CN113128071B - Reliability evaluation method for power generation system containing photovoltaic power generation - Google Patents

Reliability evaluation method for power generation system containing photovoltaic power generation Download PDF

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CN113128071B
CN113128071B CN202110500928.6A CN202110500928A CN113128071B CN 113128071 B CN113128071 B CN 113128071B CN 202110500928 A CN202110500928 A CN 202110500928A CN 113128071 B CN113128071 B CN 113128071B
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CN113128071A (en
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陈凡
何伟
王瑞驰
王浩
赵美莲
刘海涛
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Nanjing Institute of Technology
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    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]

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Abstract

The invention discloses a reliability evaluation method of a power generation system containing photovoltaic power generation, which comprises the following steps: initializing parameters; simulating to generate a photovoltaic power generation output sequence; correcting the original load sequence; establishing an equivalent load multi-state model; calculating the optimal unavailability of a generator in a power generation system by using a cross entropy important sampling method; generating a generator state sequence and a corresponding likelihood ratio sequence of the power generation system by utilizing an LHS method; and calculating the reliability index of the power generation system containing the photovoltaic power generation. On the basis of realizing the simulation of the random production of the photovoltaic output and establishing a system equivalent load model, the invention effectively improves the efficiency of random sampling of the system and accelerates the calculation speed of the reliability evaluation of the power system containing photovoltaic power generation by combining the cross entropy important sampling method and the LHS sampling method.

Description

Reliability evaluation method for power generation system containing photovoltaic power generation
Technical Field
The invention belongs to the technical field of power system analysis, and particularly relates to a method for evaluating reliability of a power generation system containing photovoltaic power generation, in particular to a method for evaluating reliability of a power generation system containing photovoltaic power generation based on improved Latin hypercube sampling (Latin hypercube sampling, LHS).
Background
Along with the gradual exhaustion of traditional fossil energy sources and the increasingly prominent environmental problems such as atmospheric pollution, greenhouse effect and the like, photovoltaic power generation is rapidly developed worldwide. However, photovoltaic output has strong randomness and uncertainty, and future grid connection of high-proportion photovoltaic power generation increases the complexity of operation analysis of the power system, so that research on reliability evaluation of the power system containing photovoltaic power generation is necessary.
The reliability evaluation method of the power generation system is mainly divided into two major categories of an analysis method and a Monte Carlo method, wherein the calculated amount of the analysis method increases exponentially along with the increase of the system scale, and meanwhile, the problem of complex modeling process of an analysis model of the new energy power generation system exists, so that the reliability evaluation method based on the Monte Carlo method is widely applied to the reliability evaluation of the power system containing new energy. Aiming at the problems of large sampling sample and low convergence speed of the traditional Monte Carlo method, researchers propose variance reduction technologies such as Latin hypercube sampling (Latin hypercube sampling, LHS), cross entropy sampling and the like. The LHS method enables the generated sample distribution to be more uniform under the condition of not changing the output random variable sample distribution by hierarchical sampling, so that the sampling efficiency can be improved under the condition of extracting a small amount of samples; under the condition of keeping the mathematical expectation of the original samples unchanged, the Cross entropy sampling (CE) method aims at finding the optimal important sampling probability density distribution by taking the minimum Cross entropy as a target, namely, the extracted samples fall in the concerned parameter value area with larger probability by changing the probability distribution of the sample space, so that the number of the samples is reduced. Therefore, the LHS method and the cross entropy sampling method improve the sampling efficiency of the system state from different angles, and the cross entropy theory is combined with LHS sampling, so that the sampling efficiency of the reliability evaluation of the power system can be further improved.
Disclosure of Invention
Aiming at the problems, the invention provides a reliability evaluation method of a power generation system containing photovoltaic power generation, which is characterized in that on the basis of realizing random production simulation of photovoltaic output and establishing a system equivalent load model, an approximate optimal probability density distribution of a power generation unit is solved by adopting a cross entropy method, and then the state of the power generation unit is sampled in layers by adopting an LHS method based on the obtained approximate optimal probability distribution function, so that the calculation speed of reliability evaluation of the power generation system containing photovoltaic power generation is accelerated.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
a power generation system reliability assessment method comprising photovoltaic power generation comprises the following steps:
step 1: initializing parameters;
step 2: simulating to generate a photovoltaic power generation output sequence based on the photovoltaic power generation statistical data;
step 3: performing point-to-point correction on the original load sequence and the photovoltaic power generation output sequence to obtain a corrected load sequence;
step 4: carrying out linearization division or clustering on the corrected load sequence, and establishing a multi-state model of equivalent load;
step 5: calculating the optimal unavailability of a generator in a power generation system by using a cross entropy important sampling method;
step 6: generating a generator state sequence and a corresponding likelihood ratio sequence of the power generation system by utilizing an LHS method according to the optimal unavailability of the generator;
step 7: and calculating the reliability index of the power generation system containing photovoltaic power generation based on the power generation system power generation state sequence, the corresponding likelihood ratio sequence and the multi-state model of the equivalent load.
