CN103311923B - A kind of method of Identification of Power System generation cascading failure - Google Patents

Abstract

The invention discloses a kind of method of Identification of Power System generation cascading failure.Consider generator speed governing and load responding, set up more realistic electric power system tide computation model, the method, in the model of Load flow calculation, overcomes the impact that traditional power flow algorithm can not reflect generator regulating action and load responding.From system cloud gray model champion angle, analyze the relation between voltage stabilization and fault in cascading failure.For the relation of quantitative analysis charge threshold level and system running state, by analyzing the change of Jacobian matrix element value, the critical value of derivation system voltage stability index and this index.Along with the increase of load, the risk of systems face cascading failure increases.In the process, system voltage stabilizes index can decline gradually, and critical value all the time critical value to maintain 0.5 (± 0.03) constant.In systems in practice, can not be changed in cascading failure by the charge threshold level calculated, choose 0.6 critical value of collapsing as line voltage in real system, whether identification electrical network faces the risk of having a power failure on a large scale.Therefore, the inventive method has good actual directive significance.

Description

A kind of method of Identification of Power System generation cascading failure

Technical field

The invention belongs to Power System and its Automation technical field, propose a kind of method of Identification of Power System generation cascading failure.

Background technology

Domestic and international electric power system large-scale blackout research is shown that the modern power network catastrophe caused by fault chain reaction shows as a series of element chain reaction tripping operation.The possibility that cascading failure occurs is minimum, but can cause serious consequence to power grid security after occurring, and causes showing great attention to of Chinese scholars.Power grid cascading fault is furtherd investigate, all significant for Electric Power Network Planning, operation of power networks decision-making and guarantee power network safety operation etc.

The research of power grid cascading fault is mainly carried out from the following aspects: 1) the self-organizing Critical Theory physics is applied in electric power system, from macroscopic perspective definition and the Evolution of identification system.This theory, by studying and disclosing critical characteristic, deeply understands large-scale blackout phenomenon from macro-level, to finding prevention, controlling the method for large-scale blackout.Research shows: real system embodies self-organized state to a certain extent, and the fault data characterizing scale of having a power failure on a large scale as North America and China's electric power system has power law tail characteristic, and is not the normal distribution on traditional understanding.Namely Power Law contains self-organized criticality behind.Data statistics research shows that domestic and international electrical network mostly has obvious small world.2) by the chain reaction in simple complex network model, the impact of network configuration on cascading failure in power system is described.Point out that betweenness and the higher contact node of the number of degrees are while guarantee electrical network connectedness, play a part to add fuel to the flames to the propagation of fault, scales-free network structure electrical network very easily causes extensive catastrophe under calculated attack, more more fragile than small-world network structure.All in all, the research based on complex network is conducive to Electric Power Network Planning and Analysis on Mechanism of having a power failure on a large scale, but its model does not consider operation characteristic and the trend constraint of actual electric network.Therefore, a lot of scholar it is also proposed some models from the angle of network analysis, and the general principle of these models is all by constantly carrying out Load flow calculation, obtains and disconnects the evolution that the out-of-limit circuit of trend carrys out cascading failure in analog electrical Force system.3) based on " being similar to " DC power flow and hidden failure mechanism hidden failure model, based on optimal load flow method (OPA) model of direct current optimal power flow (OPF), based on load excision with the Manchester model of AC power flow and based on the blackout model exchanging OPF.The hypotheses of DC power flow hidden failure model is whole bus (node) voltage per unit value is 1, and is definite value, ignores the phase angle change at circuit two ends.This hypothesis is in the higher and chain interrupting process of transmission line of system load rate and be false.Manchester model does not take into full account the regulating action of generator, thus non-power-off fault may be judged as power-off fault, or expands fault scale.Although the blackout model of optimal load flow overcomes above-mentioned deficiency, it does not consider the frequency shift (FS) in generator, part throttle characteristics and cascading failure generating process.The system power line road cascading trip stage, consequent frequency shift (FS) and generator speed regulation process cannot be ignored mostly along with the excision of load and generating set.

Therefore, first need to set up the AC power flow computational methods considering generator speed governing and load voltage, frequency characteristic.When analyzing cascading failure in power system mechanism of transmission, the frequency change of computing system and load adjustment value, describe phase angle difference change in transmission line two ends in cascading failure process accurately, more meet electric power system reality; By asking for the variable quantity analytical system load variations of Jacobian matrix diagonal element value to the impact of electrical network, defined node voltage stability index and system voltage stabilizes index, node voltage critical value when deriving voltage collapse.Along with the rising of load factor, it is constant that this critical value maintains 0.5 (± 0.03), bus voltage stability index can decline and system voltage stabilizes index can rise gradually, therefore chooses 0.6 early warning value of having a power failure on a large scale as system when actual electric network safe early warning.

