CN102707176B - Failure predication method for static security analysis of three-winding transformer - Google Patents

Abstract

The invention provides a failure predication method for static security analysis of three-winding transformers, belonging to the technical field of electric system analysis. In the invention, transformers are sorted aiming at connection modes mainly adopted by the three-winding transformers in an electric grid, and the computing mode of the on-off sensitivity of different wire connection modes is deduced. The invention is suitable for the computation of the sensitivity of load flows of most faulty three-winding transformers in the electric grid, solves the problem that the conventional sensitivity algorithm can not be applied due to local electric power shutdown caused by the failure of the three-winding transformers and can meet the requirement of the on-line real-time second grade analysis and computation of the large-scale electric grid in both accuracy and speed by acquiring comprehensive accurate operating data of power flows and reactive power flows of a system, voltage amplitudes value and voltage phases of a bus, and the like.

Description

A kind of three-winding transformer fault judgment method for static security analysis

Technical field

The invention belongs to Power System Analysis technical field, be specifically related to a kind of three-winding transformer fault judgment method for static security analysis.

Background technology

Static security analysis is the important component part of security analysis of electric power system, at present, static security analysis N-1 generally adopts the methods such as Sensitivity Method, DC power flow algorithm and penalty method, wherein, DC power flow algorithm can not calculate idle and voltage, and modern power systems is requiring to check that Branch Power Flow power, section tidal current power also need to check that whether busbar voltage is out-of-limit in whether out-of-limit; If penalty method iterations is inadequate, the error of its voltage and reactive power flow is also larger; Sensitivity Method is considered as branch breaking a kind of disturbance of normal operation, with the increment of node injecting power, simulate the impact of branch breaking, the comprehensive system performance measure that comprises meritorious, idle, node voltage, phase angle can be provided, there is very high computational accuracy and speed, have a clear superiority in.

Under the situation constantly expanding in electric system scale, intelligent grid supporting system technology has had higher requirement to the computational accuracy of static security analysis N-1 and speed, not only needs trace wiring and unit, also needs the elements such as scan transformer and bus.Wherein, three-winding transformer fault relates to multiple branch circuit and cut-offs, simultaneously mesolow side often connect separately injection element or etc. duty value and cause local dead electricity after fault, make conventional sensitivity algorithm not be suitable for the situation of the local dead electricity of electric system after fault, and again form matrix and factor table calculates in the time of need to expending a large amount of machine, can not meet the rate request that large electrical network level second is calculated in real time.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of three-winding transformer fault judgment method for static security analysis;

In order to realize foregoing invention object, the present invention takes following technical scheme:

A three-winding transformer fault judgment method for static security analysis, said method comprising the steps of:

Step 1: carry out the calculating of ground state trend, obtain Jacobi matrix J ₀, corresponding sensitivity matrix S ₀with the electrical network original state variable X being formed by node voltage and phase angle ₀;

Step 2: the mode of connection that judges the three-winding transformer that breaks down;

Step 3: calculate electric network state variable and trend power according to the mode of connection;

Step 4: judging whether electric system exists out-of-limit phenomenon, is if so, harmful fault by the fault definition occurring.

In described step 2, the mode of connection comprises that cut-offfing the mode of connection, the low-pressure side that can not cause off-the-line or dead electricity connects separately the mode of connection that injection element is connected major network connected mode with medium voltage side, connected mode that low/medium voltage side connects separately injection element separately and low/medium voltage side connect isolated island.

In described step 3, for cut-offfing, can not cause that mode of connection calculating electric network state variable X 1 process of off-the-line or dead electricity is as follows:

If three-winding transformer high-pressure side, medium voltage side and low-pressure side three side gussets are respectively node h, node m and node l, neutral node is node o, and the equivalent injecting power increment that cut-offs of node o, node m and node l is:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_o\\ \mathrm{\Δ}{Q}_o\\ \mathrm{\Δ}{P}_m\\ \mathrm{\Δ}{Q}_m\\ \mathrm{\Δ}{P}_l\\ \mathrm{\Δ}{Q}_l\end{array}\right]=H^{-1}\left[\begin{array}{c}{P}_{\mathrm{om}}+P_{\mathrm{ol}}\\ Q_{\mathrm{om}}+Q_{\mathrm{ol}}\\ P_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{lo}}\\ Q_{\mathrm{lo}}\end{array}\right]$

In formula, Δ P ₀, Δ P _mwith Δ P _lbe respectively the equivalence of cut-offfing branch breaking posterior nodal point o, node m and node l in the mode of connection that can not cause off-the-line or dead electricity and inject meritorious power increment, Δ Q _o, Δ Q _mwith Δ Q _lreactive power increment, P are injected in the equivalence that is respectively branch breaking posterior nodal point o, node m and node l _omand Q _ombe respectively the ground state trend reactive power of node o to the ground state trend active power of node m direction and node o to node m direction, P _oland Q _olbe respectively the ground state trend reactive power of node o to the ground state trend active power of node l direction and node o to node l direction, P _moand Q _mobe respectively the ground state trend reactive power of node m to the ground state trend active power of node o direction and node m to node o direction, P _loand Q _lobe respectively the ground state trend reactive power of node l to the ground state trend active power of node o direction and node l to node o direction;

Matrix H=I+LS, wherein H, I, L and S are 6 * 6 rank matrixes, and I is unit matrix;

Matrix L expression formula is as follows:

