CN102214920A - Circuit cluster-based method for analyzing grid cascading failure based on - Google Patents

Abstract

The invention discloses a circuit cluster-based method for analyzing a grid cascading failure, belonging to the technical field of safety protection of a power system. The method comprises the following steps of: applying a Bayes network failure tree theory to cascading failure analysis based on a distribution failure probability model of a self-critical circuit cluster and establishing a probability analysis model for a grid cascading failure based on cascading failure probability analysis of the self-critical circuit cluster in combination with the probability characteristic of a cascading failure developing stage; and through simulating a cascading failure process, performing risk assessment on the cascading failure by using a system load loss index and analyzing weak links of a system. By adopting the method, foundations are provided for a prevention strategy for further research on the reduction of cascading failure risk.

Description

Power grid cascading failure analysis methods based on the circuit cluster

Technical field

The invention belongs to power system security guard technology field, relate in particular to a kind of power grid cascading failure analysis methods based on the circuit cluster.

Background technology

In recent years, the a lot of particularly serious power outage that takes place all shows as cascading failure both at home and abroad, the common feature of this class power outage is: begin a certain often element and be interfered, cause the destruction of this element operate as normal, if can not in time handle, As time goes on, the linksystem that causes the accident enlarges, involve other element even whole system, cause that successively other elements disconnect in succession, cause large area blackout at last.Though the probability of happening of this class accident is little, and is very harmful, to deepening constantly that the cascading failure problem is familiar with, how to make up the focal issue that numerous experts and scholars paid close attention to that rational power grid cascading fault model has become this field along with both at home and abroad.

Up to now, do a lot of work in the cascading failure research field both at home and abroad.Scholars such as the Carreras of the U.S., Dobson begin to adopt the critical theory of self-organizing to explain the cascading failure problem of electrical network, and the OPA model of proposition, CASCADE model, HOT (Highly Optimized Tolerance) theory and branching process model etc. are constructed based on Complex System Theory and in conjunction with the reality of electric power system.Be called " hidden fault, fragility and the adaptability problem [J] of big electrical network relay automatic device " (Wang Mingjun in name, Electric Power Automation Equipment, 2005,25 (3): in document 1-5.), considered to carry out the massive blackout accident that comprises transmission line and generator cascading failure the CASCADE model of deterministic simulation and analysis.Be called " Random graphs with arbitrary degree distributions and their applications[J] in name " (Newman M E J, Strogatz S H, Watts D J.Physical Review E, 2001,64 (2): 026118,11-19.) document in, the HOT theory of power rate relation has been described, the initial distribution rule of fault statistics data can more reasonably be described.But also there is obvious deficiency in these models: in fact these models do not pay attention to the physical details of cascading failure evolution, but emphasize the initial condition of electrical network generation cascading failure and long-term macroscopical overall characteristic of electrical network generation cascading failure, be a kind of Analysis on Mechanism of cascading failure qualitatively method.

From domestic and international grid power blackout accident, cascading failure shows as the power system component of protecting action to cause and stops transport in succession, and cascading failure is the conditional probability incident in essence.Bayesian network is based on the expression and the inference pattern of a kind of uncertain knowledge of probability analysis, graph theory, can be good at representing the uncertainty at random and the correlation of variable, is fit to very much the analysis of conditional probability incident.

Method provided by the invention, will be according to from critical circuit cluster distributed faults probabilistic model, Bayesian network fault tree theory is applied to the cascading failure analysis, with the fault selectional restriction on supply path, adopt alternately trend calculating and transient stability calculating to analyze, take all factors into consideration circuit overload in the cascading failure process, stable, load loss and, power grid cascading failure risk index is analyzed the factors such as risk indicator of electrical network.

This method fully takes into account the topological relation of network configuration according to the physical process of power grid cascading fault and in conjunction with the probability characteristics of each stage incident, and system load flow shifts the Different Effects between circuit element, sets up the Bayesian network fault tree of cascading failure; When carrying out the analysis of the cascading failure mechanism of transmission, according to cascading failure take place, the physical process of development, circuit from critical characteristic when the analytical system trend shifts; In conjunction with the probability characteristics of cascading failure developing stage, based in the electric power system from the cascading failure probability analysis of critical circuit cluster, set up a kind of probability analysis model of power grid cascading fault; By simulation to the cascading failure process, with overload and system loading loss index cascading failure is carried out risk assessment, find the weak link of system, provide foundation for further studying reduction cascading failure prevention of risk strategy.

