CN104993491B - 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 of meter and voltage and idle linearisation tidal current computing method

Technical field

The invention belongs to electric power system tide computing technique field, a kind of meter and voltage and idle high-precision are specifically provided Degree linearisation tidal current computing method.

Background technology

Power flow equation is the basic physics law followed needed for the transmission of power system electric energy.Solve power flow equation process be For Load flow calculation.Used as one of three big calculating of power system, Load flow calculation is the basis of Power System Analysis.Accurate trend meter Calculate for Power System Planning, Economic Dispatch, electricity market go out clearly, Power system state estimation, line voltage control Technical support is provided Deng power system application.Therefore, it is that power system is most basic, most important scientific research to the research of power flow equation One of work.

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

Wherein, P_i、Q_iActive power and reactive power that respectively node i is injected, v_i、v_jRespectively node i and node j Voltage magnitude, G_ijAnd B_ijRespectively conductance matrix and susceptance matrix are in the i-th row, the element of jth column position, θ_ijFor node i and Phase difference of voltage between node j.

It can be seen that, AC power flow equation can reflect voltage magnitude, voltage phase angle, active injection and the idle note of electrical network simultaneously Enter.However, AC power flow equation nonlinearity, respectively quantity of state to be asked highly is coupled, it is difficult to direct solution, it usually needs pass through The numerical method iterative such as Newton-Laphson method, algorithm quicksort.However, alternative manner is difficult to ensure that calculating speed and convergence Property require.Especially for optimal power flow problems, adopt and be difficult to meet practical application based on the computational methods of AC power flow equation Require.Therefore, the simplification to AC power flow equation is very necessary with approximate.

As linear equation has more ripe method for solving, it is ensured that the optimality of result of calculation, there are a large amount of maturation business Industry software part is capable of the solution linear equation of efficient robust.Therefore, it is a kind of effectively drop AC power flow equation to be done linearization process The method that low tide flow equation solves difficulty.DC power flow equation is Typical Representative therein, now applies to power industry reality in a large number In border production and scientific research.

DC power flow equation is based on the assumption that derive：1) ignore ground connection branch road and the line resistance in electrical network.Therefore direct current Power flow equation cannot consider grid net loss.2) voltage magnitude of all nodes of system is about 1 (perunit value).3) circuit start node It is about 0 with the phase difference of voltage of terminal node.As power transmission network meets above-mentioned it is assumed that event DC power flow equation is generally to voltage Phase angle and active power are injected with preferably estimation, and this is also that DC power flow equation has good in power system actual moving process The reason for good using effect.Due to DC power flow equation cannot processing system network loss, during practical application DC power flow equation Network loss modification is generally heuristically done to load, lacks theory support.There is part it can be considered that the linearisation trend of reactive power flow Equation, but it is many based on sensitive analysis modeling, and if system running state shifts, computational accuracy will decline to a great extent.

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

The content of the invention

It is an object of the invention to be the weak point for overcoming prior art, it is proposed that a kind of meter and voltage and idle line Property tidal current computing method, it is only necessary to solve linear power flow equation, using the teaching of the invention it is possible to provide high-precision voltage magnitude, voltage phase angle and idle The estimation of injection.

A kind of meter proposed by the present invention and voltage and idle linearisation tidal current computing method, it is characterised in that the method Including：Estimate to be worth to the active injection vector of node with Losses；Calculate node is generated according to power grids circuits parameter Matrix needed for voltage phase angle；With optimal estimation method calculate node voltage phase angle；Trend side is obtained according to transmission of electricity network parameters Matrix needed for journey solution；The compensation term of reactive power is injected with voltage angle values calculate node；Transport with linearisation matrix Calculation obtains the amount to be asked in power flow equation.

The characteristics of of the invention and beneficial effect：

Actual demand of the present invention according to industrial quarters and academia to AC power flow equation linearization technique, for existing tide The deficiency of flow equation linearization technique, can counting and voltage and idle linearisation tidal current computing method for proposition, can be given Load flow calculation include voltage phase angle, voltage magnitude, it is idle be infused in the needed accurate estimation for seeking quantity of state.The present invention For existing linearisation tidal current computing method has larger improvement in computational accuracy, particularly with idle injection and voltage amplitude Value；Meanwhile, in the present invention, the computational methods that provide do not rely on current system running state, different power transmission networks is had compared with Strong adaptability.

