub.m.sup.2sin(.sub.l.sub.m)b.sub.lm0

(16) Since the loss of, the UPFC itself is negligible, the power balance is, as follows:
P.sub.ne=P.sub.smP.sub.lm

(17) The UPFC is replaced by an equivalent injection power of the corresponding nodes to obtain the model shown in FIG. 4. Since the point n is the PV node in the load flow calculation, Q.sub.ne does not need to be calculated.

(18) For the UPFC that contains more than one series branch shown in FIG. 1(b), the injection power of each series branch can be respectively calculated according formulas (1)-(3). The injection power of the shunt side can be calculated by the following formula:

(19) $P_{\mathrm{ne}}=\underset{i\mathrm{series}}{.Math.}\left(P_{\mathrm{smi}}-P_{\mathrm{lmi}}\right)$
where series represents all series lines.

(20) For the traditional UPFC topology shown in FIG. 2, the equivalent power injection model thereof is shown in FIG. 5:

(21) $\begin{array}{ccc}{P}_{\mathrm{ml}}=P_c& Q_{\mathrm{ml}}=Q_c& V_l=V_{\mathrm{nset}}\end{array}$$P_{\mathrm{lm}}=-P_c+\frac{\left(S_1^2+S_2^2\right)r_{\mathrm{lm}}}{V_m^2}$

(22) (2) The correction of the power balance equation and the Jacobian matrix.

(23) After the power injection model of the UPFC is obtained, the load flow is calculated by using the Newton-Raphson algorithm. During the calculation process, it is necessary to correct the node power balance equation and the Jacobian matrix.

(24) The power balance equation is basically consistent of that without the UPFC, and it is only necessary to consider the equivalent power injection of the UPFC at the UPFC access nodes.

(25) The correction of the power balance equation of the UPFC access nodes is as follows:

(26) $\begin{array}{cc}\begin{array}{c}{P}_l=P_{\mathrm{lo}}-P_{\mathrm{lm}}-V_l\underset{jl}{.Math.}{V}_j\left(G_{\mathrm{lj}}\cos {}_{\mathrm{lj}}+B_{\mathrm{lj}}\sin {}_{\mathrm{lj}}\right)=0\\ Q_l=Q_{\mathrm{lo}}-Q_{\mathrm{lm}}-V_l\underset{jl}{.Math.}{V}_j\left(G_{\mathrm{lj}}\sin {}_{\mathrm{lj}}-B_{\mathrm{lj}}\cos {}_{\mathrm{lj}}\right)=0\end{array}\}& \left(4\right)\\ \begin{array}{c}{P}_m=P_{\mathrm{mo}}-P_c-V_m\underset{jm}{.Math.}{V}_j\left(G_{\mathrm{mj}}\cos {}_{\mathrm{mj}}+B_{\mathrm{mj}}\sin {}_{\mathrm{mj}}\right)=0\\ Q_m=Q_{\mathrm{mo}}-Q_c-V_m\underset{jm}{.Math.}{V}_j\left(G_{\mathrm{mj}}\sin {}_{\mathrm{mj}}-B_{\mathrm{mj}}\cos {}_{\mathrm{mj}}\right)=0\end{array}\}& \left(5\right)\\ \begin{array}{c}{P}_n=P_{\mathrm{no}}-P_{\mathrm{ne}}-V_n\underset{jn}{.Math.}{V}_j\left(G_{\mathrm{nj}}\cos {}_{\mathrm{nj}}+B_{\mathrm{nj}}\sin {}_{\mathrm{nj}}\right)=0\\ Q_n=Q_{\mathrm{no}}-Q_{\mathrm{ne}}-V_n\underset{jn}{.Math.}{V}_j\left(G_{\mathrm{nj}}\sin {}_{\mathrm{nj}}-B_{\mathrm{nj}}\cos {}_{\mathrm{nj}}\right)=0\end{array}\}& \left(6\right)\end{array}$
where: P.sub.lo, Q.sub.lo, P.sub.mo, Q.sub.mo, P.sub.no and Q.sub.no respectively represent the node injection power without considering the UPFC, P.sub.lm, Q.sub.lm, P.sub.ml, Q.sub.ml, P.sub.no and Q.sub.no respectively represent the active power and the reactive power drawn from the three points of l, m, n by the UPFC. The bus node of the load flow control end at the series side of the UPFC is calculated by formula (4), and the other end of the series side is calculated by formula (5). The bus node at the shunt side of the new topology is calculated by formula (6). Since point n is a PV node, Q.sub.n does not need to be considered in the iteration, and thus does not need to be calculated.