Summary of the invention

The object of this invention is to provide a kind of AC power flow computational methods considering generator speed governing and load voltage, frequency characteristic, ask for the variable quantity of Jacobian matrix diagonal element value, thus defined node voltage stability index and system voltage stabilizes index, derive threshold values and the charge threshold level of bus voltage stability index during electric power system generation cascading failure, assessment any time, power system voltage stabilization situation under different running method and the relation between having a power failure on a large scale.

To achieve these goals, the present invention takes following technical scheme to realize:

1. assess the method for power system voltage stabilization and charge threshold level, comprise the following steps:

(1) according to power system load power, generator power, line parameter circuit value and node parameter, calculate the distribution of initial time trend according to Newton method;

(2) calculating adds Δ P by power system load _d0the power stage increment of the generator unit caused and the load power change produced due to the frequency adjustment effect of load, obtain power system frequency changes delta f.

(a) static load Equivalent Model:

P _di＝P _d0i(1+k _iΔf)(a _i+b _iV _i+c _iV _i ²)(1)

Q _di＝Q _d0i(1+k′ _iΔf)(a′ _i+b′ _iV _i+c′ _iV _i ²)

In formula: P _d0i, Q _d0i; The specified meritorious and reactive power of node i load; P _di, Q _di: node i load is gained merit and reactive power; Δ f: the frequency change of system; V _imagnitude of voltage; k _i, a _i,b _i, c _i, k ' _i, a ' _ib ' _i, c ' _ifor constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

B the meritorious contextual definition of exerting oneself between same frequency of () generator is:

$\left\{\begin{array}{c}{P}_{\mathrm{gi}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\Σ}}}{P}_{\mathrm{gik}}=\underset{k=1}{\overset{N_{\mathrm{gt}}}{\mathrm{\Σ}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\Δf})\\ P_{\min \mathrm{ik}}\≤P_{\mathrm{gi}}\≤P_{\max \mathrm{ik}}\end{array}\right.---\left(2\right)$

In formula: N _gi: generator interstitial content; P _gi: the meritorious of generator node i is exerted oneself; P _gik: meritorious the exerting oneself of generator node i kth platform unit; P _setik: the specified meritorious of generator node i kth platform unit is exerted oneself; P _minik: the minimum active power of generator node i kth platform unit; P _maxik: the maximum wattful power K of generator node i kth platform unit _gik: the unit power regulation of generator node i kth platform unit;

C () power system load adds Δ P _d0, then the power stage increment of generator unit and the load power that produces due to the frequency adjustment effect of load are changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf(3)

That is: Δ P _d0=-(K _g+ K _d) Δ f

(3) amplitude=1.0 of each node voltage vector given and phase angle initial value=0.0;

(4) each node active power amount of unbalance Δ P in electric power system is calculated _i, Δ Q _i;

A in () electric power system, the meritorious imbalance of any node is closed and is:

$\mathrm{\Δ}{P}_i=P_i-(P_{\mathrm{gi}}-P_{\mathrm{di}})=$

$V_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})-\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\Σ}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\Δf})+P_{d0i}(1+k_i\mathrm{\Δf})(a_i+b_i{V}_i+c_i{V_i}^2)---\left(4\right)$

B in () electric power system, the idle imbalance of PQ node is closed and is:

$\mathrm{\Δ}{Q}_i=Q_i-(Q_{\mathrm{gi}}-Q_{\mathrm{di}})=$

$V_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})+Q_{d0i}(1+k_i^{\′}\mathrm{\Δf})(a_i^{\′}+b_i^{\′}{V}_i+c_i^{\′}{V_i}^2)---\left(5\right)$

(5) calculate each element of Jacobian matrix in electric power system and solve equilibrium equation;

A () active balance closes:

$\left(\begin{array}{c}\mathrm{\Δ}{P}_1\\ \mathrm{\Δ}{P}_2\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{P}_{n-1}\end{array}\right)=\left(\begin{array}{ccccccccc}{H}_{11}& H_{12}& \·\·\·& H_{1,n-1}& N_{11}& N_{12}& \·\·\·& N_{1,n-1}& T_1\\ H_{21}& H_{22}& \·\·\·& H_{2,n-1}& N_{21}& N_{22}& \·\·\·& N_{2,n-1}& T_2\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ H_{n-\mathrm{1,1}}& H_{n-\mathrm{1,2}}& \·\·\·\·& H_{n-1,n-1}& N_{n-\mathrm{1,1}}& N_{n-\mathrm{1,2}}& \·\·\·& N_{n-1,n-1}& T_{n-1}\end{array}\right)\left(\begin{array}{c}\mathrm{\Δ}{\mathrm{\δ}}_1\\ \mathrm{\Δ}{\mathrm{\δ}}_2\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{\mathrm{\δ}}_{n-1}\\ \mathrm{\Δ}{V}_1/V_1\\ \mathrm{\Δ}{V}_2/V_2\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{V}_{n-1}/V_{n-1}\\ \mathrm{\Δ}\left(\mathrm{\Δf}\right)\end{array}\right)---\left(6\right)$

B () reactive balance closes:

$\left(\begin{array}{c}{\mathrm{\ΔQ}}_1\\ {\mathrm{\ΔQ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\ΔQ}}_{n-1}\end{array}\right)=\left(\begin{array}{cccccccc}{K}_{11}& K_{12}& \·\·\·& K_{1,n-1}& L_{11}& L_{12}& \·\·\·& L_{1,n-1}\\ K_{21}& K_{22}& \·\·\·& K_{2,n-1}& L_{21}& L_{22}& \·\·\·& L_{2,n-1}\\ \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·\\ K_{n-\mathrm{1,1}}& K_{n-\mathrm{1,2}}& \·\·\·& K_{n-1,n-1}& L_{n-\mathrm{1,1}}& L_{n-\mathrm{1,2}}& \·\·\·& L_{n-1,n-1}\end{array}\right)\left(\begin{array}{c}{\mathrm{\Δ\δ}}_1\\ {\mathrm{\Δ\δ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\Δ\δ}}_{n-1}\\ {\mathrm{\ΔV}}_1/V_1\\ {\mathrm{\ΔV}}_2/V_2\\ \·\\ \·\\ \·\\ {\mathrm{\ΔV}}_{n-1}/V_{n-1}\end{array}\right)---\left(7\right)$

C () Jacobian matrix element is:

$\left.\begin{array}{c}{H}_{\mathrm{ij}}=\frac{\∂\mathrm{\Δ}{P}_i}{\∂{\mathrm{\δ}}_j}=V_i{V}_j(-G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})\\ H_{\mathrm{ii}}=\frac{{\∂\mathrm{\ΔP}}_i}{{\∂\mathrm{\δ}}_i}=-V_i\underset{j\≠i}{\underset{j=1}{\stackrel{n}{\mathrm{\Σ}}}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})=-Q_i-{V_i}^2{B}_{\mathrm{ii}}\\ N_{\mathrm{ij}}=\frac{\∂\mathrm{\Δ}{P}_i}{\∂V_j}{V}_j=V_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})\\ N_{\mathrm{ii}}=\frac{{\∂\mathrm{\ΔP}}_i}{{\∂V}_i}{V}_i=V_i\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})+{{2V}_i}^2{G}_{\mathrm{ii}}+V_i{P}_{d0i}(1+k_i\mathrm{\Δf})(b_i+{2c}_i{V}_i)\\ T_i=\frac{{\∂\mathrm{\ΔP}}_i}{\∂\mathrm{\Δf}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\Σ}}}{K}_{\mathrm{gik}}+P_{d0i}{k}_i(a_i+b_i|V_i|+c_i{\left|V_i\right|}^2)\\ K_{\mathrm{ij}}=\frac{{\∂\mathrm{\ΔQ}}_i}{{\∂\mathrm{\δ}}_j}{V}_j=-V_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})\\ K_{\mathrm{ii}}=\frac{{\∂\mathrm{\ΔQ}}_i}{{\∂\mathrm{\δ}}_i}{V}_i=V_i\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})\\ L_{\mathrm{ij}}=\frac{{\∂\mathrm{\ΔP}}_i}{{\∂\mathrm{\δ}}_j}{V}_j=V_i{V}_j(-G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})\\ L_{\mathrm{ii}}=\frac{{\∂\mathrm{\ΔQ}}_i}{{\∂V}_i}{V}_i=V_i\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})-{{2V}_i}^2{B}_{\mathrm{ii}}+V_i{Q}_{d0i}(1+k_i^{\′}\mathrm{\Δf})(b_i^{\′}+{2c}_i^{\′}{V}_i)\end{array}\right\}---\left(8\right)$

(6) each node voltage amplitude and vectorial angle is revised:

${\mathrm{\θ}}_i^{\left(t\right)}={\mathrm{\θ}}_i^{(t-1)}-\mathrm{\Δ}{\mathrm{\θ}}_i^{(t-1)}$ (9)

$V_i^{\left(t\right)}=V_i^{(t-1)}-\mathrm{\Δ}{V}_i^{(t-1)}$

(7) judge whether meritorious and reactive power deviation meets the condition of convergence, obtain the trend distribution of electric power system after generator speed governing and load responding;

(8) computing node voltage status index V _vi:

$V_{\mathrm{vi}}=\frac{{\∂P}_i/{\∂\mathrm{\δ}}_i}{\underset{j\≠i}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}}{B}_{\mathrm{ij}}{V}_j}---\left(10\right)$

(9) equivalent voltage of current power system running state is calculated with critical value index V _th:

$\stackrel{\‾}{V_{\mathrm{Geq}}}=-\underset{j\≠i}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}}{V}_j\frac{B_{\mathrm{ij}}}{B_{\mathrm{ii}}}\⇒V_{\mathrm{th}}=\frac{V_{\mathrm{Geq}}}{2}$

(10) whole system voltage stability evaluation index VSI:

$\mathrm{VSI}=\underset{i\∈\mathrm{VS}}{\overset{\mathrm{NS}}{\underset{i=1}{\mathrm{\Σ}}}}{(\frac{V_{\mathrm{th}}-V_{\mathrm{vi}}}{V_{\mathrm{th}}}*100)}^2---\left(11\right)$

