CN109617123A

CN109617123A - The Reliability Sensitivity Method of wind fire system based on state space combination and cluster reduction

Info

Publication number: CN109617123A
Application number: CN201811631282.XA
Authority: CN
Inventors: 李生虎; 于新钰; 薛婧; 张�浩
Original assignee: Hefei University of Technology
Current assignee: Hefei University of Technology
Priority date: 2018-12-29
Filing date: 2018-12-29
Publication date: 2019-04-12
Anticipated expiration: 2038-12-29
Also published as: CN109617123B

Abstract

The invention discloses a kind of wind fire Reliability Sensitivity Analysis Method For Structural System based on state space combination and cluster reduction, step includes: 1 to establish N_WFThe state-space model of platform Wind turbines is simultaneously combined to obtain the state-space model of wind-powered electricity generation subsystem and carries out cluster reduction；2 establish N_FFThe state-space model of platform fired power generating unit is simultaneously combined to obtain the state-space model of thermoelectricity subsystem and carries out cluster reduction；3 combine the state-space model of the state-space model of wind-powered electricity generation subsystem and thermoelectricity subsystem to obtain the state-space model of wind fire system and carry out cluster reduction；4 calculate the sensitivity of wind fire Reliability Index and wind fire Reliability Index to Wind turbines failure rate.The present invention apparent can be fully described by wind fire system structure, to reduce the scale of wind fire system state space, and quantify influence of the Wind turbines failure rate to wind fire system reliability, and then provide reference frame for Wind turbines type selecting and maintenance.

Description

Reliability sensitivity analysis method of wind-fire system based on state space combination and cluster simplification

Technical Field

The invention relates to the field of safe operation analysis and planning of an electric power system, in particular to a wind-fire system reliability and sensitivity analysis method based on state space combination and cluster simplification.

Background

With the economic development, the scale of a power grid is continuously enlarged, new energy such as a wind power plant and the like is greatly connected to the power grid, the power load is continuously increased, the safe operation of a power system becomes more important, the reliability level and the sensitivity of each part of the power grid are evaluated, and the method has important significance for the analysis and planning of the safe operation of the power system.

Power system reliability refers to a measure of the ability of a power system to supply power and electrical energy to power consumers on an uninterrupted basis, at acceptable quality levels and in the required quantities. A multi-state time sequence random variable is modeled based on a Markov chain in a reliability analysis and calculation method for a power generation system with a wind power plant (China Motor engineering journal, 2017,37(16):4671-4679+4892) by congratulating a brocade boat, stretching a flame, increasing brightness and carrying out Suyun. Because the number of states of the wind fire system is too many, the existing multi-state model is processed approximately and is not accurate enough. The state spaces of a plurality of multi-state models are combined, Huayuting provides a method for combining transfer rate matrixes corresponding to the state spaces in 'a calculation method suitable for a transfer rate matrix of a combined state space model', and a method for combining active output corresponding to each state in the state spaces is not involved.

The sensitivity quantifies how much the parameter affects reliability. At present, the sensitivity of the reliability index of the wind power system to the fault rate of the wind turbine generator is limited by a reliability model of the wind power system, and further accuracy is needed.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a wind and fire system reliability sensitivity analysis method based on state space combination and clustering simplification so as to more clearly and completely describe the structure of the wind and fire system, thereby reducing the scale of the state space of the wind and fire system, quantifying the influence of the fault rate of a wind turbine generator on the reliability of the wind and fire system and further providing a reference basis for the type selection and the overhaul of the wind turbine generator.

The invention adopts the following technical scheme for solving the technical problems:

the invention relates to a reliability sensitivity analysis method of a wind-fire system based on state space combination and cluster simplification, wherein the wind-fire system comprises the following steps: a wind power subsystem and a fire power subsystem; the wind power subsystem comprises N_WFThe serial numbers of any wind turbine generator set are marked as i, i is 1, … and N_WF(ii) a The thermal power subsystem comprises N_FFAnd marking the number of any thermal power generating unit as o, o as 1, …, N_FF(ii) a The method is characterized by comprising the following steps:

step S1: establishing N_WFCombining the state space models of the typhoon generator sets to obtain the state space models of the wind power subsystems, and clustering and simplifying the state space models;

step S2: establishing N_FFCombining the state space models of the thermal power generating units to obtain the state space model of the thermal power subsystem, and performing clustering simplification;

step S3: combining the state space model of the wind power subsystem and the state space model of the thermal power subsystem to obtain a state space model of the wind power system and performing clustering simplification;

step S4: and calculating the reliability index of the wind-fire system and the sensitivity of the reliability index of the wind-fire system to the fault rate of the wind turbine generator.

The reliability sensitivity analysis method of the present invention is also characterized in that,

the step S1 is performed as follows:

step S1.1: obtaining a transfer rate matrix, active power output and state probability corresponding to a state space model of the ith wind generation set:

step S1.1.1: recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering random faults as A_W.i.faultAnd is andwherein, mu_W.iIndicates the repair rate, lambda, of the ith wind turbine generator system_W.iRepresenting the fault rate of the ith wind turbine generator set;

step S1.1.2: considering the windThe total number of states contained in the state space model of the ith wind generating set with speed change is N_vsWherein any one state number is q_vs，q_vs＝1,2,...,N_vs；

Step S1.1.3: recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering the change of the wind speed as A_W.i.vsAnd is and is the b th transfer rate matrix corresponding to the state space model of the ith wind generating set in consideration of the change of the wind speed_vsLine c_vsColumn element, 1. ltoreq. b_vs,c_vs≤N_vs；