Optionally, the method for generating the photovoltaic power generation output sequence comprises the following steps:
step 2-1, reading the photovoltaic output history hour sequence data in the photovoltaic power generation statistical data, and recording the data as a sample array A, wherein the sample number is N PV Discarding 0 in the sample data, and forming sample array X by the rest data PV The number of samples is n;
step 2-2, assume array X PV The n sample variables in (a) are { X ] PV,1 ,X PV,2 ,...,X PV,n Sample variable X PV The minimum value is a, the maximum value is b, and the probability density function is f (X PV ) The nonparametric kernel density of the photovoltaic output is estimated to beWherein j is 1 Is an index of the number n of samples, bandwidth +.>Sigma is the standard deviation, K (. Cndot.) represents the kernel function, and +.>
Step 2-3, variable X PV The definition domain [ a, b ] of (a)]Dividing the same into arbitrary m points, and respectively obtaining corresponding probability density estimated values of the m points by using the non-parameter kernel density estimation method in the step 2-2And calculating the probability estimated value of each point as follows:
wherein i is PV ＝1,2,...,m；
Step 2-4, estimating the value by probability of each point in step 2-3Calculate->Cumulative probability estimate at:
wherein j is PV Is i PV Is used for the indexing of (a),the minimum value of (2) is denoted as c, ">The maximum value of (2) is denoted d;
step 2-5, in each of step 2-4Dividing the cumulative probability interval into m-1 parts by taking the estimated value as an interval point, and obtaining a sample value X on each interval by using a cubic spline interpolation method in each cell PV With respect to the cumulative probability estimate y PV Is a third order polynomial of: />Wherein i is M ＝1,2,…,m-1；
Step 2-6, sequentially taking from small to largeWherein i is 1 =1, 2,..n, if +.>Will->Substituting the polynomials of the corresponding intervals in step 2-5 to obtain the required sample value +.>Otherwise->
Step 2-7, the step (N) removed in step 2-1 PV -n) 0 data and n sample values obtained in steps 2-6Arranged in a new array Z, the number of samples of Z being N PV The data are arranged from small to large, and the arrayZ is simulated photovoltaic output data;
and 2-8, sequencing the simulated photovoltaic output sequence Z in the step 2-7 according to the position characteristics of the original data to obtain a time sequence output sequence Z' of the photovoltaic power station.
Optionally, the specific process of sorting in the steps 2-8 is as follows:
step 2-8-1, marking the position of the sample array A in step 2-1, and marking the corresponding position sequence matrix as B= [1,2, …, N PV ] T ；
Step 2-8-2, arranging the data in the sample array A from small to large to obtain a new array A ', and changing the corresponding position matrix into B' = [ i ] 2 ,…,N PV ,…,j 2 ] T Wherein i is 2 ∈{1,2,...,N PV }，j 2 ∈{1,2,...,N PV }；
Step 2-8-3, newly creating an N PV 2, taking the simulated photovoltaic output sequence Z in the step 2-7 as a first column of the matrix C, and taking the position matrix B' as a second column of the matrix C to obtain a new matrix C;
and 2-8-4, arranging the matrix sequence B ' in the step 2-8-3 in a sequence from small to large, and changing the corresponding Z in the matrix C into Z ', wherein Z ' is the time sequence output data of the photovoltaic power station which accords with the original data characteristic.
Optionally, the specific acquisition method of the modified load sequence includes:
and subtracting the output sequence at the moment corresponding to the photovoltaic power generation from the original load sequence every hour to obtain a corrected equivalent load sequence.
Optionally, the multi-state equivalent load model includes: load level sequenceAnd the load level probability sequence->Wherein WP iw For load level WL iw The corresponding probability of the load is determined, iw=1, 2,.. w ；N w For multi-stage loadingTotal number of levels (I)>
Optionally, the method for calculating the optimal unavailability of the generator in the power generation system includes the following steps:
step 5-1, cross entropy parameter initialization: cross entropy significant sample size N; a quantile ρ; a smoothing factor p; maximum number of iterations N kmax The method comprises the steps of carrying out a first treatment on the surface of the Giving M generator sets output and unavailability vector u and initial iteration unavailability vector v corresponding to the generator sets 0 =u, where v 0 Is a 1 XM order vector; iterative calculation number k=1;
step 5-2, generating N system state sequences, wherein the specific method comprises the following steps: generating N [0,1 ]]Random number vector of interval and optimal unavailability sequence v of system generator used by k-1 iterative calculation k-1 Comparing, if the random numberMake->No->Wherein->Represents the nth s The first part of the random number vector>Element(s)>Represents the nth s The +.f. in the individual system generator state vector>An element;
step 5-3, calculating total output of the system generators in the N system generator states according to the system generator state sequence obtained in the step 5-2, and sequencing the total output of the N system generators from small to large to obtain a power supply total sequence of the system generators in ascending order;
step 5-4, updating the total power supply load L capable of safely supplying power according to the total output sequence of the system generators which are arranged in ascending order and obtained in step 5-3 k Determining a load shedding sign sequence of the system in N states;
step 5-5, according to the system generator state sequence obtained in step 5-2 and the optimal unavailability degree sequence v of the generator used in the iterative calculation k-1 Calculating N system state likelihood ratio sequences;
step 5-6, calculating the optimal unavailability sequence v of the system generator at the time (i.e. the kth time) according to the system generator state likelihood ratio sequence obtained in the step 5-5 k ；
Step 5-7, judging the total load L of safe power supply k Whether or not a specified average load P is reached L Or whether the number of iterations k reaches a maximum value N kmax If the condition is satisfied, i.e. L k ＝P L Or k=n kmax When the process is carried out, the process goes to the step 6; if not, let k=k+1 and return to step 5-2.
Optionally, the specific step of calculating the system load shedding sign sequence in the step 5-4 includes:
step 5-4-1, recording the total power supply sequence of the system generators which are arranged in an ascending order and obtained in the step 5-3 as P; if P t >P L Let L k ＝P t The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let L k ＝P L The method comprises the steps of carrying out a first treatment on the surface of the Thereby calculating and obtaining the safe power supply total load L of the kth iteration k Wherein ρ is quantile, P t Providing a system generator with a t-th element in a total sequence P, wherein t=ρ×n; p (P) L For a given average load, the calculation formula is
Step 5-4-2, recording the unordered pre-ordering obtained in step 5-3The total power supply sequence of the system generator is S L The method comprises the steps of carrying out a first treatment on the surface of the Record n s The state sequence of each system generator isThe load shedding mark sequence of the system in the state of N system generators is H; if->Then->Otherwise->Wherein->Indicating that the system is in generator state->Total amount of power supplied->Representation ofAnd a load shedding mark value corresponding to the system in the state.