Summary of the invention

The objective of the invention is to,, propose a kind of power grid cascading failure analysis methods based on the circuit cluster in conjunction with the probability nature behind the circuit element clustering fault in the electric power system.

For realizing above-mentioned purpose, technical scheme provided by the invention is that a kind of power grid cascading failure analysis methods based on the circuit cluster is characterized in that described method comprises:

Step 1: the Bayesian network model cascading failure tree of setting up electrical network;

Step 2: determine from critical circuit cluster;

Step 3: set up cascading failure probabilistic model from critical circuit cluster;

Step 4: calculate the cascading failure risk indicator.

Describedly determine specifically: according to constraint criteria from critical circuit cluster

$\left\{\begin{array}{c}J=\max \frac{1}{n}\{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}-\underset{i=m+1}{\overset{n}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}\}\≥\mathrm{\ϵ}\\ L_i\∈(66.7~100)\%L_{i\max }\end{array}\right.$

Judge whether each bar load circuit in the electrical network is from critical circuit, when this load bar circuit be during from critical circuit, with its adding from critical circuit cluster; Wherein, J represents weak load concentration class, and n is the load number of, lines that is connected in the electrical network, and m is the power transmission sequence quantity in the electrical network, L _ImaxBe the maximum delivery power of transmission line i correspondence, L _iBe transmission line i actual fed power, ε represents weak load convergence factor.

Described foundation from the cascading failure probabilistic model of critical circuit cluster is:

$p_{\mathrm{event}}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{p}_{\mathrm{Li}}[p_{k\left(\mathrm{Xi}\right)}{p}_{\mathrm{Xi}}{\mathrm{\λ}}^{X_i}+p_{k\left(i\right)}(1-p_{\mathrm{Xi}})]$

Wherein, L is the circuit number of electrical network, P _EventBe the cascading failure probability from critical circuit cluster, P _LiBe the probability of i bar line fault under the electrical network initial condition, P _{K (i)}Be the conditional probability that power overload takes place on the k bar circuit, X is the bar number from critical circuit, X _iFor after the circuit i fault from the bar number of critical circuit, P _XiThe expression fault occurs in the conditional probability from critical circuit cluster, P _{K (Xi)}The fault that expression causes makes the conditional probability that power overload takes place on the k bar circuit, and λ is from critical circuit cluster distributed constant.

Described from critical circuit cluster distributed constant λ=1.5.

Described calculating cascading failure risk indicator is utilized formula

R＝p _event·I _load

I _LoadBe cascading failure load loss severity index, its computing formula is

Wherein, N is an electric network fault quantity, P _Load(i) be the load capacity loss that the i time cascading failure causes, P _SBe power system capacity.

Analytical method provided by the invention, introduced constraint criteria from critical circuit, in the cascading failure analytical model, based on failure probability analysis, introducing is from critical circuit failure probability analysis, effectively weakened the defective that has difference between model prerequisite and the current conditions, thereby this is a kind of effective cascading failure Analysis on Mechanism method, more can effectively controls the development of electric network fault.

Description of drawings

Fig. 1 is based on the flow chart of the power grid cascading failure analysis methods of circuit cluster;

Fig. 2 is the Bayesian network fault tree of cascading failure;

Fig. 3 is the cascading failure characteristic of circuit cluster;

Fig. 4 is the isopleth map of IEEE 39 node system wiring;

Fig. 5 is IEEE 39 node system cascading failures risk curves step by step;

Fig. 6 is a Gansu electrical network local area network winding diagram.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.

Embodiment 1

Fig. 1 is based on the flow chart of the power grid cascading failure analysis methods of circuit cluster.Among Fig. 1, method provided by the invention comprises:

Step 1: the Bayesian network model cascading failure tree of setting up electrical network.

The present invention is cut to load, generator detachment system and grid disconnection be as the end condition of chain reaction, and the Bayesian network model cascading failure that can set up is thus set as shown in Figure 2.

Use this fault tree analysis method and can more clearly represent the evolution of cascading failure; after a circuit element is cut; the circuit overload that is closely related with this circuit and the probability of protective device malfunction improve greatly, and causing the circuit cluster to occur from critical condition is the main form of cascading failure evolution.

Step 2: determine from critical circuit cluster.