Step S1.1.4: recording active power output corresponding to the state space model of the ith wind turbine generator set considering the change of the wind speed as P_W.i.vsAnd is andwherein,q-th state space model of ith wind turbine generator set considering wind speed change_vsActive power output corresponding to each state;

step S1.1.5: combining the state space model of the ith wind turbine generator set considering the random fault and the state space model of the ith wind turbine generator set considering the wind speed change to obtain the state space model of the ith wind turbine generator set considering the random fault and the wind speed change, and marking as the state space model of the ith wind turbine generator set, wherein the state space model of the ith wind turbine generator set is 2. N in total_vsA state, wherein any one state is numbered q_W.i，q_W.i＝1,2,...,2·N_vs；

Step S1.1.6: ith wind power to consider random faultsAnd recording a transfer rate matrix obtained by combining a transfer rate matrix corresponding to the state space model of the unit and a transfer rate matrix corresponding to the state space model of the ith wind power generation unit considering the change of the wind speed as C_W.iAnd is andwherein, I_2×2Is a second order unit matrix; recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator system as A_W.iMixing C with_W.iAll diagonal elements of (A) are set as the opposite numbers of the sum of all elements except the diagonal elements of the corresponding row, and A is obtained_W.i；

Step S1.1.7: obtaining the qth state space model of the ith wind turbine generator set by using the formula (1)_W.iProbability of state corresponding to each stateThereby the state probability corresponding to the state space model of the ith wind turbine generator set is recorded as

Step S1.1.8: recording the active power output corresponding to the state space model of the ith wind turbine generator as P_W.iAnd is and

step S1.2: equivalent simplification of the state space model of the ith wind turbine generator set:

step S1.2.1: equivalently simplifying the state space model of the ith wind turbine generator set to obtain an equivalently simplified state space model of the ith wind turbine generator set, wherein the equivalently simplified state space model of the ith wind turbine generator set is N in total_WS＝N_vs+1 states, wherein any state is numbered q'_W.i，q′_W.i＝1,2,...,N_WS；

Step S1.2.2: recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set after equivalence simplification as A'_W.iAnd is and is the b-th transfer rate matrix corresponding to the state space model of the ith wind turbine generator set after equivalent simplification_WSLine c_WSElement of column, 1. ltoreq. b_WS,c_WS≤N_WS；

Step S1.2.3: obtaining a transfer rate matrix A 'corresponding to the state space model of the ith wind turbine generator set after equivalent simplification by using the formula (2)'_W.iThereby obtaining N_WFN corresponding to state space model of typhoon generator set_WFTransfer rate matrix

In the formula (2), the reaction mixture is,representing the corresponding relation matrix before and after equivalence, and the corresponding relation matrixIs to 2. N_vsOrder unit matrixIs accumulated to the last row, and then the other even rows except the last row are deletedObtaining;

step S1.2.4: recording the active power output corresponding to the state space model of the ith wind turbine generator set after equivalence simplification as the active power output corresponding to the state space model of the ith wind turbine generator setWherein,

step S1.3: n is a radical of_WFCombining state space models of the typhoon generator set:

step S1.3.1: n is a radical of_WFCombining the state space models of the typhoon generator set to obtain a state space model of the wind power subsystem, wherein the total number of states contained in the state space model of the wind power subsystem isq_wNumbering any state in the state space model of the wind power subsystem, andinitializing i to 1;

step S1.3.2: a transfer rate matrix A 'corresponding to the state space model of the ith wind turbine generator set by formula (3)'_W.iA transfer rate matrix A 'corresponding to the state space model of the (i + 1) th wind turbine generator set'_W.i+1Combining to obtain a combined transfer rate matrix C_W.i,i+1：

In expression (3), α represents a transition rate matrix A 'corresponding to the state space model of the ith wind turbine generator'_W.iThe order of (a); i is_α×αα -order unit matrix, β is a transfer rate matrix A 'corresponding to the state space model of the (i + 1) th wind turbine generator set'_W.i+1The order of (a);

step S1.3.3: combining the transfer rate matrix C_W.i,i+1Assigning to the i +1 th transfer rate matrix A'_W.i+1(ii) a Assigning the value of i +1 to i; judging that i is greater than or equal to N_WFWhether the N is true or not, if so, the N is finished_WFA combination of transfer rate matrices, C_W.i-1,iAll diagonal elements of the state space model are set as the opposite numbers of the sum of all elements except the diagonal elements of the corresponding row, and the transfer rate matrix A corresponding to the state space model of the wind power subsystem is obtained_W(ii) a Otherwise, returning to the step S1.3.2;

step S1.3.4: obtaining the qth in the state space model of the wind power subsystem by using the formula (4)_wProbability of state corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the wind power subsystem

Step S1.3.5: will N_WFAssigning a value to i, and q_W-1 to q_W；

Step S1.3.6: obtaining the state of the ith wind turbine generator set by using the formula (5)

In formula (5), f (-) is an integer function;

step S1.3.7: enabling the qth in a state space model of the wind power subsystem to be_WThe active output of the ith wind turbine generator set in the individual state is

Step S1.3.8: assign i-1 to i, willIs assigned to q_W(ii) a If i is less than 1, go to step S1.3.9; otherwise, returning to the step S1.3.6;

step S1.3.9: obtaining the qth in the state space model of the wind power subsystem by using the formula (6)_WThe active output corresponding to each state isThereby obtaining the active power output corresponding to the state space model of the wind power subsystem

Step S1.4: and (3) simplifying clustering of a state space model of the wind power subsystem:

step S1.4.1: modeling the state space of the wind power subsystemEach state is arbitrarily divided into K_WClass, K_WThe total number of states contained in the state space model of the wind power subsystem after the clustering simplification; k is a radical of_WNumbering any one state of the state space model of the clustered simplified wind electronic system, and k_W＝1,2,...,K_WCounting the number of states in each class and assigning toInitialization k is 1,