Optionally, the calculation formula of the likelihood ratio in the step 5-5 is:
wherein W represents a system generator state likelihood ratio sequence,status of the power generation system->Likelihood ratio of->Indicate->A system generator state sequence,/->Indicate->The (th) in the individual system generator state sequence>The state value of the generator, M is the number of system generators, ">Indicating system->Initial unavailability value of the counter generator, < ->For the system->The unavailability degree value of each generator is calculated and used in the k-1 th iteration; wherein->
Optionally, v as described in steps 5-6 k The calculation formula of (2) is as follows:
introducing a smoothing factor p, according to formula v' kj′ ＝pv kj′ +(1-p)v (k-1)j′ Calculating to obtain v k Wherein v is k,j′ Representing a generator unavailability sequence v obtained by the kth iterative computation k The unavailability value of the j' th generator in the system is the system state X i′ Likelihood ratio, X i′ Representing the i' th system generator state sequence, X i′j′ Represents the state value of the (j 'th) generator of the (i' th) system generator state sequence, H (X) i′ ) Representing system state X i′ I '=1, 2,..n, j' =1, 2,..m.
Optionally, the method for producing the power generation system generator state sequence and the corresponding likelihood ratio sequence comprises the following steps:
step 6-1, initializing LHS parameters: latin hypercube sampling Scale N 2 The method comprises the steps of carrying out a first treatment on the surface of the The number M of system generators;
step 6-2, according to the optimal unavailability sequence v of the system generator obtained in step 5 * Calculating an original sampling matrix R of the state of the system generator;
step 6-3, generating M×N randomly row by row 2 An order system generator state arrangement matrix, each row of which consists of [1, N 2 ]N in the range 2 The system comprises a plurality of non-repeated positive integers, wherein the value of the integer represents the arrangement position of corresponding elements of a corresponding row of a system generator state sampling matrix;
step 6-4, calculating a system generator state row correlation coefficient matrix rho according to the original sampling matrix R obtained in the step 6-2;
step 6-5, decomposing the correlation coefficient matrix rho obtained in the step 6-4 to construct a system generator state arrangement matrix Q with smaller row correlation s * ；
Step 6-6, the original sampling matrix R of the system generator state obtained in the step 6-2 is arranged according to the array matrix Q obtained in the step 6-5 s * Rearranging to generate MXN 2 The system generator state of the order samples the matrix;
step 6-7, according to the optimal unavailability sequence v of the system generator * Combining the sampling matrix obtained in step 6-6 to generate new MxN 2 A system generator state matrix WX;
step 6-8, calculating 1 XN according to the system generator state matrix WX generated in step 6-7 2 The system generator state likelihood ratio sequence WW.
Optionally, the calculation formula of the system generator state original sampling matrix R in the step 6-2 is:
wherein N is 2 For Latin hypercube sampling method, e and lambda are both constant numbers, R j*z Represents the j th of matrix R * Line z column element, v * j* For the generator unavailability sequence v * J of (j) * The unavailability value of the generator, z=1, 2,.. 2 ，j * ＝1,2,...,M；
Optionally, the calculation formula of the system generator state correlation coefficient matrix ρ in the step 6-4 is:
wherein M is the number of system generators; ρ i″j″ Representing the correlation coefficients of the ith and jth rows in the correlation coefficient matrix ρ, R i″q Represents the ith row and the qth column element of the matrix R, R j″q Represents the jth "row and qth column elements of matrix R,represents the i "th row average value of matrix R, < >>Represents the j "th row average of matrix R.
Optionally, the decomposing method of the correlation coefficient matrix ρ in the step 6-5 is as follows:
the correlation coefficient moment is determined by Cholesky decomposition methodDecomposition of the matrix ρ into DD T Wherein D is a non-singular lower triangular matrix; and then according to the arrangement matrix Q generated in the step 6-3 s Generating a matrix G with smaller row correlation, wherein the calculation formula is as followsThen according to the value of each row of element of the matrix G, replacing the element with the corresponding integer number to generate a system generator state arrangement matrix Q s * 。
Optionally, the calculation method of the reliability index of the power generation system including photovoltaic power generation comprises the following steps:
step 7-1, making the system generator state sequence index wc=0;
step 7-2, let the load level index wk=0;
step 7-3, wk=wk+1; wc=wc+1;
step 7-4, sequentially selecting a system generator state sequence WX from the system generator state matrix WX generated in step 6 wc Successively selecting load level WL wk ；WX wc For the wc-th sequence, WL in the generator state matrix WX wk The wk element in the load level sequence WL corresponds to the load probability WP wk ；
Step 7-5, updating an indication function of the system reliability index under the wk load level;
step 7-6, judging wk<N w If yes, turning to step 7-7; otherwise, go to step 7-3;
step 7-7, updating a system reliability index and a variance coefficient under a multi-level load level;
step 7-8, if the variance coefficient calculated in the step 7-7 meets the convergence condition, outputting a reliability index of the power generation system; otherwise, go to step 7-2.