$L=\left[\begin{array}{cccccc}{H}_{\mathrm{om}}+H_{\mathrm{ol}}& -2P_{\mathrm{om}}-2P_{\mathrm{ol}}+N_{\mathrm{om}}+N_{\mathrm{ol}}& -H_{\mathrm{om}}& -N_{\mathrm{om}}& -H_{\mathrm{ol}}& -N_{\mathrm{ol}}\\ M_{\mathrm{om}}+M_{\mathrm{ol}}& -2Q_{\mathrm{om}}-2Q_{\mathrm{ol}}+L_{\mathrm{om}}+L_{\mathrm{ol}}& -M_{\mathrm{om}}& -L_{\mathrm{om}}& -M_{\mathrm{ol}}& -L_{\mathrm{ol}}\\ -H_{\mathrm{mo}}& -N_{\mathrm{mo}}& H_{\mathrm{mo}}& -2P_{\mathrm{mo}}+N_{\mathrm{no}}& & \\ -M_{\mathrm{mo}}& -L_{\mathrm{mo}}& M_{\mathrm{mo}}& -2Q_{\mathrm{mo}}+L_{\mathrm{mo}}& & \\ -H_{\mathrm{lo}}& -N_{\mathrm{lo}}& & & H_{\mathrm{lo}}& -2P_{\mathrm{lo}}+N_{\mathrm{lo}}\\ -M_{\mathrm{lo}}& -L_{\mathrm{lo}}& & & M_{\mathrm{lo}}& -2Q_{\mathrm{lo}}+L_{\mathrm{lo}}\end{array}\right]$

In formula, H _om, M _om, N _om, L _om, H _mo, M _mo, N _mo, L _mo, H _ol, M _ol, N _ol, L _ol, H _lo, M _lo, N _loand L _lobe Jacobi matrix J ₀element;

The expression formula of matrix S is as follows:

$S=\left[\begin{array}{cccccc}\frac{\∂{\mathrm{\θ}}_o}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂P}_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_l}\\ \frac{\∂U_o}{U_o\∂P_o}& \frac{{\∂U}_o}{U_o{\∂Q}_o}& \frac{{\∂U}_o}{U_o{\∂P}_m}& \frac{{\∂U}_o}{U_o{\∂Q}_m}& \frac{\∂U_o}{U_o\∂P_l}& \frac{\∂U_o}{U_o\∂Q_l}\\ \frac{\∂{\mathrm{\θ}}_m}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_m}& \frac{\∂{\mathrm{\θ}}_m}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_m}{\∂Q_l}\\ \frac{\∂U_m}{U_m\∂P_o}& \frac{{\∂U}_m}{U_m{\∂Q}_o}& \frac{{\∂U}_m}{U_m{\∂P}_m}& \frac{{\∂U}_m}{U_m{\∂Q}_m}& \frac{\∂U_m}{U_m\∂P_l}& \frac{\∂U_m}{U_m\∂Q_l}\\ \frac{\∂{\mathrm{\θ}}_l}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_l}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_l}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_l}{{\∂Q}_m}& \frac{\∂{\mathrm{\θ}}_l}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_l}{\∂Q_l}\\ \frac{\∂U_l}{U_l\∂P_o}& \frac{{\∂U}_l}{U_l\∂Q_o}& \frac{{\∂U}_l}{U_l\∂P_m}& \frac{{\∂U}_l}{U_l\∂Q_m}& \frac{\∂U_l}{U_l\∂P_l}& \frac{\∂U_l}{U_l\∂Q_l}\end{array}\right]$

In formula, U _o, U _mand U _lbe respectively the voltage of node o, node m and node l, θ _o, θ _mand θ _lbe respectively the phase angle of node o, node m and node l; P _oand Q _obe respectively active power and the reactive power of node o, P _mand Q _mbe respectively the active power of node m and reactive power, P _land Q _lbe respectively active power and the reactive power of node l;

Electric network state variable X ₁for:

X ₁＝X ₀+S ₀[0,…,0,ΔP _o,ΔQ _o,ΔP _m,ΔQ _m,ΔP _l,ΔQ _l,0,…,0] ^T。

In described step 3, for low-pressure side, connect separately injection element and be connected the connected mode of major network with medium voltage side, calculate electric network state variable X ₂process is as follows:

Calculate medium voltage side branch road mo and cut-off equivalent injecting power increment:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_o^{\′}\\ \mathrm{\Δ}{Q}_o^{\′}\\ \mathrm{\Δ}{P}_m^{\′}\\ \mathrm{\Δ}{Q}_m^{\′}\end{array}\right]=H^{\′-1}\left[\begin{array}{c}{P}_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{om}}\\ Q_{\mathrm{om}}\end{array}\right]$

In formula: Δ P ' _owith Δ P ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects meritorious power increment, Δ Q ' _owith Δ Q ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects reactive power increment;

Matrix H '=I '+L ' S ', H ', I ', L ' and S ' are 4 * 4 rank matrixes, and I ' is unit matrix;

Matrix L ' expression formula be

$L^{\′}=\left[\begin{array}{cccc}{H}_{\mathrm{om}}& -2P_{\mathrm{om}}+N_{\mathrm{om}}& -H_{\mathrm{om}}& -N_{\mathrm{om}}\\ M_{\mathrm{om}}& -2Q_{\mathrm{om}}+L_{\mathrm{om}}& -M_{\mathrm{om}}& -L_{\mathrm{om}}\\ -H_{\mathrm{mo}}& -N_{\mathrm{mo}}& H_{\mathrm{mo}}& -2P_{\mathrm{mo}}+N_{\mathrm{mo}}\\ -M_{\mathrm{mo}}& -L_{\mathrm{mo}}& M_{\mathrm{mo}}& -2Q_{\mathrm{mo}}+L_{\mathrm{mo}}\end{array}\right]$

Matrix S ' expression formula as follows:

$S^{\′}=\left[\begin{array}{cccc}\frac{\∂{\mathrm{\θ}}_o}{\∂P_o}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_o}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_m}\\ \frac{\∂U_o}{U_o\∂P_o}& \frac{\∂U_o}{U_o\∂Q_o}& \frac{\∂U_o}{U_o\∂P_m}& \frac{\∂U_o}{U_o\∂Q_m}\\ \frac{\∂{\mathrm{\θ}}_m}{\∂P_o}& \frac{\∂{\mathrm{\θ}}_m}{\∂Q_o}& \frac{\∂{\mathrm{\θ}}_m}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_m}{\mathrm{\θ}{Q}_m}\\ \frac{\∂U_m}{U_m\∂P_o}& \frac{\∂U_m}{U_m\∂Q_o}& \frac{\∂U_m}{U_m\∂P_m}& \frac{\∂U_m}{U_m\∂Q_m}\end{array}\right];$

Electric network state variable X ₂for:

X ₂＝X ₀+S ₀[0,…,0,ΔP′ _o,ΔQ′ _o,ΔP′ _m,ΔQ′ _m,-P _lo,Q _lo,0,…,0] ^T。

H _om, N _om, M _om, L _om, H _mo, N _mo, M _mo, L _mo, H _ol, N _ol, M _ol, L _ol, H _lo, N _lo, M _loand L _loexpression formula be respectively:

H _om＝U _oU _m(G _omsinθ _om-B _omcosθ _om)；

N _om＝U _oU _m(G _omcosθ _om+B _omsinθ _om)；

M _om＝-N _om；

L _om＝H _om；

H _mo＝U _oU _m(G _omsinθ _mo-B _omcosθ _mo)；

N _mo＝U _oU _m(G _omcosθ _mo+B _omsinθ _mo)；

M _mo＝-N _mo；

L _mo＝H _mo；

H _ol＝U _oU _l(G _olsinθ _ol-B _omcosθ _ol)；

N _ol＝U _oU _l(G _omcosθ _ol+B _omsinθ _ol)；

M _ol＝-N _ol；

L _ol＝H _ol；

H _lo＝U _oU _l(G _olsinθ _lo-B _omcosθ _lo)；

N _lo＝U _oU _l(G _omcosθ _lo+B _omsinθ _lo)；

M _lo＝-N _lo；

L _lo＝H _lo；

In formula, θ _omfor the phase angle difference of node o and node m, θ _mo=-θ _om, θ _olfor the phase angle difference of node o and node l, θ _lo=-θ _ol, G _omand G _olthe electricity that is respectively branch road mo and branch road lo is led, B _omand B _olbe respectively the susceptance of branch road om and branch road ol.

In described step 3, for low/medium voltage side, connect separately separately the connected mode of injection element, electric network state variable X 3 expression formulas are:

X ₃＝X ₀+S ₀[0,…,0,-P _mo,-Q _mo,-P _lo,-Q _lo,0,…,0] ^T。

In described step 3, for low/medium voltage side, connect the mode of connection of isolated island, by roll-off network topological sum Jacobi matrix J ₀, carry out AC power flow iterative computation, obtain electric network state variable and trend power.

In described step 3, the process of the trend power of calculating branch road ij is as follows:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}^{/}=-U_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+t_{\mathrm{ij}}{G}_{\mathrm{ij}}{U}_i^2\\ Q_{\mathrm{ij}}^{/}=-U_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})-t_{\mathrm{ij}}{B}_{\mathrm{ij}}{U}_i^2+b_{\mathrm{ij}}{U}_i^2\end{array}\right.$

In formula: P' _ijand Q ' _ijbe respectively trend active power and the trend reactive power of branch road ij, t _ijfor branch road ij no-load voltage ratio perunit value, b _ijfor branch road ij holds half, G _ijfor the electricity of branch road ij is led, B _ijfor the susceptance of branch road ij, U _iand U _jbe respectively node i and voltage node j, θ _ijphase angle difference for node i and node j.

Compared with prior art, beneficial effect of the present invention is:

1. the present invention classifies to three-winding transformer main connected mode in electrical network, after making Calculation of Sensitivity mode can be applicable to polytype three-winding transformer fault, trend is calculated, computing velocity is fast, meets the requirement of modern intelligent grid to static security analysis module level second computing velocity;

2. the classified calculating mode that the present invention proposes can access after three-winding transformer fault that accurate system is meritorious, the comprehensive service data such as reactive power trend and busbar voltage amplitude, phase place, not only can accurately judge the out-of-limit situation of power of circuit and transformer in electric system, and can judge the out-of-limit situation of busbar voltage, there is very high practical value;

3. the present invention is applicable in electrical network the Calculation of Sensitivity of trend after most three-winding transformer faults, has solved three-winding transformer fault and has easily caused local dead electricity to make the not applicable problem of conventional sensitivity algorithm.

Accompanying drawing explanation

Fig. 1 is the three-winding transformer fault judgment method process flow diagram of static security analysis in the embodiment of the present invention;

Fig. 2 cut-offs the mode of connection schematic diagram that can not cause off-the-line or dead electricity in the embodiment of the present invention;

Fig. 3 is that embodiment of the present invention mesolow side connects separately injection element is connected major network connected mode schematic diagram with medium voltage side;

Fig. 4 is the connected mode schematic diagram that low in the embodiment of the present invention/medium voltage side connects separately injection element separately;

Fig. 5 is the front Branch Power Flow schematic diagram of fault in three-winding transformer.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

As Fig. 1, a kind of three-winding transformer fault judgment method for static security analysis, said method comprising the steps of:

Step 1: carry out the calculating of ground state trend, obtain Jacobi matrix J ₀, corresponding sensitivity matrix S ₀with the electrical network original state variable X being formed by node voltage and phase angle ₀;

Step 2: the mode of connection that judges the three-winding transformer that breaks down;

Step 3: calculate electric network state variable and trend power according to the mode of connection;

Step 4: judging whether electric system exists out-of-limit phenomenon, is if so, harmful fault by the fault definition occurring.