Step S1.4.2: obtaining kth by the formula (7)_WClass center

In the formula (7), s_WRepresents any one state in each class, and

step S1.4.3: step S1.4.2 is repeated, thereby obtaining K_WClass center:

step S1.4.4: obtaining the qth in the state space model of the wind power subsystem by using the formula (8)_WActive output corresponding to each stateAnd k is_WClass centerIs a distance of

Step S1.4.5: repeating the step S1.4.4 to obtainA state and K_WDistance of class centerAnd a distanceIn which comprisesSubsets of the q-th in a state space model of the wind power subsystem_WEach state corresponds to the qth_WA subset of

Step S1.4.6: obtaining the total error of classification by using the formula (9)

Step S1.4.7: select the qth_WEach state is respectively equal to K_WMinimum of distance of class center, and q-th_WDividing each state into a class corresponding to the minimum value; thereby will beThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

Step S1.4.8: if it isIf true, go to step S1.4.9; otherwise, assigning k +1 to k, and returning to the step S1.4.2 for execution;

step S1.4.9: obtaining the kth state space model of the wind power subsystem after cluster simplification by using the formula (10)_WActive power output corresponding to each stateObtaining the active output corresponding to the state space model of the wind power subsystem after the clustering simplification

Step S1.4.10: recording a transfer rate matrix corresponding to the state space model of the wind power subsystem after cluster simplification as A'_W(ii) a And is Is the b th transfer rate matrix corresponding to the state space model of the wind power subsystem after cluster simplification_WLine c_WElement of column, 1. ltoreq. b_W,c_W≤K_W；

Step S1.4.11: obtaining a transfer rate matrix A 'corresponding to the state space model of the wind power subsystem after the clustering simplification by using the formula (11)'_W：

In the formula (11), the reaction mixture is,representing a corresponding relation matrix before and after cluster simplification; correspondence matrixIs obtained by judging row by row and column by column if the q th_WAfter clustering, put into the kth_WClass, then order the kth_WLine q_WThe elements of the column are 1, otherwise 0;

step S1.4.12: obtaining the kth in the state space model of the wind power subsystem after the clustering simplification by using the formula (13)_WState probability corresponding to each stateThereby obtaining the steady state probability corresponding to the state space model of the wind power subsystem after the clustering simplification

The step S2 is performed as follows:

step S2.1: obtaining a transfer rate matrix, active power output and a state probability corresponding to a state space model of the No. o thermal power generating unit:

step S2.1.1: recording a transfer rate matrix corresponding to the state space model of the o-th thermal power generating unit as A_F.oAnd is andwherein, mu_F.oIndicates the repair rate, lambda, of the o-th thermal power generating unit_F.oRepresenting the fault rate of the No. o thermal power generating unit; thereby obtaining N_FFN corresponding to state space model of thermal power generating unit_FFTransfer rate matrix

Step S2.1.2: and respectively recording active outputs corresponding to 2 states in the state space model of the o-th thermal power generating unit AS AS_F.o.1And AS_F.o.2And the active output corresponding to the state space model of the No. o thermal power generating unit is recorded as P_F.oAnd is and

step S2.1.3: obtaining state probabilities EP corresponding to two states in state space model of the o-th thermal power generating unit by using formula (14)_F.o.1And EP_F.o.2Thereby obtaining the state probability p corresponding to the state space model of the o-th thermal power generating unit_F.o＝[EP_F.o.1EP_F.o.2]：

Step S2.2: will N_FFCombining state space models of the thermal power generating units:

step S2.2.1: will N_FFCombining the state space models of the thermal power generating units to obtain a state space model of the thermal power subsystem, wherein the total number of states contained in the state space model of the thermal power subsystem isq_FNumbering any state in a state space model of the thermal power subsystem, andinitializing o to be 1;

step S2.2.2: utilizing an equation (15) to obtain a transfer rate matrix A corresponding to the state space model of the o-th thermal power generating unit_F.oAnd the transfer corresponding to the state space model of the (o + 1) th thermal power generating unitRate matrix A_F.o+1Combining to obtain a combined transfer rate matrix C_F.o,o+1：

In the formula (14), α represents a transfer rate matrix a corresponding to the state space model of the o-th thermal power generating unit_F.oβ is a transfer rate matrix A corresponding to the state space model of the (o + 1) th thermal power generating unit_F.o+1The order of (a);

step S2.2.3: combining the transfer rate matrix C_F.o,o+1Assigning to the (o + 1) th transfer rate matrix A_F.o+1(ii) a Then assigning the value of o +1 to o; judging o is more than or equal to N_FFWhether the N is true or not, if so, the N is finished_FFA combination of transfer rate matrices, a transfer rate matrix C_F.o-1,oAll diagonal elements are set as the inverse number of the sum of all elements except the diagonal elements in the corresponding row, and a transfer rate matrix A corresponding to the state space model of the thermal power subsystem is obtained_F(ii) a Otherwise, return to step S2.2.2;

step S2.2.4: obtaining the qth in a state space model of the thermal power subsystem by using the formula (16)_FProbability of state corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the thermal power subsystem

Step S2.2.5: will N_FFAssigning q to o, and_F-1 to q_F；

Step S2.2.6: obtaining the state of the o-th thermal power generating unit by using the formula (17)

In the formula (16), f (-) is an integer function;

step S2.2.7: enabling the qth in a state space model of the thermal power subsystem to be_FThe active power output of the o-th thermal power generating unit in the state is

