CN105281329A - Single-phase reclosing time sequence setting method for improving transient frequency stability of 2-generator power system - Google Patents

Abstract

The invention relates to a single-phase reclosing time sequence setting method for improving transient frequency stability of a 2-generator power system, and belongs to the technical field of power system stabilization and control. The single-phase reclosing time sequence setting method comprises the steps of: inversing an admittance matrix of each sequence to obtain an impedance matrix of each sequence; adopting a dual-port theory to acquire port impedance matrixes and further acquire an integrated impedance matrix, and inversing the integrated impedance matrix to obtain an integrated admittance matrix; correcting a positive sequence network according to the integrated admittance matrix to obtain an extension positive sequence admittance matrix; and calculating equivalent mutual admittance between nodes of two generators by using a Ward equivalent method. Therefore, generator frequency variation trajectories under two kinds of reclosing time sequences are calculated, the quantitative evaluation on frequency variation trajectories is achieved to obtain transient frequency stability margins, and the reclosing time sequence corresponding to the greater transient frequency stability margin is selected as an optimized reclosing scheme. The single-phase reclosing time sequence setting method greatly simplifies the analytical calculation of complicated faults, can effectively improve the transient frequency stability of the 2-generator power system in single-phase reclosing, and has good effect.

Description

The single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities

Technical field

The present invention relates to the single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities, belong to power system stability and control technical field.

Background technology

Frequency is an important operating index in electric power system, is also the pith that power system stability runs.It reflects the dynamic equilibrium relation between active power that generator sends and load (comprising the burden with power that loss burden with power in burden with power that power plant consumes, network and various power consumption equipment consume).In order to meet consumers' demand, ± the fluctuation range of 0.2 Η z generally can not be exceeded in the skew of electric power system medium frequency, when system is not strict demand, the frequency of system can not exceed ± fluctuation range of 0.5Hz, so the fluctuation of frequency to exceed allowed scope when electric power system normally works.If the fluctuation of frequency is beyond allowed scope, frequency will be maintained in allowed limits by corresponding control measure.

When after generation disturbance, the distribution that the dynamic process of frequency of each department is not only free, and the distribution of having living space, also just says when different when, the dynamic process of frequency difference of same node or areal; At synchronization, the dynamic process of different node or different regional frequencies is also different.The amplitude of different regions hunting of frequency is also different.

Transient frequency is generally divided into the transient frequency of system-wide transient frequency, regional transient frequency, generator transient frequency and general bus.System-wide transient frequency refers to act on incremental speed that the total equivalent moment of inertia of system produces over time by system imbalance power summation.Area transient frequency refers to that this area's imbalance power summation acts on incremental speed that the total equivalent rotary inertia in the center of inertia, this area produces over time.Generator node transient frequency is generator speed increment over time, also namely directly corresponding with generator speed frequency.General bus transient frequency be the incremental speed that rotates in phase plane of space vector of voltage of its two-phase instantaneous voltage synthesis over time.

Adjusting of single-pole reclosing sequential, object is that minimizing, to the Secondary Shocks again of system and uneven energy, weakens the adverse effect to electrical network as far as possible when coinciding with permanent fault, improves the transmittability of network.Needs index of adjusting of single-pole reclosing sequential under transient frequency stablizes visual angle, and this index is exactly transient frequency stability margin.When system transient modelling frequency stabilization nargin is greater than 0, system is stable, and numerical value is more conducive to system stability more greatly; When system transient modelling frequency stabilization nargin is less than 0, system is unstable, and is more littlely more unfavorable for the stable of system, is carried out the optimum Match of single-pole reclosing sequential by the size of transient frequency stability margin value.

The simplifying method that dual-port is theoretical, Ward equivalent method is a kind of network, it by complexity, the electric power networks abbreviation of high-order is simple low order network, carrying out such simplification can not only ensure computational accuracy, greatly can improve computational efficiency simultaneously.Patent of the present invention calculates generator frequency curve over time under two kinds of time sequence of coincidence, and computing system transient frequency stability margin realizes the quantitative evaluation to frequency variation track in time, single-phase time sequence of coincidence corresponding to selecting system transient frequency margin of safety the greater is as the coincidence setting program of the best.

Summary of the invention

The invention provides the single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities, stablize visual angle for transient frequency in solution 2 electro-mechanical force system and to place an order the optimization problem of timing scheme of coinciding.

Technical scheme of the present invention is: the single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities, when there is single phase ground fault in the transmission line of alternation current of 2 electro-mechanical force systems, there is two kinds of faults and single phase ground fault and single-phase wire break fault when single-phase coincidence, form the fault network of dual-port; Utilize symmetrical component method to obtain three sequence sequence nets according to fault type, arrange according to positive sequence, negative phase-sequence, zero-sequence network the admittance battle array writing each sequence, the admittance battle array of each sequence is inverted and obtains the Impedance Matrix of each sequence; Adopt dual-port theory first to try to achieve port Impedance battle array, and then try to achieve comprehensive impedance battle array, inverting to it obtains complex admittance battle array; According to complex admittance battle array amendment positive sequence network, thus the positive sequence admittance battle array that is expanded; Ward equivalent method is utilized to calculate equivalent transadmittance between 2 generator nodes, calculate the generator frequency variation track under two kinds of reclosing time sequences thus, realize the quantitative evaluation of frequency change track thus obtain transient frequency stability margin, choosing time sequence of coincidence corresponding to transient frequency stability margin the greater is the coincidence scheme optimized.

The concrete steps of described method are as follows:

(1) analog line head end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line head end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ₁, Y ₂, Y ₀; Wherein, the method forming admittance battle array is as follows: in admittance battle array each row off-diagonal element, the number of nonzero element equals the connected earth-free circuitry number of corresponding node; The each diagonal element of admittance battle array, i.e. the self-admittance Y of each node _iiequal the admittance sum on respective nodes institute's chord road: the transadmittance Yij of each off-diagonal element of admittance battle array just to equal between 2 nodes connect the negative value of admittance: Y _ij=-y _ij;

In formula, y _ijfor the admittance on institute's chord road between node i and node j;

2) positive sequence, negative phase-sequence, zero sequence impedance battle array is asked for

To positive sequence, negative phase-sequence, zero sequence admittance battle array Y ₁, Y ₂, Y ₀invert, shown in (1), obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ₁, Z ₂, Z ₀;

$Z_1=Y_1^{-1},Z_2=Y_2^{-1},Z_0=Y_0^{-1}---\left(1\right)$

3) apply dual-port theory and ask for port Impedance

1. the positive sequence of port one and port 2, negative phase-sequence, zero sequence self-impedance and mutual impedance is asked for;

If node serial number single phase ground fault place occurring corresponding is m, n, n is the earth 0 node; Node serial number corresponding to single-phase end disconnection fault place is p, q; Be that the port that m, n are corresponding is denoted as port one by node serial number; Node serial number is that the port that p, q are corresponding is denoted as port 2;

By step 2) in the three sequence Impedance Matrixes that calculate corresponding element substitute in formula (2), try to achieve the positive sequence of port one and port 2, negative phase-sequence, the self-impedance of zero sequence and mutual impedance;

Z ₁₁₍₁₎＝Z ₁₁₍₂₎＝Z _mm(1)+Z _nn(1)-2Z _mn(1)

Z ₁₂₍₁₎＝Z ₁₂₍₂₎＝Z _mp(1)+Z _nq(1)-Z _mq(1)-Z _np(1)

Z ₂₁₍₁₎＝Z ₂₁₍₂₎＝Z _pm(1)+Z _qn(1)-Z _pn(1)-Z _qm(1)

Z ₂₂₍₁₎＝Z ₂₂₍₂₎＝Z _pp(1)+Z _qq(1)-2Z _pq(1)

Z ₁₁₍₀₎＝Z _mm(0)+Z _nn(0)-2Z _mn(0)(2)

Z ₁₂₍₀₎＝Z _mp(0)+Z _nq(0)-Z _mq(0)-Z _np(0)

Z ₂₁₍₀₎＝Z _pm(0)+Z _qn(0)-Z _pn(0)-Z _qm(0)

Z ₂₂₍₀₎＝Z ₂₂₍₀₎＝Z _pp(0)+Z _qq(0)-2Z _pq(0)

In formula, Z _{11 (1)}, Z _{22 (1)}represent the positive sequence self-impedance of port one and port 2 respectively; Z _{12 (1)}, Z _{21 (1)}represent the positive sequence mutual impedance between port one and port 2 respectively; Z _{11 (2)}, Z _{22 (2)}represent the negative phase-sequence self-impedance of port one and port 2 respectively; Z _{12 (2)}, Z _{21 (2)}represent the negative phase-sequence mutual impedance between port one and port 2 respectively; Z _{11 (0)}, Z _{22 (0)}represent the zero sequence self-impedance of port one and port 2 respectively; Z _{12 (0)}, Z _{21 (0)}represent the zero sequence mutual impedance between port one and port 2 respectively; Z _{uv (1)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₁in the capable v column element of u, Z _{uv (2)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₂in the capable v column element of u, Z _{uv (0)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₀in the capable v column element of u;

2. the port Impedance battle array of the positive sequence of port one and port 2, negative phase-sequence, zero sequence is asked

The each sequence impedance calculated by formula (2), forms positive sequence, negative phase-sequence, zero sequence port Impedance battle array, is denoted as Z respectively ₍₁₎, Z ₍₂₎, Z ₍₀₎, shown in (3);

$Z_{\left(1\right)}=\left(\begin{array}{cc}{Z}_{11\left(1\right)}& Z_{12\left(1\right)}\\ Z_{21\left(1\right)}& Z_{22\left(1\right)}\end{array}\right),Z_{\left(2\right)}=\left(\begin{array}{cc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}\end{array}\right),Z_{\left(0\right)}=\left(\begin{array}{cc}{Z}_{11\left(0\right)}& Z_{12\left(0\right)}\\ Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right)---\left(3\right)$

4) comprehensive impedance battle array Z is asked for _f

1. according to each sequence impedance element calculated by formula (2), row write negative phase-sequence, zero sequence port comprehensive impedance battle array Z, shown in (4);

$Z=\left[\begin{array}{cccc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}& 0& 0\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}& 0& 0\\ 0& 0& Z_{11\left(0\right)}& Z_{12\left(0\right)}\\ 0& 0& Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right]---\left(4\right)$

2. negative phase-sequence formula (4) Suo Shi, zero sequence port comprehensive impedance battle array Z are substituted into formula (5) counter circuit Impedance Matrix Z _l;

$Z_L=C^{T}ZC=\left[\begin{array}{ccc}{Z}_{aa}^{\′}& Z_{ab}^{\′}& Z_{ac}^{\′}\\ Z_{ba}^{\′}& Z_{bb}^{\′}& Z_{bc}^{\′}\\ Z_{ca}^{\′}& Z_{cb}^{\′}& Z_{cc}^{\′}\end{array}\right]---\left(5\right)$

In formula, $C=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& -1\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ C ^tfor the transposition of C; Z ' _st(s=a, b, c; L=a, b, c), during s=l, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l;

3. by formula (5) by impedance element corresponding to formula (6) cancellation closed-loop path c, the impedance element of retention loop a and loop b, obtains comprehensive impedance battle array Z _f, shown in (7);

$Z_{sl}=Z_{sl}^{\′}-\frac{Z_{sc}^{\′}{Z}_{cl}^{\′}}{Z_{cc}^{\′}}---\left(6\right)$