The present invention is based on the AC power flow computational methods considering generator speed governing and load voltage, frequency characteristic, according to the change of Jacobian matrix diagonal element value under malfunction, derive charge threshold level when system voltage stabilizes evaluation index and system are in voltage collapse critical point.This Identification of Power System generation cascading failure is applied in power grid security early warning, and real-time node voltage and system voltage stabilizes state are quantized, identification more accurately faces the node of Voltage Instability and the operation risk of whole Network Voltage Stability.The present invention has following technique effect: 1, by considering the AC power flow computational methods of generator speed governing and load voltage, frequency characteristic, more meet electric power system actual needs; 2, in Load flow calculation, Jacobian matrix element derives critical value and the system stabilization of power grids evaluation index of voltage collapse, calculates simple physical meaning clear and definite.3, the node voltage critical value of this index can not change along with the impact of the conditions such as electrical network scale, load, clearly can show the relation between system node voltage running status and voltage collapse.

Accompanying drawing explanation

Fig. 1 is two node system geographical wiring diagrams.

Fig. 2 is IEEE-39 node system geographical wiring diagram.

Fig. 3 is Guangdong Power Grid 500kv side topology diagram.

Embodiment

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

Embodiment 1

Be two node system geographical wiring diagrams as shown in Figure 1, this is for illustrate power system voltage stabilization index VSI and charge threshold level V for 2 node systems _thderivation.Symbol in figure represent generator, perpendicular solid line represents transmission of electricity bus, | g _ij+ jb _ij| represent the impedance of transmission line, arrow represents load.

(1) any two node power systems are had:

$S_i^{*}=\stackrel{\‾}{Y_{\mathrm{ii}}}{V_i}^2+{{\stackrel{\‾}{V}}^{*}}_j\stackrel{\‾}{V_j}\stackrel{\‾}{Y_{\mathrm{ij}}}\⇒{V_i}^2+{{\stackrel{\‾}{V}}^{*}}_j\stackrel{\‾}{V_j}\frac{\stackrel{\‾}{Y_{\mathrm{ij}}}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}=\frac{S_i^{*}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}$

P _i＝G _iiV _i ²+V _iV _j(G _ijcosδ _ij+B _ijsinδ _ij)(1)

Q _i＝-B _iiV _i ²+V _iV _j(G _ijsinδ _ij-B _ijcosδ _ij)

The Jacobian matrix of (2) two node power systems is:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ΔPi}}{\∂\mathrm{\δi}}=\mathrm{ViVj}(-\mathrm{Gij}\sin \mathrm{\δij}+\mathrm{Bij}\cos \mathrm{\δij})\\ \frac{\∂\mathrm{Pi}}{\∂\mathrm{Vi}}=\mathrm{Vj}(\mathrm{Gij}\cos \mathrm{\δij}+\mathrm{Bij}\sin \mathrm{\δij})+{2V}_i\mathrm{Gii}\\ \frac{{\∂Q}_i}{{\∂\mathrm{\δ}}_i}=V_i{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})\\ \frac{{\∂Q}_i}{{\∂V}_i}=V_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})-{2V}_i{B}_{\mathrm{ii}}\end{array}\right.---\left(2\right)$

(3) during electric power system generation cascading failure, Jacobian matrix is unusual, namely satisfy condition as:

$\frac{{\∂\mathrm{\ΔP}}_i}{{\∂\mathrm{\δ}}_i}\frac{{\∂\mathrm{\ΔQ}}_i}{{\∂V}_i}=\frac{{\∂P}_i}{{\∂V}_i}\frac{{\∂\mathrm{\ΔQ}}_i}{{\∂\mathrm{\δ}}_i}---\left(3\right)$

(4) (3) are substituted into (2) abbreviation then to have:

[V _iV _j(-G _ijsinδ _ij+B _ijcosδ _ij)][V _j(G _ijsinδ _ij-B _ijcosδ _ij)-2V _iB _ii](4)

＝[V _j(G _ijcosδ _ij+B _ijsinδ _ij)+2V _iG _ii[V _iV _j(G _ijcosδ _ij+B _ijsinδ _ij)]

$\begin{array}{c}{2V}_i{B}_{\mathrm{ii}}(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})-{2V}_i{G}_{\mathrm{ii}}(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})\\ =V_j{(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})}^2+V_j{(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}})}^2\\ \⇓\\ V_i\sin {\mathrm{\δ}}_{\mathrm{ij}}[B_{\mathrm{ii}}{G}_{\mathrm{ij}}-B_{\mathrm{ij}}{G}_{\mathrm{ii}}]-V_i\cos {\mathrm{\δ}}_{\mathrm{ij}}[B_{\mathrm{ij}}{B}_{\mathrm{ii}}+G_{\mathrm{ij}}{G}_{\mathrm{ii}}]=\frac{V_j[{G_{\mathrm{ij}}}^2+{B_{\mathrm{ij}}}^2]}{2}\end{array}---\left(5\right)$

