CN103311923A - Method for identifying cascading failure of power system - Google Patents

Abstract

The invention discloses a method for identifying the cascading failure of a power system. Considering the speed governing and load response of a power generator, a more practical power system load flow calculation model is established, and the method overcomes the impact that a traditional load flow calculation model cannot reflect the regulation action and load response of the power generator in the load flow calculation model. From the perspective of the operation status of the system, the method analyzes the relationship between stable voltage and the failure in the cascading failure; and deducts the stable indicator of the system voltage and the critical value of the indicator by analyzing the change of a Jacobi matrix element value in order to quantitatively analyze the relationship between the critical value of the voltage and the operation status of the system. As the load is increased, the system has higher risk of the cascading failure. During the process, the stable indicator of the system voltage is gradually reduced, and the critical value is always maintained at 0.5 (+/-0.03). In an actual system, the critical value of the voltage which is calculated remains unchanged in the cascading failure, 0.6 is selected as the critical value of voltage collapse in a power grid in the actual system, so as to identify whether the power grid faces the risk of large-scale power-off or not. In such a manner, the method has better actual guiding significance.

Description

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

Technical field

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

Background technology

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

Research to the power grid cascading fault is mainly carried out from the following aspects: 1) the self-organizing Critical Theory the physics is applied in the electric power system, from the Evolution of macroscopic perspective definition and identification system.This theory is by research and disclose critical characteristic, deeply understands the accident phenomenon of having a power failure on a large scale from macro-level, to finding prevention, controlling the method for the accident of having a power failure on a large scale.Studies show that: real system embodies the self-organizing critical characteristic to a certain extent, and the fault data that characterizes the scale of having a power failure on a large scale such as North America and China electric power system has power law tail characteristic, and is not the normal distribution on the traditional understanding.Power Law is namely containing self-organized criticality behind.Data statistics studies show that domestic and international electrical network mostly has obvious worldlet characteristic.2) network configuration is described on the impact of cascading failure in power system by the chain reaction in the simple complex network model.Point out that the higher contact node of betweenness and the number of degrees is when guaranteeing the electrical network connectedness, propagation to fault plays a part to add fuel to the flames, scale-free networks network structure electrical network very easily causes extensive catastrophe under calculated attack, more more fragile than small-world network structure.All in all, be conducive to Electric Power Network Planning and the Analysis on Mechanism of having a power failure on a large scale based on the research of complex network, but its model is not considered operation characteristic and the trend constraint of actual electric network.Therefore, a lot of scholars have also proposed some models from the angle of network analysis, and the basic principle of these models all is to calculate by constantly carrying out trend, obtain and disconnect the evolution that the out-of-limit circuit of trend is simulated cascading failure in the electric power system.3) based on the hidden failure model of " being similar to " DC power flow and hidden failure mechanism, based on optimal load flow method (OPA) model of direct current optimal power flow (OPF), based on the Manchester model of load excision and AC power flow and based on the blackout model that exchanges OPF.The hypotheses of DC power flow hidden failure model is that whole buses (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.The Manchester model does not take into full account the regulating action of generator, thereby non-power-off fault may be judged as power-off fault, has perhaps enlarged the fault scale.Although the blackout model of optimal load flow has overcome above-mentioned deficiency, it does not consider the frequency shift (FS) in generator, part throttle characteristics and the cascading failure generating process.System is accompanied by the excision of load and generating set the transmission line cascading trip stage mostly, and consequent frequency shift (FS) and generator speed regulation process cannot be ignored.

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

Summary of the invention

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

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

1. the method for assessment power system voltage stabilization and charge threshold level comprises the following steps:

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

(2) calculating has increased Δ P by power system load _D0The power stage increment of the generator unit that causes and the load power that produces owing to the frequency adjustment effect of loading change, and 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 the formula: P _D0i, Q _D0iThe specified meritorious and reactive power of node i load; P _Di, Q _Di: the 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 ' _iBe constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

(b) the meritorious contextual definition of exerting oneself between the 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 the formula: N _Gi: the generator interstitial content; P _Gi: the meritorious of generator node i exerted oneself; P _Gik: meritorious the exerting oneself of generator node i k platform unit; P _Setik: specified meritorious the exerting oneself of generator node i k platform unit; P _Minik: the minimum active power of generator node i k platform unit; P _Maxik: the maximum wattful power K of generator node i k platform unit _Gik: the unit power regulation of generator node i k platform unit;

(c) power system load has increased Δ P _D0, then the power stage increment of generator unit and since the load power that produces of frequency adjustment effect of load be changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf (3)

That is: Δ P _D0=-(K _G+ K _D) Δ f

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

(4) calculate each node active power amount of unbalance Δ P in the electric power system _i, Δ Q _i