Optionally, in said step 7-5, the wk-th load level WL is updated wk The following specific method of the system reliability index indication function is as follows: for the system state sequence WX in step 7-4 wc Performing system state analysis to judge the system state WX wc Whether or not a cut load is generated; if a cut load is generated, the index indication function isWherein SD is the cut load, and its size is the load level WL wk In state WX with system M generator wc A difference in total amount of lower power generation; if no load shedding occurs, i.e. the system M generators are in state WX wc The total amount of lower power generation is greater than the load level WL wk The index indication function is F LOLP (WX wc )＝0，F EENS (WX wc )＝0。
Optionally, the calculation formula of the system reliability index and the variance coefficient under the multi-stage load level updated in the step 7-7 is as follows:
compared with the prior art, the invention has the beneficial effects that:
the invention adopts the piecewise cubic spline interpolation function to solve the problem that the LHS method cannot be applied when the inverse function of the cumulative probability distribution function of the photovoltaic output cannot write a specific expression, and can accurately simulate the photovoltaic power generation output sequence while ensuring that the sampling precision and the efficiency of the LHS method are high enough.
The invention takes the minimum cross entropy of the important sampling probability density function and the theoretical optimal important sampling probability density function as an objective function, obtains the approximate optimal important sampling probability distribution, improves the occurrence probability of rare events on the basis of ensuring that the expected value of the reliability index is approximately unchanged, greatly reduces the reliability evaluation sampling times of the power system and improves the sampling efficiency; the LHS method is further applied on the basis, the optimal important sampling probability distribution obtained by cross entropy optimization is used for hierarchical sampling, the full coverage of the sample point interval is ensured on the basis of improving the probability of rare events, and the tail cutting phenomenon of data is avoided, so that the sampling efficiency of the system state is further improved. The method provided by the invention fully utilizes the advantages of the cross entropy sampling and LHS sampling methods, and effectively improves the calculation speed of the reliability evaluation of the power system.
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In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings, in which:
FIG. 1 is a flow chart of a method for evaluating reliability of a power generation system according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of optimizing the system generator for optimal unavailability using cross entropy important sampling;
FIG. 3 is a schematic flow chart of a system generator state sequence and likelihood ratio sequence determination using Latin hypercube sampling;
fig. 4 is a schematic flow chart of calculating a reliability index of a power generation system including photovoltaic power generation.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The principle of application of the invention is described in detail below with reference to the accompanying drawings.
The invention provides a power generation system reliability evaluation method based on improved LHS and comprising the following steps: initializing parameters; simulating to generate a photovoltaic power generation output sequence; correcting the original load sequence; establishing an equivalent load multi-state model; calculating the optimal unavailability of a generator in a power generation system by using a cross entropy important sampling method; generating a generator state sequence and a corresponding likelihood ratio sequence of the power generation system by utilizing an LHS method; and calculating the reliability index of the power generation system containing the photovoltaic power generation. On the basis of realizing the simulation of the random production of the photovoltaic output and establishing a system equivalent load model, the invention effectively improves the efficiency of random sampling of the system and accelerates the calculation speed of the reliability evaluation of the power system containing photovoltaic power generation by combining the cross entropy important sampling method and the LHS sampling method. The systems mentioned in this invention are all referred to as power systems.
As shown in fig. 1, the method for evaluating the reliability of the power generation system containing photovoltaic power generation based on the improved LHS comprises the following steps:
step 1: initializing parameters;
step 2: simulating to generate a photovoltaic power generation output sequence based on the photovoltaic power generation statistical data;
in a specific implementation manner of the embodiment of the present invention, the step 2 specifically includes the following steps:
step 2-1, reading the photovoltaic output history hour sequence data in the photovoltaic power generation statistical data, marking the data as a sample array A, and marking the length of the array A as N PV The method comprises the steps of carrying out a first treatment on the surface of the Truncating 0 in the sample data, the remaining data forming array X PV Array X PV Is n in length;
step 2-2, assume array X PV The n sample variables in (a) are { X ] PV,1 ,X PV,2 ,...,X PV,n Sample variable X PV The minimum value is a, the maximum value is b, and the probability density function is f (X PV ) The nonparametric kernel density of the photovoltaic output is estimated to be
Wherein j is 1 Index of the number n of samples, bandwidthSigma is the standard deviation, K (. Cndot.) represents the kernel function, and +.>
Step 2-3, variable X PV The definition domain [ a, b ] of (a)]Dividing the same into arbitrary m points, and respectively obtaining corresponding probability density estimated values of the m points by using the non-parameter kernel density estimation method in the step 2-2Calculating the probability estimated value of each point as follows;
wherein i is PV ＝1,2,...,m；
Step 2-4, estimating the value by probability of each point in step 2-3Calculate->Cumulative probability estimate at:
wherein j is PV Is i PV Is used for the indexing of (a),the minimum value of (2) is denoted as c, ">The maximum value of (2) is denoted d;
step 2-5, in each of step 2-4Dividing the cumulative probability interval into m-1 parts by taking the estimated value as an interval point, and obtaining a sample value X on each interval by using a cubic spline interpolation method in each cell PV With respect to the cumulative probability estimate y PV Three or more of (2)The formula: />Wherein i is M ＝1,2,…,m-1；
Step 2-6, sequentially taking from small to largeWherein i is 1 =1, 2,..n, if +.>Will beSubstituting the polynomials of the corresponding intervals in step 2-5 to obtain the required sample value +.>Otherwise->
Step 2-7, the step (N) removed in step 2-1 PV -n) 0 data and n sample values obtained in steps 2-6Arranged in a new array Z, the number of samples of Z being N PV The data are arranged from small to large, and the array Z is simulated photovoltaic output data;
step 2-8, sequencing the simulated photovoltaic output sequence Z in the step 2-7 according to the position characteristics of the original data to obtain a time sequence output sequence Z' of the photovoltaic power station;
the specific process of sequencing in the steps 2-8 is as follows:
step 2-8-1, marking the position of the sample array A in step 2-1, and marking the corresponding position sequence matrix as B= [1,2, …, N PV ] T ；
Step 2-8-2, arranging the data in the sample array A from small to large to obtain a new array A ', and changing the corresponding position matrix into B' = [ i ] 2 ,…,N PV ,…,j 2 ] T Wherein i is 2 ∈{1,2,...,N PV }，j 2 ∈{1,2,...,N PV }；
Step 2-8-3, newly creating an N PV 2, taking the simulated photovoltaic output sequence Z in the step 2-7 as a first column of the matrix C, and taking the position matrix B' as a second column of the matrix C to obtain a new matrix C;
and 2-8-4, arranging the matrix sequence B ' in the step 2-8-3 in a sequence from small to large, and changing the corresponding Z in the matrix C into Z ', wherein Z ' is the time sequence output data of the photovoltaic power station which accords with the original data characteristic.