(5) ignore node self-admittance over the ground, then have:

$\begin{array}{c}{B}_{\mathrm{ii}}=b_{\mathrm{ij}},B_{\mathrm{ij}}=-\mathrm{bij},G_{\mathrm{ii}}=g_{\mathrm{ij}},G_{\mathrm{ij}}=-g_{\mathrm{ij}}\\ V_i\sin {\mathrm{\δ}}_{\mathrm{ij}}[-b_{\mathrm{ij}}{g}_{\mathrm{ij}}+b_{\mathrm{ij}}{g}_{\mathrm{ij}}]-V_i\cos {\mathrm{\δ}}_{\mathrm{ij}}[-b_{\mathrm{ij}}{b}_{\mathrm{ij}}-g_{\mathrm{ij}}{g}_{\mathrm{ij}}]=\frac{V_j[{g_{\mathrm{ij}}}^2+{b_{\mathrm{ij}}}^2]}{2}\\ \⇒\frac{V_i}{V_j}\cos {\mathrm{\δ}}_{\mathrm{ij}}=\frac{1}{2}\end{array}---\left(6\right)$

(6) partial derivative with numerical value relative to with be very little, then have:

(7) fast decoupling zero tidal current computing method as:

ΔP/ΔV＝B′Δδ(8)

ΔQ/ΔV＝B″ΔV

(8) when voltage collapse, load bus j load is 0, can obtain:

${\∂P}_i/{\∂\mathrm{\δ}}_i={B_{\mathrm{ii}}}^{\′}{V}_i^0$ (9)

${\∂Q}_i/{\∂V}_i={B^{\′\′}}_{\mathrm{ii}}{V}_i^0$

(9) load bus j load is 0, then have:

$\begin{array}{c}{V}_i^0\≈V_j,{B_{\mathrm{ii}}}^{\′}={B_{\mathrm{ii}}}^{\′}=-B_{\mathrm{ii}}=B_{\mathrm{ij}}\\ \⇒I_{\mathrm{pi}}=\frac{{\∂P}_i/{\∂\mathrm{\δ}}_i}{{B_{\mathrm{ii}}}^{\′}{V_i}^0}=\frac{V_j^2}{{{2V}_i}^0}\end{array}---\left(10\right)$

(10) formula (6) is substituted into formula (10), then has:

$I_{\mathrm{pi}}=\frac{V_j}{2}---\left(11\right)$

(11) for multi-node system, arbitrary node injecting power meets equation:

$S_i^{*}=\stackrel{\‾}{Y_{\mathrm{ii}}}{V_i}^2+\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{{\stackrel{\‾}{V}}^{*}}_j\stackrel{\‾}{V_j}\stackrel{\‾}{Y_{\mathrm{ij}}}\⇒{V_i}^2+\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{{\stackrel{\‾}{V}}^{*}}_j\stackrel{\‾}{V_j}\frac{\stackrel{\‾}{Y_{\mathrm{ij}}}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}=\frac{S_i^{*}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}---\left(12\right)$

(12) contrast two node system equations (1), can obtain equivalent voltage such as formula:

$\stackrel{\‾}{V_{\mathrm{Geq}}}=-\underset{j\≠i}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}}\stackrel{\‾}{V_j}\frac{\stackrel{\‾}{Y_{\mathrm{ij}}}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}---\left(13\right)$

$I_{\mathrm{pi}}=\frac{{\∂P}_i/{\∂\mathrm{\δ}}_i}{-B_{\mathrm{ii}}}$

(13) in actual high-voltage electrical network, G _ij< < B _ij, that is:

$\stackrel{\&OverBar;}{V_{\mathrm{Geq}}}=-\underset{j\&NotEqual;i}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}}{V}_j\frac{B_{\mathrm{ij}}}{B_{\mathrm{ii}}}$

$V_{\mathrm{Vi}}=\frac{I_{\mathrm{pi}}}{V_{\mathrm{Geq}}}=\frac{{\&PartialD;P}_i/{\&PartialD;\mathrm{\&delta;}}_i}{\underset{j\&NotEqual;i}{\overset{n}{\underset{j=1}{\mathrm{\&Sigma;}}}}{B}_{\mathrm{ij}}{V}_j}---\left(14\right)$

(14) there is following relational expression during voltage collapse:

$V_{\mathrm{th}}=\frac{V_{\mathrm{Geq}}}{2}---\left(15\right)$

Embodiment 2

Be IEEE-39 node system geographical wiring diagram as shown in Figure 2, as research standard electrical network of the present invention, comprise 10 generators, 34 transmission lines.Symbol in figure represent generator, fine line represents transmission line, and heavy line represents node bus, and arrow represents load.