In described step 2, the mode of connection comprises that cut-offfing the mode of connection, the low-pressure side that can not cause off-the-line or dead electricity connects separately the mode of connection that injection element is connected major network connected mode with medium voltage side, connected mode that low/medium voltage side connects separately injection element separately and low/medium voltage side connect isolated island.

As Fig. 2, for cut-offfing the mode of connection calculating electric network state variable X that can not cause off-the-line or dead electricity ₁process is as follows:

If three-winding transformer high-pressure side, medium voltage side and low-pressure side three side gussets are respectively node h, node m and node l, neutral node is node o, and the equivalent injecting power increment that cut-offs of node o, node m and node l is:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_o\\ \mathrm{\Δ}{Q}_o\\ \mathrm{\Δ}{P}_m\\ \mathrm{\Δ}{Q}_m\\ \mathrm{\Δ}{P}_l\\ \mathrm{\Δ}{Q}_l\end{array}\right]=H^{-1}\left[\begin{array}{c}{P}_{\mathrm{om}}+P_{\mathrm{ol}}\\ Q_{\mathrm{om}}+Q_{\mathrm{ol}}\\ P_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{lo}}\\ Q_{\mathrm{lo}}\end{array}\right]$

In formula, Δ P _o, Δ P _mwith Δ P _lbe respectively the equivalence of cut-offfing branch breaking posterior nodal point o, node m and node l in the mode of connection that can not cause off-the-line or dead electricity and inject meritorious power increment, Δ Q _o, Δ Q _mwith Δ Q _lreactive power increment, P are injected in the equivalence that is respectively branch breaking posterior nodal point o, node m and node l _omand Q _ombe respectively the ground state trend reactive power of node o to the ground state trend active power of node m direction and node o to node m direction, P _oland Q _olbe respectively the ground state trend reactive power of node o to the ground state trend active power of node l direction and node o to node l direction, P _moand Q _mobe respectively the ground state trend reactive power of node m to the ground state trend active power of node o direction and node m to node o direction, P _loand Q _lobe respectively the ground state trend reactive power of node l to the ground state trend active power of node o direction and node l to node o direction;

Matrix H=I+LS, wherein H, I, L and S are 6 * 6 rank matrixes, and I is unit matrix;

Matrix L expression formula is as follows:

$L=\left[\begin{array}{cccccc}{H}_{\mathrm{om}}+H_{\mathrm{ol}}& -2P_{\mathrm{om}}-2P_{\mathrm{ol}}+N_{\mathrm{om}}+N_{\mathrm{ol}}& -H_{\mathrm{om}}& -N_{\mathrm{om}}& -H_{\mathrm{ol}}& -N_{\mathrm{ol}}\\ M_{\mathrm{om}}+M_{\mathrm{ol}}& -2Q_{\mathrm{om}}-2Q_{\mathrm{ol}}+L_{\mathrm{om}}+L_{\mathrm{ol}}& -M_{\mathrm{om}}& -L_{\mathrm{om}}& -M_{\mathrm{ol}}& -L_{\mathrm{ol}}\\ -H_{\mathrm{mo}}& -N_{\mathrm{mo}}& H_{\mathrm{mo}}& -2P_{\mathrm{mo}}+N_{\mathrm{no}}& & \\ -M_{\mathrm{mo}}& -L_{\mathrm{mo}}& M_{\mathrm{mo}}& -2Q_{\mathrm{mo}}+L_{\mathrm{mo}}& & \\ -H_{\mathrm{lo}}& -N_{\mathrm{lo}}& & & H_{\mathrm{lo}}& -2P_{\mathrm{lo}}+N_{\mathrm{lo}}\\ -M_{\mathrm{lo}}& -L_{\mathrm{lo}}& & & M_{\mathrm{lo}}& -2Q_{\mathrm{lo}}+L_{\mathrm{lo}}\end{array}\right]$

In formula, H _om, M _om, N _om, L _om, H _mo, M _mo, N _mo, L _mo, H _ol, M _ol, N _ol, L _ol, H _lo, M _lo, N _loand L _lobe Jacobi matrix J ₀element;

The expression formula of matrix S is as follows:

$S=\left[\begin{array}{cccccc}\frac{\∂{\mathrm{\θ}}_o}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂P}_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_l}\\ \frac{\∂U_o}{U_o\∂P_o}& \frac{{\∂U}_o}{U_o{\∂Q}_o}& \frac{{\∂U}_o}{U_o{\∂P}_m}& \frac{{\∂U}_o}{U_o{\∂Q}_m}& \frac{\∂U_o}{U_o\∂P_l}& \frac{\∂U_o}{U_o\∂Q_l}\\ \frac{\∂{\mathrm{\θ}}_m}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_m}& \frac{\∂{\mathrm{\θ}}_m}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_m}{\∂Q_l}\\ \frac{\∂U_m}{U_m\∂P_o}& \frac{{\∂U}_m}{U_m{\∂Q}_o}& \frac{{\∂U}_m}{U_m{\∂P}_m}& \frac{{\∂U}_m}{U_m{\∂Q}_m}& \frac{\∂U_m}{U_m\∂P_l}& \frac{\∂U_m}{U_m\∂Q_l}\\ \frac{\∂{\mathrm{\θ}}_l}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_l}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_l}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_l}{{\∂Q}_m}& \frac{\∂{\mathrm{\θ}}_l}{\∂P_l}& \frac{\∂{\mathrm{\θ}}_l}{\∂Q_l}\\ \frac{\∂U_l}{U_l\∂P_o}& \frac{{\∂U}_l}{U_l\∂Q_o}& \frac{{\∂U}_l}{U_l\∂P_m}& \frac{{\∂U}_l}{U_l\∂Q_m}& \frac{\∂U_l}{U_l\∂P_l}& \frac{\∂U_l}{U_l\∂Q_l}\end{array}\right]$