By the network configuration topological analysis, the inhomogeneities that the system loading vulnerability has seriously caused circuit element to distribute, the weak failure risk that has strengthened element between two nodes that connects of circuit, make power system network possess weak gathering load and line construction simultaneously from critical characteristic, line related is called from critical circuit.Verify whether a circuit is as follows from the constraint criteria of critical circuit:

$\left\{\begin{array}{c}J=\max \frac{1}{n}\{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}-\underset{i=m+1}{\overset{n}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}\}\≥\mathrm{\ϵ}\\ L_i\∈(66.7~100)\%L_{i\max }\end{array}\right.---\left(1\right)$

Wherein, J represents weak load concentration class, and n is the load number of, lines that is connected in the electrical network, and m is the power transmission sequence quantity in the electrical network, L _ImaxBe the maximum delivery power of transmission line i correspondence, L _iBe transmission line i actual fed power, ε represents weak load convergence factor.

Owing to from the vulnerability of critical circuit institute on-load, make, cause that other relevant probability of malfunction from the critical line circuit component improves greatly from the fault of critical circuit.And along with the variation of network topology after the fault and the reallocation of load, system may produce new for critical circuit, and what these were closely related is referred to as from critical circuit cluster from critical line set.

Step 3: set up cascading failure probabilistic model from critical circuit cluster.

1, determines the cascading failure characteristic of circuit cluster

In the power network line fault, relevant with the number of lines Z in the circuit cluster from the probability of critical circuit overload, the security settings cluster value of initial condition is Z _S, as Z≤Z _SThe time, the probability of the overload that breaks down in the cluster circuit is a constant P _WAs Z＞Z _SThe time, the probability of circuit overload increases sharply by index law:

$P_{\mathrm{line}}=\left\{\begin{array}{cc}{P}_W& Z\≤Z_S\\ P_W\·e^{(\frac{Z}{Z_S}-1)},& Z>Z_S\end{array}\right.---\left(2\right)$

P in the formula _LineFor occur the probability of overload in the circuit cluster from critical circuit; P _WBe cluster circuit overload probability constant; Z _SBe the security settings cluster value of system initial state, Z is the number of lines in the circuit cluster.The cascading failure characteristic of circuit cluster as shown in Figure 3; when the power network line cluster topology is optimized; after the fault that reduces the circuit cluster distributes, from critical circuit reduce and overload protection arrangement littler than former line fault overload action probability, thereby reduced the risk of system's generation cascading failure.

2, determine circuit cluster cascading failure probabilistic model

This method adopts the integration probabilistic model to describe the cascading failure of electric power system based on the circuit cluster.If electrical network has L bar circuit, definition line fault causes and shifts overload order of severity function:

$\mathrm{\Δ}{I}_i=\left|\frac{P_i}{P_{i\max }}\right|\underset{k=1}{\overset{L}{\mathrm{\Σ}}}{\left(\frac{\mathrm{\Δ}{P}_k}{P_{k\max }}\right)}^2---\left(3\right)$

P in the formula _iBe the actual active power of circuit i; P _ImaxFor circuit i allows maximum active power value; P _KmaxFor circuit k can transmit maximum active power; Δ P _kFor circuit i fault causes circuit k transmission active power variable quantity.

P _LiBe the probability of i bar line fault under the electrical network initial condition, P _{K (i)}Be the conditional probability that power overload takes place on the k bar circuit, X is the bar number from critical circuit, X _iFor after the circuit i fault from the bar number of critical circuit, P _XiThe expression fault occurs in the conditional probability from critical circuit cluster, P _{K (Xi)}The fault that expression causes makes the conditional probability that power overload takes place on the k bar circuit, can obtain the cascading failure Probability p _EventFor

$p_{\mathrm{event}}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{p}_{\mathrm{Li}}[p_{k\left(\mathrm{Xi}\right)}{p}_{\mathrm{Xi}}{\mathrm{\λ}}^{X_i}+p_{k\left(i\right)}(1-p_{\mathrm{Xi}})]---\left(4\right)$

Wherein, λ is a circuit cluster distributed constant, gets empirical value 1.5.

Step 4: calculate the cascading failure risk indicator.

