CN104993491A - Linear power flow calculation method with voltage and reactive power being taken into consideration - Google Patents

Abstract

The invention relates to a linear power flow calculation method with voltage and reactive power being taken into consideration and belongs to the technical field of load flow calculation of an electrical power system. The method comprises the following steps: obtaining active power injection vectors of nodes by utilizing network loss estimated value of a power transmission network; generating a matrix required for calculating node voltage phase angles according to power transmission network line parameters; estimating the node voltage phase angles by utilizing an optimal estimation method; obtaining matrixes required for calculating a power flow equation according to the power transmission network parameters; calculating reactive power injection compensation terms of the nodes according to the voltage phase angle values; and obtaining parameters to be calculated in the power flow equation through linear matrix operation. The calculation method makes the most of the characteristics of the power flow equation and provides the linear power flow equation, and thus state parameters to be calculated of the nodes can be estimated accurately. The method does not need iterative solving, is high in calculating efficiency and small in development difficulty, and has higher industrial application values.

Description

A kind ofly take into account voltage and idle linearisation tidal current computing method

Technical field

The invention belongs to electric power system tide computing technique field, specifically provide and a kind ofly take into account voltage and idle high accuracy linearization tidal current computing method.

Background technology

Power flow equation is the basic physics law followed needed for electric power system delivery of electrical energy.The process solving power flow equation is Load flow calculation.One of calculate greatly as electric power system three, Load flow calculation is the basis of power system analysis.The electric power system application such as Load flow calculation is power system planning accurately, Economic Dispatch, electricity market go out clearly, Power system state estimation, line voltage control provide technical support.Therefore, be one of the most basic, most important research work of electric power system to the research of power flow equation.

Power flow equation can accurately be described by AC power flow equation.The power flow equation of node i is as follows:

Wherein, P _i, Q _ibe respectively active power and the reactive power of node i injection, v _i, v _jbe respectively the voltage magnitude of node i and node j, G _ijand B _ijbe respectively conductance matrix and the susceptance matrix element at the i-th row, jth column position, θ _ijfor the phase difference of voltage between node i and node j.

Visible, AC power flow equation can reflect voltage magnitude, the voltage phase angle of electrical network, gain merit injection and idle injection simultaneously.But AC power flow equation nonlinearity, respectively quantity of state height coupling to be asked, is difficult to direct solution, usually needs by the numerical method such as Newton-Laphson method, algorithm quicksort iterative.But alternative manner is difficult to ensure computational speed and convergence requirement.Especially for optimal power flow problems, the computational methods based on AC power flow equation are adopted to be difficult to meet application request.Therefore, to the simplification of AC power flow equation and approximate very necessary.

Because linear equation has more ripe method for solving, the optimality of result of calculation can be ensured, have a large amount of ripe business software can efficiently robust solve linear equation.Therefore, AC power flow equation being done linearization process is a kind of method that effective reduction power flow equation solves difficulty.DC power flow equation is Typical Representative wherein, now applies in a large number in power industry actual production and scientific research.

DC power flow equation is derived based on supposing as follows: 1) ignore the ground connection branch road in electrical network and line resistance.Therefore DC power flow equation cannot consider grid net loss.2) voltage magnitude of all nodes of system is about 1 (perunit value).3) phase difference of voltage of circuit start node and terminal node is about 0.Because electric power transmission network meets above-mentioned hypothesis, therefore DC power flow equation is injected with good estimation to voltage phase angle and active power usually, and this is also the reason that DC power flow equation has good result of use in electric power system actual moving process.Because DC power flow equation cannot treatment system network loss, in practical application DC power flow equation process, network loss modification is done to load usually heuristicly, lack theory support.There is part can consider the linearisation power flow equation of reactive power flow, but many based on sensitivity analysis modeling, and if system running state offsets, then computational accuracy will decline to a great extent.

In sum, existing power flow equation computational methods are difficult to ensure high computational accuracy, Computationally efficient and good convergence simultaneously.

Summary of the invention

The object of the invention is to the weak point for overcoming prior art, proposing and a kind ofly taking into account voltage and idle linearisation tidal current computing method, the only linear power flow equation of demand solution, the estimation of high-precision voltage magnitude, voltage phase angle and idle injection can be provided.