Below the inventive method is described in detail:

(1) basic parameter is arranged: part throttle characteristics parameter k _i=1.5, a _i=0.85, b _i=0.1, c _i=0.05, k ' _i=1.5, a ' _i=0.8, b ' _i=0.15, c ' _i=0.05, generator speed governing parameter: K _g=20, K _d=1.5.Adopt basic Newton method computing system trend; The part trend distribution of IEEE-39 node system is as following table, and fiducial value is 1000MW:

Node serial number	Node voltage	Node injecting power
			1	0.982	(0.663008934734+1.27060976311j)
2	1.029835	(2.82883070315e-15+1.82477065053e-14j)
			3	1.027007	(-0.322-0.00239999999999j)
4	1.016467	(-0.5-0.184j)
			5	1.017305	(-4.90521167858e-16+1.15684904535e-13j)
6	1.016289	(2.06166250556e-15+1.44079678474e-14j)
			7	1.019193	(-0.2338-0.084j)
8	1.020629	(-0.522-0.176j)
			9	1.039258	(-0.0065+0.066j)
10	0.990573	(1.61787560937e-15+1.05565119752e-13j)
			11	0.999115	(3.39690612331e-15+2.12529456274e-14j)
12	0.995958	(-0.0085-0.088j)

13	0.996717	(-3.03450806585e-15-2.82903311553e-14j)
			14	1.008742	(-9.52697759268e-16-2.86578456633e-14j)
15	1.014377	(-0.32-0.153j)
			16	1.015958	(-0.329-0.0323j)
17	1.025529	(3.88016945604e-15+3.63669115512e-14j)
			18	1.026777	(-0.158-0.03j) 7 -->
19	0.963324	(1.83822337135e-15+4.10635007442e-14j)
			20	1.011711	(-0.68-0.103j)
21	1.024088	(-0.274-0.115j)
			22	1.030669	(3.28541784273e-16-1.46484753346e-14j)
23	1.037307	(-0.2475-0.0846j)
			24	1.020492	(-0.3086+0.0922j)
25	1.028155	(-0.224-0.0472j)
			26	1.042588	(-0.139-0.017j)
27	1.036275	(-0.281-0.0755j)
			28	1.035207	(-0.206-0.0276j)
29	1.025522	(-0.2835-0.0269j)
			30	1.0499	(0.25-0.313129851904j)
31	1.040813	(-0.097-0.0442j)
			32	0.9841	(0.65-3.25364307747j)
33	0.9972	(0.632-2.08519629732j)
			34	1.0123	(0.508-0.49331847078j)
35	1.0494	(0.65-0.488558512955j)
			36	1.0636	(0.56+1.02145828193j)
37	1.0275	(0.54-1.12149065659j)
			38	1.0265	(0.83-1.58076125956j)
39	1.03	-0.104-1.85710686275j)

Table 1

(2) increase by 10% load, the frequency change of computing system, node load and generator output;

A () system loading adds Δ P _d0, then the power stage increment of generator unit and the load power that produces due to the frequency adjustment effect of load are changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf

(1)

That is: Δ P _d0=-(K _g+ K _d) Δ f

(b) static load Equivalent Model:

P _di＝P _d0i(1+k _iΔf)(a _i+b _iV _i+c _iV _i ²)

Q _di＝Q _d0i(1+k′ _iΔf)(a′ _i+b′ _iV _i+c′ _iV _i ²)

In formula: P _d0i, Q _d0i; The specified meritorious and reactive power of node i load; P _di, Q _di: node i load is gained merit and reactive power; Δ f: the frequency change of system; V _imagnitude of voltage; k _i, a _ib _i, c _i, k ' _i, a ' _i, b ' _i, c ' _ifor constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

C the meritorious contextual definition of exerting oneself between same frequency of () generator is:

$\left\{\begin{array}{c}{P}_{\mathrm{gi}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gik}}=\underset{k=1}{\overset{N_{\mathrm{gt}}}{\mathrm{\&Sigma;}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\&Delta;f})\\ P_{\min \mathrm{ik}}\&le;P_{\mathrm{gi}}\&le;P_{\max \mathrm{ik}}\end{array}\right.---\left(3\right)$

In formula: N _gi: generator interstitial content; P _gi: the meritorious of generator node i is exerted oneself; P _gik: meritorious the exerting oneself of generator node i kth platform unit; P _setik: the specified meritorious of generator node i kth platform unit is exerted oneself; P _minik: the minimum active power of generator node i kth platform unit; P _maxik: the maximum wattful power K of generator node i kth platform unit _gik: the unit power regulation of generator node i kth platform unit;

(4) trend adopting Newton method to calculate now distributes, and obtain node admittance matrix, Jacobian matrix coefficient, node voltage, result of calculation is as table 2;

As can be seen from Table 2, along with the increase of load factor, node voltage states value reduces gradually along with the increase of load factor, and V _thbasic maintenance about 0.5 is constant, therefore, can choose V when the policy development of actual electric network safe early warning _th=0.6 threshold values assessed as the voltage stabilization operation of system., be it can also be seen that by table 1, along with the increase of system load rate, system voltage stabilizes assessed value VSI also increases gradually meanwhile, and therefore, more Iarge-scale system level of security is lower can to think VSI.