In formula, Z _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s behind cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l; Z ' _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l; Z ' _sc(s=a, b) represents the mutual impedance between loop s and loop c; Z ' _cl(l=a, b) represents the mutual impedance between loop c and loop l; Z ' _ccrepresent the self-impedance of loop c;

$Z_F=\left[\begin{array}{cc}{Z}_{aa}& Z_{ab}\\ Z_{ba}& Z_{bb}\end{array}\right]---\left(7\right)$

In formula, Z _sl(s=a, b; L=a, b), during s=l, the self-impedance of loop s behind expression cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l;

5) formula (8) is inverted obtain complex admittance battle array, be denoted as Y _f, shown in (8)

$Y_F={Z_F}^{-1}=\left[\begin{array}{cc}{y}_{aa}& y_{ab}\\ y_{ba}& y_{bb}\end{array}\right]---\left(8\right)$

In formula, y _sl(s=a, b; L=a, b), during s=l, the self-admittance of loop s behind expression cancellation closed-loop path; During s ≠ l, the transadmittance behind expression cancellation closed-loop path between loop s and loop l;

6) complex admittance battle array Y is utilized _fin element amendment positive sequence admittance battle array Y ₁middle corresponding element, amending method is shown in formula (9), the positive sequence that is expanded admittance battle array Y _1E

$\left\{\begin{array}{c}{y}_{mm\left(1\right)}^{\′}=y_{mm\left(1\right)}+y_{aa},y_{mn\left(1\right)}^{\′}=y_{mn\left(1\right)}+y_{ab},y_{nm\left(1\right)}^{\′}=y_{nm\left(1\right)}+y_{ba},y_{nn\left(1\right)}^{\′}=y_{nn\left(1\right)}+y_{bb}\\ y_{pp\left(1\right)}^{\′}=y_{pp\left(1\right)}+y_{aa},y_{pq\left(1\right)}^{\′}=y_{pq\left(1\right)}+y_{ab},y_{qp\left(1\right)}^{\′}=y_{qp\left(1\right)}+y_{ba},y_{qq\left(1\right)}^{\′}=y_{qq\left(1\right)}+y_{bb}\end{array}\right.---\left(9\right)$

In formula, y ' _uv(1) (u=m, n; V=m, n) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=m, n; V=m, n) represent admittance battle array Y ₁in the capable v column element of u;

Y ' _{uv (1)}(u=p, q; V=p, q) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=p, q; V=p, q) represent admittance battle array Y ₁in the capable v column element of u;

7) according to expansion positive sequence admittance battle array Y _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ₁₂; Concrete grammar is as follows:

1. the set of generator 1 and generator 2 corresponding node composition is denoted as boundary node B, in network, the set of all the other nodes composition is denoted as external node E, will expand positive sequence admittance battle array Y _1Ewriting matrix in block form form, can obtain network equation that matrix in block form represents such as formula shown in (10);

$\left[\begin{array}{cc}{Y}_{BB}& Y_{BE}\\ Y_{EB}& Y_{EE}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{V}}_B\\ {\stackrel{\·}{V}}_E\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{I}}_B\\ {\stackrel{\·}{I}}_E\end{array}\right]---\left(10\right)$

In formula, Y _bBrepresent the admittance battle array corresponding to all boundary nodes; Y _bErepresent all boundary nodes and the admittance battle array corresponding to all external nodes, and Y _bEequal Y _eBtransposition; Y _eErepresent the admittance battle array corresponding to all external nodes; represent the column voltage vector of all boundary points; represent the column voltage vector of all external nodes; represent the Injection Current of all boundary nodes; represent the Injection Current of all external nodes;

2. the matrix in block form in formula (10) is substituted in (11) formula and calculate, obtain boundary admittance battle array

${\tilde{Y}}_{BB}=Y_{BB}-Y_{BE}{Y}_{EE}^{-1}{Y}_{EB}---\left(11\right)$

In formula, the boundary admittance battle array after equivalence, the contribution of the equivalent branch road that it produces after including external network abbreviation; Therefore the equivalent transadmittance between generator 1 node retained in 2 machine systems and generator 2 node be exactly equivalence after boundary admittance, so there is formula (12) to set up:

${\tilde{Y}}_{BB}=Y_{12}=G_{12}+{\mathrm{jB}}_{12}---\left(12\right)$

In formula, G ₁₂for equivalent transadmittance Y ₁₂real part, be called conductance, and G ₁₂> 0; B ₁₂for equivalent transadmittance Y ₁₂imaginary part, be called susceptance, and B ₁₂> 0;

8) by step 7) in equivalent transadmittance Y between the generator 1 that calculates and generator 2 ₁₂in substitution formula (13), the active power of calculating generator 1 and generator 2 is to the local derviation K at respective merit angle respectively ₁₁, K ₂₂;

$\left\{\begin{array}{c}{K}_{11}=\frac{\∂P_{G1}}{\∂{\mathrm{\δ}}_1}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin (\mathrm{\γ}-{\mathrm{\δ}}_0)\\ K_{22}=\frac{\∂P_{G2}}{\∂{\mathrm{\δ}}_2}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin (\mathrm{\γ}+{\mathrm{\δ}}_0)\end{array}\right.---\left(13\right)$

In formula, P _g1, P _g2be respectively the active power of generator 1 and generator 2; δ ₁, δ ₂be respectively the merit angle of generator 1 and generator 2; represent that the active power of generator 1 and generator 2 is to the numerical value of the partial derivative of generator's power and angle at initial time respectively; E _q1, E _q2be respectively the electromotive force of generator 1 and generator 2; δ ₀the phase angle at expression system initial work location place; | Y ₁₂| represent equivalent transadmittance Y ₁₂amplitude, γ represents equivalent transadmittance Y ₁₂phase angle, γ=arctg (B ₁₂/ G ₁₂), and γ ∈ (0, pi/2);

9) by step 8) in the K that calculates ₁₁, K ₂₂calculate the transient state angular frequency of 2 machine systems when head end is single-phase to be overlapped in substitution formula (14), the transient state angular frequency of generator 1 and generator 2 is denoted as Δ ω respectively ₁(t), Δ ω ₂(t);

$\left\{\begin{array}{c}{\mathrm{\Δ\ω}}_1\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\ΔP}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\ΔP}}_{m20})(1-e^{-\mathrm{\σ}t})+\frac{K_{11}}{M_1}\mathrm{\Δ}\stackrel{*}{\mathrm{\ω}}\left(t\right)\\ {\mathrm{\Δ\ω}}_2\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\ΔP}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\ΔP}}_{m20})(1-e^{-\mathrm{\σ}t})-\frac{K_{22}}{M_2}\mathrm{\Δ}\stackrel{*}{\mathrm{\ω}}\left(t\right)\end{array}\right.---\left(14\right)$

In formula, D ₁, D ₂represent the damping coefficient of generator 1 and generator 2 respectively; Δ P _m10, Δ P _m20represent the chugging that generator 1 and generator 2 occur respectively; m ₁, M ₂represent the moment of inertia of generator 1,2; $\mathrm{\Δ}\stackrel{*}{\mathrm{\ω}}\left(t\right)=\frac{D_1{D}_2}{K_{11}{D}_2+K_{22}{D}_1}(\frac{{\mathrm{\ΔP}}_{m10}}{D_1}-\frac{{\mathrm{\ΔP}}_{m20}}{D_2})e^{-\frac{\mathrm{\σ}}{2}t}\frac{sin\left(\mathrm{\β}t\right)}{\mathrm{\β}};$ $\mathrm{\β}=\sqrt{{\mathrm{\ω}}_0(\frac{K_{11}}{M_1}+\frac{K_{22}}{M_2})-{\left(\frac{\mathrm{\σ}}{2}\right)}^2};$ ω ₀for the rated angular velocity of generator, t is the time;

10) because the relation between angular frequency and frequency meets formula (15), by step 9) in the angular frequency Δ ω of generator 1,2 that calculates ₁(t), Δ ω ₂t () substitutes into formula (16), calculate the transient frequency Δ f of generator 1,2 when head end is single-phase to be overlapped ₁(t), Δ f ₂(t);

f＝ω/2π(15)

$\mathrm{\Δ}f\left(t\right)=\frac{\mathrm{\Δ}\mathrm{\ω}\left(t\right)}{2\mathrm{\π}}---\left(16\right)$

In formula, f is frequency; ω is angular frequency;

(2) analog line end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase head end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ' ₁, Y ' ₂, Y ' ₀;

2) by Y ' ₁, Y ' ₂, Y ' ₀substitution formula (1), invert obtain line end single-phase overlap time positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ' ₁, Z ' ₂, Z ' ₀;

3) 3 in step (1) is repeated) application dual-port theory asks for port Impedance, is designated as Z ' ₍₁₎, Z ' ₍₂₎, Z ' ₍₀₎;

4) 4 in step (1) is repeated) ask for comprehensive impedance battle array, be designated as Z ' _f;

5) 5 in step (1) is repeated) obtain complex admittance battle array, be denoted as Y ' _f;

6) 6 in step (1) is repeated) utilize complex admittance battle array Y ' _fmiddle element amendment positive sequence admittance battle array Y ' ₁middle corresponding element, the positive sequence that is expanded admittance battle array Y ' _1E;

7) 7 in step (1) is repeated) according to expansion positive sequence admittance battle array Y ' _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ' ₁₂;

8) 8 in step (1) is repeated) distinguish the active power of calculating generator 1 and generator 2 to the local derviation K ' at respective merit angle ₁₁, K ' ₂₂;

9) 9 in step (1) is repeated) the transient state angular frequency that calculates generator 1 and generator 2 when end is single-phase to be overlapped is denoted as Δ ω ' respectively ₁(t), Δ ω ' ₂(t);

10) 10 in step (1) is repeated) calculate the transient frequency Δ f ' of generator 1,2 when end is single-phase to be overlapped ₁(t), Δ f ' ₂(t);

(3) frequency shift (FS) fail safe quantitative evaluation index

Utilize formula (17) to carry out quantitative evaluation to the generator transient frequency that step (1), (2) calculate, obtain the transient frequency stability margin η of generator 1,2 when circuit head end is single-phase to be overlapped _g1, η _g2, line end single-phase overlap time generator 1,2 transient frequency stability margin η ' _g1, η ' _g2;

η＝[f _ext-(f _cr-kT _cr)]×100％(17)

In formula, f _crand T _crthe frequency shift (FS) threshold value of generator and the duration of permission respectively, f _extrefer to the limiting value of generator frequency in transient process, k is commutation factor critical frequency shift duration being converted into frequency, and η is that plus or minus value represents that transient frequency is stable or unstable respectively;

Obtain the transient frequency stability margin of each generator in 2 machine systems, get the transient frequency stability margin of each generator transient frequency stability margin minimum value as system;

Head end single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (18), be denoted as η ₁;

η ₁＝min{η _G1,η _G2}(18)

End single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (19), be denoted as η ₂;

η ₂＝min{η′ _G1,η′ _G2}(19)

(4) reach a conclusion

Alternative route first and end single-phase overlap time system transient modelling frequency stabilization nargin η ₁, η ₂, choose single-phase time sequence of coincidence corresponding to the greater as the optimization time sequence of coincidence scheme exported; If η ₁> η ₂, then single-phase coincidence is first dropped into by circuit head end; Otherwise, first drop into single-phase coincidence by line end.