The a kind of of the present invention's proposition takes into account voltage and idle linearisation tidal current computing method, and it is characterized in that, the method comprises: use Losses estimated value to obtain the meritorious injection vector of node; The matrix needed for computing node voltage phase angle is generated according to power grids circuits parameter; Use optimal estimation method computing node voltage phase angle; According to power transmission network parameter obtain power flow equation solve in required matrix; The compensation term of reactive power is injected with voltage angle values computing node; Utilization linearisation matrix operation obtains the amount to be asked in power flow equation.

Feature of the present invention and beneficial effect:

The present invention according to industrial quarters and academia to the actual demand of AC power flow equation linearization technique, for the deficiency of existing power flow equation linearization technique, what propose can take into account voltage and idle linearisation tidal current computing method, can provide Load flow calculation and comprise voltage phase angle, voltage magnitude, is idlely infused in interior the accurate estimation needing to be asked quantity of state.The present invention has larger improvement, especially for idle injection and voltage magnitude for existing linearisation tidal current computing method in computational accuracy; Meanwhile, the computational methods provided in the present invention do not rely on current system running state, have stronger adaptability to different electric power transmission networks.

Accompanying drawing explanation

The linearisation tidal current computing method flow chart that Fig. 1 the present invention proposes.

Fig. 2 is the node voltage phase angle that the linearisation tidal current computing method using the present invention to propose obtains.

Fig. 3 is the node voltage amplitude that the linearisation tidal current computing method using the present invention to propose obtains.

Fig. 4 is the idle injection of node that the linearisation tidal current computing method using the present invention to propose obtains.

Embodiment

Below in conjunction with drawings and the embodiments, the present invention is further detailed explanation.Should be appreciated that embodiment described herein in order to explain the present invention, but can not limit the present invention.

The a kind of of the present invention's proposition takes into account voltage and idle linearisation tidal current computing method, as shown in Figure 1, it is characterized in that,

If power transmission network has N number of node, node has three classes: V θ node, also referred to as slack bus, voltage magnitude and voltage phase angle given, meritorious inject and be idlely injected to amount to be asked, in conventional Load Flow calculating, only having a V θ node; PV node, is generally generating set place node, meritorious inject and voltage magnitude known, idle injection and voltage phase angle are amount to be asked; PQ node, is generally load bus, meritorious inject and idle injection known, voltage magnitude and voltage phase angle are amount to be asked; Suppose to have 1 V θ node in power transmission network, m-1 PV node, N-m PQ node; Without loss of generality, if the sequence of node serial number is: node 1 is V θ node, and node 2 ~ node m is PV node, and node m+1 ~ node N is PQ node, and the phase angle of V θ node is set to 0;

The method comprises the following steps:

(1) Losses estimated value P is used _lossobtain the vectorial P of meritorious injection of node 1 ~ node N:

According to node type, the meritorious injection of node 2 ~ node N is known, and injection of being gained merit by node 2 ~ node N forms (N-1) × 1 dimensional vector in order, uses P _rrepresent; The vectorial P of meritorious injection that can obtain electrical network interior joint 1 ~ node N according to power conservation is:

Wherein, e _r=[1 ... 1] ^t, be the column vector that (N-1) × 1 is tieed up, all elements is 1;

2) according to the reactance parameter of circuits all in power transmission network, the matrix B needed for estimation node voltage phase angle is generated ₀with

B ₀for N × N ties up matrix, its generation method is such as formula shown in (2):

Wherein, B _{0, ij}for matrix B ₀at the element of the i-th row, jth row, x _ijfor being connected to the reactance of the circuit between node i and node j, if there is not circuit between node i and node j, then x _ij→ ∞, B _{0, ij}=0;

By B ₀writing matrix in block form form, shown in (3):

Wherein, B ₁₁for B ₀element on matrix the 1st row the 1st column position, b ₁for B ₀matrix the 1st arranges, the column vector of 2nd ~ N-th row element composition, and dimension is (N-1) × 1, B _rfor B ₀the matrix that matrix is remaining after removing the first row and first row, dimension is (N-1) × (N-1);

If for B ₀submatrix remaining after matrix removing first row, dimension is N × (N-1), and expression formula is as follows;

3) node 2 ~ voltage N voltage phase angle is estimated:

The voltage phase angle of node 1 is known (being 0), the voltage phase angle vector θ of node 2 ~ node N _{oE, R}available following formula solves:

θ _{oE, R}for (N-1) × 1 is tieed up;

Therefore the voltage phase angle θ of node 1 ~ node N _oEcan be expressed as:

4) obtain the intermediary matrix needing in following Load flow calculation step to use according to power transmission network admittance matrix Y, comprising: G _p, B _p, B _q, G _q, l _vm, L _qm, L _vn, L _qn;