Step S2.2.8: assign o-1 to o, willIs assigned to q_F(ii) a If o < 1, go to step S2.2.9; otherwise, return to step S2.2.6;

step S2.2.9: obtaining the qth in a state space model of the thermal power subsystem by using the formula (18)_FThe active output corresponding to each state isThereby obtaining the active power output corresponding to the state space model of the thermal power subsystem

Step S2.3: and (3) simplifying clustering of a state space model of the thermal power subsystem:

step S2.3.1: will be describedOf state-space models of thermal power sub-systemsEach state is arbitrarily divided into K_FClass, K_WThe total number of states contained in the state space model of the wind power subsystem after the clustering simplification; k is a radical of_WNumbering any state of the state space model of the wind power subsystem after the clustering simplification, and k_W＝1,2,...,K_WCounting the number of states in each class and assigning toThe initialization k is 1 and the initialization k is,

step S2.3.2: obtaining kth by the formula (18)_FClass center

In the formula (18), s_FRepresents any one state in each class, and

step S2.3.3: step S2.3.2 is repeated, thereby obtaining K_FClass center

Step S2.3.4: obtaining the qth in a state space model of the thermal power subsystem by using the formula (19)_FActive output corresponding to each stateAnd k is_FClass centerIs a distance of

Step S2.3.5: repeating the step S2.3.4 to obtainA state and K_FDistance of class centerAnd a distanceIn which comprisesA subset of q-th elements of a state space model of the thermal power sub-system_FEach state corresponds to the qth_FA subset of

Step S2.3.6: the total error of classification is obtained by using the formula (20)

Step S2.3.7: select the qth_FEach state is respectively equal to K_FMinimum of distance of class center, and q-th_FA stateClassifying into the class corresponding to the minimum value; thereby will beThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

Step S2.3.8: if it isIf true, go to step S2.3.9; otherwise, assigning k +1 to k, and returning to the step S2.3.2 for execution;

step S2.3.9: obtaining the kth state space model of the thermal power subsystem after cluster simplification by using the formula (21)_FActive power output corresponding to each stateObtaining the active output corresponding to the state space model of the thermal power subsystem after the clustering simplification

Step S2.3.10: recording a transfer rate matrix corresponding to the state space model of the thermal power subsystem after cluster simplification as A'_F(ii) a And is Is the b th transfer rate matrix corresponding to the state space model of the thermal power subsystem after cluster simplification_FLine c_FElement of column, 1. ltoreq. b_F,c_F≤K_F；

Step S2.3.11: obtaining a transfer rate matrix A 'corresponding to the state space model of the thermal power subsystem after the cluster simplification by using a formula (22)'_F：

In the formula (22), the reaction mixture is,representing a corresponding relation matrix before and after cluster simplification; correspondence matrixIs obtained by judging row by row and column by column, if the q th_FAfter clustering, put into the kth_FClass, then order the kth_FLine q_FThe column element is 1, otherwise 0;

step S2.3.12: obtaining the kth in the state space model of the thermal power subsystem after the clustering simplification by using the formula (23)_FState probability corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the thermal power subsystem after the clustering simplification

The step S3 is performed as follows:

step S3.1: combining the state space model of the wind power subsystem and the state space model of the thermal power subsystem:

step S3.1.1: combining the state space model of the wind power subsystem and the state space model of the thermal power subsystem to obtain the state space model of the wind power system, wherein the state space model of the wind power system has K_W·K_FA state, wherein any one state is numbered q_GAnd q is_G＝1,2,...,K_W·K_F；

Step S3.1.2: converting rate matrix A 'corresponding to state space model of wind power subsystem'_WA transfer rate matrix A corresponding to the state space model of the thermal power subsystem_F' the transfer rate matrix obtained by combining is recorded as C_W,FAnd is andwherein,is K_WAn order identity matrix; recording a transfer rate matrix corresponding to a state space model of the wind-fire system as A_GThe transfer rate matrix is denoted A_GIs to mix C_W,FAll diagonal elements of the corresponding row are obtained by setting the sum of all elements except the diagonal elements as the inverse number of the sum of all elements of the corresponding row;

step S3.1.3: obtaining the qth in the state space model of the wind-fire system by using the formula (24)_GState probability corresponding to each stateThereby obtaining the state probability corresponding to the state space model of the wind-fire system

Step S3.1.4: q is to be_G-1 to q_G；

Step S3.1.5: the state of the thermal power subsystem is obtained by using a formula (25)

In the formula (25), f (·) is an integer function;

step S3.1.6: enabling the qth in a state space model of the wind-fire system_GThe active power output of the thermal power subsystem in each state is

Step S3.1.7: the state of the wind power subsystem is obtained by using the formula (26)

Step S3.1.8: enabling the qth in a state space model of the wind-fire system_GThe active power of the wind power system in one state is

Step S3.1.9: obtaining the qth of a state space model of the wind fire system by using an equation (29)_GThe active power corresponding to each state isThereby obtaining the active power output corresponding to the state space model of the wind-fire system

Step S3.2: and (3) simplifying clustering of a state space model of the wind-fire system:

step S3.2.1: k of state space model of wind power subsystem_W·K_FEach state is arbitrarily divided into K_GClass, K_GThe total number of states contained in the state space model of the clustered simplified wind-fire system; k is a radical of_GNumbering any one state of the state space model of the clustered simplified wind-fire system, and k_G＝1,2,...,K_G(ii) a Counting the number of states in each class and assigning toThe initialization k is 1 and the initialization k is,

step S3.2.2: obtaining kth by equation (30)_GClass center

In the formula (30), s_GRepresents any one state in each class, and

step S3.2.3: step S3.2.2 is repeated, thereby obtaining K_GClass center:

step S3.2.4: obtaining the qth in the state space model of the wind fire system by using the formula (31)_GActive power output corresponding to each stateAnd k is_GClass centerIs a distance of