Description of the drawings

Fig. 1 linearisation tidal current computing method flow charts proposed by the present invention.

Fig. 2 is the node voltage phase angle obtained with linearisation tidal current computing method proposed by the present invention.

Fig. 3 is the node voltage amplitude obtained with linearisation tidal current computing method proposed by the present invention.

Fig. 4 is the idle injection of node obtained with linearisation tidal current computing method proposed by the present invention.

Specific embodiment

Below in conjunction with the accompanying drawings and embodiment the present invention is further detailed explanation.It should be appreciated that described herein Specific embodiment may be used to explain the present invention, but limit the present invention.

A kind of meter proposed by the present invention and voltage and idle linearisation tidal current computing method, as shown in figure 1, its feature exists In,

If power transmission network has N number of node, node has three classes：V θ nodes, also referred to as slack bus, voltage magnitude and voltage Phase angle gives, and active injection is injected to amount to be asked with idle, and conventional Load Flow only has a V θ node in calculating；PV node, generally For generating set place node, active injection and voltage magnitude, it is known that idle injection and voltage phase angle are amount to be asked；PQ nodes, Usually load bus, active injection and idle injection are, it is known that voltage magnitude and voltage phase angle are amount to be asked；In assuming power transmission network Have 1 V θ node, m-1 PV node, N-m PQ node；Without loss of generality, if node serial number is ordered as：Node 1 is V θ Node, 2～node of node m are PV node, and node m+1～node N is PQ nodes, and the phase angle of V θ nodes is set to 0；

The method is comprised the following steps：

(1) with Losses estimated value P_LossObtain the active injection vector P of node 1～node N：

According to node type, the active injection of node 2～node N is, it is known that by node 2～node N active injection in order The composition composition dimensional vector of (N-1) × 1, uses P_RRepresent；The active note of electrical network interior joint 1～node N can be obtained according to power conservation Incoming vector P is：

Wherein, e_R=[1 ... 1]^T, it is the column vector of the dimension of (N-1) × 1, all elements are 1；

2) reactance parameter according to all circuits in power transmission network, generates the matrix B needed for estimation node voltage phase angle₀With

B₀For N × N-dimensional matrix, shown in its generation method such as formula (2)：

B_0,ij=-1/x_ij,B_0,ii=-∑_j≠iB_0,ij (2)

Wherein, B_0,ijFor matrix B₀In the element that the i-th row, jth are arranged, x_ijFor the circuit that is connected between node i and node j Reactance, if there is no circuit, x between node i and node j_ij→ ∞, B_0,ij=0；

By B₀Writing matrix in block form form, as shown in formula (3)：

Wherein, B₁₁For B₀Element on the 1st column position of the 1st row of matrix, b₁For B₀The row of matrix the 1st, 2～Nth row element group Into column vector, dimension be (N-1) × 1, B_RFor B₀Matrix removes remaining matrix after the first row and first row, and dimension is (N-1) ×(N-1)；

IfFor B₀Matrix removes remaining submatrix after first row, and dimension is N × (N-1), and expression formula is as follows；

3) node 2～voltage N voltage phase angles are estimated：

(being 0), the voltage phase angle vector θ of node 2～node N known to the voltage phase angle of node 1_OE,RAvailable following formula is solved：

θ_OE,RTie up for (N-1) × 1；

Therefore the voltage phase angle θ of node 1～node N_OEIt is represented by：

4) intermediary matrix for needing to use in following Load flow calculation steps is obtained according to power transmission network admittance matrix Y, including： 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 are respectively the real part and imaginary part, i.e. Y=G+jB of Y matrixes, if G_ij、 B_ijThe place element of respectively matrix G, the i-th row of matrix B jth row, generates G according to matrix G and matrix B first_P、B_P、B_Q、G_Q：

Wherein, G_P,ij、B_P,ij、B_Q,ij、G_Q,ijG is represented 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_QIt is expressed as matrix in block form form：

Wherein,The dimension of matrix be m × m, remaining matrix in block form can the like,

And then intermediary matrix H needed for Load flow calculation can be obtained^(m,m)、H^(m,n)、H^(n,m)、H^(n,n)It is as follows：