If Y is power transmission network admittance matrix, matrix G and B is respectively real part and the imaginary part of Y matrix, i.e. Y=G+jB, if G _ij, B _ijbe respectively the place element of matrix G, matrix B i-th row jth row, first generate G according to matrix G and matrix B _p, B _p, B _q, G _q:

Wherein, G _{p, ij}, B _{p, ij}, B _{q, ij}, G _{q, ij}represent G respectively _p, B _p, B _q, G _qthe place element of the i-th row jth row;

By G _p, B _p, B _q, G _qbe expressed as matrix in block form form:

Wherein, the dimension of matrix is m × m, all the other matrixs in block form can the like,

And then required intermediary matrix H in Load flow calculation can be obtained ^{(m, m)}, H ^{(m, n)}, H ^{(n, m)}, H ^{(n, n)}as follows:

By matrix H ^{(m, m)}, H ^{(m, n)}, H ^{(n, m)}, H ^{(n, n)}splicing can obtain matrix H:

H is write matrix in block form form, as follows:

Wherein, H ₁₁for the element on H matrix the 1st row the 1st column position, h ₁for H ₀matrix the 1st arranges the column vector of the 2nd ~ the N bit element composition, and dimension is (N-1) × 1, H _rfor H ₀the matrix that matrix is remaining after removing the first row and first row, dimension is (N-1) × (N-1);

If for submatrix remaining after H matrix removing first row, dimension is N × (N-1), and expression formula is as follows;

Matrix L _vm, L _qm, L _vn, L _qncomputational methods are as follows:

5) computing node 1 ~ node N injects the compensation term of reactive power:

Node i idle injecting compensating item W _icomputing formula is as follows:

Wherein, B _ijfor admittance matrix B i-th row jth column element, θ _ij=θ _{oE, i}-θ _{oE, j}, be the phase difference of voltage of formula (5) gained node i and node j.

Can obtain the idle injecting compensating column vector of node is thus W:W=[W ₁..., W _n] ^t, dimension is N × 1

6) amount to be asked in Load flow calculation is asked in utilization matrix operation, comprises the idle injection of node 1 ~ node m, the voltage phase angle of node 2 ~ node N, the voltage magnitude of node m+1 ~ node N;

If the intermediate column vector introduced in Load flow calculation is as follows: v _s, δ ' _s, dimension is N × 1;

Column vector v _s, δ ' _s, the Partitioning Expression of A of P, Q, W is as follows:

Column vector can be obtained by Q and W as follows:

According to the known parameter of V θ node, PQ node, PV node, in known Load Flow Solution, given power transmission network estimation network loss P _loss, column vector P, Q ⁽ⁿ⁾, all elements be known quantity;

First amount to be asked in Load flow calculation and intermediate variable can be obtained according to following equalities:

And then the amount to be asked that can obtain in power flow equation is as follows:

Comprise the idle injection of node 1 ~ node m:

The voltage phase angle of node 2 ~ node N, is the δ ' that formula (33) obtains:

θ _i＝δ′ _i，i＝1，...，N (36)

If v _s,ifor vector v _sin i-th element, its physical significance be voltage magnitude square, therefore the voltage magnitude of node m+1 ~ node N can be obtained:

So far, amount to be asked in all Load flow calculation (comprising the meritorious injection of V θ node and idle injection, the idle injection of PV node and voltage phase angle, the voltage magnitude of PQ node and voltage phase angle) is all drawn by linear matrix computing.

The inventive method adopts IEEE-118 node example to calculate, and data are from the emulation tool Matpower4.1 that increases income.

The contrast of the result of calculation of the node voltage phase angle that put forward the methods of the present invention obtains, PV node is idle injection, PQ node voltage amplitude and AC power flow equation, Traditional DC power flow equation respectively as shown in Figure 2, Figure 3, Figure 4.In figure, the curve of solid line composition is the result of calculation that existing AC power flow equation obtains, the dashed curve of some composition is the result of calculation that existing DC power flow equation obtains, and the curve of triangle mark, line segment composition is the result of calculation of the linearisation power flow equation acquisition that the present invention proposes.Can find out, contrast with traditional DC power flow equation, the estimation of injection that institute of the present invention extracting method can obtain precision better node voltage phase angle, PV node is idle and PQ node voltage amplitude, and the result of calculation that obtains of method that proposes of the present invention and AC power flow equation comparatively close.

