CN106681133A - Method for identifying hydroelectric generating set model improved type subspace closed loop - Google Patents

Abstract

The invention discloses an improved subspace closed-loop identification method for a hydroelectric unit model, which belongs to the technical field of hydroelectric unit model modeling and identification, and applies the simplified subspace identification method based on PSO parameter optimization to the hydroelectric unit model closed-loop identification, including The following steps are as follows: (1) Establish a hydraulic turbine speed regulation closed-loop system model with output frequency noise; (2) Consider the influence of parameters p and f on the identification in the predictive form parsimony subspace identification method (PARSIM‑K), and use the PSO algorithm Optimize the parameters p, f; (3) use the improved algorithm to identify the no-load model of the closed-loop hydroelectric unit. This method has the advantages of fast algorithm, high reliability, and easy programming, etc. It can optimize the appropriate algorithm parameters according to different hydroelectric unit models in practice, and the improved algorithm effectively improves the identification accuracy.

Description

An improved subspace closed-loop identification method for hydroelectric unit models

technical field

The invention belongs to the technical field of hydroelectric unit model modeling and identification, and in particular relates to an improved subspace closed-loop identification method for a hydroelectric unit model.

Background technique

With the increasing scale of the power system, the safety and stability of the system put forward higher requirements for the accuracy of the hydroelectric unit model. The hydraulic turbine speed control system has the unique characteristics of non-minimum phase, nonlinearity, and complexity. Therefore, a more accurate identification of the model of the hydroelectric unit is essential for large-scale grid connection of hydropower generation, timely adjustment of dispatching strategies for power systems containing hydropower generation, and It is of great practical significance to realize its safe, stable and economical operation.

Open-loop identification can be performed on the load model, but in the no-load condition, the frequency dead zone is 0, the unit frequency tracks the grid frequency, and the no-load model identification belongs to closed-loop identification. Previous studies on model identification of hydroelectric units focused on open-loop identification methods. In comparison, closed-loop identification methods are scarce. Compared with open-loop identification, closed-loop identification is convenient, fast, and widely used in industry. However, the current identification method for hydroelectric unit no-load model is based on the identification method of closed-loop to open-loop.

The subspace identification method realizes the identification through the SVD reduced-order state-space model and the linear projection to the data matrix. Predictive Form Reduced Subspace Identification Method (PARSIM-K) is an optimized subspace identification method. Predictor form PARSIMonious algorithm for closed-loop subspace identification (PARSIM-K) is a subspace closed-loop identification method, such as references (PannocchiaG, Calosi MA predictor form PARSIMonious algorithm for closed-loop subspace identification. Journal of Process Control, 2010, 20: 517-524 ) made a more specific introduction to PARSIM-K. Specifically, the method is mainly divided into two steps: 1) Estimation [(Γ ^f L _z ), H _K ^f , G _K ^f ] term; 2) Realization of weighted SVD and estimated system matrix. This algorithm makes full use of and develops the characteristics of H ^f and G ^f being the lower triangular Toeplitz matrix, effectively solves the closed-loop identification problem of the correlation between noise and input data, improves the calculation efficiency, and ensures the consistency of the algorithm, so as to realize the No-load model identification of hydroelectric units with frequency noise. However, due to the small number of parameters of the PARSIM-K algorithm, the identification results of the algorithm are greatly affected by the parameters p and f, so that the current PARSIM-K algorithm still has insufficient reliability and accuracy, and it is difficult to meet the requirements of the closed-loop identification of the current hydroelectric unit model .

Contents of the invention

Aiming at the deficiency of current hydroelectric unit model closed-loop identification method, the present invention proposes an improved subspace closed-loop identification method for hydroelectric unit model, which is based on PSO parameter optimization prediction form parsimony subspace identification method (PARSIM-K) for hydroelectric unit model Identification, this method makes full use of the Toplitz structure of the Markov matrix parameters and SVD reduction order to obtain the extended observable matrix, estimate the system matrix, and optimize the parameters p and f with PSO, which can greatly improve the reliability of the closed-loop identification of the hydroelectric unit model and precision.