In formula, U _o, U _mand U _lbe respectively the voltage of node o, node m and node l, θ _o, θ _mand θ _lbe respectively the phase angle of node o, node m and node l; P _oand Q _obe respectively active power and the reactive power of node o, P _mand Q _mbe respectively the active power of node m and reactive power, P _land Q _lbe respectively active power and the reactive power of node l;

Electric network state variable X ₁for:

X ₁＝X ₀+S ₀[0,…,0,ΔP _o,ΔQ _o,ΔP _m,ΔQ _m,ΔP _l,ΔQ _l,0,…,0] ^T。

As Fig. 3, for low-pressure side, connect separately injection element and be connected the connected mode of major network with medium voltage side, calculate electric network state variable X ₂process is as follows:

Calculate medium voltage side branch road mo and cut-off equivalent injecting power increment:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_o^{\′}\\ \mathrm{\Δ}{Q}_o^{\′}\\ \mathrm{\Δ}{P}_m^{\′}\\ \mathrm{\Δ}{Q}_m^{\′}\end{array}\right]=H^{\′-1}\left[\begin{array}{c}{P}_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{om}}\\ Q_{\mathrm{om}}\end{array}\right]$

In formula: Δ P ' _owith Δ P ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects meritorious power increment, Δ Q ' _owith Δ Q ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects reactive power increment;

Matrix H '=I '+L ' S ', H ', I ', L ' and S ' are 4 * 4 rank matrixes, and I ' is unit matrix;

Matrix L ' expression formula be

$L^{\′}=\left[\begin{array}{cccc}{H}_{\mathrm{om}}& -2P_{\mathrm{om}}+N_{\mathrm{om}}& -H_{\mathrm{om}}& -N_{\mathrm{om}}\\ M_{\mathrm{om}}& -2Q_{\mathrm{om}}+L_{\mathrm{om}}& -M_{\mathrm{om}}& -L_{\mathrm{om}}\\ -H_{\mathrm{mo}}& -N_{\mathrm{mo}}& H_{\mathrm{mo}}& -2P_{\mathrm{mo}}+N_{\mathrm{mo}}\\ -M_{\mathrm{mo}}& -L_{\mathrm{mo}}& M_{\mathrm{mo}}& -2Q_{\mathrm{mo}}+L_{\mathrm{mo}}\end{array}\right]$

Matrix S ' expression formula as follows:

$S^{\′}=\left[\begin{array}{cccc}\frac{\∂{\mathrm{\θ}}_o}{\∂P_o}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_o}& \frac{\∂{\mathrm{\θ}}_o}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_o}{\∂Q_m}\\ \frac{\∂U_o}{U_o\∂P_o}& \frac{\∂U_o}{U_o\∂Q_o}& \frac{\∂U_o}{U_o\∂P_m}& \frac{\∂U_o}{U_o\∂Q_m}\\ \frac{\∂{\mathrm{\θ}}_m}{\∂P_o}& \frac{\∂{\mathrm{\θ}}_m}{\∂Q_o}& \frac{\∂{\mathrm{\θ}}_m}{\∂P_m}& \frac{\∂{\mathrm{\θ}}_m}{\mathrm{\θ}{Q}_m}\\ \frac{\∂U_m}{U_m\∂P_o}& \frac{\∂U_m}{U_m\∂Q_o}& \frac{\∂U_m}{U_m\∂P_m}& \frac{\∂U_m}{U_m\∂Q_m}\end{array}\right];$

Electric network state variable X ₂for:

X ₂＝X ₀+S ₀[0,…,0,ΔP′ _o,ΔQ′ _o,ΔP′ _m,ΔQ′ _m,-P _lo,-Q _lo,0,…,0] ^T。

H _om, N _om, M _om, L _om, H _mo, N _mo, M _mo, L _mo, H _ol, N _ol, M _ol, L _ol, H _lo, N _lo, M _loand L _loexpression formula be respectively:

H _om＝U _oU _m(G _omsinθ _om-B _omcosθ _om)；

N _om＝U _oU _m(G _omcosθ _om+B _omsinθ _om)；

M _om＝-N _om；

L _om＝H _om；

H _mo＝U _oU _m(G _omsinθ _mo-B _omcosθ _mo)；

N _mo＝U _oU _m(G _omcosθ _mo+B _omsinθ _mo)；

M _mo＝-N _mo；

L _mo＝H _mo；

H _ol＝U _oU _l(G _olsinθ _ol-B _omcosθ _ol)；

N _ol＝U _oU _l(G _omcosθ _ol+B _omsinθ _ol)；

M _ol＝-N _ol；

L _ol＝H _ol；

H _lo＝U _oU _l(G _olsinθ _lo-B _omcosθ _lo)；

N _lo＝U _oU _l(G _omcosθ _lo+B _omsinθ _lo)；

M _lo＝-N _lo；

L _lo＝H _lo；

In formula, θ _omfor the phase angle difference of node o and node m, θ _mo=-θ _om, θ _olfor the phase angle difference of node o and node l, θ _lo=-θ _ol, G _omand G _olthe electricity that is respectively branch road mo and branch road lo is led, B _omand B _olbe respectively the susceptance of branch road om and branch road ol.