Operation principle of the present invention is:

1. dual-port is theoretical

(1) apply dual-port theory and ask for port Impedance

When there is unbalanced fault at F1 place and F2 place in electric power system simultaneously, be equivalent to the impedance simultaneously accessing asymmetrical three-phase at F1 place and F2 place, be made up of two parts circuit at fault place, a part is the unsymmetric circuit of faults situation, and another part is the original system of reflection triphase parameter symmetry.Owing to there being two place's faults, in sequence net, each fault place shows as a port, and therefore the sequence net of double fault is two-port network, i.e. two-port network.

1. the positive sequence of port one and port 2, negative phase-sequence, zero sequence self-impedance and mutual impedance is asked for.

If it is m, n (n is the earth 0 node) that node serial number corresponding to single phase ground fault place occurs; Node serial number corresponding to line end single-phase wire break place is p, q.Be that the port that m, n are corresponding is denoted as port one by node serial number; Node serial number is that the port that p, q are corresponding is denoted as port 2.

Corresponding element in positive sequence, negative phase-sequence, zero sequence impedance battle array is substituted in formula (20), tries to achieve the positive sequence of port one and port 2, negative phase-sequence, the self-impedance of zero sequence and mutual impedance.

Z ₁₁₍₁₎＝Z ₁₁₍₂₎＝Z _mm(1)+Z _nn(1)-2Z _mn(1)

Z ₁₂₍₁₎＝Z ₁₂₍₂₎＝Z _mp(1)+Z _nq(1)-Z _mq(1)-Z _np(1)

Z ₂₁₍₁₎＝Z ₂₁₍₂₎＝Z _pm(1)+Z _qn(1)-Z _pn(1)-Z _qm(1)

Z ₂₂₍₁₎＝Z ₂₂₍₂₎＝Z _pp(1)+Z _qq(1)-2Z _pq(1)

Z ₁₁₍₀₎＝Z _mm(0)+Z _nn(0)-2Z _mn(0)(20)

Z ₁₂₍₀₎＝Z _mp(0)+Z _nq(0)-Z _mq(0)-Z _np(0)

Z ₂₁₍₀₎＝Z _pm(0)+Z _qn(0)-Z _pn(0)-Z _qm(0)

Z ₂₂₍₀₎＝Z ₂₂₍₀₎＝Z _pp(0)+Z _qq(0)-2Z _pq(0)

In formula, Z _{11 (1)}, Z _{22 (1)}represent the positive sequence self-impedance of port one and port 2 respectively; Z _{12 (1)}, Z _{21 (1)}represent the positive sequence mutual impedance between port one and port 2 respectively; Z _{11 (2)}, Z _{22 (2)}represent the negative phase-sequence self-impedance of port one and port 2 respectively; Z _{12 (2)}, Z _{21 (2)}represent the negative phase-sequence mutual impedance between port one and port 2 respectively; Z _{11 (0)}, Z _{22 (0)}represent the zero sequence self-impedance of port one and port 2 respectively; Z _{12 (0)}, Z _{21 (0)}represent the zero sequence mutual impedance between port one and port 2 respectively; Z _{uv (1)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₁in the capable v column element of u, Z _{uv (2)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₂in the capable v column element of u, Z _{uv (0)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₀in the capable v column element of u;

2. the port Impedance battle array of the positive sequence of port one and port 2, negative phase-sequence, zero sequence is asked.

The each sequence impedance calculated by formula (20), forms positive sequence, negative phase-sequence, zero sequence port Impedance battle array, is denoted as Z respectively ₍₁₎, Z ₍₂₎, Z ₍₀₎, shown in (21).

$Z_{\left(1\right)}=\left(\begin{array}{cc}{Z}_{11\left(1\right)}& Z_{12\left(1\right)}\\ Z_{21\left(1\right)}& Z_{22\left(1\right)}\end{array}\right),Z_{\left(2\right)}=\left(\begin{array}{cc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}\end{array}\right),Z_{\left(0\right)}=\left(\begin{array}{cc}{Z}_{11\left(0\right)}& Z_{12\left(0\right)}\\ Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right)---\left(21\right)$

(2) comprehensive impedance battle array is asked for

1. negative phase-sequence, zero sequence port comprehensive impedance battle array Z is write, shown in (22) according to two-port network row.

$Z=\left[\begin{array}{cccc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}& 0& 0\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}& 0& 0\\ 0& 0& Z_{11\left(0\right)}& Z_{12\left(0\right)}\\ 0& 0& Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right]---\left(22\right)$

2. negative phase-sequence formula (22) Suo Shi, zero sequence port comprehensive impedance battle array Z are substituted into formula (23) counter circuit Impedance Matrix Z _l.

$Z_L=C^{T}ZC=\left[\begin{array}{ccc}{Z}_{aa}^{\′}& Z_{ab}^{\′}& Z_{ac}^{\′}\\ Z_{ba}^{\′}& Z_{bb}^{\′}& Z_{bc}^{\′}\\ Z_{ca}^{\′}& Z_{cb}^{\′}& Z_{cc}^{\′}\end{array}\right]---\left(23\right)$

In formula, $C=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& -1\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ C ^tfor the transposition of C; Z ' _st(s=a, b, c; L=a, b, c), during s=l, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l;

3. by formula (23) by impedance element corresponding to formula (24) cancellation closed-loop path c, the impedance element of retention loop a and loop b, obtains comprehensive impedance battle array Z _f, shown in (25).

$Z_{sl}=Z_{sl}^{\′}-\frac{Z_{sc}^{\′}{Z}_{cl}^{\′}}{Z_{cc}^{\′}}---\left(24\right)$

In formula, Z _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s behind cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l; Z ' _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l; Z ' _sc(s=a, b) represents the mutual impedance between loop s and loop c; Z ' _cl(l=a, b) represents the mutual impedance between loop c and loop l; Z ' _ccrepresent the self-impedance of loop c;

$Z_F=\left[\begin{array}{cc}{Z}_{aa}& Z_{ab}\\ Z_{ba}& Z_{bb}\end{array}\right]---\left(25\right)$

In formula, Z _sl(s=a, b; L=a, b), during s=l, the self-impedance of loop s behind expression cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l;

(3) formula (25) is inverted obtain complex admittance battle array, be denoted as Y _f, shown in (26).

$Y_F={Z_F}^{-1}=\left[\begin{array}{cc}{y}_{aa}& y_{ab}\\ y_{ba}& y_{bb}\end{array}\right]---\left(26\right)$

In formula, y _sl(s=a, b; L=a, b), during s=l, the self-admittance of loop s behind expression cancellation closed-loop path; During s ≠ l, the transadmittance behind expression cancellation closed-loop path between loop s and loop l;

(4) complex admittance battle array Y is utilized _fin element amendment positive sequence admittance battle array Y ₁middle corresponding element, amending method is shown in formula (27), and be expanded admittance battle array Y _1E.

$\left\{\begin{array}{c}{y}_{mm\left(1\right)}^{\′}=y_{mm\left(1\right)}+y_{aa},y_{mn\left(1\right)}^{\′}=y_{mn\left(1\right)}+y_{ab},y_{nm\left(1\right)}^{\′}=y_{nm\left(1\right)}+y_{ba},y_{nn\left(1\right)}^{\′}=y_{nn\left(1\right)}+y_{bb}\\ y_{pp\left(1\right)}^{\′}=y_{pp\left(1\right)}+y_{aa},y_{pq\left(1\right)}^{\′}=y_{pq\left(1\right)}+y_{ab},y_{qp\left(1\right)}^{\′}=y_{qp\left(1\right)}+y_{ba},y_{qq\left(1\right)}^{\′}=y_{qq\left(1\right)}+y_{bb}\end{array}\right.---\left(27\right)$

In formula, y ' _{uv (1)}(u=m, n; V=m, n) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=m, n; V=m, n) represent admittance battle array Y ₁in the capable v column element of u;

Y ' _{uv (1)}(u=p, q; V=p, q) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=p, q; V=p, q) represent admittance battle array Y ₁in the capable v column element of u.

2.Ward equivalent method

The node of former network represents with set N.The part fallen for abbreviation is called external network, and its set of node E represents.The node of reserve part network represents with reservation collection G.Then there is G ∩ E=N.Retaining the node composition boundary node set concentrated and be associated with external network node, represent with B.The part of discord outside segments point set association is internal node collection, represents with I.If the network equation of short for admittance matrix representation is pressed I, B, E set to divide, then can write out the network equation represented by matrix in block form form as follows:

$\left[\begin{array}{ccc}{Y}_{EE}& Y_{EB}& 0\\ Y_{BE}& Y_{BB}& Y_{BI}\\ 0& Y_{IB}& Y_{II}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{V}}_E\\ {\stackrel{\·}{V}}_B\\ {\stackrel{\·}{V}}_I\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{I}}_E\\ {\stackrel{\·}{I}}_B\\ {\stackrel{\·}{I}}_I\end{array}\right]---\left(28\right)$

The voltage quantities of cancellation external node have

$\left[\begin{array}{cc}{\tilde{Y}}_{BB}& Y_{BI}\\ Y_{IB}& Y_{II}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{V}}_B\\ {\stackrel{\·}{V}}_I\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{\tilde{I}}}_B\\ {\stackrel{\·}{I}}_I\end{array}\right]---\left(29\right)$

${\tilde{Y}}_{BB}=Y_{BB}-Y_{BE}{Y^{-1}}_{EE}{Y}_{EB}---\left(30\right)$

In formula, the boundary admittance matrix after equivalence, the contribution of the equivalent branch road that it produces after including external network abbreviation.

The order of the secondary comparatively formula (28) of order of equation of formula (29) is low, therefore easily calculates.Due to equivalent boundary admittance matrix add an addition Item relative to original YBB, and addition Item is full battle array under many circumstances, so non-zero entry more than YBB, namely by sparse for some lost.When dimension is lower, solves the network equation (29) after simplification faster than solving former network equation (28) when namely boundary node is less.

3. single-phase time sequence of coincidence is to the Influencing Mechanism of system transient modelling frequency stability

The formation of 3.1 admittance battle arrays

Under static load model, 2 machine systems as shown in Figure 1.2 machine systems are powered to load through double back transmission line of alternation current.When on circuit during non-head end any point generation single phase ground fault, when dropping into single-pole reclosing by circuit head end and end respectively, calculate first close head end and first conjunction end time bus frequency change.

The Changing Pattern of 2 machine systems each using internal potential frequency of generator when original machine power is undergone mutation, does not consider the impact of regulating system and part throttle characteristics in analysis, focus on disturbance place and the empty research to distributing of frequency.For ease of the comprehensive analysis to various phenomenon, first carry out relevant theory deduction.

If 1 ^#with 2 ^#equivalent transadmittance between machine interior nodes is Y ₁₂=G ₁₂+ jB ₁₂, the discussion of 2 machine system equivalent transadmittances, in FIG, if line impedance is Z _l=r _l+ jx _l, load impedance constant impedance represents, i.e. Z _di=R _di+ jX _dior Y _di=G _di-jB _di, i=1,2.Wherein, Z _lfor line impedance, r _lfor line resistance, x _lfor line reactance; Z _difor load constant impedance, R _difor load resistance, X _difor load reactance; Y _difor load constant admittance, G _difor load conductance, B _difor susceptance.