Step S3.2.5: step S3.2.4 is repeated, thereby obtaining K_W·K_FA state and K_GDistance of class centerAnd a distanceIn which contains K_W·K_FSubset of status space model of wind-fire system_GEach state corresponds to the qth_GA subset of

Step S3.2.6: the total error of classification is obtained by equation (32)

Step S3.2.7: select the qth_GEach state is respectively equal to K_GMinimum of distance of class center, and q-th_GThe states are classified into the class corresponding to the minimum value; thereby will K_W·K_FThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

Step S3.2.8: if it isIf true, go to step S3.2.9; otherwise, assigning k +1 to k, and returning to the step S3.2.2 for execution;

step S3.2.9: obtaining the kth state space model of the wind fire system after the cluster simplification by using the formula (33)_GActive power output corresponding to each stateThus obtaining the active output corresponding to the state space model of the clustered and simplified wind-fire system

Step S3.2.10: recording a transfer rate matrix corresponding to the state space model of the wind-fire system after cluster simplification as A'_G(ii) a And is Is the b th transfer rate matrix corresponding to the state space model of the wind fire system after cluster simplification_GLine c_GElement of column, 1. ltoreq. b_G,c_G≤K_G；

Step S3.2.11: obtaining a transfer rate matrix A 'corresponding to the state space model of the wind-fire system after the cluster simplification by using the formula (34)'_G：

In the formula (34), the reaction mixture is,representing a corresponding relation matrix before and after cluster simplification; correspondence matrixIs obtained by judging row by row and column by column if the q th_GAfter clustering, put into the kth_GClass, then order the kth_GLine q_GThe elements of the column are 1, otherwise 0;

step S3.2.12: obtaining the kth in the state space model of the clustered and simplified wind-fire system by using the formula (35)_GState probability corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the clustered and simplified wind-fire system

The step S4 is performed as follows:

step S4.1: calculating the reliability index of the wind fire system:

step S4.1.1: the state space model of the load comprises N_LSIn one of the states, the state of the mobile terminal,the state number is q_LAnd q is_L＝1,2,...,N_LSQ is the number q_LThe active power corresponding to each state is recorded asThe active power output corresponding to the state space model of the load is recorded as P_LAnd is and

step S4.1.2: let q be_LThe state probability corresponding to each state is recorded asThe state probability corresponding to the state space model of the load is recorded as p_LAnd is and

step S4.1.3: the reliability calculation of the wind fire system comprises K_G·N_LSIn each case, the number of the case is q_SAnd q is_L＝1,2,...,N_LS(ii) a Recording the load loss probability of the wind fire system as LOLP; the expected shortage of the wind and fire system is recorded as ENDS; the q th_SThe system state corresponding to the situation is recorded as I_f(q_S) (ii) a The q th_SThe load reduction corresponding to the situation is recorded as L_C(q_S) (ii) a The q th_SThe probability corresponding to each case is denoted as p (q)_S) (ii) a Initializing q_G＝1，q_L＝1，q_S＝1，LOLP＝0， ENDS＝0；

Step S4.1.4: if it isThen order I_f(q_S) Is 1, willIs assigned to L_C(q_S) (ii) a Otherwise order I_f(q_S) Is 0, let L_C(q_S) Is 0;

step S4.1.5: to EP_G.qG·EP_L.qLIs given to p (q)_S) (ii) a LOLP + I_f(q_S)·p(q_S) Assigning an LOLP; will ENDS + I_f(q_S)·p(q_S)·L_C(q_S) Assigning to ENDS; q is to be_L+1 to q_L(ii) a Q is to be_S+1 to q_S；

Step S4.1.6: if q is_L＞N_LSThen q is_G+1 to q_GLet q stand for_LIs 1; otherwise, q_GAnd q is_LKeeping the same;

step S4.1.7: if q is_S＞K_G·N_LSIf yes, executing step S4.2; otherwise, return to step S4.1.4;

step S4.2: calculating the sensitivity of the reliability index of the wind fire system to the fault rate of the wind turbine generator:

step S4.2.1: recording the failure rate of the wind turbine generator as z, and obtaining the sensitivity of the load loss probability of the wind fire system to the failure rate of the wind turbine generator by using a formula (36)

Step S4.2.2: sensitivity of wind turbine generator failure rate to power shortage expectation of wind-fire system obtained by equation (37)

Compared with the prior art, the invention has the beneficial effects that:

1. the invention provides a method for combining the active power output corresponding to each state in the state space during the combination of the state spaces, and solves the problem of calculating the active power output of the state spaces.

2. By adopting a clustering algorithm, the state space is simplified, and the problem that the number of states of the wind-fire system is too large and difficult to calculate is solved under the condition of ensuring certain accuracy; the clustering algorithm can obtain a state combination corresponding relation matrix, so that the transfer rate matrix corresponding to the simplified state space can be conveniently obtained from the transfer rate matrix corresponding to the state space before simplification, and the complicated and complicated equivalent calculation of one-by-one manual searching and accumulation calculation is avoided.

3. According to the method, the state space model of the wind-fire system is obtained through state space combination and clustering simplification, the complex conditions of random transfer and multi-state operation of the system state along with element faults or repair can be described more comprehensively, certain accuracy is guaranteed, reliability index and sensitivity calculation are carried out on the basis, the problem of accuracy of reliability and sensitivity analysis is solved, and therefore a more accurate reference basis is provided for safe operation of a power system, and a basis is provided for reasonably selecting the model of a wind turbine generator and reasonably arranging, repairing and repairing.