(27) Since the equivalent injection power of the UPFC is relevant to the bus voltage amplitude and phase angle of its access node, it is necessary to consider the impact of this part in the Jacobian matrix, i.e., the partial derivatives of the equivalent injection power of the UPFC is subtracted from the corresponding elements in the original Jacobian matrix Y:

(28) $Y-\left[\begin{array}{cccc}\frac{P_{\mathrm{lm}}}{{}_l}& \frac{P_{\mathrm{lm}}}{{}_m}& \frac{P_{\mathrm{lm}}}{V_l}& \frac{P_{\mathrm{lm}}}{V_m}\\ \frac{Q_{\mathrm{lm}}}{{}_l}& \frac{Q_{\mathrm{lm}}}{{}_m}& \frac{Q_{\mathrm{lm}}}{V_l}& \frac{Q_{\mathrm{lm}}}{V_m}\\ \frac{P_{\mathrm{ne}}}{{}_l}& \frac{P_{\mathrm{ne}}}{{}_m}& \frac{P_{\mathrm{ne}}}{V_l}& \frac{P_{\mathrm{ne}}}{V_m}\end{array}\right]$

(29) The calculation formulas of the partial derivatives are as follows:

(30) $\frac{P_{\mathrm{lm}}}{{}_l}=\frac{V_l}{V_m}\left(S_1+b_{\mathrm{lm}0}\left(C_{m1}+S_2{r}_{\mathrm{lm}}-S_1{x}_{\mathrm{lm}}\right)\right)$$\begin{array}{cc}\frac{P_{\mathrm{lm}}}{{}_m}=-\frac{P_{\mathrm{lm}}}{{}_l}& \frac{P_{\mathrm{lm}}}{V_l}=\frac{P_{\mathrm{lm}}}{V_l}\end{array}$$\frac{P_{\mathrm{lm}}}{V_m}=\frac{V_l}{V_m^2}\left(-S_2+b_{\mathrm{lm}0}\left(\begin{array}{c}3C_{m2}+\left(S_1-2C_{m1}{b}_{\mathrm{lm}0}\right)r_{\mathrm{lm}}-\\ \left(-S_2+2C_{m2}{b}_{\mathrm{lm}0}\right)x_{\mathrm{lm}}\end{array}\right)\right)$$\frac{Q_{\mathrm{lm}}}{{}_l}=\frac{V_l}{V_m}\left(S_2-b_{\mathrm{lm}0}\left(-C_{m2}+S_1{r}_{\mathrm{lm}}+S_2{x}_{\mathrm{lm}}\right)\right)$$\begin{array}{cc}\frac{Q_{\mathrm{lm}}}{{}_m}=-\frac{Q_{\mathrm{lm}}}{{}_m}& \frac{Q_{\mathrm{lm}}}{V_l}=\frac{Q_{\mathrm{lm}}}{V_l}\end{array}$$\frac{Q_{\mathrm{lm}}}{V_m}=\frac{V_l}{V_m^2}\left(S_1+b_{\mathrm{lm}0}\left(\begin{array}{c}-3C_{m1}-\left(-S_2+2C_{m2}{b}_{\mathrm{lm}0}\right)r_{\mathrm{lm}}-\\ \left(S_1-2C_{m1}{b}_{\mathrm{lm}0}\right)x_{\mathrm{lm}}\end{array}\right)\right)$$\begin{array}{ccc}\frac{P_{\mathrm{ne}}}{{}_l}=-\frac{P_{\mathrm{lm}}}{{}_l}& \frac{P_{\mathrm{ne}}}{{}_m}=-\frac{P_{\mathrm{lm}}}{{}_m}& \frac{P_{\mathrm{ne}}}{V_l}=-\frac{P_{\mathrm{lm}}}{V_l}\end{array}$$\frac{P_{\mathrm{ne}}}{V_m}=\frac{P_{\mathrm{sm}}}{V_m}-\frac{P_{\mathrm{lm}}}{V_m}$$\mathrm{where}\text{:}$$\frac{P_{\mathrm{sm}}}{V_m}=-\frac{2r_{\mathrm{lm}}}{V_m^3}\left(P_c^2+Q_c^2-V_m^4{b}_{\mathrm{lm}0}^2\right)$$C_{m1}=V_m^2\cos \left({}_l-{}_m\right)$$C_{m2}=V_m^2\sin \left({}_l-{}_m\right)$

(31) (3) Calculating the Load Flow by Iteration

(32) The flow chart for calculating the load flow shown in FIG. 6 is described in detail as follows:

(33) 3.1 the original system data is loaded, and the initial state of the system is set;

(34) 3.2 the equivalent injection power of the UPFC is calculated according to the voltage amplitude and phase angle of the UPFC access node based on the above-mentioned method;

(35) 3.3 P and Q of each node are calculated according to the corrected node power balance equation;

(36) 3.4 V and are calculated by using the corrected Jacobian matrix and the voltage amplitude and phase angle of each node are updated;

(37) 3.5 whether the convergence condition is satisfied is determined, if yes, the calculation is completed, and the load flow is convergent; otherwise, the next step is performed:

(38) 3.6 whether the number of iterations reaches the limit is determined; if yes, the calculation is completed, and the load flow is not convergent; otherwise, the number of the iterations plus 1 is established, and go back to step 3.2.

(39) The foregoing description of the embodiments is intended to allow those of ordinary skill in the art to understand and implement the present invention. It is apparent that various modifications can be derived from the above-mentioned embodiments and the generic principles described herein can be applied to other embodiments without creative or inventive efforts by those skilled in the art. Therefore, the present invention is not limited to the above embodiments. The improvements and modifications derived from the disclosure of the present invention by those skilled in the art should be deemed within the scope of the present invention.