In order to achieve the above object, according to the present invention, an improved subspace closed-loop identification method for a hydroelectric unit model is provided, which includes the following steps:

S1 establishes a hydraulic turbine speed regulation closed-loop system model with output frequency noise;

S2 determines the excitation signal and unit frequency noise signal, and collects guide vane opening and unit frequency;

S3 optimizes the parameters p and f in the PARSIM-K algorithm, and obtains the optimized parameters p and f, where f and p represent future time domain parameters and past time domain parameters respectively;

S4 improves the PARSIM-K algorithm with the optimized parameters p and f, and uses the improved PARSIM-K algorithm to identify the no-load model of the closed-loop hydropower unit, so that the closed-loop identification of the no-load model of the hydropower unit can be realized.

As a further preference of the present invention, wherein, the specific process of the parameter p, f in the described PSO optimization PARSIM-K algorithm is:

S31 sets the initial particle position, velocity range and learning factor;

S32 evaluates the particle, calculates the individual extremum and group extremum of the current particle according to the fitness evaluation function;

S33 update particles;

S34 Estimate [(Γ ^f L _z ), H _K ^f , G _K ^f ] item, realize weighted SVD and estimate system matrix, and update individual extremum and group extremum;

S35 checks whether the end condition is met, if the current iteration number reaches the maximum number, then end, output the particles of the optimal solution, namely parameters p, f, and obtain the best estimated model, otherwise go to step S32.

As a further preference of the present invention, the fitness evaluation function is Among them, L represents the number of sampled data, k represents the k-th iteration, j represents the j-th sampled data, y(j) is the actual measurement output data, y _k (j) represents the estimated model when the input is the actual measurement input Output Data.

As a further preference of the present invention, the unit output frequency noise is white noise with a mean value of 0 and a constant variance.

Noise is a non-negligible factor in closed-loop identification, and the system model with noise is more in line with the actual situation. In this scheme, the established water turbine speed control closed-loop system model takes into account the influence of frequency noise on closed-loop identification, and establishes a water turbine speed control system model with output frequency noise. The mean value of the unit output frequency noise is 0, and the variance is a constant value. of white noise.

As a further preference of the present invention, wherein the given frequency step signal is determined as the excitation signal, so that the guide vane opening signal satisfies the continuous excitation condition rank(UL ) _≥f +p.

Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

1) The method of the present invention proposes a closed-loop identification method directly applicable to hydroelectric unit models, without using the previous open-loop identification or closed-loop to open-loop identification methods, and considers the influence of unit frequency noise on closed-loop identification;

2) The method of the present invention improves the prediction form contracted subspace identification method, optimizes the parameters p and f by the PSO algorithm, and improves the accuracy and reliability of the algorithm;

3) The method algorithm of the present invention has low complexity and is easy to program and apply in engineering.

Description of drawings

The invention can be best understood by referring to the following description taken in conjunction with the accompanying drawings. In the drawings, the same parts may be denoted by the same reference numerals.

Fig. 1 is the block diagram of the hydraulic turbine system model with noise established;

Figure 2 is a structural block diagram of the controller and the actuator;

Fig. 3 is the hydro turbine generator and load model;

Fig. 4 is algorithm flow chart;

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and exemplary embodiments. It should be understood that the exemplary embodiments described here are only used to explain the present invention, and are not intended to limit the applicable scope of the present invention.

An improved subspace closed-loop identification method for a hydroelectric unit model according to an embodiment of the present invention. On the basis of analyzing the influence of the hydraulic turbine speed regulation closed-loop system and the output frequency noise of the unit on the closed-loop identification, the PSO algorithm is used to identify the reduced subspace of the prediction form. The parameters p and f of the method are iteratively optimized, and the optimized predictive form reduction subspace identification method is applied to the closed-loop identification of the no-load model of the hydroelectric unit.

Specifically, the improved subspace closed-loop identification method of the hydroelectric unit model in this embodiment specifically includes the following steps:

Step 1 establishes the model of the hydraulic turbine speed regulation closed-loop system with frequency noise, and sets the model parameters.

The block diagram of the system model established in this embodiment is shown in FIG. 1 . Figure 2 is the PID controller model and electro-hydraulic servo system model. Figure 3 is the turbine generator and load model. Parameter variables are defined in Table 1:

Table 1 Definition of parameters and variables of the model of hydraulic turbine regulating system with noise

In Figure 1, x is the frequency of the unit; x _r is the given frequency of the unit; y _PID is the output signal of the PID controller; y is the opening of the servomotor guide vane.