Drawings

FIG. 1 is a block diagram of a wind fire system of the present invention;

FIG. 2 is a flow chart of the present invention;

FIG. 3 is a flow chart of the state combination of the present invention;

FIG. 4 is a simplified flow chart of clustering in accordance with the present invention;

FIG. 5 shows N according to the present invention_WFA state space combination diagram of the typhoon generator set;

FIG. 6 is a simplified state space diagram of clustering for a wind power subsystem according to the present invention.

Detailed Description

The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.

The invention relates to a wind-fire system reliability sensitivity analysis method based on state space combination and cluster simplification, wherein the wind-fire system comprises the following steps: a wind power subsystem and a fire power subsystem; the wind power subsystem comprises N_WFThe serial numbers of any wind turbine generator set are marked as i, i is 1, … and N_WF(ii) a The thermal power subsystem comprises N_FFAnd marking the number of any thermal power generating unit as o, o as 1, …, N_FF(ii) a The structure diagram of the wind fire system is shown in figure 1;

the flow chart of the invention, as shown in FIG. 2; a state combination flow chart, as shown in FIG. 3; a clustering simplified flow chart, as shown in fig. 4; the method for analyzing the reliability and sensitivity of the wind fire system based on state space combination and cluster simplification is carried out according to the following steps:

step S1.1.2: the total number of states contained in the state space model of the ith wind generating set considering the change of the wind speed is N_vsWherein any one state number is q_vs，q_vs＝1,2,...,N_vs；

Step S1.1.6: recording a transfer rate matrix obtained by combining a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering the random faults and a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering the wind speed changes as C_W.iAnd is andwherein, I_2×2Is a second order unit matrix; recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator system as A_W.iMixing C with_W.iAll diagonal elements of (A) are set as the opposite numbers of the sum of all elements except the diagonal elements of the corresponding row, and A is obtained_W.i；

In the formula (2), the reaction mixture is,representing the corresponding relation matrix before and after equivalence, and the corresponding relation matrixIs to 2. N_vsOrder unit matrixAccumulating the even lines to the last line, and then deleting other even lines except the last line to obtain the final product;

N_WFthe state space combination diagram of the typhoon generator set is shown in figure 5;

Step S1.3.5: will N_WFAssigning a value to i, and q_W-1 to q_W；

In formula (5), f (-) is an integer function;

step S1.3.7: enabling the qth in a state space model of the wind power subsystem to be_WStation i under the stateThe active output of the wind turbine is

a clustering simplified state space diagram of the wind power subsystem is shown in FIG. 6;

Step S1.4.2: obtaining kth by the formula (7)_WClass center

In the formula (7), s_WRepresents any one state in each class, and

step S1.4.3: step S1.4.2 is repeated, thereby obtaining K_WClass center:

step S2.2.2: utilizing an equation (15) to obtain a transfer rate matrix A corresponding to the state space model of the o-th thermal power generating unit_F.oA transfer rate matrix A corresponding to the state space model of the (o + 1) th thermal power generating unit_F.o+1Combining to obtain a combined transfer rate matrix C_F.o,o+1：

Step S2.2.5: will N_FFAssigning q to o, and_F-1 to q_F；

In the formula (16), f (-) is an integer function;

step S2.3.1: modeling a state space of the thermal power subsystemEach state is arbitrarily divided into K_FClass, K_WThe total number of states contained in the state space model of the wind power subsystem after the clustering simplification; k is a radical of_WNumbering any state of the state space model of the wind power subsystem after the clustering simplification, and k_W＝1,2,...,K_WCounting the number of states in each class and assigning toThe initialization k is 1 and the initialization k is,

step S2.3.2: obtaining kth by the formula (18)_FClass center

In the formula (18), s_FRepresents any one state in each class, and

step S2.3.3: step S2.3.2 is repeated, thereby obtaining K_FClass center

Step S2.3.7: select the qth_FEach state is respectively equal to K_FMinimum of distance of class center, and q-th_FThe states are classified into the class corresponding to the minimum value; thereby will beThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

Step S2.3.10: recording a transfer rate matrix corresponding to the state space model of the thermal power subsystem after clustering simplification as A_F'; and is Is the b th transfer rate matrix corresponding to the state space model of the thermal power subsystem after cluster simplification_FLine c_FElement of column, 1. ltoreq. b_F,c_F≤K_F；

step S3.1.1: combining the state space model of the wind power subsystem and the state space model of the thermal power subsystem to obtain the state space model of the wind power system, wherein the state space models of the wind power system and the thermal power system are combinedWith K_W·K_FA state, wherein any one state is numbered q_GAnd q is_G＝1,2,...,K_W·K_F；

Step S3.1.2: converting rate matrix A 'corresponding to state space model of wind power subsystem'_WAnd a transfer rate matrix A 'corresponding to a state space model of the thermal power subsystem'_FThe transfer rate matrix obtained by combination is marked as C_W,FAnd is andwherein,is K_WAn order identity matrix; recording a transfer rate matrix corresponding to a state space model of the wind-fire system as A_GThe transfer rate matrix is denoted A_GIs to mix C_W,FAll diagonal elements of the corresponding row are set as the opposite numbers of the sum of all elements except the diagonal elements;

Step S3.1.4: q is to be_G-1 to q_G；

In the formula (25), f (·) is an integer function;

step S3.2.2: obtaining kth by equation (30)_GClass center

In the formula (30), s_GRepresents any one state in each class, and

step S3.2.3: step S3.2.2 is repeated, thereby obtaining K_GClass center:

Step S3.2.6: the total error of classification is obtained by equation (32)