1, cascading failure loses the load computational methods

Along with the transfer of primary fault system load flow, the circuit cluster occurs from critical condition, by the cascading failure Probability p _EventComputational methods as can be seen, the order of severity that power overload takes place on the circuit is the principal element of electrical network generation cascading failure.The order of severity that can measure cascading failure with the size of load loss total quantity index in the cascading failure evolution.Load loss mainly comprises 3 aspects: 1) grid disconnection is several isolated islands, causes the load that loses for keeping the trend balance; 2) circuit overload protects action or under-voltage protection action to cause generator or the load that loses; 3) add under not convergence of the trend situation and cause the load that loses after the control measure.Minimum with the system loss load is target function:

$\min P_B=\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\left(\underset{i\∈Q}{\mathrm{\Σ}}{P}_{\mathrm{ji}}\right)---\left(5\right)$

Wherein, K is the number of stages of control measure; But Q is the set of cutting load node; P _JiRepresent the cutting load amount on the j stage load bus i.

2, power grid cascading failure risk assessment

The factor of the possibility of the risk indicator assurance accident quantitatively of electric power system and seriousness and decision systems reliability, thereby than the influence of more comprehensive reflection accident to whole electric power system.The risk indicator of system is defined as the product of contingency occurrence probability and accident severity, and expression formula is as follows:

R＝p _e·I _e (6)

Wherein, R is the risk probability index, p _eBe accident probability, I _eBe accident severity.

When electric power system generation cascading failure, because the cascading trip of circuit may cause load cut, then cascading failure can reflect by load loss the risk that whole system causes.For ease of the comparison between the different system, this method is carried out the standardization processing to the power loss of load, and cascading failure load loss severity index is

$I_{\mathrm{load}}=\frac{1}{P_S\×N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{\mathrm{load}}\left(i\right)---\left(7\right)$

Wherein, N is a number of faults; P _Load(i) be the load capacity loss that the i time cascading failure causes; P _SBe power system capacity.

3, calculate the risk indicator of large power grid cascading fault

According to the index definition of risk in the assessment of power grid cascading failure risk, the cascading failure risk indicator is

R＝p _event·I _load (8)

With the probability calculation of cascading failure p as a result _EventThe substitution following formula can calculate the risk indicator of system's cascading failure.

Embodiment 2

IEEE 39 node systems are carried out the cascading failure emulation experiment, and system node and electrical wiring are as shown in Figure 4.This method is carried out the example computational analysis by adopting IEEE 39 node systems, can reflect the variation step by step of electric power system value-at-risk in the chain reaction process intuitively.39 node systems are chosen the full shipping line mode of generator standard-sized sheet, and 5 circuits of initial trend maximum are as shown in table 1:

5 circuits of table 1 39 node system trend maximums

The initial trend of initialization system is constant, is example to cut off transmission line L16 and L1 accident, and by the analysis that this 39 node system circuit cluster is distributed, the trend that the computational scheme fault causes shifts.According to the cascading failure end condition, obtain causing the Probability p of cascading failure step by step _EventWith the total load loss I on the cascading failure path _Load, according to the computing formula of cascading failure risk indicator, obtain after normalized the cascading failure risk indicator that changes step by step, as shown in table 2.

Table 2 cascading failure is risk indicator step by step

Cascading failure is risk curve result such as table 2 and shown in Figure 5 step by step, and the 4th grade of fault, behind the excision circuit L16, cascading failure value-at-risks at different levels significantly raise.Its reason is that the trend transfer of fault in the cascading failure process enlarges the distribution of circuit cluster, causes circuit overload, and the circuit cluster runs their course to from critical condition, makes system the cascading failure probability occur and improves greatly.

By contrast, behind the excision circuit L1, trend shifts the distribution of circuit cluster is enlarged, and the system line cluster remains enough subcritical states, 3rd level system risk value at cascading failure just reduces to 0, and initial incident will can not cause more serious cascading failure.By such curve, the operations staff can see the development of faults at different levels and intuitively to the influence of system safety.

Embodiment 3

With China's Gansu electrical network region linkage fault example demonstration, draw this province's zone power grid cascading failure operation mode and weak link below,, summary of the invention of the present invention is described further as one embodiment of the present of invention.

In Gansu 09 year winter large load operation mode is example, Gansu electrical network part trunk rack and inter-provincial interconnection as shown in Figure 6:

Gansu and Shaanxi electrical network adopt eastern electric west to send limit mode, at first utilize synthesizer PSASP that the Gansu electrical network is carried out fault scanning, determine that line faults such as Pingliang-Qian County are the most dangerous, and they are set at level fault, are used for the analysis of consequent malfunction.