By matrix H^(m,^m)、H^(m,n)、H^(n,m)、H^(n,n)Splicing can obtain matrix H：

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

Wherein, H₁₁For the element on the 1st column position of the 1st row of H-matrix, h₁For H₀Matrix the 1st arranges the 2nd～the N-bit element group Into column vector, dimension be (N-1) × 1, H_RFor H₀Matrix removes remaining matrix after the first row and first row, and dimension is (N-1) ×(N-1)；

IfRemaining submatrix after first row is removed for H-matrix, 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) 1～node of calculate node N injects the compensation term of reactive power：

Node iIdle injecting compensating item W_iComputing formula is as follows：

Wherein, B_ijFor admittance matrix B the i-th row jth column elements, θ_ij=θ_OE,i-θ_OE,j, it is node i and section obtained by formula (5) The phase difference of voltage of point j.

Thus the idle injecting compensating column vector of node can be obtained for W：W=[W₁,...,W_N]^T, dimension is N × 1

6) amount to be asked in Load flow calculation, including the idle injection of node 1～node m, node 2 are asked for matrix operationss The voltage phase angle of～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 WIt is as follows：

According to V θ nodes, PQ nodes, PV node known parameter, it is known that in Load Flow Solution, give power transmission network estimation network loss P_Loss, column vector P, Q⁽ⁿ⁾、All elements be known quantity；

Amount to be asked and the intermediate variable in Load flow calculation can be obtained first according to following equalities：

The amount to be asked that further can be obtained in power flow equation is as follows：

Including the idle injection of node 1～node m：

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

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 node m+1 can be obtained The voltage magnitude of～node N：

So far, amount to be asked in all Load flow calculations (includes active injection and idle injection, the nothing of PV node of V θ nodes Work(injects and voltage phase angle, the voltage magnitude of PQ nodes and voltage phase angle) drawn by linear matrix computing.

The inventive method is calculated using IEEE-118 nodes example, and data are from the emulation tool Matpower4.1 that increases income.

Node voltage phase angle that proposition method of the present invention is obtained, PV node is idle injection, the calculating of PQ node voltage amplitudes As a result distinguish as shown in Figure 2, Figure 3, Figure 4 with the contrast of AC power flow equation, Traditional DC power flow equation.Solid line composition in figure Curve is the result of calculation that existing AC power flow equation is obtained, and the dashed curve for putting composition is obtained for existing DC power flow equation The result of calculation for obtaining, triangle mark, the curve of line segment composition are the calculating knot that linearisation power flow equation proposed by the present invention is obtained Really.As can be seen that contrasting with traditional DC power flow equation, institute's extracting method of the present invention is obtained in that the more preferable node voltage of precision Injection that phase angle, PV node are idle and the estimation of PQ node voltage amplitudes, and the result of calculation that method proposed by the present invention is obtained It is closer to AC power flow equation.

It can be seen that, tidal current computing method proposed by the present invention has higher computational accuracy, and institute's extracting method of the present invention only demand Linear power flow equation is solved, there is no convergence problem.

Above implementation steps are only to illustrative and not limiting technical scheme.Without departing from spirit and scope of the invention Any modification or partial replacement, all should cover in the middle of scope of the presently claimed invention.

Claims (1)

1. it is a kind of to count and voltage and idle linearisation tidal current computing method, it is characterised in that the method includes：With power transmission network Network loss is estimated to be worth to the active injection vector of node；Square according to needed for power grids circuits parameter generates calculate node voltage phase angle Battle array；Node voltage phase angle is estimated with optimal estimation method；Square according to needed for transmission of electricity network parameters obtain power flow equation solution Battle array；The compensation term of reactive power is injected with voltage angle values calculate node；Obtain in power flow equation with linearisation matrix operationss Amount to be asked；

The method sets power transmission network and has N number of node, wherein having 1 V θ node, m-1 PV node, N-m PQ node；Will section Putting numbering rearrangement is：Node 1 be V θ nodes, 2～node of node m be PV node, node m+1～node N be PQ nodes, V θ The phase angle of node is set to 0；V θ node voltage amplitudes and voltage phase angle are given, and active injection is injected to amount to be asked with idle；PV is saved The active injection of point and voltage magnitude are, it is known that idle injection and voltage phase angle are waited to ask；PQ nodes it is active injection and it is idle injection, it is known that Voltage magnitude and voltage phase angle are waited to ask；The method specifically includes following steps：