Step S3.2.7: select the qth_GEach state is respectively equal to K_GMinimum of distance of class center, and q-th_GThe states are classified into the class corresponding to the minimum value; thereby will K_W·K_FThe state is drawn into the corresponding minimum valueCorresponding classes are counted, and the number of states in each class is assigned to

5. The wind-fire system reliability sensitivity analysis method based on state space combination and cluster simplification according to claim 1, characterized in that: the step S4 is performed as follows:

step S4.1: calculating the reliability index of the wind fire system:

step S4.1.1: the state space model of the load comprises N_LSA state with state number q_LAnd q is_L＝1,2,...,N_LSQ is the number q_LThe active power corresponding to each state is recorded asThe active power output corresponding to the state space model of the load is recorded as P_LAnd is and

step S4.1.5: will be provided withIs given to p (q)_S) (ii) a LOLP + I_f(q_S)·p(q_S) Assigning an LOLP; will ENDS + I_f(q_S)·p(q_S)·L_C(q_S) Assigning to ENDS; q is to be_L+1 to q_L(ii) a Q is to be_S+1 to q_S；

Claims

1. A reliability sensitivity analysis method of a wind fire system based on state space combination and cluster simplification is disclosed, wherein the wind fire system comprises: a wind power subsystem and a fire power subsystem; the wind power subsystem comprises N_WFThe serial numbers of any wind turbine generator set are marked as i, i is 1, … and N_WF(ii) a The thermal power subsystem comprises N_FFAnd marking the number of any thermal power generating unit as o, o as 1, …, N_FF(ii) a The reliability and sensitivity analysis method is characterized by comprising the following steps of:

step S1: establishing N_WFCombining the state space models of the typhoon generator sets to obtain a state space model of the wind power subsystem, and clustering and simplifying the state space model;

step S2: establishing N_FFCombining the state space models of the thermal power generating units to obtain a state space model of the thermal power subsystem, and performing clustering simplification;

2. The reliability sensitivity analysis method according to claim 1, wherein the step S1 is performed as follows:

step S1.1.5: combining the state space model of the ith wind turbine generator set considering the random fault and the state space model of the ith wind turbine generator set considering the wind speed change to obtain the state space model of the ith wind turbine generator set considering the random fault and the wind speed change, and marking the state space model as the state space model of the ith wind turbine generator set, wherein the state space model of the ith wind turbine generator set is 2 & N in total_vsA state, wherein any one state is numbered q_W.i，q_W.i＝1,2,...,2·N_vs；

Step S1.1.6: recording a transfer rate matrix obtained by combining a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering the random faults and a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set considering the wind speed changes as C_W.iAnd is andwherein, I_2×2Is a second order identity matrix; recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator system as A_W.iMixing C with_W.iIs set as the corresponding row dividing pairThe sum of all elements except the angle line element is the opposite number to obtain A_W.i；

Step S1.1.7: obtaining the qth state space model of the ith wind turbine generator set by using the formula (1)_W.iState probability corresponding to each stateThereby the state probability corresponding to the state space model of the ith wind turbine generator set is recorded as

Step S1.2.2: recording a transfer rate matrix corresponding to the state space model of the ith wind turbine generator set after equivalence simplification as A'_W.iAnd is and is an equivalence simplificationThe b th in the transfer rate matrix corresponding to the state space model of the ith wind turbine generator set_WSLine c_WSElement of column, 1. ltoreq. b_WS,c_WS≤N_WS；

step S1.3.1：N_WFCombining the state space models of the typhoon generator set to obtain a state space model of the wind power subsystem, wherein the total number of states contained in the state space model of the wind power subsystem isq_wNumbering any state in a state space model of the wind power subsystem, andinitializing i to 1;

step S1.3.4: obtaining the qth in the state space model of the wind power subsystem by using the formula (4)_wA state pairProbability of corresponding stateThereby obtaining the steady-state probability corresponding to the state space model of the wind power subsystem

Step S1.3.5: will N_WFAssigning a value to i, and q_W-1 to q_W；

In formula (5), f (-) is an integer function;

step S1.3.7: enabling the qth in a state space model of the wind power subsystem to be_WThe active power of the ith wind turbine generator set in each state is

step S1.3.9: obtaining the qth in the state space model of the wind power subsystem by using the formula (6)_WThe active power corresponding to each state isThereby obtaining the active power output corresponding to the state space model of the wind power subsystem

step S1.4.1: modeling the state space of the wind power subsystemEach state is arbitrarily divided into K_WClass, K_WThe total number of states contained in the state space model of the wind power subsystem after the clustering simplification; k is a radical of_WNumbering any state of the state space model of the wind power subsystem after the clustering simplification, and k_W＝1,2,...,K_WCounting the number of states in each class and assigning toInitialization k is 1,

Step S1.4.2: obtaining kth by the formula (7)_WClass center

In the formula (7), s_WRepresents any one state in each class, and

step S1.4.3: step S1.4.2 is repeated, thereby obtaining K_WClass center:

step S1.4.4: obtaining the qth in the state space model of the wind power subsystem by using the formula (8)_WActive power output corresponding to each stateAnd k is_WClass centerIs a distance of

step S1.4.9: obtaining the kth state space model of the wind power subsystem after cluster simplification by using the formula (10)_WActive power output corresponding to each stateObtaining the active power output corresponding to the state space model of the wind power subsystem after the clustering simplification

step S1.4.12: obtaining the kth in the state space model of the wind power subsystem after the clustering simplification by using the formula (13)_WState probability corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the wind power subsystem after the clustering simplification