(a) meritorious uneven the closing of arbitrary node is in the electric power system:

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

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

(b) idle uneven the closing of PQ node is in the electric power system:

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

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

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

(a) active balance closes and is:

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

(b) reactive balance closes and is:

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

(c) the 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) revise each node voltage amplitude and vectorial angle:

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

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

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

(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 calculating current power system running state

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 of consideration generator speed governing and load voltage, frequency characteristic, according to the variation of Jacobian matrix diagonal element value under the malfunction, the charge threshold level when deriving system voltage Stability Assessment index and system and being in the voltage collapse critical point.This Identification of Power System generation cascading failure is applied in the power grid security early warning, and real-time node voltage and system voltage stable state are quantized, and more accurately identification 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 the electric power system actual needs; 2, the Jacobian matrix element was derived critical value and system's stabilization of power grids evaluation index of voltage collapse during trend was calculated, and calculated the 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, can clearly show the relation between system node voltage running status and the voltage collapse.

Description of drawings

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

The present invention is further illustrated below in conjunction with accompanying drawing.

Embodiment 1

Be two node system geographical wiring diagrams as shown in Figure 1, this is explanation power system voltage stabilization index VSI and charge threshold level V as an example of 2 node systems example _ThDerivation.Symbol among the figure The expression generator, perpendicular solid line represents the bus of transmitting electricity, | g _Ij+ jb _Ij| the impedance of expression transmission line, arrow represents load.

(1) have for any two node power systems:

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

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) Jacobian matrix is unusual during electric power system generation cascading failure, 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) substitution (2) and abbreviation are then had:

[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 with respect to

With Be very little, then have:

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

ΔP/ΔV＝B′Δδ (8)

ΔQ/ΔV＝B″ΔV

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

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

(10) with formula (6) substitution formula (10), then have:

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

(11) for multi-node system, the arbitrary node injecting power satisfies 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 suc 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 the actual high-voltage electrical network, G _Ij＜＜B _Ij, that is:

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

$V_{\mathrm{Vi}}=\frac{I_{\mathrm{pi}}}{V_{\mathrm{Geq}}}=\frac{{\∂P}_i/{\∂\mathrm{\δ}}_i}{\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{B}_{\mathrm{ij}}{V}_j}---\left(14\right)$

(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 among the figure

The expression generator, fine line represents transmission line, and heavy line represents the node bus, and arrow represents load.

The below is described in detail the inventive method:

(1) basic parameter setting: 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 of IEEE-39 node system distributes such as following table, and fiducial value is 1000MW:

Node serial number	Node voltage	The 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)
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 has increased Δ P _D0, then the power stage increment of generator unit and since the load power that produces of frequency adjustment effect of load be 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 the formula: P _D0i, Q _D0iThe specified meritorious and reactive power of node i load; P _Di, Q _Di: the 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 ' _iBe constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

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

$\left\{\begin{array}{c}{P}_{\mathrm{gi}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\Σ}}}{P}_{\mathrm{gik}}=\underset{k=1}{\overset{N_{\mathrm{gt}}}{\mathrm{\Σ}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\Δf})\\ P_{\min \mathrm{ik}}\≤P_{\mathrm{gi}}\≤P_{\max \mathrm{ik}}\end{array}\right.---\left(3\right)$

In the formula: N _Gi: the generator interstitial content; P _Gi: the meritorious of generator node i exerted oneself; P _Gik: meritorious the exerting oneself of generator node i k platform unit; P _Setik: specified meritorious the exerting oneself of generator node i k platform unit; P _Minik: the minimum active power of generator node i k platform unit; P _Maxik: the maximum wattful power K of generator node i k platform unit _Gik: the unit power regulation of generator node i k platform unit;

(4) trend that adopts Newton method to calculate this moment distributes, and obtains node admittance matrix, Jacobian matrix coefficient, node voltage, result of calculation such as table 2;

As can be seen from Table 2, along with the increase of load factor, the node voltage state value reduces gradually along with the increase of load factor, and V _ThBasic 0.5 left and right sides that keeps is constant, therefore, can choose V when the policy development of actual electric network safe early warning _Th=0.6 voltage stabilization as system moves the threshold values of assessing.Simultaneously, be it can also be seen that by table 1, along with the increase of system load rate, system voltage stability assessment value VSI also increases gradually, therefore, can think that the larger security of system level of VSI is lower.