Step 3: performing point-to-point correction on the original load sequence and the photovoltaic output sequence generated in the step 2 to obtain a corrected load sequence;
the correction method comprises the following steps: and subtracting the output sequence at the moment corresponding to the photovoltaic power generation from the original load sequence every hour.
Step 4: carrying out linearization division or clustering on the corrected load sequence, and establishing a multi-state model of equivalent load;
wherein the multi-state equivalent load model comprises a load level sequenceLoad level probability sequence->Wherein WP iw For load level WL iw The corresponding probability of the load is determined, iw=1, 2,.. w ；N w For the total number of multi-level load levels, +.>
Step 5: calculating the optimal unavailability of a generator in the system by using a cross entropy important sampling method;
as shown in fig. 2, in a specific implementation manner of the embodiment of the present invention, the step 5 specifically includes the following steps:
step 5-1Cross entropy parameter initialization: cross entropy significant sample size N; a quantile ρ; a smoothing factor p; maximum number of iterations N kmax The method comprises the steps of carrying out a first treatment on the surface of the Giving M generator sets output and unavailability vector u and initial iteration unavailability vector v corresponding to the generator sets 0 =u, where v 0 Is a 1 XM order vector; iterative calculation number k=1;
step 5-2, generating N system state sequences, wherein the specific method comprises the following steps: generating N [0,1 ]]Random number vector of interval and optimal unavailability sequence v of system generator used by k-1 iterative calculation k-1 Comparing, if the random numberMake->No->Wherein->Represents the nth s The first part of the random number vector>Element(s)>Represents the nth s The +.f. in the individual system generator state vector>The elements.
Step 5-3, calculating total output of the system generators in the N system generator states according to the system generator state sequence obtained in the step 5-2, and sequencing the total output of the N system generators from small to large to obtain a power supply total sequence of the system generators in ascending order;
step 5-4, according to the ascending order obtained in step 5-3The total output sequence of the system generators is arranged, and the total load L capable of safely supplying power is updated k Determining a load shedding sign sequence of the system in N states;
the specific method for calculating the load shedding mark sequence of the system comprises the following steps:
step 5-4-1, recording the total power supply sequence of the system generators which are arranged in an ascending order and obtained in the step 5-3 as P; if P t >P L Let L k ＝P t The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let L k ＝P L The method comprises the steps of carrying out a first treatment on the surface of the Thereby calculating and obtaining the safe power supply total load L of the kth iteration k Wherein ρ is quantile, P t Providing a system generator with a t-th element in a total sequence P, wherein t=ρ×n; p (P) L For a given average load, the calculation formula is
Step 5-4-2, recording the total power supply sequence of the system generators before unordered obtained in step 5-3 as S L The method comprises the steps of carrying out a first treatment on the surface of the Record n s The state sequence of each system generator isThe load shedding mark sequence of the system in the state of N system generators is H; if->Then->Otherwise->Wherein->Indicating that the system is in generator state->Total amount of power supplied->Representation->And a load shedding mark value corresponding to the system in the state.
Step 5-5, according to the system generator state sequence obtained in step 5-2 and the optimal unavailability degree sequence v of the generator used in the iterative calculation k-1 Calculating N system state likelihood ratio sequences;
wherein, the calculation formula of likelihood ratio:
wherein W represents a system generator state likelihood ratio sequence,for the system state->Is used for the likelihood ratio of (a),indicate->A system generator state sequence,/->Indicate->The (th) in the individual system generator state sequence>The state value of the generator, M is the number of system generators, ">Indicating system->Initial unavailability value of the counter generator, < ->For the system->The unavailability degree value of each generator is calculated and used in the k-1 th iteration; wherein->
Step 5-6, calculating the optimal unavailability sequence v of the system generator at the time (i.e. the kth time) according to the system generator state likelihood ratio sequence obtained in the step 5-5 k ；
Wherein v is k Is calculated according to the formula:and introducing a smoothing factor p according to formula v' kj′ ＝pv kj′ +(1-p)v (k-1)j′ Calculating to obtain v k Wherein v is k,j′ Representing a generator unavailability sequence v obtained by the kth iterative computation k Unavailability value of the j' th generator, W (X i′ ；u,v k-1 ) For system state X i′ Likelihood ratio, X i′ Representing the i' th system generator state sequence, X i′j′ Represents the state value of the (j 'th) generator of the (i' th) system generator state sequence, H (X) i′ ) Representing system state X i′ I '=1, 2,..n, j' =1, 2,..m.
Step 5-7, judging the total load L of safe power supply k Whether or not a specified average load P is reached L Or whether the number of iterations k reaches a maximum value N kmax If the condition is satisfied, i.e. L k ＝P L Or k=N kmax When the process is carried out, the process goes to the step 6; if not, let k=k+1 and return to step 5-2.