Establish again and (wherein, x _difor the reactance of generator, y _ibe the admittance of two generator nodes, y _lfor the admittance of circuit.) the admittance battle array that can obtain 2 machine systems is:

$\left[\begin{array}{cccc}{y}_1& 0& -y_1& 0\\ 0& y_2& 0& -y_2\\ -y_1& 0& y_1+y_L+y_{D1}& -y_L\\ 0& -y_2& -y_L& y_2+y_L+y_{D2}\end{array}\right]$

Cancellation load bus obtains: $y_{12}=-\frac{y_1{y}_2{y}_L}{\mathrm{\Δ}}$ In formula $\mathrm{\Δ}=(y_1+y_L+y_{D1})(y_1+y_L+y_{D2})-y_L^2$

Order $R_{12}+{\mathrm{jX}}_{12}=\frac{1}{Y_{12}}=\frac{1}{G_{12}+{\mathrm{jB}}_{12}}$

Can obtain:

R ₁₂＝-r _L(x _d2B _D2+x _d1B _D1+1)+r _L(G _D1G _D2-B _D1B _D2)x _d1x _d2

+x _L(x _d1G _D1+x _d2G _D2)+x _d1x _d2(G _D1+G _D2)+x _d1x _d2x _L(G _D1B _D2+G _D2B _D1)

X ₁₂＝-(x _d1+x _d2+x _L)-r _L(x _d1x _d2+x _d2G _D2+x _d1x _d2(G _D1B _D2+G _D2B _D1))

-x _d1x _d2(B _D1+B _D2)-x _L(x _d1B _D1+x _d2B _D2)-x _d1x _d2x _L(B _D1B _D2-G _D1G _D2)

General r _lvery little, so there is R ₁₂> 0, X ₁₂< 0, therefore G ₁₂> 0, B ₁₂> 0.Y ₁₂=G ₁₂+ jB ₁₂as order γ=arctg (B ₁₂/ G ₁₂), γ ∈ (0, pi/2).

The transient frequency of 3.2 systems

When system is uniform damping, i.e. D ₁/ M ₁=D ₂/ M ₂during=σ, the analytic solutions of frequency procedure can be obtained:

$\left\{\begin{array}{c}{\mathrm{\&Delta;\&omega;}}_1\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20})(1-e^{-\mathrm{\&sigma;}t})+\frac{K_{11}}{M_1}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\\ {\mathrm{\&Delta;\&omega;}}_2\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20})(1-e^{-\mathrm{\&sigma;}t})-\frac{K_{22}}{M_2}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\end{array}\right.---\left(31\right)$

In formula, $\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)=\frac{D_1{D}_2}{K_{11}{D}_2+K_{22}{D}_1}(\frac{{\mathrm{\&Delta;P}}_{m10}}{D_1}-\frac{{\mathrm{\&Delta;P}}_{m20}}{D_2})e^{-\mathrm{\&sigma;}t}\frac{sin\left(\mathrm{\&beta;}t\right)}{\mathrm{\&beta;}};$ Y ₁₂=G ₁₂+ jB ₁₂, wherein, G ₁₂the real part of admittance, and G ₁₂> 0; B ₁₂the imaginary part of admittance, and B ₁₂> 0.| Y ₁₂| represent equivalent transadmittance Y ₁₂amplitude, and γ represents admittance Y ₁₂phase angle, and γ=arctg (B ₁₂/ G ₁₂), then there is γ ∈ (0, pi/2); The active power of generator 1 and generator 2 is respectively to the local derviation K at respective merit angle ₁₁, K ₂₂; P _g1, P _g2what represent generator 1 and generator 2 respectively has power; δ ₁, δ ₂represent the merit angle of generator 1 and generator 2 respectively; δ ₀the phase angle at expression system initial work location place; D _i, (i=1,2) represent the damping coefficient of generator; Δ P _mi0(i=1,2) represents the chugging that prime mover occurs; $\mathrm{\&sigma;}=D_1/M_1=\frac{D_2}{M_2};$ M ₁, M ₂represent the moment of inertia of generator; $\mathrm{\&beta;}=\sqrt{{\mathrm{\&omega;}}_0(\frac{K_{11}}{M_1}+\frac{K_{22}}{M_2})-{\left(\frac{\mathrm{\&sigma;}}{2}\right)}^2},$ ω ₀for the rated angular velocity of generator.

4. transient frequency stability margin

Shown in Fig. 2 one group two-element list [(f _cr1, T _cr1), (f _cr2, T _cr2) ..., (f _crl, T _crl)] be used to the TFDA problem of a description bus.If for the threshold value f of each frequency _crllower than electrical network rated frequency (f _r) two-element list, bus actual frequency is lower than threshold value f _crlduration be all less than corresponding threshold value T _crl; Meanwhile, for each threshold value f _crlhigher than electrical network rated frequency (f _r) two-element list, bus actual frequency exceedes threshold value f _crlduration be all less than corresponding threshold value T _crl, then think that the transient frequency of this bus is stable.Otherwise, think that the transient frequency of this bus is unstable.Wherein, f _cr1..., f _crlit is one group of given frequency threshold value; T _cr1..., T _crlfor the threshold value of given frequency threshold value corresponding duration.

According to the stability margin of transient frequency curve calculation transient frequency over time, generally transient frequency stability margin is denoted as η _fb, formula (32) is its definition:

η _fb＝[f _ext-(f _cr-kT _cr)]×100％(32)

Wherein f _crand T _crthe frequency shift (FS) threshold value of generator and the duration of permission respectively, f _extrefer to the limiting value of generator frequency in transient process, k is commutation factor critical frequency shift duration being converted into frequency, η _fbfor just (or negative) value represents transient frequency stable (or unstable).

The invention has the beneficial effects as follows:

1, apply dual-port theory and solve single-phase port battle array when coinciding with permanent fault, the analytical calculation of complex fault is greatly simplified.

2, when asking for the internodal equivalent transadmittance of 2 generators, adopting Ward equivalent method to carry out abbreviation to expansion positive sequence admittance battle array, not only reducing network size, and improve computational efficiency.

3, the stable of general frequency is compared with given threshold value by the steady-state value of frequency response, thus determination frequency to stablize or unstable.The present invention utilizes the quantitative evaluation of transient frequency to obtain the quantizating index of characterization system transient frequency stability, thus realizes the preferred of single-phase time sequence of coincidence scheme.

4, a large amount of simulation result shows, patent of the present invention effectively can improve transient frequency stability when 2 machine systems carry out single-phase lock, respond well.

Accompanying drawing explanation

Fig. 1 is 2 machine system wiring figure; Comprise 2 generator G ₁, G ₂with 2 transformer T ₁, T ₂through transmission line of alternation current, load is powered; E in figure _q1, E _q2be respectively G ₁, G ₂electromotive force; P _dA, Q _dAbe respectively load active power and the reactive power of bus A; P _dC, Q _dCbe respectively load active power and the reactive power of bus C; P _dD, Q _dDbe respectively load active power and the reactive power of bus D;

Fig. 2 is the two-element list describing TFDA; In figure, f is frequency; f _rfor electrical network rated frequency; f _cr1, f _cr2, f _cr3be respectively different frequency threshold values; T ₁, T ₂, T ₃be respectively frequency threshold value f _cr1, f _cr2, f _cr3corresponding time gate threshold value; T/s be time/second;

Fig. 3 is bus 1-bus D circuit head end single phase ground fault, generator G during head end first single-phase coincidence ₁frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 4 is bus 1-bus D circuit head end single phase ground fault, generator G during head end first single-phase coincidence ₂frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 5 is bus 1-bus D circuit head end single phase ground fault, generator G during end first single-phase coincidence ₁frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 6 is bus 1-bus D circuit head end single phase ground fault, generator G during end first single-phase coincidence ₂frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 7 is bus 2-bus D circuit head end single phase ground fault, generator G during head end first single-phase coincidence ₁frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 8 is bus 2-bus D circuit head end single phase ground fault, generator G during head end first single-phase coincidence ₂frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Fig. 9 is bus 2-bus D circuit head end single phase ground fault, generator G during end first single-phase coincidence ₁frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second);

Figure 10 is bus 2-bus D circuit head end single phase ground fault, generator G during end first single-phase coincidence ₂frequency variation curve; In figure, generator frequency curve (Hz) is generator frequency (hertz); Time (s) is the time (second).

Embodiment

Embodiment 1: as Figure 1-10 shows, the single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities, when there is single phase ground fault in the transmission line of alternation current of 2 electro-mechanical force systems, there is two kinds of faults and single phase ground fault and single-phase wire break fault when single-phase coincidence, form the fault network of dual-port; Utilize symmetrical component method to obtain three sequence sequence nets according to fault type, arrange according to positive sequence, negative phase-sequence, zero-sequence network the admittance battle array writing each sequence, the admittance battle array of each sequence is inverted and obtains the Impedance Matrix of each sequence; Adopt dual-port theory first to try to achieve port Impedance battle array, and then try to achieve comprehensive impedance battle array, inverting to it obtains complex admittance battle array; According to complex admittance battle array amendment positive sequence network, thus the positive sequence admittance battle array that is expanded; Ward equivalent method is utilized to calculate equivalent transadmittance between 2 generator nodes, calculate the generator frequency variation track under two kinds of reclosing time sequences thus, realize the quantitative evaluation of frequency change track thus obtain transient frequency stability margin, choosing time sequence of coincidence corresponding to transient frequency stability margin the greater is the coincidence scheme optimized.

The concrete steps of described method are as follows:

(1) analog line head end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line head end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ₁, Y ₂, Y ₀; Wherein, the method forming admittance battle array is as follows: in admittance battle array each row off-diagonal element, the number of nonzero element equals the connected earth-free circuitry number of corresponding node; The each diagonal element of admittance battle array, i.e. the self-admittance Y of each node _iiequal the admittance sum on respective nodes institute's chord road: the transadmittance Y of each off-diagonal element of admittance battle array _ijjust to equal between 2 nodes connect the negative value of admittance: Y _ij=-y _ij;

In formula, y _ijfor the admittance on institute's chord road between node i and node j;

2) positive sequence, negative phase-sequence, zero sequence impedance battle array is asked for

To positive sequence, negative phase-sequence, zero sequence admittance battle array Y ₁, Y ₂, Y ₀invert, shown in (1), obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ₁, Z ₂, Z ₀;

$Z_1=Y_1^{-1},Z_2=Y_2^{-1},Z_0=Y_0^{-1}---\left(1\right)$

3) apply dual-port theory and ask for port Impedance

1. the positive sequence of port one and port 2, negative phase-sequence, zero sequence self-impedance and mutual impedance is asked for;

If node serial number single phase ground fault place occurring corresponding is m, n, n is the earth 0 node; Node serial number corresponding to single-phase end disconnection fault place is p, q; Be that the port that m, n are corresponding is denoted as port one by node serial number; Node serial number is that the port that p, q are corresponding is denoted as port 2;

By step 2) in the three sequence Impedance Matrixes that calculate corresponding element substitute in formula (2), try to achieve the positive sequence of port one and port 2, negative phase-sequence, the self-impedance of zero sequence and mutual impedance;

Z ₁₁₍₁₎＝Z ₁₁₍₂₎＝Z _mm(1)+Z _nn(1)-2Z _mn(1)

Z ₁₂₍₁₎＝Z ₁₂₍₂₎＝Z _mp(1)+Z _nq(1)-Z _mq(1)-Z _np(1)

Z ₂₁₍₁₎＝Z ₂₁₍₂₎＝Z _pm(1)+Z _qn(1)-Z _pn(1)-Z _qm(1)

Z ₂₂₍₁₎＝Z ₂₂₍₂₎＝Z _pp(1)+Z _qq(1)-2Z _pq(1)

Z ₁₁₍₀₎＝Z _mm(0)+Z _nn(0)-2Z _mn(0)(2)

Z ₁₂₍₀₎＝Z _mp(0)+Z _nq(0)-Z _mq(0)-Z _np(0)