Table 2

The charge threshold level V of (a) computing system _th:

$\stackrel{\&OverBar;}{V_{\mathrm{Geq}}}=-\underset{j\&NotEqual;i}{\overset{n}{\underset{j=1}{\mathrm{\&Sigma;}}}}\stackrel{\&OverBar;}{V_j}\frac{\stackrel{\&OverBar;}{Y_{\mathrm{ij}}}}{\stackrel{\&OverBar;}{Y_{\mathrm{ii}}}}\&DoubleRightArrow;V_{\mathrm{th}}=\frac{V_{\mathrm{Geq}}}{2}---\left(4\right)$

(b) computing node voltage status value I _vi:

$I_{\mathrm{vi}}=\frac{I_{\mathrm{pi}}}{V_{\mathrm{Geq}}}=\frac{{\&PartialD;P}_i/{\&PartialD;\mathrm{\&delta;}}_i}{\underset{j\&NotEqual;i}{\overset{n}{\underset{j=1}{\mathrm{\&Sigma;}}}}{B}_{\mathrm{ij}}{V}_j}---\left(5\right)$

C () calculates whole system voltage stability evaluation index VSI.

$\mathrm{VSI}=\underset{i\&Element;\mathrm{VS}}{\overset{\mathrm{NS}}{\underset{i=1}{\mathrm{\&Sigma;}}}}{(\frac{V_{\mathrm{th}}-V_{\mathrm{vi}}}{V_{\mathrm{th}}}*100)}^2---\left(6\right)$

Embodiment 3

Electrical network 500kv side, Guangdong topology diagram as shown in Figure 3, as the actual electric network of the present invention's research.Figure interior joint represents bus and transformer station, and fine rule represents transmission line.

Below the inventive method is described in detail:

(1) basic parameter is arranged: part throttle characteristics parameter k _i=1.5, a _i=0.85, b _i=0.1, c _i=0.05, k ' _i=1.5, a ' _i=0.8, b ' _i=0.15, c ' _i=0.05, generator speed governing parameter: K _g=20, K _d=1.5, adopt basic Newton method computing system trend as table 3;

Node serial number	Node voltage p.u	Node injecting power (1000MW)
			1	1.006	(27.2326710998-30.0611882767j)
2	1.053763	(-19.931-1.272j)
			3	1.019433	(15.716+1.154j)
4	1.042896	(-9.739+0.788j)
			5	1.068123	(-24.554+4.374j)
6	1.055256	-0.189+0.197999999966j)
			7	1.055	(28.188-27.0068180726j)
8	1.078657	(-3.264+0.091999999998j)
			9	1.12264	(8.774+0.877000000029j)
10	1.227566	(10.884+1.31600000013j)
			11	1.180265	(10.0750000001-0.190999999936j)

12	1.17957	(-6.85700000004-0.524000000049j)
			13	0.995075	(8.562+5.49700000004j)
14	0.973891	(-2.975-0.293j)
			15	1.010586	(2.119+1.254j)
16	0.983075	(-22.946+4.78999999998j)
			17	1.042656	(9.008+0.00400000000146j)
18	1.044034	(-32.99-2.05100000001j)
			19	1.272854	(-3.606+0.912999999944j)
20	1.467194	(17.232-2.69599999941j)
			21	1.118044	(29.3930000002-0.381000000026j)
22	0.879714	(-27.7699999984+2.15899999614j)
			23	0.951284	(-28.098+2.668j)
24	0.963875	(-14.234+1.114j)
			25	1.046355	(-8.971-0.281999999997j)
26	1.048414	(-6.863+0.187j)
			27	0.988382	(-8.908+2.438j)
28	1.030075	(-6.69-0.406j)
			29	0.996123	(1.10000000001+1.186j)
30	0.951999	(-2.991+0.629j)
			31	0.921728	(-8.194+1.69j)
32	0.905192	(11.804-0.6j)
			33	0.907202	(-14.542-0.967j)
34	0.913569	(-21.576+1.311j)
			35	0.936206	(-9.248-0.0820000000003j)
36	0.997585	(8.166-0.998j)
			37	0.908557	(23.127-1.04j) 10 -->
38	0.906191	(-18.916+1.618j)
			39	0.899466	(-14.115+1.375j)
40	0.896843	(-1.949+1.608j)
			41	1.005701	(-3.93923977421e-15+1.46348783314e-11j)
42	0.997957	(6.714+0.233999999988j)

43	0.913684	(-2.358+2.325j)
			44	1.006658	(6.948+0.26j)
45	0.996	(21.01-12.2693374769j)
			46	0.998	(30.412+4.31295787781j)
47	0.988	(17.634-698.977912824j)
			48	1.002	(16.444+693.917293916j)
49	1.046	(22.835-37.1324786923j)

Table 3

(2) regulating load rate, the frequency change of computing system, node load and generator output;

A () arranges system loading increment is 10%, and the load factor of system initial time is 0.1.Now load system load is Δ P _d0, then the power stage increment of generator unit and the load power that produces due to the frequency adjustment effect of load are changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf

That is: Δ P _d0=-(K _g+ K _d) Δ f (1)