Step 2 selects the continuous excitation signal and the unit output frequency noise signal.

In this embodiment, the simulation excitation signal of the no-load model of the hydroelectric unit is selected according to the definition of the continuous excitation signal and the actual requirements of the project.

The continuous excitation signal is defined as: the input signal u is a deterministic sequence of length L, which satisfies u∈R ^m . If formula (1) holds, then u is continuous excitation of order hm.

The PARSIM-K algorithm requires that the input sequence u is a continuous excitation of order f+p, and the selected excitation signal can not only ensure the stability of the system, but also meet the requirements of the excitation order. In this embodiment, the given frequency step signal is selected as the excitation signal, and whether the model input (guide vane opening signal u) satisfies the continuous excitation condition rank(UL ) _≥f +p is checked in the simulation.

In addition, in this embodiment, the no-load model of the hydroelectric unit is selected according to the signal-to-noise ratio to simulate the frequency noise signal. Noise is a non-negligible factor in closed-loop identification, and the system model with noise is more in line with the actual situation. Therefore, in the present embodiment, a water turbine speed-governing system model with output noise is established, wherein the unit output frequency noise is set to mean value 0 and variance to be a constant value (for example ) band-limited white noise. Specifically, Equation (2) defines the output signal-to-noise ratio, and after the output data is collected, the noise variance of the unit frequency can be determined.

SNR=10*lg(var(y)/var(o))=20*lg(V(y)/V(o)) (2)

Among them, var represents the variance; V represents the signal amplitude; y is the output; o is the output noise, which is assumed to be white noise with a mean value of 0 and a constant variance.

Step 3: Use the PSO algorithm to optimize the parameters p and f in the PARSIM-K algorithm to obtain the optimized parameters p and f.

In this scheme, the influence of parameters p and f in the PARSIM-K algorithm on identification is considered. Specifically, first, in this embodiment, the linear time-invariant system in the form of a predictor is:

x _k+1 ＝A _K x _k +B _K u _k +Ky _k (3a)

y _k =Cx _k +Du _k +e _k (3b)

Among them, x∈R ⁿ represents state; u∈R ^m represents input; y∈R ^l represents output; e∈R ^l represents new information; K represents Kalman filter gain matrix; A _K ＝A-KC; B _K ＝B -KD. And the model satisfies the following assumptions:

a) The matrix (A, B) is controllable, the matrix (A, C) is observable, and the matrix A _K =A-KC is a strict Hurwitz matrix (in a discrete sense).

b) The new information {e _k } is a fixed, zero-mean, white noise process, and its self-variance is: when i≠j, ε(e _j e' _j )=R _e ,ε(e _i e' _j ) =0. Among them, R _e is positive definite.

c) Data is collected over L sampling times. In an open-loop system, the following condition holds: ε(u _i e' _j )=0 for all i and j. In a closed-loop system, if D=0, then when i<j, ε(u _i e' _j )=0, that is, u _{i can be estimated by feeding back y i ;} if D=0, then when i≤j , ε(u _i e' _j )=0, that is, u _i can be estimated by feeding back y _i-1 (or earlier output).

d) The input {u _k } is quasi-stable and f+p order continuous excitation. Among them, f and p represent the future time-domain parameters and the past time-domain parameters respectively.

The basic idea of the subspace identification algorithm is to divide the measured input and output data into past and future parts. Define the output sequence y and the state sequence x of known length L(L>>max(f, p)) as follows:

y _fi =[y _p+i-1 y _p+i ... y _L-f+i-1 ], y _pi =[y _i-1 y _i ... y _Lf-p+i-1 ]

Y _f = [y ^T _f1 y ^T _f2 ... y ^T _ff ] ^T , Y _p = [y ^T _p1 y ^T _p2 ... y ^T _pf ] ^T

X _kp = [x _kp x _k-p+1 ... x _k-p+L-1 ], X _k = [x _k x _k+1 ... x _k+L-1 ]

Wherein, i=1,...,L. The input data u and the innovation e are similarly defined, and the block Hankel matrix U _f ∈ R ^mf×N , U _p ∈ R ^mp×N , E _f ∈ R ^lf×N , E _p ∈ R ^lp×N , Y _f ∈ R ^lf×N , Y _p ∈ R ^lp×N (N=Lf−p+1).