Z ₂₁₍₀₎＝Z _pm(0)+Z _qn(0)-Z _pn(0)-Z _qm(0)

Z ₂₂₍₀₎＝Z ₂₂₍₀₎＝Z _pp(0)+Z _qq(0)-2Z _pq(0)

In formula, Z _{11 (1)}, Z _{22 (1)}represent the positive sequence self-impedance of port one and port 2 respectively; Z _{12 (1)}, Z _{21 (1)}represent the positive sequence mutual impedance between port one and port 2 respectively; Z _{11 (2)}, Z _{22 (2)}represent the negative phase-sequence self-impedance of port one and port 2 respectively; Z _{12 (2)}, Z _{21 (2)}represent the negative phase-sequence mutual impedance between port one and port 2 respectively; Z _{11 (0)}, Z _{22 (0)}represent the zero sequence self-impedance of port one and port 2 respectively; Z _{12 (0)}, Z _{21 (0)}represent the zero sequence mutual impedance between port one and port 2 respectively; Z _{uv (1)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₁in the capable v column element of u, Z _{uv (2)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₂in the capable v column element of u, Z _{uv (0)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₀in the capable v column element of u;

2. the port Impedance battle array of the positive sequence of port one and port 2, negative phase-sequence, zero sequence is asked

The each sequence impedance calculated by formula (2), forms positive sequence, negative phase-sequence, zero sequence port Impedance battle array, is denoted as Z respectively ₍₁₎, Z ₍₂₎, Z ₍₀₎, shown in (3);

$Z_{\left(1\right)}=\left(\begin{array}{cc}{Z}_{11\left(1\right)}& Z_{12\left(1\right)}\\ Z_{21\left(1\right)}& Z_{22\left(1\right)}\end{array}\right),Z_{\left(2\right)}=\left(\begin{array}{cc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}\end{array}\right),Z_{\left(0\right)}=\left(\begin{array}{cc}{Z}_{11\left(0\right)}& Z_{12\left(0\right)}\\ Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right)---\left(3\right)$

4) comprehensive impedance battle array Z is asked for _f

1. according to each sequence impedance element calculated by formula (2), row write negative phase-sequence, zero sequence port comprehensive impedance battle array Z, shown in (4);

$Z=\left[\begin{array}{cccc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}& 0& 0\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}& 0& 0\\ 0& 0& Z_{11\left(0\right)}& Z_{12\left(0\right)}\\ 0& 0& Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right]---\left(4\right)$

2. negative phase-sequence formula (4) Suo Shi, zero sequence port comprehensive impedance battle array Z are substituted into formula (5) counter circuit Impedance Matrix Z _l;

$Z_L=C^{T}ZC=\left[\begin{array}{ccc}{Z}_{aa}^{\&prime;}& Z_{ab}^{\&prime;}& Z_{ac}^{\&prime;}\\ Z_{ba}^{\&prime;}& Z_{bb}^{\&prime;}& Z_{bc}^{\&prime;}\\ Z_{ca}^{\&prime;}& Z_{cb}^{\&prime;}& Z_{cc}^{\&prime;}\end{array}\right]---\left(5\right)$

In formula, $C=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& -1\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ C ^tfor the transposition of C; Z ' _st(s=a, b, c; L=a, b, c), during s=l, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l;

3. by formula (5) by impedance element corresponding to formula (6) cancellation closed-loop path c, the impedance element of retention loop a and loop b, obtains comprehensive impedance battle array Z _f, shown in (7);

$Z_{sl}=Z_{sl}^{\&prime;}-\frac{Z_{sc}^{\&prime;}{Z}_{cl}^{\&prime;}}{Z_{cc}^{\&prime;}}---\left(6\right)$

In formula, Z _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s behind cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l; Z ' _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l; Z ' _sc(s=a, b) represents the mutual impedance between loop s and loop c; Z ' _cl(l=a, b) represents the mutual impedance between loop c and loop l; Z ' _ccrepresent the self-impedance of loop c;

$Z_F=\left[\begin{array}{cc}{Z}_{aa}& Z_{ab}\\ Z_{ba}& Z_{bb}\end{array}\right]---\left(7\right)$

In formula, Z _sl(s=a, b; L=a, b), during s=l, the self-impedance of loop s behind expression cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l;

5) formula (8) is inverted obtain complex admittance battle array, be denoted as Y _f, shown in (8)

$Y_F={Z_F}^{-1}=\left[\begin{array}{cc}{y}_{aa}& y_{ab}\\ y_{ba}& y_{bb}\end{array}\right]---\left(8\right)$

In formula, y _sl(s=a, b; L=a, b), during s=l, the self-admittance of loop s behind expression cancellation closed-loop path; During s ≠ l, the transadmittance behind expression cancellation closed-loop path between loop s and loop l;

6) complex admittance battle array Y is utilized _fin element amendment positive sequence admittance battle array Y ₁middle corresponding element, amending method is shown in formula (9), the positive sequence that is expanded admittance battle array Y _1E

$\left\{\begin{array}{c}{y}_{mm\left(1\right)}^{\&prime;}=y_{mm\left(1\right)}+y_{aa},y_{mn\left(1\right)}^{\&prime;}=y_{mn\left(1\right)}+y_{ab},y_{nm\left(1\right)}^{\&prime;}=y_{nm\left(1\right)}+y_{ba},y_{nn\left(1\right)}^{\&prime;}=y_{nn\left(1\right)}+y_{bb}\\ y_{pp\left(1\right)}^{\&prime;}=y_{pp\left(1\right)}+y_{aa},y_{pq\left(1\right)}^{\&prime;}=y_{pq\left(1\right)}+y_{ab},y_{qp\left(1\right)}^{\&prime;}=y_{qp\left(1\right)}+y_{ba},y_{qq\left(1\right)}^{\&prime;}=y_{qq\left(1\right)}+y_{bb}\end{array}\right.---\left(9\right)$

In formula, y ' _{uv (1)}(u=m, n; V=m, n) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u;

Y _{uv (1)}(u=m, n; V=m, n) represent admittance battle array Y ₁in the capable v column element of u;

Y ' _{uv (1)}(u=p, q; V=p, q) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=p, q; V=p, q) represent admittance battle array Y ₁in the capable v column element of u;

7) according to expansion positive sequence admittance battle array Y _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ₁₂; Concrete grammar is as follows:

1. the set of generator 1 and generator 2 corresponding node composition is denoted as boundary node B, in network, the set of all the other nodes composition is denoted as external node E, will expand positive sequence admittance battle array Y _1Ewriting matrix in block form form, can obtain network equation that matrix in block form represents such as formula shown in (10);

$\left[\begin{array}{cc}{Y}_{BB}& Y_{BE}\\ Y_{EB}& Y_{EE}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_B\\ {\stackrel{\&CenterDot;}{V}}_E\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_B\\ {\stackrel{\&CenterDot;}{I}}_E\end{array}\right]---\left(10\right)$

In formula, Y _bBrepresent the admittance battle array corresponding to all boundary nodes; Y _bErepresent all boundary nodes and the admittance battle array corresponding to all external nodes, and Y _bEequal Y _eBtransposition; Y _eErepresent the admittance battle array corresponding to all external nodes; represent the column voltage vector of all boundary points; represent the column voltage vector of all external nodes; represent the Injection Current of all boundary nodes; represent the Injection Current of all external nodes;

2. the matrix in block form in formula (10) is substituted in (11) formula and calculate, obtain boundary admittance battle array

${\tilde{Y}}_{BB}=Y_{BB}-Y_{BE}{Y}_{EE}^{-1}{Y}_{EB}---\left(11\right)$

In formula, the boundary admittance battle array after equivalence, the contribution of the equivalent branch road that it produces after including external network abbreviation; Therefore the equivalent transadmittance between generator 1 node retained in 2 machine systems and generator 2 node be exactly equivalence after boundary admittance, so there is formula (12) to set up:

${\tilde{Y}}_{BB}=Y_{12}=G_{12}+{\mathrm{jB}}_{12}---\left(12\right)$

In formula, G ₁₂for the real part of equivalent transadmittance Y12, be called conductance, and G ₁₂> 0; B ₁₂for equivalent transadmittance Y ₁₂imaginary part, be called susceptance, and B ₁₂> 0;

8) by step 7) in equivalent transadmittance Y between the generator 1 that calculates and generator 2 ₁₂in substitution formula (13), the active power of calculating generator 1 and generator 2 is to the local derviation K at respective merit angle respectively ₁₁, K ₂₂;

$\left\{\begin{array}{c}{K}_{11}=\frac{\&part;P_{G1}}{\&part;{\mathrm{\&delta;}}_1}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin (\mathrm{\&gamma;}-{\mathrm{\&delta;}}_0)\\ K_{22}=\frac{\&part;P_{G2}}{\&part;{\mathrm{\&delta;}}_2}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin (\mathrm{\&gamma;}+{\mathrm{\&delta;}}_0)\end{array}\right.---\left(13\right)$

In formula, P _g1, P _g2be respectively the active power of generator 1 and generator 2; δ ₁, δ ₂be respectively the merit angle of generator 1 and generator 2; represent that the active power of generator 1 and generator 2 is to the numerical value of the partial derivative of generator's power and angle at initial time respectively; E _q1, E _q2be respectively the electromotive force of generator 1 and generator 2; δ ₀the phase angle at expression system initial work location place; | Y ₁₂| represent equivalent transadmittance Y ₁₂amplitude, γ represents equivalent transadmittance Y ₁₂phase angle, γ=arctg (B ₁₂/ G ₁₂), and γ ∈ (0, pi/2);

9) by step 8) in the K that calculates ₁₁, K ₂₂calculate the transient state angular frequency of 2 machine systems when head end is single-phase to be overlapped in substitution formula (14), the transient state angular frequency of generator 1 and generator 2 is denoted as Δ ω respectively ₁(t), Δ ω ₂(t);

$\left\{\begin{array}{c}{\mathrm{\&Delta;\&omega;}}_1\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20})(1-e^{-\mathrm{\&sigma;}t})+\frac{K_{11}}{M_1}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\\ {\mathrm{\&Delta;\&omega;}}_2\left(t\right)=(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20})(1-e^{-\mathrm{\&sigma;}t})-\frac{K_{22}}{M_2}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\end{array}\right.---\left(14\right)$

In formula, D ₁, D ₂represent the damping coefficient of generator 1 and generator 2 respectively; Δ P _m10, Δ P _m20represent the chugging that generator 1 and generator 2 occur respectively; m ₁, M ₂represent the moment of inertia of generator 1,2; $\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)=\frac{D_1{D}_2}{K_{11}{D}_2+K_{22}{D}_1}(\frac{{\mathrm{\&Delta;P}}_{m10}}{D_1}-\frac{{\mathrm{\&Delta;P}}_{m20}}{D_2})e^{-\frac{\mathrm{\&sigma;}}{2}t}\frac{sin\left(\mathrm{\&beta;}t\right)}{\mathrm{\&beta;}};$ $\mathrm{\&beta;}=\sqrt{{\mathrm{\&omega;}}_0(\frac{K_{11}}{M_1}+\frac{K_{22}}{M_2})-{\left(\frac{\mathrm{\&sigma;}}{2}\right)}^2};$ ω ₀for the rated angular velocity of generator, t is the time;

10) because the relation between angular frequency and frequency meets formula (15), by step 9) in the angular frequency Δ ω of generator 1,2 that calculates ₁(t), Δ ω ₂t () substitutes into formula (16), calculate the transient frequency Δ f of generator 1,2 when head end is single-phase to be overlapped ₁(t), Δ f ₂(t);

f＝ω/2π(15)