3. The wind-fire system reliability sensitivity analysis method based on state space combination and cluster simplification according to claim 1, characterized in that: the step S2 is performed as follows:

step S2.1: obtaining a transfer rate matrix, active power output and state probability corresponding to a state space model of the No. o thermal power generating unit:

step S2.1.3: obtaining state probabilities EP corresponding to two states in state space model of the o-th thermal power generating unit by using formula (14)_F.o.1And EP_F.o.2To obtain the o-th thermal power generatorState probabilities p corresponding to the state space models of the group_F.o＝[EP_F.o.1EP_F.o.2]：

step S2.2.1: will N_FFCombining state space models of the thermal power generating unit to obtain a state space model of the thermal power subsystem, wherein the total number of states contained in the state space model of the thermal power subsystem isq_FNumbering any state in a state space model of the thermal power subsystem, andinitializing o to be 1;

step S2.2.3: combining the transfer rate matrix C_F.o,o+1Assigning to the (o + 1) th transfer rate matrix A_F.o+1(ii) a Then assigning the value of o +1 to o; judging o is more than or equal to N_FFWhether the N is true or not, if so, the N is finished_FFTransfer rate matrixA transfer rate matrix C_F.o-1,oAll diagonal elements are set as the opposite numbers of the sum of all elements except the diagonal elements in the corresponding row, and a transfer rate matrix A corresponding to the state space model of the thermal power subsystem is obtained_F(ii) a Otherwise, return to step S2.2.2;

step S2.2.4: obtaining the qth in a state space model of the thermal power subsystem by using the formula (16)_FState probability corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the thermal power subsystem

Step S2.2.5: will N_FFAssigning q to o, and_F-1 to q_F；

In the formula (16), f (-) is an integer function;

step S2.2.9: obtaining the qth in a state space model of the thermal power subsystem by using the formula (18)_FThe active power corresponding to each state isThereby obtaining the active power output corresponding to the state space model of the thermal power subsystem

step S2.3.2: obtaining kth by the formula (18)_FClass center

In the formula (18), s_FRepresents any one state in each class, and

step S2.3.3: step S2.3.2 is repeated, thereby obtaining K_FClass center

Step S2.3.4: obtaining the qth in a state space model of the thermal power subsystem by using the formula (19)_FActive power output corresponding to each stateAnd k is_FClass centerIs a distance of

Step S2.3.7: select the qth_FEach state is respectively equal to K_FMinimum of distance of class center, and q-th_FDividing each state into a class corresponding to the minimum value; thereby will beThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

Step S2.3.11: obtaining a transfer rate matrix A corresponding to the state space model of the thermal power subsystem after the clustering simplification by using the formula (22)_F′：

In the formula (22), the reaction mixture is,representing a corresponding relation matrix before and after cluster simplification; correspondence matrixIs obtained by judging row by row and column by column if the q th_FAfter clustering, put into the kth_FClass, then order the kth_FLine q_FThe column element is 1, otherwise0；

4. The wind-fire system reliability sensitivity analysis method based on state space combination and cluster simplification according to claim 1, characterized in that: the step S3 is performed as follows:

Step S3.1.2: converting rate matrix A 'corresponding to state space model of wind power subsystem'_WA transfer rate matrix A corresponding to the state space model of the thermal power subsystem_F' the transfer rate matrix obtained by combining is recorded as C_W,FAnd is andwherein,is K_WAn order identity matrix; recording a transfer rate matrix corresponding to a state space model of the wind-fire system as A_GThe transfer rate matrix is denoted A_GIs to mix C_W,FAll diagonal elements of the corresponding row are set as the opposite numbers of the sum of all elements except the diagonal elements;

Step S3.1.4: q is to be_G-1 to q_G；

In the formula (25), f (·) is an integer function;

step S3.2.2: obtaining kth by equation (30)_GClass center

In the formula (30), s_GRepresents any one state in each class, and

step S3.2.3: step S3.2.2 is repeated, thereby obtaining K_GClass center:

Step S3.2.5: step S3.2.4 is repeated, thereby obtaining K_W·K_FA state and K_GDistance of class centerAnd a distanceIn which contains K_W·K_FSubset of q-th in a state space model of the wind-fire system_GEach state corresponds to the qth_GA subset of

Step S3.2.6: the total error of classification is obtained by equation (32)

Step S3.2.7: select the qth_GEach state is respectively equal to K_GMinimum of distance of class center, and q-th_GDividing each state into a class corresponding to the minimum value; thereby will K_W·K_FThe states are classified into the classes corresponding to the corresponding minimum values, and the number of the states in each class is counted and assigned to the classes

step S3.2.9: obtaining the kth state space model of the wind fire system after the cluster simplification by using the formula (33)_GActive power output corresponding to each stateThereby obtaining the clusterActive power output corresponding to state space model of simplified wind-fire system

Step S3.2.11: obtaining a transfer rate matrix A 'corresponding to the state space model of the clustered and simplified wind-fire system by using the formula (34)'_G：

step S3.2.12: obtaining the clustered and simplified wind using equation (35)Kth in state space model of fire system_GState probability corresponding to each stateThereby obtaining the steady-state probability corresponding to the state space model of the clustered and simplified wind-fire system

step S4.1: calculating the reliability index of the wind fire system:

step S4.1.3: the reliability calculation of the wind fire system comprises K_G·N_LSIn each case, the number of the case is q_SAnd q is_L＝1,2,...,N_LS(ii) a Recording the load loss probability of the wind fire system as LOLP; the expected shortage of the wind and fire system is recorded as ENDS; the q th_SThe system state corresponding to the situation is recorded as I_f(q_S) (ii) a The q th_SThe load reduction corresponding to the situation is recorded as L_C(q_S) (ii) a The q th_SThe probability corresponding to each case is denoted as p (q)_S) (ii) a Initializing q_G＝1，q_L＝1，q_S＝1，LOLP＝0，ENDS＝0；