(b) static load Equivalent Model:

P _di＝P _d0i(1+k _iΔf)(a _i+b _iV _i+c _iV _i ²)(2)

Q _di＝Q _d0i(1+k′ _iΔf)(a′ _i+b′ _iV _i+c′ _iV _i ²)

In formula: P _d0i, Q _d0i; The specified meritorious and reactive power of node i load; P _di, Q _di: node i load is gained merit and reactive power; Δ f: the frequency change of system; V _imagnitude of voltage; k _i, a _i, b _i, c _i, k ' _i, a ' _i, b ' _i, c ' _ifor constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

C the meritorious contextual definition of exerting oneself between same frequency of () generator is:

$\left\{\begin{array}{c}{P}_{\mathrm{gi}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gik}}=\underset{k=1}{\overset{N_{\mathrm{gt}}}{\mathrm{\&Sigma;}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\&Delta;f})\\ P_{\min \mathrm{ik}}\&le;P_{\mathrm{gi}}\&le;P_{\max \mathrm{ik}}\end{array}\right.---\left(3\right)$

In formula: N _gi: generator interstitial content; P _gi: the meritorious of generator node i is exerted oneself; P _gik: meritorious the exerting oneself of generator node i kth platform unit; P _setik: the specified meritorious of generator node i kth platform unit is exerted oneself; P _minik: the minimum active power of generator node i kth platform unit; P _maxik: the maximum wattful power K of generator node i kth platform unit _gik: the unit power regulation of generator node i kth platform unit;

(3) trend adopting Newton method to calculate now distributes, and obtain node admittance matrix, Jacobian matrix coefficient, node voltage, result of calculation is as table 4;

Load factor	I vi	V th	Load factor	I vi	V th
						0.1	0.9745	0.51139	0.6	0.80317	0.51903 11 -->
0.2	0.93199	0.51301	0.7	0.77298	0.51784
						0.3	0.89103	0.51397	0.8	0.74987	0.51652
0.4	0.85233	0.51447	0.9	0.737063	0.51519
						0.5	0.80317	0.51463	1.0	0.744353	0.51429
0.6	0.80317	0.51903	1.1	0.640641	0.50244

Table 4

As can be seen from Table 5, along with the increase of load factor, node voltage states value reduces gradually along with the increase of load factor, and V _thbasic maintenance about 0.5 is constant, therefore, can choose V when the policy development of actual electric network safe early warning _th=0.6 threshold values assessed as the voltage stabilization operation of system., be it can also be seen that by table 4 meanwhile, along with the increase of system load rate, voltage stability assessed value I _vialso reduce approach to criticality value gradually, therefore, this value can reflect operation of power networks state and relation between having a power failure on a large scale intuitively.

Claims (1)

1. a method for Identification of Power System generation cascading failure, comprises the following steps:

(1) according to power system load power, generator power, line parameter circuit value and node parameter, calculate the distribution of initial time trend according to Newton method;

(2) calculating adds Δ P by power system load _d0the power stage increment of the generator unit caused and the load power change produced due to the frequency adjustment effect of load, obtain system frequency changes delta f;

(a) static load Equivalent Model:

In formula: P _di, Q _di: for node i load is meritorious and reactive power; P _d0i, Q _d0i; For the specified meritorious and reactive power of node i load; Δ f: be the frequency change of system; V _imagnitude of voltage; k _i, a _i, b _i, c _i, k ' _i, a ' _i, b ' _i, c ' _ifor constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

B the meritorious contextual definition of exerting oneself between same frequency of () generator is:

In formula: P _gi: be the active power of generator node i; N _gi: be generator interstitial content; P _gik: be the active power of generator node i kth platform unit; P _setik: for the specified meritorious of generator node i kth platform unit is exerted oneself; P _minik: be the minimum active power of generator node i kth platform unit; P _maxik: be the maximum active power K of generator node i kth platform unit _gik: the unit power regulation of generator node i kth platform unit;

C () power system load adds Δ P _d0, then the power stage increment of generator unit and the load power that produces due to the frequency adjustment effect of load are changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf(3)

I.e. Δ P _d0=-(K _g+ K _d) Δ f

(3) amplitude of each node voltage vector given and phase angle initial value;

(4) each node active power and reactive power amount of unbalance Δ P is calculated _i, Δ Q _i;

A the active power imbalance of () electric power system any node is closed and is:

B the reactive power imbalance of () PQ node is closed and is:

(5) calculate each element of Jacobian matrix and solve equilibrium equation;

A in () electric power system, active power balance closes and is:

B in () electric power system, reactive power equilibrium is closed and is:

C in () electric power system, Jacobian matrix element is:

(6) each node voltage amplitude and vectorial angle in electric power system is revised:

(7) judge whether meritorious and reactive power deviation meets the condition of convergence, obtain the trend distribution of electric power system after generator speed governing and load responding;

(8) computing node voltage status index V _vi:

(9) equivalent voltage of current power system running state is calculated with critical value index V _th:

(10) whole system voltage stability evaluation index I _vSI:

。