$\mathrm{\&Delta;}f\left(t\right)=\frac{\mathrm{\&Delta;}\mathrm{\&omega;}\left(t\right)}{2\mathrm{\&pi;}}---\left(16\right)$

In formula, f is frequency; ω is angular frequency;

(2) analog line end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase head end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ' ₁, Y ' ₂, Y ' ₀;

2) by Y ' ₁, Y ' ₂, Y ' ₀substitution formula (1), invert obtain line end single-phase overlap time positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ' ₁, Z ' ₂, Z ' ₀;

3) 3 in step (1) is repeated) application dual-port theory asks for port Impedance, is designated as Z ' ₍₁₎, Z ' ₍₂₎, Z ' ₍₀₎;

4) 4 in step (1) is repeated) ask for comprehensive impedance battle array, be designated as Z ' _f;

5) 5 in step (1) is repeated) obtain complex admittance battle array, be denoted as Y ' _f;

6) 6 in step (1) is repeated) utilize complex admittance battle array Y ' _fmiddle element amendment positive sequence admittance battle array Y ' ₁middle corresponding element, the positive sequence that is expanded admittance battle array Y ' _1E;

7) 7 in step (1) is repeated) according to expansion positive sequence admittance battle array Y ' _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ' ₁₂;

8) 8 in step (1) is repeated) distinguish the active power of calculating generator 1 and generator 2 to the local derviation K ' at respective merit angle ₁₁, K ' ₂₂;

9) 9 in step (1) is repeated) the transient state angular frequency that calculates generator 1 and generator 2 when end is single-phase to be overlapped is denoted as Δ ω ' respectively ₁(t), Δ ω ' ₂(t);

10) 10 in step (1) is repeated) calculate the transient frequency Δ f ' of generator 1,2 when end is single-phase to be overlapped ₁(t), Δ f ' ₂(t);

(3) frequency shift (FS) fail safe quantitative evaluation index

Utilize formula (17) to carry out quantitative evaluation to the generator transient frequency that step (1), (2) calculate, obtain the transient frequency stability margin η of generator 1,2 when circuit head end is single-phase to be overlapped _g1, η _g2, line end single-phase overlap time generator 1,2 transient frequency stability margin η ' _g1, η ' _g2;

η＝[f _ext-(f _cr-kT _cr)]×100％(17)

In formula, f _crand T _crthe frequency shift (FS) threshold value of generator and the duration of permission respectively, f _extrefer to the limiting value of generator frequency in transient process, k is commutation factor critical frequency shift duration being converted into frequency, and η is that plus or minus value represents that transient frequency is stable or unstable respectively;

Obtain the transient frequency stability margin of each generator in 2 machine systems, get the transient frequency stability margin of each generator transient frequency stability margin minimum value as system;

Head end single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (18), be denoted as η ₁;

η ₁＝min{η _G1,η _G2}(18)

End single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (19), be denoted as η ₂;

η ₂＝min{η′ _G1,η′ _G2}(19)

(4) reach a conclusion

Alternative route first and end single-phase overlap time system transient modelling frequency stabilization nargin η ₁, η ₂, choose single-phase time sequence of coincidence corresponding to the greater as the optimization time sequence of coincidence scheme exported; If η ₁> η ₂, then single-phase coincidence is first dropped into by circuit head end; Otherwise, first drop into single-phase coincidence by line end.

Embodiment 2: as Figure 1-10 shows, the single-phase time sequence of coincidence setting method of a kind of raising 2 electro-mechanical force system transient modelling frequency stabilities, when there is single phase ground fault in the transmission line of alternation current of 2 electro-mechanical force systems, there is two kinds of faults and single phase ground fault and single-phase wire break fault when single-phase coincidence, form the fault network of dual-port; Utilize symmetrical component method to obtain three sequence sequence nets according to fault type, arrange according to positive sequence, negative phase-sequence, zero-sequence network the admittance battle array writing each sequence, the admittance battle array of each sequence is inverted and obtains the Impedance Matrix of each sequence; Adopt dual-port theory first to try to achieve port Impedance battle array, and then try to achieve comprehensive impedance battle array, inverting to it obtains complex admittance battle array; According to complex admittance battle array amendment positive sequence network, thus the positive sequence admittance battle array that is expanded; Ward equivalent method is utilized to calculate equivalent transadmittance between 2 generator nodes, calculate the generator frequency variation track under two kinds of reclosing time sequences thus, realize the quantitative evaluation of frequency change track thus obtain transient frequency stability margin, choosing time sequence of coincidence corresponding to transient frequency stability margin the greater is the coincidence scheme optimized.

Embodiment 3: as Figure 1-10 shows,

For 2 machine systems shown in Fig. 1, have 8 buses in system, the node parameter of each generator and bus is as shown in table 1, and generator 1 electric pressure is 18.0kV, and generator 1 electric pressure is 13.8kV, and busbar voltage grade is 230kV.Resistance, the circuit per unit value parameter such as reactance and admittance of circuit are as shown in table 2.Article 8, line voltage distribution grade is 230kV.Resistance, the parameter such as reactance and no-load voltage ratio of transformer are as shown in table 3, and the parameter such as inertia time constant, the reactance of d-axis transient state, the reactance of quadrature axis transient state of generator is as shown in table 4.The power reference value of the parameter per unit value related in table 2-table 4 all gets 100MVA.

There is A phase single phase ground fault in 2 machine system busbar 1-bus D circuit head end 0s shown in Fig. 1,0.1s circuit A phase head end trips, and 0.2s circuit A phase end trips, and 1s circuit A phase head end overlaps, and 1.2s faulty line first and end three-phase trips.Form faulty line A phase head end when 1s to overlap, positive sequence during end broken string, negative phase-sequence, zero sequence admittance battle array, to positive sequence, negative phase-sequence, zero sequence admittance battle array is inverted, obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, application two-port network theory asks for positive sequence, negative phase-sequence, zero sequence port Impedance battle array, behind cancellation closed-loop path, obtain comprehensive impedance battle array, comprehensive impedance battle array is inverted, obtain complex admittance battle array, utilize WARD equivalent method, after cancellation removes the external node of generator 1 and generator 2, obtain the equivalent transadmittance between generator 1 and generator 2, substituted into the transient state angular frequency that formula (14) tries to achieve generator 1 and generator 2 when bus 1-bus D circuit A phase head end overlaps, according to transformation relation formula (15) Suo Shi between angular frequency and frequency, obtain the transient frequency of generator 1 and generator 2 when bus 1-bus D circuit A phase head end overlaps.

There is A phase single phase ground fault in bus 1-bus D circuit head end 0s, 0.1s circuit A phase head end trips, and 0.2s circuit A phase end trips, and 1s circuit A phase end overlaps, and 1.2s faulty line first and end three-phase trips.Form faulty line A phase end when 1s to overlap, positive sequence during head end broken string, negative phase-sequence, zero sequence admittance battle array, to positive sequence, negative phase-sequence, zero sequence admittance battle array is inverted, obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, application two-port network theory asks for positive sequence, negative phase-sequence, zero sequence port Impedance battle array, behind cancellation closed-loop path, obtain comprehensive impedance battle array, comprehensive impedance battle array is inverted, obtain complex admittance battle array, utilize WARD equivalent method, after cancellation removes the external node of generator 1 and generator 2, obtain the equivalent transadmittance between generator 1 and generator 2, substituted into the transient state angular frequency that formula (14) tries to achieve generator 1 and generator 2 when bus 1-bus D circuit A phase end overlaps, according to transformation relation formula (15) Suo Shi between angular frequency and frequency, obtain the transient frequency of generator 1 and generator 2 when bus 1-bus D circuit A phase end overlaps.

When overlapping to bus 1-bus D circuit A phase head end, the transient frequency change curve of generator 1 and generator 2 carries out quantitative evaluation (as shown in Figure 3,4), choose the transient frequency stability margin of system when generator 1 and generator 2 transient frequency stability margin smaller 74.12% overlap as head end, be shown in table 5.When overlapping to bus 1-bus D circuit A phase end, the transient frequency change curve of generator 1 and generator 2 carries out quantitative evaluation (as shown in Figure 5,6), choose the transient frequency stability margin of system when generator 1 and generator 2 transient frequency stability margin smaller 78.44% overlap as end, be shown in table 5.Bus 1-bus D circuit A phase head end fault, the transient frequency stability margin of system when contrast first and end overlaps, the end choosing the greater 78.44% correspondence overlaps as the time sequence of coincidence scheme optimized, and is shown in table 6.

Embodiment 4: as Figure 1-10 shows,

For 2 machine systems shown in Fig. 1, have 8 buses in system, the node parameter of each generator and bus is as shown in table 1, and generator 1 electric pressure is 18.0kV, and generator 1 electric pressure is 13.8kV, and busbar voltage grade is 230kV.Resistance, the circuit per unit value parameter such as reactance and admittance of circuit are as shown in table 2.Article 8, line voltage distribution grade is 230kV.Resistance, the parameter such as reactance and no-load voltage ratio of transformer are as shown in table 3, and the parameter such as inertia time constant, the reactance of d-axis transient state, the reactance of quadrature axis transient state of generator is as shown in table 4.The power reference value of the parameter per unit value related in table 2-table 4 all gets 100MVA.

There is A phase single phase ground fault in 2 machine system busbar 2-bus D circuit head end 0s shown in Fig. 1,0.1s circuit A phase head end trips, and 0.2s circuit A phase end trips, and 1s circuit A phase head end overlaps, and 1.2s faulty line first and end three-phase trips.Form faulty line A phase head end when 1s to overlap, positive sequence during end broken string, negative phase-sequence, zero sequence admittance battle array, to positive sequence, negative phase-sequence, zero sequence admittance battle array is inverted, obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, application two-port network theory asks for positive sequence, negative phase-sequence, zero sequence port Impedance battle array, behind cancellation closed-loop path, obtain comprehensive impedance battle array, comprehensive impedance battle array is inverted, obtain complex admittance battle array, utilize WARD equivalent method, after cancellation removes the external node of generator 1 and generator 2, obtain the equivalent transadmittance between generator 1 and generator 2, substituted into the transient state angular frequency that formula (14) tries to achieve generator 1 and generator 2 when bus 2-bus D circuit A phase head end overlaps, according to transformation relation formula (15) Suo Shi between angular frequency and frequency, obtain the transient frequency of generator 1 and generator 2 when bus 2-bus D circuit A phase head end overlaps.

There is A phase single phase ground fault in bus 2-bus D circuit head end 0s, 0.1s circuit A phase head end trips, and 0.2s circuit A phase end trips, and 1s circuit A phase end overlaps, and 1.2s faulty line first and end three-phase trips.Form faulty line A phase end when 1s to overlap, positive sequence during head end broken string, negative phase-sequence, zero sequence admittance battle array, to positive sequence, negative phase-sequence, zero sequence admittance battle array is inverted, obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, application two-port network theory asks for positive sequence, negative phase-sequence, zero sequence port Impedance battle array, behind cancellation closed-loop path, obtain comprehensive impedance battle array, comprehensive impedance battle array is inverted, obtain complex admittance battle array, utilize WARD equivalent method, after cancellation removes the external node of generator 1 and generator 2, obtain the equivalent transadmittance between generator 1 and generator 2, substituted into the transient state angular frequency that formula (14) tries to achieve generator 1 and generator 2 when bus 2-bus D circuit A phase end overlaps, according to transformation relation formula (15) Suo Shi between angular frequency and frequency, obtain the transient frequency of generator 1 and generator 2 when bus 2-bus D circuit A phase end overlaps.