Visible, the tidal current computing method that the present invention proposes has higher computational accuracy, and the institute of the present invention extracting method only linear power flow equation of demand solution, there is not convergence problem.

Above implementation step is the unrestricted technical scheme of the present invention in order to explanation only.Do not depart from any modification or partial replacement of spirit and scope of the invention, all should be encompassed in the middle of right of the present invention.

Claims (2)

1. take into account voltage and an idle linearisation tidal current computing method, it is characterized in that, the method comprises: use Losses estimated value to obtain the meritorious injection vector of node; The matrix needed for computing node voltage phase angle is generated according to power grids circuits parameter; Use optimal estimation method estimation node voltage phase angle; According to power transmission network parameter obtain power flow equation solve in required matrix; The compensation term of reactive power is injected with voltage angle values computing node; Utilization linearisation matrix operation obtains the amount to be asked in power flow equation.

2. method as claimed in claim 1, it is characterized in that, the method establishes power transmission network to have N number of node, wherein has 1 V θ node, m-1 PV node, N-m PQ node; By node serial number rearrangement be: node 1 is V θ node, and node 2 ~ node m is PV node, and node m+1 ~ node N is PQ node, and the phase angle of V θ node is set to 0; V θ node voltage amplitude and voltage phase angle given, meritorious inject and be idlely injected to amount to be asked; PV node is meritorious inject and voltage magnitude known, idle injection and voltage phase angle are waited to ask; PQ node is meritorious inject and idle injection known, voltage magnitude and voltage phase angle are waited to ask; The method specifically comprises the following steps:

(1) Losses estimated value P is used _lossobtain the vectorial P of meritorious injection of node 1 ~ node N:

The meritorious injection of known node 2 ~ node N, injection of being gained merit by node 2 ~ node N forms (N-1) × 1 dimensional vector in order, uses P _rrepresent; The vectorial P of meritorious injection that can obtain electrical network interior joint 1 ~ node N according to power conservation is:

$P=\left(\begin{array}{c}-e_R^T{P}_R+P_{Loss}\\ P_R\end{array}\right)---\left(1\right)$

Wherein, e _r=[1 ... 1] ^t, be the column vector that (N-1) × 1 is tieed up, all elements is 1;

2) according to the reactance parameter of circuits all in power transmission network, the matrix B needed for computing node voltage phase angle is generated ₀and B

B ₀for N × N ties up matrix, its computational methods are such as formula shown in (2):

B _0,ij＝-1/x _ij,B _0,ii＝-Σ _j≠iB _0,ij(2)

Wherein, B _{0, ij}for matrix B ₀at the element of the i-th row, jth row, x _ijfor being connected to the reactance of the circuit between node i and node j, if there is not circuit between node i and node j, then x _ij→ ∞, B _{0, ij}=0;

By B ₀writing matrix in block form form, shown in (3):

$B_0=\left(\begin{array}{cc}{B}_{11}& b_1^T\\ b_1& B_R\end{array}\right)---\left(3\right)$

Wherein, B ₁₁for B ₀element on matrix the 1st row the 1st column position, b ₁for B ₀matrix the 1st arranges the column vector of the 2nd ~ the N bit element composition, and dimension is (N-1) × 1, B _rfor B ₀the matrix that matrix is remaining after removing the first row and first row, dimension is (N-1) × (N-1);

If for B ₀submatrix remaining after matrix removing first row, dimension is N × (N-1), and expression formula is as follows;

3) computing node 2 ~ voltage N voltage phase angle:

Due to the voltage phase angle of node 1 known (being 0), the voltage phase angle of node 2 ~ node N is waited to ask, the voltage phase angle vector θ of node 2 ~ node N _{oE, R}available following formula solves:

θ _{oE, R}for (N-1) × 1 is tieed up;

Therefore the voltage phase angle θ of node 1 ~ node N _oEcan be expressed as:

${\mathrm{\θ}}_{OE}=\left(\begin{array}{c}0\\ {\mathrm{\θ}}_{OE,R}\end{array}\right)---\left(6\right)$

4) Load flow calculation is asked for according to power transmission network admittance matrix and impedance matrix, if the trend intermediary matrix used in computational process is respectively: G _p, B _p, B _q, G _q, l _vm, L _qm, L _vn, L _qn;

If Y is power transmission network admittance matrix, matrix G and B is respectively real part and the imaginary part of Y matrix, i.e. Y=G+jB, if G _ij, B _ijbe respectively the place element of matrix G, matrix B i-th row jth row, first generate G according to matrix G and matrix B _p, B _p, B _q, G _q:

$G_{P,ii}=\frac{1}{2}\underset{j=1}{\overset{N}{\Σ}}{G}_{ij}+\frac{1}{2}{G}_{ii},G_{P,ij}=\frac{1}{2}{G}_{ij}---\left(7\right)$

$B_{P,ii}=-\underset{j=1,j\≠i}{\overset{N}{\Σ}}{B}_{ij},B_{P,ij}=B_{ij}---\left(8\right)$

$B_{Q,ii}=\frac{1}{2}\underset{j=1}{\overset{N}{\Σ}}{B}_{ij}+\frac{1}{2}{B}_{ii},B_{P,ij}=\frac{1}{2}{B}_{ij}---\left(9\right)$

$G_{Q,ii}=-\underset{j=1}{\overset{N}{\Σ}}{G}_{ij},G_{Q,ij}=G_{ij}---\left(10\right)$

Wherein, G _{p, ij}, B _{p, ij}, B _{q, ij}, G _{q, ij}represent G respectively _p, B _p, B _q, G _qthe place element of the i-th row jth row;

By G _p, B _p, B _q, G _qbe expressed as matrix in block form form:

$G_P=\left(\begin{array}{cc}{G}_P^{(m,m)}& G_P^{(m,n)}\\ G_P^{(n,m)}& G_P^{(n,n)}\end{array}\right)---\left(11\right)$

$B_P=\left(\begin{array}{cc}{B}_P^{(m,m)}& B_P^{(m,n)}\\ B_P^{(n,m)}& B_P^{(n,n)}\end{array}\right)---\left(12\right)$

$B_Q=\left(\begin{array}{cc}{B}_Q^{(m,m)}& B_Q^{(m,n)}\\ B_Q^{(n,m)}& B_Q^{(n,n)}\end{array}\right)---\left(13\right)$

$G_Q=\left(\begin{array}{cc}{G}_Q^{(m,m)}& G_Q^{(m,n)}\\ G_Q^{(n,m)}& G_Q^{(n,n)}\end{array}\right)---\left(14\right)$

Wherein, the dimension of matrix is m × m, all the other matrixs in block form can the like,

And then required intermediary matrix H in Load flow calculation can be obtained ^{(m, m)}, H ^{(m, n)}, H ^{(n, m)}, H ^{(n, n)}as follows:

$H^{(m,m)}=-B_P^{(m,m)}-G_P^{(m,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,m)}---\left(15\right)$

$H^{(m,n)}=-B_P^{(m,n)}-G_P^{(m,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,n)}---\left(16\right)$

$H^{(n,m)}=-B_P^{(n,m)}-G_P^{(n,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,m)}---\left(17\right)$

$H^{(n,n)}=-B_P^{(n,n)}-G_P^{(n,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,n)}---\left(18\right)$

By matrix H ^{(m, m)}, H ^{(m, n)}, H ^{(n, m)}, H ^{(n, n)}splicing can obtain matrix H:

$H=\left(\begin{array}{cc}{H}^{(m,m)}& H^{(m,n)}\\ H^{(n,m)}& H^{(n,n)}\end{array}\right)---\left(19\right)$

H is write matrix in block form form, as follows:

$H=\left(\begin{array}{cc}{H}_{11}& h_1^T\\ h_1& H_R\end{array}\right)---\left(20\right)$

Wherein, H ₁₁for the element on H matrix the 1st row the 1st column position, h ₁for H ₀matrix the 1st arranges the column vector of the 2nd ~ the N bit element composition, and dimension is (N-1) × 1, H _rfor H ₀the matrix that matrix is remaining after removing the first row and first row, dimension is (N-1) × (N-1);

If for submatrix remaining after H matrix removing first row, dimension is N × (N-1), and expression formula is as follows;

Matrix L _vm, L _qm, L _vn, L _qncomputational methods are as follows:

$L_{vm}=G_P^{(m,m)}-G_P^{(m,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{B}_Q^{(n,m)}---\left(22\right)$

$L_{vn}=G_P^{(n,n)}-G_P^{(m,n)}{\left(B_Q^{(n,n)}\right)}^{-1}{B}_Q^{(n,m)}---\left(23\right)$

$L_{Qm}=-G_P^{(m,n)}{\left(B_Q^{(n,n)}\right)}^{-1}---\left(24\right)$

$L_{Qm}=-G_P^{(n,n)}{\left(B_Q^{(n,n)}\right)}^{-1}---\left(25\right)$

5) computing node 1 ~ node N injects the compensation term of reactive power:

Node idle injecting compensating item W _icomputing formula is as follows:

$W_i=\underset{j=1}{\overset{N}{\Σ}}{B}_{ij}\frac{{\mathrm{\θ}}_{ij}^2}{2}---\left(26\right)$

Wherein, B _ijfor admittance matrix B i-th row jth column element, θ _ij=θ _{oE, i}-θ _{oE, j}, be the phase difference of voltage of formula (5) gained node i and node j.