If let x _f ＝A _K ^p x _p +L _z Z _p , iteratively derived from formula (3):

Y _f ＝Γ _K ^f x _f +H _K ^f U _f +G _K ^f Y _f +E _f

＝Γ _K ^f (A _K ^p x _p +L _z Z _p )+H _K ^f U _f +G _K ^f Y _f +E _f

(4)

Among them, x _f =x _f1 ∈ R ^n×N , L _z is the inverse extended controllable matrix, Γ _K ^f is the extended observable matrix, H _K ^f and G _K ^f are lower triangular Toeplitz matrices. The specific structure of the matrix is as follows:

in,

In this embodiment, the PARSIM-K algorithm is specifically implemented through steps 3.1) and 3.2).

3.1) Estimate the [(Γ ^f L _z ), H _K ^f , G _K ^f ] term.

The matrices H _K ^f and G _K ^f are strictly block lower triangular structures, known from formula (4):

y _f1 ＝Γ _K ^f1 (A _K ^p x _p +L _z Z _p )+H _K ^f1 u _f1 +e _f1 (5a)

When i=2,...,f, y _fi ＝Γ _K ^fi (A _K ^p x _p +L _z Z _p )+H _K ^fi u _f1 +G _K ^fi y _f1 +y _fi +e _fi

(5b)

Among them, y _f2 =H _K ^f1 u _f2 ; when i=3,...,f,

Since A _K is a strict Hulvitz matrix, it is assumed that the selected parameter p is large enough such that Then the [(Γ ^fi L _z ), H _K ^fi , G _K ^fi ] term is estimated by formula (5).

3.2) Realize weighted SVD and estimate system matrix.

pair matrix Implement weighted SVD:

Wherein, (U _n , S _n , V _n ) are the SVD items associated with the n largest singular values, R _n represents the error associated with the remaining (fl-n) SVD items, and the weight matrix W ₁ =I,

Finally, yes with The least square method is used to calculate the system estimation matrix.

The above analysis of the PARSIM-K algorithm shows that after the parameters p and f are set, the measured input and output data can be used to perform matrix operations to obtain identification results. For different closed-loop systems, the parameters p and f applicable to the system are also different. If the parameter setting is too small, it may lead to large errors in the identification results; if the parameter setting is too large, unnecessary calculations will be added. Therefore, when applying the PARSIM-K algorithm to different closed-loop systems, it is necessary to select appropriate algorithm parameters p and f. The definitions of PSO algorithm parameter variables in this scheme are shown in Table 2.

Table 2 PSO algorithm parameter variable definition

To simulate the no-load model of the hydroelectric unit, in one embodiment, the parameter of the PARSIM-K algorithm after PSO optimization is p=f=29. The flow chart of the improved algorithm is shown in Figure 4.

For different closed-loop systems, the parameters p and f applicable to the system are also different. The steps of PSO to optimize parameters p and f of PARSIM-K algorithm are as follows:

Step (3.3.1) initialization. Set the initial particle position, velocity range, learning factor, etc.

Step (3.3.2) evaluates the particles. Calculate the individual extremum and group extremum of the current particle according to the fitness evaluation function. The fitness evaluation function is Among them, L represents the number of sampled data; k represents the k-th iteration; j represents the j-th sampled data; y(j) is the actual measurement output data; y _k (j) represents the estimated model when the input is the actual measurement input Output Data.

Step (3.3.3) update of particles. The speed update equation and position update equation are respectively Among them, v is the speed; x is the position; i represents the i-th sampled data c ₁ and c ₂ are the learning factors; rand _{1, 2} are random numbers between [0,1]; pbest and gbest respectively represent the individual extremum and group extremum.

Step (3.3.4) Estimate the [(Γ ^f L _z ), H _K ^f , G _K ^f ] term, realize weighted SVD and estimate the system matrix. Update individual extremum and group extremum.

Step (3.3.5) detects whether the end condition is met. If the current number of iterations reaches the maximum number, then end, output the particles of the optimal solution (ie parameters p, f), and obtain the best estimated model, otherwise go to step (3.3.2).