Table 2

(a) the charge threshold level V of computing system _Th:

$\stackrel{\‾}{V_{\mathrm{Geq}}}=-\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}\stackrel{\‾}{V_j}\frac{\stackrel{\‾}{Y_{\mathrm{ij}}}}{\stackrel{\‾}{Y_{\mathrm{ii}}}}\⇒V_{\mathrm{th}}=\frac{V_{\mathrm{Geq}}}{2}---\left(4\right)$

(b) computing node voltage status value I _Vi:

$I_{\mathrm{vi}}=\frac{I_{\mathrm{pi}}}{V_{\mathrm{Geq}}}=\frac{{\∂P}_i/{\∂\mathrm{\δ}}_i}{\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{B}_{\mathrm{ij}}{V}_j}---\left(5\right)$

(c) calculate whole system voltage stability evaluation index VSI.

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

Embodiment 3

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

The below is described in detail the inventive method:

(1) basic parameter setting: 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 such 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)
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) the system loading increment being set is 10%, and the load factor of system's initial time is 0.1.This moment, the load system load was Δ P _D0, then the power stage increment of generator unit and since the load power that produces of frequency adjustment effect of load be 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 the formula: P _D0i, Q _D0iThe specified meritorious and reactive power of node i load; P _Di, Q _Di: the 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 ' _iBe constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

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

$\left\{\begin{array}{c}{P}_{\mathrm{gi}}=\underset{k=1}{\overset{N_{\mathrm{gi}}}{\mathrm{\Σ}}}{P}_{\mathrm{gik}}=\underset{k=1}{\overset{N_{\mathrm{gt}}}{\mathrm{\Σ}}}(P_{\mathrm{setik}}-K_{\mathrm{gik}}\mathrm{\Δf})\\ P_{\min \mathrm{ik}}\≤P_{\mathrm{gi}}\≤P_{\max \mathrm{ik}}\end{array}\right.---\left(3\right)$

In the formula: N _Gi: the generator interstitial content; P _Gi: the meritorious of generator node i exerted oneself; P _Gik: meritorious the exerting oneself of generator node i k platform unit; P _Setik: specified meritorious the exerting oneself of generator node i k platform unit; P _Minik: the minimum active power of generator node i k platform unit; P _Maxik: the maximum wattful power K of generator node i k platform unit _Gik: the unit power regulation of generator node i k platform unit;

(3) trend that adopts Newton method to calculate this moment distributes, and obtains node admittance matrix, Jacobian matrix coefficient, node voltage, result of calculation such 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
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, the node voltage state value reduces gradually along with the increase of load factor, and V _ThBasic 0.5 left and right sides that keeps is constant, therefore, can choose V when the policy development of actual electric network safe early warning _Th=0.6 voltage stabilization as system moves the threshold values of assessing.Simultaneously, be it can also be seen that by table 4, along with the increase of system load rate, voltage stability assessed value I _ViAlso reduce gradually the approach to criticality value, therefore, this value can reflect intuitively the operation of power networks state and have a power failure on a large scale between relation.

Claims (1)

1. the method for an 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 initial time trend according to Newton method and distribute;

(2) calculating has increased Δ P by power system load _D0The power stage increment of the generator unit that causes and the load power that produces owing to the frequency adjustment effect of loading change, and obtain system frequency changes delta f

(a) static load Equivalent Model:

In the formula: P _Di, Q _Di: the meritorious and reactive power for the node i load; P _D0i, Q _D0iBe 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 ' _iBe constant, a _i+ b _i+ c _i=1, a ' _i+ b ' _i+ c ' _i=1;

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

In the formula: P _Gi: for the meritorious of generator node i exerted oneself; N _Gi: be the generator interstitial content; P _Gik: be meritorious the exerting oneself of generator node i k platform unit; P _Setik: be specified meritorious the exerting oneself of generator node i k platform unit; P _Minik: be the minimum active power of generator node i k platform unit; P _Maxik: be the maximum wattful power K of generator node i k platform unit _Gik: the unit power regulation of generator node i k platform unit;

(c) power system load has increased Δ P _D0, then the power stage increment of generator unit and since the load power that produces of frequency adjustment effect of load be changed to:

ΔP _D0+ΔP _D＝ΔP _G＝-K _GΔf (3)

That is: Δ P _D0=-(K _G+ K _D) Δ f

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

(4) calculate each node active power amount of unbalance Δ P _i, Δ Q _i

(a) meritorious uneven the closing of the arbitrary node of electric power system is:

(b) idle uneven the closing of PQ node is:

(5) calculate each element of Jacobian matrix and find the solution equilibrium equation;

(a) the active balance pass is in the electric power system:

(b) the reactive balance pass is in the electric power system:

(c) the Jacobian matrix element is in the electric power system:

(6) revise each node voltage amplitude and vectorial angle in the electric power system:

(9)

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

(8) computing node voltage status index V _Vi:

(9) equivalent voltage of calculating current power system running state

With critical value index V _Th:

(10) whole system voltage stability evaluation index VSI:

。

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