Can obtain the idle injecting compensating column vector of node is thus W:W=[W ₁..., W _n] ^t, dimension is N × 1

6) amount to be asked in Load flow calculation is asked in utilization matrix operation, comprises the idle injection of node 1 ~ node m, the voltage phase angle of node 2 ~ node N, the voltage magnitude of node m+1 ~ node N;

If the intermediate column vector introduced in Load flow calculation is as follows: v _s, δ ' _s, dimension is N × 1;

Column vector v _s, δ ' _s, the Partitioning Expression of A of P, Q, W is as follows:

$v_s=\left(\begin{array}{c}{v}_S^{\left(m\right)}\\ v_S^{\left(n\right)}\end{array}\right)---\left(27\right)$

${\mathrm{\δ}}_s^{\′}=\left(\begin{array}{c}{\mathrm{\δ}}^{\′\left(m\right)}\\ {\mathrm{\δ}}^{\′\left(n\right)}\end{array}\right)---\left(28\right)$

$P=\left(\begin{array}{c}{P}^{\left(m\right)}\\ P^{\left(n\right)}\end{array}\right)---\left(29\right)$

$Q=\left(\begin{array}{c}{Q}^{\left(m\right)}\\ Q^{\left(n\right)}\end{array}\right)---\left(30\right)$

$W=\left(\begin{array}{c}{W}^{\left(m\right)}\\ W^{\left(n\right)}\end{array}\right)---\left(31\right)$

Column vector can be obtained by Q and W as follows:

$\stackrel{\‾}{Q}=\left(\begin{array}{c}{\stackrel{\‾}{Q}}^{\left(m\right)}\\ {\stackrel{\‾}{Q}}^{\left(n\right)}\end{array}\right)=Q-W=\left(\begin{array}{c}{Q}^{\left(m\right)}\\ Q^{\left(n\right)}\end{array}\right)-\left(\begin{array}{c}{W}^{\left(m\right)}\\ W^{\left(n\right)}\end{array}\right)---\left(32\right)$

According to the known parameter of V θ node, PQ node, PV node, in Load Flow Solution, given power transmission network estimation network loss P _loss, column vector P, Q ⁽ⁿ⁾, all elements be known quantity;

First amount to be asked in Load flow calculation and intermediate variable can be obtained according to following equalities:

$\begin{array}{c}{v}_S^{\left(n\right)}=-{\left(B_Q^{(n,n)}\right)}^{-1}{\stackrel{\‾}{Q}}^{\left(n\right)}-{\left(B_Q^{(n,n)}\right)}^{-1}{B}_Q^{(n,m)}{v}_S^{\left(m\right)}\\ -{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,m)}{\mathrm{\δ}}^{\′\left(m\right)}-{\left(B_Q^{(n,n)}\right)}^{-1}{G}_Q^{(n,n)}{\mathrm{\δ}}^{\′\left(n\right)}\end{array}---\left(34\right)$

And then the amount to be asked that can obtain in power flow equation is as follows:

Comprise the idle injection of node 1 ~ node m:

$\begin{array}{c}{Q}^{\left(m\right)}=-B_Q^{(m,m)}{v}_S^{\left(m\right)}-B_Q^{(m,n)}{v}_S^{\left(n\right)}\\ -G_Q^{(m,m)}{\mathrm{\δ}}^{\′\left(m\right)}-G_Q^{(m,n)}{\mathrm{\δ}}^{\′\left(n\right)}+W^{\left(m\right)}\end{array}---\left(35\right)$

The voltage phase angle of node 2 ~ node N, is the voltage phase angle that formula (5) obtains:

θ _i＝θ _OE,i,i＝2,...,N(36)

If v _s,ifor vector v _sin i-th element, its physical significance be voltage magnitude square, therefore the voltage magnitude of node m+1 ~ node N can be obtained:

$v_i^2=v_{s,i},i=m+1,\mathrm{...},N---\left(37\right)$

So far, the amount to be asked in all Load flow calculation is all drawn by linear matrix computing.