Analyze according to circuit cluster probabilistic model, draw possible secondary failure and corresponding index result of calculation, after fast transient scanning, only have 5 faults need carry out detailed transient state verification.According to the information of I and II fault, utilize institute the residue circuit to be scanned again, can determine three grades of circuits that the failure risk index is high, the results are shown in table 3 to index:

5 circuits of table 3 cascading failure risk indicator maximum

Repeat said process, can further determine the consequent malfunction of system's higher level.As can be seen from Table 3, under close overload index, cause the probability maximum of three grades of chain faults behind society's hall-Baoji line failure, the fragile link that has shown system, section interconnection overlond running during Pingliang-Qian County circuit generation parallel lines on same tower secondary failure, circuit cluster distributed faults enlarges, and its cutting load counts maximum and approaching failure is the most serious.If therefore this circuit goes wrong, the operations staff should give enough attention and take appropriate measures.

Electrical network analysis shows:

This method has proposed the cascading failure probabilistic model of the circuit cluster of electrical network from critical condition based on failure probability analysis, has invented a kind of large power grid cascading failure analysis methods based on the circuit cluster.This method combines self-organizing critical model and cluster distributed model, demonstrate the circuit cluster from the main effect of critical condition in the cascading failure developing stage, and the utilization Risk Theory is carried out risk assessment from the load loss angle to the electric power system cascading failure, be convenient in time find the weak link of system, for the control and the design of electric power system provides theoretical foundation more accurately.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection range of claim.

Claims (5)

1. power grid cascading failure analysis methods based on the circuit cluster is characterized in that described method comprises:

Step 1: the Bayesian network model cascading failure tree of setting up electrical network;

Step 2: determine from critical circuit cluster;

Step 3: set up cascading failure probabilistic model from critical circuit cluster;

Step 4: calculate the cascading failure risk indicator.

2. a kind of power grid cascading failure analysis methods based on the circuit cluster according to claim 1 is characterized in that describedly determining from critical circuit cluster specifically: according to constraint criteria

$\left\{\begin{array}{c}J=\max \frac{1}{n}\{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}-\underset{i=m+1}{\overset{n}{\mathrm{\Σ}}}\frac{\left|L_i\right|}{L_{i\max }}\}\≥\mathrm{\ϵ}\\ L_i\∈(66.7~100)\%L_{i\max }\end{array}\right.$

Judge whether each bar load circuit in the electrical network is from critical circuit, when this load bar circuit be during from critical circuit, with its adding from critical circuit cluster; Wherein, J represents weak load concentration class, and n is the load number of, lines that is connected in the electrical network, and m is the power transmission sequence quantity in the electrical network, L _ImaxBe the maximum delivery power of transmission line i correspondence, L _iBe transmission line i actual fed power, ε represents weak load convergence factor.

3. a kind of power grid cascading failure analysis methods based on the circuit cluster according to claim 2 is characterized in that described foundation from the cascading failure probabilistic model of critical circuit cluster is:

$p_{\mathrm{event}}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{p}_{\mathrm{Li}}[p_{k\left(\mathrm{Xi}\right)}{p}_{\mathrm{Xi}}{\mathrm{\λ}}^{X_i}+p_{k\left(i\right)}(1-p_{\mathrm{Xi}})]$

Wherein, L is the circuit number of electrical network, P _EventBe the cascading failure probability from critical circuit cluster, P _LiBe the probability of i bar line fault under the electrical network initial condition, P _{K (i)}Be the conditional probability that power overload takes place on the k bar circuit, X is the bar number from critical circuit, X _iFor after the circuit i fault from the bar number of critical circuit, P _XiThe expression fault occurs in the conditional probability from critical circuit cluster, P _{K (Xi)}The fault that expression causes makes the conditional probability that power overload takes place on the k bar circuit, and λ is from critical circuit cluster distributed constant.

4. a kind of power grid cascading failure analysis methods based on the circuit cluster according to claim 3 is characterized in that described from critical circuit cluster distributed constant λ=1.5.

5. a kind of power grid cascading failure analysis methods based on the circuit cluster according to claim 3 is characterized in that described calculating cascading failure risk indicator utilizes formula

R＝p _event·I _load

I _LoadBe cascading failure load loss severity index, its computing formula is

Wherein, N is an electric network fault quantity, P _Load(i) be the load capacity loss that the i time cascading failure causes, P _SBe power system capacity.

Images