When overlapping to bus 2-bus D circuit A phase head end, the transient frequency change curve of generator 1 and generator 2 carries out quantitative evaluation (as shown in Figure 7,8), choose the transient frequency stability margin of system when generator 1 and generator 2 transient frequency stability margin smaller 89.01% overlap as head end, be shown in table 5.When overlapping to bus 2-bus D circuit A phase end, the transient frequency change curve of generator 1 and generator 2 carries out quantitative evaluation (as shown in Fig. 9,10), choose the transient frequency stability margin of system when generator 1 and generator 2 transient frequency stability margin smaller 69.73% overlap as end, be shown in table 5.Bus 2-bus D circuit A phase head end fault, the transient frequency stability margin of system when contrast first and end overlaps, the head end choosing the greater 89.01% correspondence overlaps as the time sequence of coincidence scheme optimized, and is shown in table 6.

For in above-described embodiment, table 1-table 6 is as follows:

Table 12 machine system node parameter

Table 22 machine system line per unit value parameter

Note: power reference value is 100MWA

Table 32 machine system transformer parameter

Note: power reference value is 100MWA

Table 42 machine system generator parameter

Note: power reference value is 100MWA

In table 4, T _jfor the inertia time constant of generator, unit is s; X ' _dfor the reactance of d-axis transient state; X ' _qfor the reactance of quadrature axis transient state; x _dfor the unsaturated synchronous reactance of d-axis; x _qfor the unsaturated synchronous reactance of quadrature axis; T ' _d0for d-axis transient state open circuit time constant; T ' _q0for quadrature axis transient state open circuit time constant; x _lfor stator leakage reactance; X " _dfor d axle subtranient reactance; X " _qfor q axle subtranient reactance; T " _d0for d axle time time constant; T " _q0for q axle time time constant.

When the transmission line of alternation current single phase ground fault fault of 2 machine systems, generator 1 is shown in table 5 with the transient frequency stability margin of generator 2 system under difference single-phase time sequence of coincidence.Choose single-phase time sequence of coincidence corresponding to nargin the greater as the coincidence scheme optimized, obtain the single-phase time sequence of coincidence scheme of raising transient frequency stability as shown in table 6.

Table 5 transient frequency stability margin

Time sequence of coincidence scheme optimized by table 6

By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned execution mode, in the ken that those of ordinary skill in the art possess, can also make a variety of changes under the prerequisite not departing from present inventive concept.

Claims (2)

1. one kind is improved the single-phase time sequence of coincidence setting method of 2 electro-mechanical force system transient modelling frequency stabilities, it is characterized in that: when single phase ground fault occurs in the transmission line of alternation current of 2 electro-mechanical force systems, there is two kinds of faults and single phase ground fault and single-phase wire break fault when single-phase coincidence, form the fault network of dual-port; Utilize symmetrical component method to obtain three sequence sequence nets according to fault type, arrange according to positive sequence, negative phase-sequence, zero-sequence network the admittance battle array writing each sequence, the admittance battle array of each sequence is inverted and obtains the Impedance Matrix of each sequence; Adopt dual-port theory first to try to achieve port Impedance battle array, and then try to achieve comprehensive impedance battle array, inverting to it obtains complex admittance battle array; According to complex admittance battle array amendment positive sequence network, thus the positive sequence admittance battle array that is expanded; Ward equivalent method is utilized to calculate equivalent transadmittance between 2 generator nodes, calculate the generator frequency variation track under two kinds of reclosing time sequences thus, realize the quantitative evaluation of frequency change track thus obtain transient frequency stability margin, choosing time sequence of coincidence corresponding to transient frequency stability margin the greater is the coincidence scheme optimized.

2. the single-phase time sequence of coincidence setting method of raising 2 electro-mechanical force system transient modelling frequency stability according to claim 1, is characterized in that: the concrete steps of described method are as follows:

(1) analog line head end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line head end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ₁, Y ₂, Y ₀; Wherein, the method forming admittance battle array is as follows: in admittance battle array each row off-diagonal element, the number of nonzero element equals the connected earth-free circuitry number of corresponding node; The each diagonal element of admittance battle array, i.e. the self-admittance Y of each node _iiequal the admittance sum on respective nodes institute's chord road: the transadmittance Y of each off-diagonal element of admittance battle array _ijjust to equal between 2 nodes connect the negative value of admittance: Y _ij=-y _ij;

In formula, y _ijfor the admittance on institute's chord road between node i and node j;

2) positive sequence, negative phase-sequence, zero sequence impedance battle array is asked for

To positive sequence, negative phase-sequence, zero sequence admittance battle array Y ₁, Y ₂, Y ₀invert, shown in (1), obtain positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ₁, Z ₂, Z ₀;

$Z_1=Y_1^{-1},Z_2=Y_2^{-1},Z_0=Y_0^{-1}---\left(1\right)$

3) apply dual-port theory and ask for port Impedance

1. the positive sequence of port one and port 2, negative phase-sequence, zero sequence self-impedance and mutual impedance is asked for;

If node serial number single phase ground fault place occurring corresponding is m, n, n is the earth 0 node; Node serial number corresponding to single-phase end disconnection fault place is p, q; Be that the port that m, n are corresponding is denoted as port one by node serial number; Node serial number is that the port that p, q are corresponding is denoted as port 2;

By step 2) in the three sequence Impedance Matrixes that calculate corresponding element substitute in formula (2), try to achieve the positive sequence of port one and port 2, negative phase-sequence, the self-impedance of zero sequence and mutual impedance;

Z ₁₁₍₁₎＝Z ₁₁₍₂₎＝Z _mm(1)+Z _nn(1)-2Z _mn(1)

Z ₁₂₍₁₎＝Z ₁₂₍₂₎＝Z _mp(1)+Z _nq(1)-Z _mq(1)-Z _np(1)

Z ₂₁₍₁₎＝Z ₂₁₍₂₎＝Z _pm(1)+Z _qn(1)-Z _pn(1)-Z _qm(1)

Z ₂₂₍₁₎＝Z ₂₂₍₂₎＝Z _pp(1)+Z _qq(1)-2Z _pq(1)

Z ₁₁₍₀₎＝Z _mm(0)+Z _nn(0)-2Z _mn(0)(2)

Z ₁₂₍₀₎＝Z _mp(0)+Z _nq(0)-Z _mq(0)-Z _np(0)

Z ₂₁₍₀₎＝Z _pm(0)+Z _qn(0)-Z _pn(0)-Z _qm(0)

Z ₂₂₍₀₎＝Z ₂₂₍₀₎＝Z _pp(0)+Z _qq(0)-2Z _pq(0)

In formula, Z _{11 (1)}, Z _{22 (1)}represent the positive sequence self-impedance of port one and port 2 respectively; Z _{12 (1)}, Z _{21 (1)}represent the positive sequence mutual impedance between port one and port 2 respectively; Z _{11 (2)}, Z _{22 (2)}represent the negative phase-sequence self-impedance of port one and port 2 respectively; Z _{12 (2)}, Z _{21 (2)}represent the negative phase-sequence mutual impedance between port one and port 2 respectively; Z _{11 (0)}, Z _{22 (0)}represent the zero sequence self-impedance of port one and port 2 respectively; Z _{12 (0)}, Z _{21 (0)}represent the zero sequence mutual impedance between port one and port 2 respectively; Z _{uv (1)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₁in the capable v column element of u, Z _{uv (2)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₂in the capable v column element of u, Z _{uv (0)}(u=m, n, p, q; V=m, n, p, q) represent Impedance Matrix Z ₀in the capable v column element of u;

2. the port Impedance battle array of the positive sequence of port one and port 2, negative phase-sequence, zero sequence is asked

The each sequence impedance calculated by formula (2), forms positive sequence, negative phase-sequence, zero sequence port Impedance battle array, is denoted as Z respectively ₍₁₎, Z ₍₂₎, Z ₍₀₎, shown in (3);

$Z_{\left(1\right)}=\left(\begin{array}{cc}{Z}_{11\left(1\right)}& Z_{12\left(1\right)}\\ Z_{21\left(1\right)}& Z_{22\left(1\right)}\end{array}\right),Z_{\left(2\right)}=\left(\begin{array}{cc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}\end{array}\right),Z_{\left(0\right)}=\left(\begin{array}{cc}{Z}_{11\left(0\right)}& Z_{12\left(0\right)}\\ Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right)---\left(3\right)$

4) comprehensive impedance battle array Z is asked for _f

1. according to each sequence impedance element calculated by formula (2), row write negative phase-sequence, zero sequence port comprehensive impedance battle array Z, shown in (4);

$Z=\left[\begin{array}{cccc}{Z}_{11\left(2\right)}& Z_{12\left(2\right)}& 0& 0\\ Z_{21\left(2\right)}& Z_{22\left(2\right)}& 0& 0\\ 0& 0& Z_{11\left(0\right)}& Z_{12\left(0\right)}\\ 0& 0& Z_{21\left(0\right)}& Z_{22\left(0\right)}\end{array}\right]---\left(4\right)$

2. negative phase-sequence formula (4) Suo Shi, zero sequence port comprehensive impedance battle array Z are substituted into formula (5) counter circuit Impedance Matrix Z _l;

$Z_L=C^{T}ZC=\left[\begin{array}{ccc}{Z}_{aa}^{\&prime;}& Z_{ab}^{\&prime;}& Z_{ac}^{\&prime;}\\ Z_{ba}^{\&prime;}& Z_{bb}^{\&prime;}& Z_{bc}^{\&prime;}\\ Z_{ca}^{\&prime;}& Z_{cb}^{\&prime;}& Z_{cc}^{\&prime;}\end{array}\right]---\left(5\right)$

In formula, $C=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& -1\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ C ^tfor the transposition of C; Z ' _st(s=a, b, c; L=a, b, c), during s=l, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l;

3. by formula (5) by impedance element corresponding to formula (6) cancellation closed-loop path c, the impedance element of retention loop a and loop b, obtains comprehensive impedance battle array Z _f, shown in (7);

$Z_{sl}=Z_{sl}^{\&prime;}-\frac{Z_{sc}^{\&prime;}{Z}_{cl}^{\&prime;}}{Z_{cc}^{\&prime;}}---\left(6\right)$

In formula, Z _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s behind cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l; Z ' _sl(s=a, b; L=a, b) s=l time, represent the self-impedance of loop s; During s ≠ l, represent the mutual impedance between loop s and loop l; Z ' _sc(s=a, b) represents the mutual impedance between loop s and loop c; Z ' _cl(l=a, b) represents the mutual impedance between loop c and loop l; Z ' _ccrepresent the self-impedance of loop c;

$Z_F=\left[\begin{array}{cc}{Z}_{aa}& Z_{ab}\\ Z_{ba}& Z_{bb}\end{array}\right]---\left(7\right)$

In formula, Z _sl(s=a, b; L=a, b), during s=l, the self-impedance of loop s behind expression cancellation closed-loop path; During s ≠ l, the mutual impedance behind expression cancellation closed-loop path between loop s and loop l;

5) formula (8) is inverted obtain complex admittance battle array, be denoted as Y _f, shown in (8)

$Y_F={Z_F}^{-1}=\left[\begin{array}{cc}{y}_{aa}& y_{ab}\\ y_{ba}& y_{bb}\end{array}\right]---\left(8\right)$