As Fig. 4, for low/medium voltage side, connect separately separately the connected mode of injection element, electric network state variable X ₃expression formula is:

X ₃＝X ₀+S ₀[0,…,0,-P _mo,-Q _mo,-P _lo,-Q _lo,0,…,0] ^T。

In described step 3, for low/medium voltage side, connect the mode of connection of isolated island, by roll-off network topological sum Jacobi matrix J ₀, carry out AC power flow iterative computation, obtain electric network state variable and trend power.

In described step 3, the process of the trend power of calculating branch road ij is as follows:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}^{/}=-U_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+t_{\mathrm{ij}}{G}_{\mathrm{ij}}{U}_i^2\\ Q_{\mathrm{ij}}^{/}=-U_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})-t_{\mathrm{ij}}{B}_{\mathrm{ij}}{U}_i^2+b_{\mathrm{ij}}{U}_i^2\end{array}\right.$

In formula: P' _ijand Q ' _ijbe respectively trend active power and the trend reactive power of branch road ij, t _ijfor branch road ij no-load voltage ratio perunit value, b _ijfor branch road ij holds half, G _ijfor the electricity of branch road ij is led, B _ijfor the susceptance of branch road ij, U _iand U _jbe respectively node i and voltage node j, θ _ijphase angle difference for node i and node j.

Fig. 5 is Branch Power Flow schematic diagram before three-winding transformer fault.

The present invention classifies to three-winding transformer main connected mode in electrical network, after making Calculation of Sensitivity mode can be applicable to polytype three-winding transformer fault, trend is calculated, computing velocity is fast, Central China Power Grid and the North China Power Telecommunication Network system of national grid dispatching center intelligent grid dispatching technique supporting platform of take is example, meet the requirement of modern intelligent grid to static security analysis module level second computing velocity, concrete computing time is as shown in table 1.

Table 1

The classified calculating mode that the present invention proposes can access after three-winding transformer fault that accurate system is meritorious, the comprehensive service data such as reactive power trend and busbar voltage amplitude, phase place, not only can accurately judge the out-of-limit situation of power of circuit and transformer in electric system, and can judge the out-of-limit situation of busbar voltage, there is very high practical value.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit, although the present invention is had been described in detail with reference to above-described embodiment, those of ordinary skill in the field are to be understood that: still can modify or be equal to replacement the specific embodiment of the present invention, and do not depart from any modification of spirit and scope of the invention or be equal to replacement, it all should be encompassed in the middle of claim scope of the present invention.

Claims (7)

1. for a three-winding transformer fault judgment method for static security analysis, it is characterized in that: said method comprising the steps of:

Step 1: carry out the calculating of ground state trend, obtain Jacobi matrix J ₀, corresponding sensitivity matrix S ₀with the electrical network original state variable X being formed by node voltage and phase angle ₀;

Step 2: the mode of connection that judges the three-winding transformer that breaks down;

Step 3: calculate electric network state variable according to the mode of connection, and calculate in the following manner branch road ij trend power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}^{/}={-U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+t_{\mathrm{ij}}{G}_{\mathrm{ij}}{U}_i^2\\ Q_{\mathrm{ij}}^{/}={-U}_i{U}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})-t_{\mathrm{ij}}{B}_{\mathrm{ij}}{U}_i^2+b_{\mathrm{ij}}{U}_i^2\end{array}\right.$

In formula: P' _ijand Q' _ijbe respectively trend active power and the trend reactive power of branch road ij, t _ijfor branch road ij no-load voltage ratio perunit value, b _ijfor branch road ij holds half, G _ijfor the electricity of branch road ij is led, B _ijfor the susceptance of branch road ij, U _iand U _jbe respectively node i and voltage node j, θ _ijphase angle difference for node i and node j;

Step 4: judging whether electric system exists out-of-limit phenomenon, is if so, harmful fault by the fault definition occurring.

2. the three-winding transformer fault judgment method for static security analysis according to claim 1, it is characterized in that: in described step 2, the mode of connection comprises that cut-offfing the mode of connection, the low-pressure side that can not cause off-the-line or dead electricity connects separately the mode of connection that injection element is connected major network connected mode with medium voltage side, connected mode that low/medium voltage side connects separately injection element separately and low/medium voltage side connect isolated island.

3. the three-winding transformer fault judgment method for static security analysis according to claim 2, is characterized in that: in described step 3, for cut-offfing the mode of connection calculating electric network state variable X that can not cause off-the-line or dead electricity ₁process is as follows:

If three-winding transformer high-pressure side, medium voltage side and low-pressure side three side gussets are respectively node h, node m and node l, neutral node is node o, and the equivalent injecting power increment that cut-offs of node o, node m and node l is:

$\left[\begin{array}{c}\mathrm{\Δ}{P}_o\\ \mathrm{\Δ}{Q}_o\\ \mathrm{\Δ}{P}_m\\ \mathrm{\Δ}{Q}_m\\ \mathrm{\Δ}{P}_l\\ \mathrm{\Δ}{Q}_l\end{array}\right]=H^{-1}\left[\begin{array}{c}{P}_{\mathrm{om}}+P_{\mathrm{ol}}\\ Q_{\mathrm{om}}+Q_{\mathrm{ol}}\\ P_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{lo}}\\ Q_{\mathrm{lo}}\end{array}\right]$