Step 4 Substitute the parameters p and f optimized by the PSO algorithm into the PARSIM-K algorithm, repeat steps 3.1 and 3.2, and apply it to the identification of the no-load model of the closed-loop hydropower unit to realize the closed-loop identification of the no-load model of the hydropower unit.

In order to verify the effectiveness of the method of the present invention, two groups of parameters can be randomly selected (parameter 1 is p=28, f=14, parameter 2 is p=25, f=48) and compared with the parameters after PSO optimization. The no-load model of the hydroelectric unit adopts the discrete model a ₀ , a ₁ , b ₀ and b ₁ are the parameters to be identified, and the following two model accuracy evaluation indexes are defined.

Root mean square error (root mean square error, RMSE):

Mean absolute percentage error (mean absolute percentage error, MAPE):

Table 3 is a comparison of real parameters and estimated model parameters.

It can be seen from Table 3 that the estimated model parameters of the PARSIM-K algorithm using PSO optimized parameters are closest to the real parameter values, and the frequency curve is in good agreement with the actual curve; In particular, the parameters b ₀ and b ₁ have seriously deviated from the true value, and the steady-state value of the estimated model output frequency curve of parameter 2 has deviated from the actual steady-state value of the frequency curve.

Table 3 True model and estimated model parameters

Table 4 is a comparison of model accuracy indicators. It can be seen from Table 4 that the model accuracy indicators RMSE and MAPE of the algorithm estimation model after PSO optimized parameters are both smaller than the model accuracy of parameters 1 and 2, indicating that the PARSIM-K algorithm with PSO optimized parameters can effectively improve the algorithm identification accuracy.

Table 4 Comparison of model accuracy indicators

In this embodiment, the no-load estimation model of the hydroelectric unit based on the closed-loop identification of the PARSIM-K method with PSO optimized parameters is highly consistent with the real model, which demonstrates the superiority of the method of the present invention compared with the PARSIM-K method with unoptimized parameters.

Those skilled in the art can easily understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (5)

1. A method for identifying an improved subspace closed loop of a hydroelectric generating set model comprises the following steps:

s1, establishing a water turbine speed regulation closed-loop system model with output frequency noise;

s2, determining an excitation signal and a unit frequency noise signal, and acquiring the opening of a guide vane and the unit frequency;

s3, optimizing parameters p and f in the PARSIM-K algorithm, and obtaining the optimized parameters p and f, wherein f and p respectively represent future time domain parameters and past time domain parameters;

s4, improving the PARSIM-K algorithm by the optimized parameters p and f, and identifying the no-load model of the closed-loop hydroelectric generating set by using the improved PARSIM-K algorithm, so that the closed-loop identification of the no-load model of the hydroelectric generating set can be realized.

2. The improved subspace closed-loop identification method of the hydroelectric generating set model according to claim 1, wherein the parameters p and f in the optimized PARSIM-K algorithm in the step S3 are realized through a PSO algorithm, and the specific process is as follows:

s31 setting initial particle position, speed range and learning factor;

s32, evaluating the particles, and calculating the individual extreme value and the group extreme value of the current particles according to the fitness evaluation function;

s33 updating the particles;

s34 estimates [ ((S))^fL_z),H_K ^f,G_K ^f]Item, realizing weighted SVD and estimation system matrix, and updating individual extreme value and group extreme value;

s35, whether the end condition is met is detected, if the current iteration times reach the maximum times, the process is ended, the particles of the optimal solution, namely the parameters p and f, are output, the optimal estimation model is obtained, and if not, the process goes to the step S32.

3. The method according to claim 2, wherein the fitness evaluation function isWherein, L represents the number of sampling data, k represents the kth iteration, j represents the jth sampling data, y (j) is the actual measurement output data, y (j)_k(j) Representing the output data of the estimation model at the input of the actual measurement.

4. The improved subspace closed-loop identification method of the hydroelectric generating set model according to claim 2 or 3, wherein the set output frequency noise is white noise with a mean value of 0 and a variance of a fixed value.

5. The method according to any one of claims 1 to 4, wherein a frequency-given step signal is determined as the excitation signal, such that a guide vane opening signal satisfies a continuous excitation condition rank (U)_L)≥f+p。