(1) with Losses estimated value P_LossObtain the active injection vector P of node 1～node N：

The active injection of known node 2～node N, by node 2～node N active injection, composition composition (N-1) × 1 is tieed up in order Column vector, uses P_RRepresent；According to the active injection vector P that power conservation can obtain electrical network interior joint 1～node N it 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, it is the column vector of the dimension of (N-1) × 1, all elements are 1；

2) reactance parameter according to all circuits in power transmission network, generates the matrix B needed for calculate node voltage phase angle₀WithB₀For N × N-dimensional matrix, shown in its computational methods such as formula (2)：

B_0,ij=-1/x_ij,B_0,ii=-∑_j≠iB_0,ij (2)

Wherein, B_0,ijFor matrix B₀In the element that the i-th row, jth are arranged, x_ijThe reactance of the circuit to be connected between node i and node j, If there is no circuit, x between node i and node j_ij→ ∞, B_0,ij=0；

By B₀Writing matrix in block form form, as shown in formula (3)：

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

Wherein, B₁₁For B₀Element on the 1st column position of the 1st row of matrix, b₁For B₀Matrix the 1st arranges the 2nd～the N-bit element composition Column vector, dimension are (N-1) × 1, B_RFor B₀Matrix removes remaining matrix after the first row and first row, dimension be (N-1) × (N-1)；

IfFor B₀Matrix removes remaining submatrix after first row, and dimension is N × (N-1), and expression formula is as follows；

3) 2～voltage of calculate node N voltage phase angles：

Due to node 1 voltage phase angle known to (be 0), the voltage phase angle of node 2～node N is waited to ask, the electricity of node 2～node N Pressure phase angle vector θ_OE,RAvailable following formula is solved：

θ_OE,RTie up for (N-1) × 1；

Therefore the voltage phase angle θ of node 1～node N_OEIt is represented by：

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

4) Load flow calculation is asked for according to power transmission network admittance matrix and impedance matrix, designs square in the middle of the trend used in calculation process Battle array 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 are respectively the real part and imaginary part, i.e. Y=G+jB of Y matrixes, if G_ij、B_ijRespectively For the place element that matrix G, the i-th row of matrix B jth are arranged, G is generated according to matrix G and matrix B first_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,ijG is represented 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_QIt is 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 be m × m, remaining matrix in block form can the like,

And then intermediary matrix H needed for Load flow calculation can be obtained^(m,m)、H^(m,n)、H^(n,m)、H^(n,n)It is 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 into matrix in block form form, it is as follows：

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

Wherein, H₁₁For the element on the 1st column position of the 1st row of H-matrix, h₁For H₀Matrix the 1st arranges the row of the 2nd～the N-bit element composition Vector, dimension are (N-1) × 1, H_RFor H₀Matrix removes remaining matrix after the first row and first row, and dimension is (N-1) × (N- 1)；

IfRemaining submatrix after first row is removed for H-matrix, 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) 1～node of calculate node N injects the compensation term of reactive power：

NodeIdle 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 the i-th row jth column elements, θ_ij=θ_OE,i-θ_OE,j, it is node i and node j obtained by formula (5) Phase difference of voltage；

Thus the idle injecting compensating column vector of node can be obtained for W：W=[W₁,...,W_N]^T, dimension is N × 1；

6) amount to be asked in Load flow calculation, including the idle injection of node 1～node m, 2～section of node are asked for matrix operationss The voltage phase angle of point 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 WIt is 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 V θ nodes, PQ nodes, PV node known parameter, in Load Flow Solution, give power transmission network estimation network loss P_Loss, arrange to Amount P, Q⁽ⁿ⁾、All elements be known quantity；

Amount to be asked and the intermediate variable in Load flow calculation can be obtained first according to following equalities：

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

The amount to be asked that further can be obtained in power flow equation is as follows：

Including 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, the voltage phase angle that as formula (5) is obtained：

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 node m+1～section can be obtained The voltage magnitude of point N：

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

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