In formula, Δ P _o, Δ P _mwith Δ P _lbe respectively the equivalence of cut-offfing branch breaking posterior nodal point o, node m and node l in the mode of connection that can not cause off-the-line or dead electricity and inject meritorious power increment, Δ Q _o, Δ Q _mwith Δ Q _lreactive power increment, P are injected in the equivalence that is respectively branch breaking posterior nodal point o, node m and node l _omand Q _ombe respectively the ground state trend reactive power of node o to the ground state trend active power of node m direction and node o to node m direction, P _oland Q _olbe respectively the ground state trend reactive power of node o to the ground state trend active power of node l direction and node o to node l direction, P _moand Q _mobe respectively the ground state trend reactive power of node m to the ground state trend active power of node o direction and node m to node o direction, P _loand Q _lobe respectively the ground state trend reactive power of node l to the ground state trend active power of node o direction and node l to node o direction;

Matrix H=I+LS, wherein H, I, L and S are 6 * 6 rank matrixes, and I is unit matrix;

Matrix L expression formula is as follows:

$L=\left[\begin{array}{cccccc}{H}_{\mathrm{om}}+H_{\mathrm{ol}}& {-2P}_{\mathrm{om}}-{2P}_{\mathrm{ol}}+N_{\mathrm{om}}+N_{\mathrm{ol}}& {-H}_{\mathrm{om}}& {-N}_{\mathrm{om}}& {-H}_{\mathrm{ol}}& {-N}_{\mathrm{ol}}\\ M_{\mathrm{om}}+M_{\mathrm{ol}}& {-2Q}_{\mathrm{om}}-{2Q}_{\mathrm{ol}}+L_{\mathrm{om}}+L_{\mathrm{ol}}& {-M}_{\mathrm{om}}& {-L}_{\mathrm{om}}& {-M}_{\mathrm{ol}}& {-L}_{\mathrm{ol}}\\ {-H}_{\mathrm{mo}}& {-N}_{\mathrm{mo}}& H_{\mathrm{mo}}& {-2P}_{\mathrm{mo}}+N_{\mathrm{mo}}& & \\ {-M}_{\mathrm{mo}}& {-L}_{\mathrm{mo}}& M_{\mathrm{mo}}& {-2Q}_{\mathrm{mo}}+L_{\mathrm{mo}}& & \\ {-H}_{\mathrm{lo}}& {-N}_{\mathrm{lo}}& & & H_{\mathrm{lo}}& {-2P}_{\mathrm{lo}}+N_{\mathrm{lo}}\\ {-M}_{\mathrm{lo}}& {-L}_{\mathrm{lo}}& & & M_{\mathrm{lo}}& {-2Q}_{\mathrm{lo}}+L_{\mathrm{lo}}\end{array}\right]$

In formula, H _om, M _om, N _om, L _om, H _mo, M _mo, N _mo, L _mo, H _ol, M _ol, N _ol, L _ol, H _lo, M _lo, N _loand L _lobe Jacobi matrix J ₀element;

The expression formula of matrix S is as follows:

$S=\left[\begin{array}{cccccc}\frac{{\∂\mathrm{\θ}}_o}{{\∂P}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_m}& \frac{{\∂\mathrm{\θ}}_o}{\∂P_l}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_l}\\ \frac{{\∂U}_o}{U_o{\∂P}_o}& \frac{\∂U_o}{U_o{\∂Q}_o}& \frac{{\∂U}_o}{U_o{\∂P}_m}& \frac{\∂U_o}{U_o{\∂Q}_m}& \frac{{\∂U}_o}{U_o{\∂P}_l}& \frac{{\∂U}_o}{U_o{\∂Q}_l}\\ \frac{{\∂\mathrm{\θ}}_m}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_o}& \frac{\∂{\mathrm{\θ}}_m}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_m}& \frac{\∂{\mathrm{\θ}}_m}{{\∂P}_l}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_l}\\ \frac{\∂U_m}{U_m\∂P_o}& \frac{\∂U_m}{U_m\∂Q_o}& \frac{\∂U_m}{U_m\∂P_m}& \frac{\∂U_m}{U_m\∂Q_m}& \frac{{\∂U}_m}{U_m\∂P_l}& \frac{{\∂U}_m}{U_m\∂Q_l}\\ \frac{{\∂\mathrm{\θ}}_l}{\∂P_o}& \frac{{\∂\mathrm{\θ}}_l}{\∂Q_o}& \frac{{\∂\mathrm{\θ}}_l}{\∂P_m}& \frac{{\∂\mathrm{\θ}}_l}{\∂Q_m}& \frac{\∂{\mathrm{\θ}}_l}{\∂P_l}& \frac{{\∂\mathrm{\θ}}_l}{{\∂Q}_l}\\ \frac{\∂U_l}{U_l\∂P_o}& \frac{\∂U_l}{U_l\∂Q_o}& \frac{\∂U_l}{U_l\∂P_m}& \frac{\∂U_l}{U_l\∂Q_m}& \frac{\∂U_l}{U_l\∂P_l}& \frac{{\∂U}_l}{U_l{\∂Q}_l}\end{array}\right]$

In formula, U _o, U _mand U _lbe respectively the voltage of node o, node m and node l, θ _o, θ _mand θ _lbe respectively the phase angle of node o, node m and node l; P _oand Q _obe respectively active power and the reactive power of node o, P _mand Q _mbe respectively the active power of node m and reactive power, P _land Q _lbe respectively active power and the reactive power of node l;

Electric network state variable X ₁for:

X ₁＝X ₀+S ₀[0,…,0,ΔP _o,ΔQ _o,ΔP _m,ΔQ _m,ΔP _l,ΔQ _l,0,…,0] ^T。

4. the three-winding transformer fault judgment method for static security analysis according to claim 3, is characterized in that: in described step 3, connect separately injection element be connected the connected mode of major network with medium voltage side for low-pressure side, calculate electric network state variable X ₂process is as follows:

Calculate medium voltage side branch road mo and cut-off equivalent injecting power increment:

$\left[\begin{array}{c}{\mathrm{\ΔP}}_o^{\′}\\ \mathrm{\Δ}{Q}_o^{\′}\\ \mathrm{\Δ}{P}_m^{\′}\\ \mathrm{\Δ}{Q}_m^{\′}\end{array}\right]=H^{{\′}^{-1}}\left[\begin{array}{c}{P}_{\mathrm{mo}}\\ Q_{\mathrm{mo}}\\ P_{\mathrm{om}}\\ Q_{\mathrm{om}}\end{array}\right]$

In formula: Δ P ' _owith Δ P ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects meritorious power increment, Δ Q ' _owith Δ Q ' _mbeing respectively low-pressure side connects separately the equivalence of branch breaking posterior nodal point o and node m in injection element is connected major network connected mode with medium voltage side and injects reactive power increment;

Matrix H '=I '+L ' S ', H ', I ', L ' and S ' are 4 * 4 rank matrixes, and I ' is unit matrix;

Matrix L ' expression formula be

$L^{\′}=\left[\begin{array}{cccc}{H}_{\mathrm{om}}& -2P_{\mathrm{om}}& -H_{\mathrm{om}}& {-N}_{\mathrm{om}}\\ M_{\mathrm{om}}& -2Q_{\mathrm{om}}+L_{\mathrm{om}}& -M_{\mathrm{om}}& {-N}_{\mathrm{om}}\\ -H_{\mathrm{om}}& -N_{\mathrm{om}}& H_{\mathrm{om}}& -2P_{\mathrm{om}}+N_{\mathrm{om}}\\ -M_{\mathrm{mo}}& {-L}_{\mathrm{om}}& M_{\mathrm{om}}& -2Q_{\mathrm{om}}+L_{\mathrm{om}}\end{array}\right]$

Matrix S ' expression formula as follows:

$S^{\′}=\left[\begin{array}{cccc}\frac{{\∂\mathrm{\θ}}_o}{{\∂P}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_o}{{\∂P}_m}& \frac{{\∂\mathrm{\θ}}_o}{{\∂Q}_m}\\ \frac{{\∂U}_o}{U_o{\∂P}_o}& \frac{{\∂U}_o}{U_o{\∂Q}_o}& \frac{{\∂U}_o}{U_o{\∂P}_m}& \frac{{\∂U}_o}{U_o{\∂Q}_m}\\ \frac{{\∂\mathrm{\θ}}_m}{{\∂P}_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_o}& \frac{{\∂\mathrm{\θ}}_m}{{\∂U}_m}& \frac{{\∂\mathrm{\θ}}_m}{{\∂Q}_m}\\ \frac{{\∂U}_m}{U_m{\∂P}_o}& \frac{{\∂U}_m}{U_m{\∂Q}_o}& \frac{{\∂U}_m}{U_m{\∂P}_m}& \frac{{\∂U}_m}{U_m{\∂Q}_m}\end{array}\right];$

Electric network state variable X ₂for:

X ₂＝X ₀+S ₀[0,…,0,ΔP′ _o,ΔQ′ _o,ΔP′ _m,ΔQ′ _m,-P _lo,-Q _lo,0,…,0] ^T。

5. according to the three-winding transformer fault judgment method for static security analysis described in claim 3 or 4, it is characterized in that: H _om, N _om, M _om, L _om, H _mo, N _mo, M _mo, L _mo, H _ol, N _ol, M _ol, L _ol, H _lo, N _lo, M _loand L _loexpression formula be respectively:

H _om＝U _oU _m(G _omsinθ _om-B _omcosθ _om)；

N _om＝U _oU _m(G _omcosθ _om+B _omsinθ _om)；

M _om＝-N _om；

L _om＝H _om；

H _mo＝U _oU _m(G _omsinθ _mo-B _omcosθ _mo)；

N _mo＝U _oU _m(G _omcosθ _mo+B _omsinθ _mo)；

M _mo＝-N _mo；

L _mo＝H _mo；

H _ol＝U _oU _l(G _olsinθ _ol-B _omcosθ _ol)；

N _ol＝U _oU _l(G _omcosθ _ol+B _omsinθ _ol)；

M _ol＝-N _ol；

L _ol＝H _ol；

H _lo＝U _oU _l(G _olsinθ _lo-B _omcosθ _lo)；

N _lo＝U _oU _l(G _omcosθ _lo+B _omsinθ _lo)；

M _lo＝-N _lo；

L _lo＝H _lo；

In formula, θ _omfor the phase angle difference of node o and node m, θ _mo=-θ _om, θ _olfor the phase angle difference of node o and node l, θ _lo=-θ _ol, G _omand G _olthe electricity that is respectively branch road mo and branch road lo is led, B _omand B _olbe respectively the susceptance of branch road om and branch road ol.

6. the three-winding transformer fault judgment method for static security analysis according to claim 4, is characterized in that: in described step 3, for low/medium voltage side, connect separately separately the connected mode of injection element, electric network state variable X ₃expression formula is:

X ₃＝X ₀+S ₀[0,…,0,-P _mo,-Q _mo,-P _lo,-Q _lo,0,…,0] ^T。

7. the three-winding transformer fault judgment method for static security analysis according to claim 1, is characterized in that: in described step 3, connect the mode of connection of isolated island for low/medium voltage side, by roll-off network topological sum Jacobi matrix J ₀, carry out AC power flow iterative computation, obtain electric network state variable and trend power.