Step 6: generating a generator state sequence and a corresponding likelihood ratio sequence of the power generation system by utilizing an LHS method according to the optimal unavailability of the generator;
as shown in fig. 3, in a specific implementation manner of the embodiment of the present invention, the step 6 specifically includes the following steps:
step 6-1, initializing parameters; latin hypercube sampling Scale N 2 The method comprises the steps of carrying out a first treatment on the surface of the The number M of system generators;
step 6-2, according to the optimal unavailability sequence v of the system generator obtained in step 5 * Calculating an original sampling matrix R of the state of the system generator;
wherein N is 2 For Latin hypercube sampling method, e and lambda are both constant numbers, R j*z Represents the j th of matrix R * Line z column element, v * j* For the generator unavailability sequence v * J of (j) * The unavailability value of the generator, z=1, 2,.. 2 ，j * ＝1,2,...,M；
Step 6-3, generating M×N randomly row by row 2 An order system generator state arrangement matrix, each row of which consists of [1, N 2 ]N in the range 2 The system comprises a plurality of non-repeated positive integers, wherein the value of the integer represents the arrangement position of corresponding elements of a corresponding row of a system generator state sampling matrix;
step 6-4, calculating a system generator state row correlation coefficient matrix rho according to the original sampling matrix R obtained in the step 6-2;
wherein, the formula for calculating the correlation coefficient matrix ρ is:
/>
wherein the method comprises the steps ofM is the number of system generators; ρ i″j″ Representing the correlation coefficients of the ith and jth rows in the correlation coefficient matrix ρ, R i″q Represents the ith row and the qth column element of the matrix R, R j″q Represents the jth "row and qth column elements of matrix R,represents the i "th row average value of matrix R, < >>Represents the j "th row average of matrix R.
Step 6-5, decomposing the correlation coefficient matrix rho obtained in the step 6-4 to construct a system generator state arrangement matrix Q with smaller row correlation s * ；
The correlation coefficient matrix decomposition method is Cholesky decomposition method. This approach decomposes the correlation coefficient matrix ρ into DD T Wherein D is a non-singular lower triangular matrix; and then according to the arrangement matrix Q generated in the step 6-3 s Generating a matrix G with smaller row correlation, wherein the calculation formula is as followsThen according to the value of each row of element of the matrix G, replacing the element with the corresponding integer number to generate a system generator state arrangement matrix Q s * 。
Step 6-6, the original sampling matrix R of the system generator state obtained in the step 6-2 is arranged according to the array matrix Q obtained in the step 6-5 s * Rearranging to generate MXN 2 The system generator state of the order samples the matrix;
step 6-7, according to the optimal unavailability sequence v of the system generator * Combining the sampling matrix obtained in step 6-6 to generate new MxN 2 A system generator state matrix WX;
wherein the method of generating the system generator state sequence is the same as mentioned in step 5-2.
Step 6-8, generating a System Generator according to step 6-7State matrix WX, calculate 1 xn 2 A generator state likelihood ratio sequence WW of the order system;
wherein the formula for calculating the likelihood ratio sequence is the same as in step 5-5, it should be noted that the optimal unavailability sequence v of the system generator is brought in * The generator state is the system generator state calculated in the step 6-7.
Step 7: and calculating the reliability index of the power generation system containing photovoltaic power generation based on the power generation system power generation state sequence, the corresponding likelihood ratio sequence and the multi-state model of the equivalent load.
As shown in fig. 4, in a specific implementation manner of the embodiment of the present invention, the step 7 specifically includes the following steps:
step 7-1, making the system generator state sequence index wc=0;
step 7-2, let the load level index wk=0;
step 7-3, wk=wk+1; wc=wc+1;
step 7-4, sequentially selecting a system generator state sequence WX from the system generator state matrix WX generated in step 6 wc Successively selecting load level WL wk ；WX wc For the wc-th sequence, WL in the generator state matrix WX wk The wk element in the load level sequence WL corresponds to the load probability WP wk ；
Step 7-5, updating an indication function of the system reliability index under the wk load level;
wherein the wk load level WL is updated wk The following specific method of the system reliability index indication function is as follows: for the system state sequence WX in step 7-4 wc Performing system state analysis to judge the system state WX wc Whether or not a cut load is generated; if a cut load is generated, the index indicates the function:
F LOLP (WX wc )＝WW(WX wc )×WP wk
F EENS (WX wc )＝8760×SD×WW(WX wc )×WP wk
wherein SD is the cut load, and its size is the load level WL wk In state WX with system M generator wc A difference in total amount of lower power generation; if no load shedding occurs, i.e. the system M generators are in state WX wc The total amount of lower power generation is greater than the load level WL wk The index indication function is F LOLP (WX wc )＝0，F EENS (WX wc )＝0。
Step 7-6, judging wk<N w If yes, turning to step 7-7; otherwise, go to step 7-3;
step 7-7, updating a system reliability index and a variance coefficient under a multi-level load level;
the calculation formula for updating the system reliability index and the variance coefficient under the multistage load level is as follows:
step 7-8, if the variance coefficient calculated in the step 7-7 meets the convergence condition, outputting a reliability index of the power generation system; otherwise, go to step 7-2.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. The method for evaluating the reliability of the power generation system containing the photovoltaic power generation is characterized by comprising the following steps of:
step 1: initializing parameters;
step 2: simulating to generate a photovoltaic power generation output sequence based on the photovoltaic power generation statistical data;
step 3: performing point-to-point correction on the original load sequence and the photovoltaic power generation output sequence to obtain a corrected load sequence;
step 4: carrying out linearization division or clustering on the corrected load sequence, and establishing a multi-state model of equivalent load;
step 5: calculating the optimal unavailability of a generator in a power generation system by using a cross entropy important sampling method;
step 6: generating a generator state sequence and a corresponding likelihood ratio sequence of the power generation system by utilizing an LHS method according to the optimal unavailability of the generator;