In formula, y _sl(s=a, b; L=a, b), during s=l, the self-admittance of loop s behind expression cancellation closed-loop path; During s ≠ l, the transadmittance behind expression cancellation closed-loop path between loop s and loop l;

6) complex admittance battle array Y is utilized _fin element amendment positive sequence admittance battle array Y ₁middle corresponding element, amending method is shown in formula (9), the positive sequence that is expanded admittance battle array Y _1E

$\left\{\begin{array}{c}{y}_{mm\left(1\right)}^{\&prime;}=y_{mm\left(1\right)}+y_{aa},y_{mn\left(1\right)}^{\&prime;}=y_{mn\left(1\right)}+y_{ab},y_{nm\left(1\right)}^{\&prime;}=y_{nm\left(1\right)}+y_{ba},y_{nn\left(1\right)}^{\&prime;}=y_{nn\left(1\right)}+y_{bb}\\ y_{pp\left(1\right)}^{\&prime;}=y_{pp\left(1\right)}+y_{aa},y_{pq\left(1\right)}^{\&prime;}=y_{pq\left(1\right)}+y_{ab},y_{qp\left(1\right)}^{\&prime;}=y_{qp\left(1\right)}+y_{ba},y_{qq\left(1\right)}^{\&prime;}=y_{qq\left(1\right)}+y_{bb}\end{array}\right.---\left(9\right)$ In formula, y ' _{uv (1)}(u=m, n; V=m, n) represent expansion positive sequence admittance battle array Y _1Ein the capable v column element of u; y _{uv (1)}(u=m, n; V=m, n) represent admittance battle array Y ₁in the capable v column element of u;

Y ' _{uv (1)}(u=p, q; V=p, q) represent the capable v column element of u in expansion positive sequence admittance battle array Y1E; y _{uv (1)}(u=p, q; V=p, q) represent admittance battle array Y ₁in the capable v column element of u;

7) according to expansion positive sequence admittance battle array Y _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ₁₂; Concrete grammar is as follows:

1. the set of generator 1 and generator 2 corresponding node composition is denoted as boundary node B, in network, the set of all the other nodes composition is denoted as external node E, will expand positive sequence admittance battle array Y _1Ewriting matrix in block form form, can obtain network equation that matrix in block form represents such as formula shown in (10);

$\left[\begin{array}{cc}{Y}_{BB}& Y_{BE}\\ Y_{EB}& Y_{EE}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_B\\ {\stackrel{\&CenterDot;}{V}}_E\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_B\\ {\stackrel{\&CenterDot;}{I}}_E\end{array}\right]---\left(10\right)$

In formula, Y _bBrepresent the admittance battle array corresponding to all boundary nodes; Y _bErepresent all boundary nodes and the admittance battle array corresponding to all external nodes, and Y _bEequal Y _eBtransposition; Y _eErepresent the admittance battle array corresponding to all external nodes; represent the column voltage vector of all boundary points; represent the column voltage vector of all external nodes; represent the Injection Current of all boundary nodes; represent the Injection Current of all external nodes;

2. the matrix in block form in formula (10) is substituted in (11) formula and calculate, obtain boundary admittance battle array

${\tilde{Y}}_{BB}=Y_{BB}-Y_{BE}{Y}_{EE}^{-1}{Y}_{EB}---\left(11\right)$

In formula, the boundary admittance battle array after equivalence, the contribution of the equivalent branch road that it produces after including external network abbreviation; Therefore the equivalent transadmittance between generator 1 node retained in 2 machine systems and generator 2 node be exactly equivalence after boundary admittance, so there is formula (12) to set up:

${\tilde{Y}}_{BB}=Y_{12}=G_{12}+{\mathrm{jB}}_{12}---\left(12\right)$

In formula, G ₁₂for equivalent transadmittance Y ₁₂real part, be called conductance, and G ₁₂> 0; B ₁₂for equivalent transadmittance Y ₁₂imaginary part, be called susceptance, and B ₁₂> 0;

8) by step 7) in equivalent transadmittance Y between the generator 1 that calculates and generator 2 ₁₂in substitution formula (13), the active power of calculating generator 1 and generator 2 is to the local derviation K at respective merit angle respectively ₁₁, K ₂₂;

$\left\{\begin{array}{c}{K}_{11}=\frac{\&part;P_{G1}}{\&part;{\mathrm{\&delta;}}_1}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin \left(\mathrm{\&gamma;}-{\mathrm{\&delta;}}_0\right)\\ K_{22}=\frac{\&part;P_{G2}}{\&part;{\mathrm{\&delta;}}_2}{|}_0=\left|Y_{12}\right|E_{q1}{E}_{q2}\sin \left(\mathrm{\&gamma;}+{\mathrm{\&delta;}}_0\right)\end{array}\right.---\left(13\right)$

In formula, P _g1, P _g2be respectively the active power of generator 1 and generator 2; δ ₁, δ ₂be respectively the merit angle of generator 1 and generator 2; represent that the active power of generator 1 and generator 2 is to the numerical value of the partial derivative of generator's power and angle at initial time respectively; E _q1, E _q2be respectively the electromotive force of generator 1 and generator 2; δ ₀the phase angle at expression system initial work location place; | Y ₁₂| represent equivalent transadmittance Y ₁₂amplitude, γ represents equivalent transadmittance Y ₁₂phase angle, γ=arctg (B ₁₂/ G ₁₂), and γ ∈ (0, pi/2);

9) by step 8) in the K that calculates ₁₁, K ₂₂calculate the transient state angular frequency of 2 machine systems when head end is single-phase to be overlapped in substitution formula (14), the transient state angular frequency of generator 1 and generator 2 is denoted as Δ ω respectively ₁(t), Δ ω ₂(t);

$\left\{\begin{array}{c}{\mathrm{\&Delta;\&omega;}}_1\left(t\right)=\left(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20}\right)\left(1-e^{-\mathrm{\&sigma;}t}\right)+\frac{K_{11}}{M_1}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\\ {\mathrm{\&Delta;\&omega;}}_2\left(t\right)=\left(\frac{K_{22}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m10}+\frac{K_{11}}{K_{11}{D}_2+K_{22}{D}_1}{\mathrm{\&Delta;P}}_{m20}\right)\left(1-e^{-\mathrm{\&sigma;}t}\right)-\frac{K_{22}}{M_2}\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)\end{array}\right.---\left(14\right)$

In formula, D ₁, D ₂represent the damping coefficient of generator 1 and generator 2 respectively; Δ P _m10, Δ P _m20represent the chugging that generator 1 and generator 2 occur respectively; m ₁, M ₂represent the moment of inertia of generator 1,2; $\mathrm{\&Delta;}\stackrel{*}{\mathrm{\&omega;}}\left(t\right)=\frac{D_1{D}_2}{K_{11}{D}_2+K_{22}{D}_1}(\frac{{\mathrm{\&Delta;P}}_{m10}}{D_1}-\frac{{\mathrm{\&Delta;P}}_{m20}}{D_2})e^{-\frac{\mathrm{\&sigma;}}{2}t}\frac{\sin \left(\mathrm{\&beta;}t\right)}{\mathrm{\&beta;}};$ $\mathrm{\&beta;}=\sqrt{{\mathrm{\&omega;}}_0\left(\frac{K_{11}}{M_1}+\frac{K_{22}}{M_2}\right)-{\left(\frac{\mathrm{\&sigma;}}{2}\right)}^2};$ ω ₀for the rated angular velocity of generator, t is the time;

10) because the relation between angular frequency and frequency meets formula (15), by step 9) in the angular frequency Δ ω of generator 1,2 that calculates ₁(t), Δ ω ₂t () substitutes into formula (16), calculate the transient frequency Δ f of generator 1,2 when head end is single-phase to be overlapped ₁(t), Δ f ₂(t);

f＝ω/2π(15)

$\mathrm{\&Delta;}f\left(t\right)=\frac{\mathrm{\&Delta;}\mathrm{\&omega;}\left(t\right)}{2\mathrm{\&pi;}}---\left(16\right)$

In formula, f is frequency; ω is angular frequency;

(2) analog line end drops into single-pole reclosing

1) positive sequence, negative phase-sequence, zero sequence admittance battle array is formed

Analog line end drops into single-pole reclosing, is equivalent to there occurs the multiple fault of single-phase earthing and single-phase head end broken string, first forms positive sequence, negative phase-sequence, zero sequence admittance battle array under this multiple fault, is designated as Y ' ₁, Y ' ₂, Y ' ₀;

2) by Y ' ₁, Y ' ₂, Y ' ₀substitution formula (1), invert obtain line end single-phase overlap time positive sequence, negative phase-sequence, zero sequence impedance battle array, be designated as Z ' ₁, Z ' ₂, Z ' ₀;

3) 3 in step (1) is repeated) application dual-port theory asks for port Impedance, is designated as Z ' ₍₁₎, Z ' ₍₂₎, Z ' ₍₀₎;

4) 4 in step (1) is repeated) ask for comprehensive impedance battle array, be designated as Z ' _f;

5) 5 in step (1) is repeated) obtain complex admittance battle array, be denoted as Y ' _f;

6) 6 in step (1) is repeated) utilize complex admittance battle array Y ' _fmiddle element amendment positive sequence admittance battle array Y ' ₁middle corresponding element, the positive sequence that is expanded admittance battle array Y ' _1E;

7) 7 in step (1) is repeated) according to expansion positive sequence admittance battle array Y ' _1E, utilize ward equivalent method to calculate equivalent transadmittance between 2 generator nodes, be designated as Y ' ₁₂;

8) 8 in step (1) is repeated) distinguish the active power of calculating generator 1 and generator 2 to the local derviation K ' at respective merit angle ₁₁, K ' ₂₂;

9) 9 in step (1) is repeated) the transient state angular frequency that calculates generator 1 and generator 2 when end is single-phase to be overlapped is denoted as Δ ω ' respectively ₁(t), Δ ω ' ₂(t);

10) 10 in step (1) is repeated) calculate the transient frequency Δ f ' of generator 1,2 when end is single-phase to be overlapped ₁(t), Δ f ' ₂(t);

(3) frequency shift (FS) fail safe quantitative evaluation index

Utilize formula (17) to carry out quantitative evaluation to the generator transient frequency that step (1), (2) calculate, obtain the transient frequency stability margin η of generator 1,2 when circuit head end is single-phase to be overlapped _g1, η _g2, line end single-phase overlap time generator 1,2 transient frequency stability margin η ' _g1, η ' _g2;

η＝[f _ext-(f _cr-kT _cr)]×100％(17)

In formula, f _crand T _crthe frequency shift (FS) threshold value of generator and the duration of permission respectively, f _extrefer to the limiting value of generator frequency in transient process, k is commutation factor critical frequency shift duration being converted into frequency, and η is that plus or minus value represents that transient frequency is stable or unstable respectively;

Obtain the transient frequency stability margin of each generator in 2 machine systems, get the transient frequency stability margin of each generator transient frequency stability margin minimum value as system;

Head end single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (18), be denoted as η ₁;

η ₁＝min{η _G1,η _G2}(18)

End single-phase overlap time system transient modelling frequency stabilization nargin calculate by formula (19), be denoted as η ₂;

η ₂＝min{η′ _G1,η′ _G2}(19)

(4) reach a conclusion

Alternative route first and end single-phase overlap time system transient modelling frequency stabilization nargin η ₁, η ₂, choose single-phase time sequence of coincidence corresponding to the greater as the optimization time sequence of coincidence scheme exported; If η ₁> η ₂, then single-phase coincidence is first dropped into by circuit head end; Otherwise, first drop into single-phase coincidence by line end.