step 7: calculating a reliability index of the power generation system containing photovoltaic power generation based on the power generation system power generation state sequence, the corresponding likelihood ratio sequence and the multi-state model of the equivalent load;
the method for calculating the optimal unavailability of the generator of the power generation system comprises the following steps:
step 5-1, cross entropy parameter initialization: cross entropy significant sample size N; a quantile ρ; a smoothing factor p; maximum number of iterations N kmax The method comprises the steps of carrying out a first treatment on the surface of the Giving M generator sets output and unavailability vector u and initial iteration unavailability vector v corresponding to the generator sets 0 =u, where v 0 Is a 1 XM order vector; iterative calculation number k=1;
step 5-2, generating N system state sequences, wherein the specific method comprises the following steps: generating N [0,1 ]]Random number vector of interval and optimal unavailability sequence v of system generator used by k-1 iterative calculation k-1 Comparing, if the random numberMake->No->Wherein->Represents the nth s The first part of the random number vector>Element(s)>Represents the nth s The +.f. in the individual system generator state vector>An element;
step 5-3, calculating total output of the system generators in the N system generator states according to the system generator state sequence obtained in the step 5-2, and sequencing the total output of the N system generators from small to large to obtain a power supply total sequence of the system generators in ascending order;
step 5-4, updating the total power supply load L capable of safely supplying power according to the total output sequence of the system generators which are arranged in ascending order and obtained in step 5-3 k Determining a load shedding sign sequence of the system in N states;
step 5-5, according to the system generator state sequence obtained in step 5-2 and the optimal unavailability degree sequence v of the generator used in the iterative calculation k-1 Calculating N system state likelihood ratio sequences;
step 5-6, calculating the optimal unavailability sequence v of the system generator at the time according to the system generator state likelihood ratio sequence obtained in the step 5-5, namely the kth time k ；
Step 5-7, judging the total load L of safe power supply k Whether or not a specified average load P is reached L Or also iterateWhether the number k reaches the maximum value N kmax If the condition is satisfied, i.e. L k ＝P L Or k=n kmax When the process is carried out, the process goes to the step 6; if not, let k=k+1, and return to step 5-2;
the production method of the power generation system generator state sequence and the corresponding likelihood ratio sequence comprises the following steps:
step 6-1, initializing LHS parameters: latin hypercube sampling Scale N 2 The method comprises the steps of carrying out a first treatment on the surface of the The number M of system generators;
step 6-2, according to the optimal unavailability sequence v of the system generator obtained in step 5 * Calculating an original sampling matrix R of the state of the system generator;
step 6-3, generating M×N randomly row by row 2 An order system generator state arrangement matrix, each row of which consists of [1, N 2 ]N in the range 2 The system comprises a plurality of non-repeated positive integers, wherein the value of the integer represents the arrangement position of corresponding elements of a corresponding row of a system generator state sampling matrix;
step 6-4, calculating a system generator state row correlation coefficient matrix rho according to the original sampling matrix R obtained in the step 6-2;
step 6-5, decomposing the correlation coefficient matrix rho obtained in the step 6-4 to construct a system generator state arrangement matrix Q with smaller row correlation s * ；
Step 6-6, the original sampling matrix R of the system generator state obtained in the step 6-2 is arranged according to the array matrix Q obtained in the step 6-5 s * Rearranging to generate MXN 2 The system generator state of the order samples the matrix;
step 6-7, according to the optimal unavailability sequence v of the system generator * Combining the sampling matrix obtained in step 6-6 to generate new MxN 2 A system generator state matrix WX;
step 6-8, calculating 1 XN according to the system generator state matrix WX generated in step 6-7 2 The system generator state likelihood ratio sequence WW.
2. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 1, wherein the method for generating the photovoltaic power generation output sequence comprises the steps of:
step 2-1, reading the photovoltaic output history hour sequence data in the photovoltaic power generation statistical data, and recording the data as a sample array A, wherein the sample number is N PV Discarding 0 in the sample data, and forming sample array X by the rest data PV The number of samples is n; step 2-2, assume array X PV The n sample variables in (a) are { X ] PV,1 ,X PV,2 ,...,X PV,n Sample variable X PV The minimum value is a, the maximum value is b, and the probability density function is f (X PV ) The nonparametric kernel density of the photovoltaic output is estimated to beWherein j is 1 Is an index of the number n of samples, bandwidth +.>Sigma is the standard deviation, K (·) represents the kernel function, and
step 2-3, variable X PV The definition domain [ a, b ] of (a)]Dividing the same into arbitrary m points, and respectively obtaining corresponding probability density estimated values of the m points by using the non-parameter kernel density estimation method in the step 2-2And calculating the probability estimated value of each point as follows:
wherein i is PV ＝1,2,...,m；
Step 2-4, estimating the value by probability of each point in step 2-3Calculate->Cumulative probability estimate at:
wherein j is PV Is i PV Is used for the indexing of (a),the minimum value of (2) is denoted as c, ">The maximum value of (2) is denoted d;
step 2-5, in each of step 2-4Dividing the cumulative probability interval into m-1 parts by taking the estimated value as an interval point, and obtaining a sample value X on each interval by using a cubic spline interpolation method in each cell PV With respect to the cumulative probability estimate y PV Is a third order polynomial of: />Wherein i is M ＝1,2,…,m-1
Step 2-6, sequentially taking from small to largeWherein i is 1 =1, 2,..n, if +.>Will->Substituted into the corresponding step 2-5The polynomial of the interval determines the desired sample value +.>Otherwise->
Step 2-7, the step (N) removed in step 2-1 PV -n) 0 data and n sample values obtained in steps 2-6Arranged in a new array Z, the number of samples of Z being N PV The data are arranged from small to large, and the array Z is simulated photovoltaic output data;
and 2-8, sequencing the simulated photovoltaic output sequence Z in the step 2-7 according to the position characteristics of the original data to obtain a time sequence output sequence Z' of the photovoltaic power station.
3. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 2, characterized by: the specific process of sequencing in the steps 2-8 is as follows:
step 2-8-1, marking the position of the sample array A in step 2-1, and marking the corresponding position sequence matrix as B= [1,2, …, N PV ] T ；
Step 2-8-2, arranging the data in the sample array A from small to large to obtain a new array A ', and changing the corresponding position matrix into B' = [ i ] 2 ,…,N PV ,…,j 2 ] T Wherein i is 2 ∈{1,2,...,N PV }，j 2 ∈{1,2,...,N PV }；
Step 2-8-3, newly creating an N PV 2, taking the simulated photovoltaic output sequence Z in the step 2-7 as a first column of the matrix C, and taking the position matrix B' as a second column of the matrix C to obtain a new matrix C;
and 2-8-4, arranging the matrix sequence B ' in the step 2-8-3 in a sequence from small to large, and changing the corresponding Z in the matrix C into Z ', wherein Z ' is the time sequence output data of the photovoltaic power station which accords with the original data characteristic.
4. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 1, characterized by: the specific steps of calculating the system load shedding mark sequence in the step 5-4 comprise the following steps:
step 5-4-1, recording the total power supply sequence of the system generators which are arranged in an ascending order and obtained in the step 5-3 as P; if P t ＞P L Let L k ＝P t The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let L k ＝P L The method comprises the steps of carrying out a first treatment on the surface of the Thereby calculating and obtaining the safe power supply total load L of the kth iteration k Wherein ρ is quantile, P t Providing a system generator with a t-th element in a total sequence P, wherein t=ρ×n; p (P) L For a given average load, the calculation formula is
Step 5-4-2, recording the total power supply sequence of the system generators before unordered obtained in step 5-3 as S L The method comprises the steps of carrying out a first treatment on the surface of the Record n s The state sequence of each system generator isThe load shedding mark sequence of the system in the state of N system generators is H; if->Then->Otherwise->Wherein->Indicating that the system is in generator state->Total amount of power supplied->Representation->And a load shedding mark value corresponding to the system in the state.
5. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 1, characterized by: the calculation formula of the likelihood ratio is as follows:
wherein W represents a system generator likelihood ratio sequence,for the system state->Likelihood ratio of->Represent the firstA system generator state sequence,/->Indicate->The (th) in the individual system generator state sequence>The state value of the generator, M is the number of system generators, ">Indicating system->Initial unavailability value of the counter generator, < ->For the system->The unavailability degree value of each generator is calculated and used in the k-1 th iteration; wherein->
The v is k The calculation formula of (2) is as follows:
introducing a smoothing factor p, according to formula v' kj′ ＝pv kj′ +(1-p)v (k-1)j′ Calculating to obtain v k Wherein v is k,j′ Representing a generator unavailability sequence v obtained by the kth iterative computation k The unavailability value of the j' th generator in the system is the system state X i′ Likelihood ratio, X i′ Representing the i' th system generator state sequence, X i′j′ Represents the state value of the (j 'th) generator of the (i' th) system generator state sequence, H (X) i′ ) Representing system state X i′ I '=1, 2,..n, j' =1, 2,..m.
6. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 1, characterized by: the calculation formula of the system generator state original sampling matrix R is as follows:
wherein N is 2 For the Latin hypercube method of sampling scale, e and lambda are both constant numbers,represents the j th of matrix R * Column z element->For the generator unavailability sequence v * J of (j) * The unavailability value of the generator, z=1, 2,.. 2 ，j * ＝1,2,...,M；
The calculation formula of the generator state correlation coefficient matrix rho of the power generation system is as follows:
wherein M is the number of generators of the power generation system; ρ i″j″ Representing the correlation coefficients of the ith and jth rows in the correlation coefficient matrix ρ, R i″q Represents the ith row and the qth column element of the matrix R, R j″q Represents the jth "row and qth column elements of matrix R,represents the i "th row average value of matrix R, < >>Represents the j "th row average of matrix R.
7. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 1, characterized by: the calculation method of the reliability index of the power generation system comprising the photovoltaic power generation comprises the following steps:
step 7-1, making the system generator state sequence index wc=0;
step 7-2, let the load level index wk=0;
step 7-3, wk=wk+1; wc=wc+1;
step 7-4, sequentially selecting a system generator state sequence WX from the system generator state matrix WX generated in step 6 wc Successively selecting load level WL wk ；WX wc For the wc-th sequence, WL in the generator state matrix WX wk The wk element in the load level sequence WL corresponds to the load probability WP wk ；
Step 7-5, updating an indication function of the system reliability index under the wk load level;
step 7-6, judging wk is less than N w If yes, turning to step 7-7; otherwise, go to step 7-3;
step 7-7, updating a system reliability index and a variance coefficient under a multi-level load level;
step 7-8, if the variance coefficient calculated in the step 7-7 meets the convergence condition, outputting a reliability index of the power generation system;
otherwise, go to step 7-2.
8. The method for evaluating the reliability of a power generation system including photovoltaic power generation according to claim 7, characterized by: in said step 7-5, the wk load level WL is updated wk The following specific method of the system reliability index indication function is as follows: for the system state sequence WX in step 7-4 wc Performing system state analysis to judge the system state WX wc Whether or not a cut load is generated; if a cut load is generated, the index indication function isWherein SD is the tangential load, whichThe size is the load level WL wk In state WX with system M generator wc A difference in total amount of lower power generation; if no load shedding occurs, i.e. the system M generators are in state WX wc The total amount of lower power generation is greater than the load level WL wk The index indication function is F LOLP (WX wc )＝0，F EENS (WX wc )＝0。
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