CN103853881A

CN103853881A - Water turbine parameter identification method based on self-adaptive chaotic and differential evolution particle swarm optimization

Info

Publication number: CN103853881A
Application number: CN201410048930.4A
Authority: CN
Inventors: 李兴源; 王曦; 刘俊敏; 黄睿; 苗淼; 丁理杰
Original assignee: Sichuan University
Current assignee: Sichuan University
Priority date: 2014-02-12
Filing date: 2014-02-12
Publication date: 2014-06-11

Abstract

The invention discloses a water turbine parameter identification method based on adaptive chaos and differential evolution particle swarm algorithm, which is characterized by the following steps: (1) determining the nonlinear model of the water turbine; (2) obtaining frequency step test data; (3) Determine the fitness function of adaptive chaos and differential evolution particle swarm optimization; (4) set the basic parameters of the identification algorithm; (5) calculate the fitness function value of the particles in the group, the individual extremum of the particle and the global extremum of the group, and update (6) Carry out premature judgment, if it is judged to be premature, perform operations such as differential mutation, intersection and selection to avoid falling into local optimum; (7) Check whether the algorithm satisfies the termination condition, and if so, output the most Excellent solution. If not satisfied, the inertia factor changes adaptively, and steps 5-7 are performed again. The invention identifies the water hammer time constant of the water turbine, and the algorithm convergence speed is fast and the convergence precision is high, and the invention can utilize the water turbine test data at any load level, thereby effectively reducing the test cost.

Description

Based on the turbine parameter discrimination method of self-adaptation chaos and differential evolution particle cluster algorithm

Technical field

The present invention relates to a kind of turbine parameter discrimination method based on self-adaptation chaos and differential evolution particle cluster algorithm, belong to parameters of electric power system identification field.

Background technology

For hydraulic generator unit; the hydraulic turbine and governing system thereof are as genset important composition part; not only bearing the vital task of start and stop unit, regulating frequency, adjusting active power; and be the final topworks of primary frequency modulation, frequency modulation frequency modulation, Automatic Generation Control (AGC); its accurate mathematical model not only has great value for the efficient operation that improves mains side generating plant, and to electric power system design, planning, stability analysis have significant impact under the new situation.

In traditional Power System Analysis, the normal hydraulic turbine model adopting ideally, ignored the impact of Adaptive System of Water-Turbine Engine variable working condition, variable element, the factor such as non-linear, in order to make result more accurate, electromagnetic transient simulation adopts non-linear hydraulic turbine model conventionally in analyzing.Set up accurate mathematical model and also depend on the identification of model parameter, conventional parameter identification method, as all applicable linear models only such as least square method, pencil of matrix, TLS-ESPRIT algorithm, poor to nonlinear system parameter identification effect.Intelligent algorithm as particle cluster algorithm can well the non-linear hydraulic turbine model of identification, [yellow pine, Xu Guangwen. the self-defined modeling of Turbine Governor System and application [J]. Automation of Electric Systems, 2012,36 (16): 115-117.] [what is ever victorious. Water turbine governing system simulation and parameter identification [D]. and Xi'an University of Technology, 2009.] but it is easily absorbed in local optimum, cause resultant error larger.In recent years, the improvement of particle cluster algorithm becomes a study hotspot, improves convergence precision and speed, avoids being absorbed in the common purpose that local optimum is various improvement algorithms.Improved particle cluster algorithm is had to good practical value for the identification of non-linear hydraulic turbine model parameter.

Summary of the invention

The object of the invention is for the deficiency of present identification technique and a kind of turbine parameter discrimination method based on self-adaptation chaos and differential evolution particle cluster algorithm is provided, be characterized in the accurately non-linear hydraulic turbine model parameter of identification of the method, and its speed of convergence is very fast.

Object of the present invention is realized by following technical measures

Turbine parameter discrimination method based on self-adaptation chaos and differential evolution particle cluster algorithm comprises the following steps:

1) determine Nonlinear hydraulic turbine model and parameter to be identified, Mathematical Model for Hydraulic Turbine is:

\{\begin{matrix} P_{m} = qh \\ q = y \sqrt{h} \\ - T_{w} \frac{dq}{dt} = 1 - h \end{matrix}

Comprising aperture y, flow q, head h, mechanical output P _m4 variablees, think that the hydraulic turbine is taking aperture y as input, mechanical output P _mfor the nonlinear function of output, water hammer time constant T _wfor parameter to be identified;

2) hydraulic turbine is carried out to frequency step test, measure guide vanes of water turbine aperture and mechanical output, because guide vanes of water turbine aperture is difficult to direct measurement, adopt servomotor stroke to substitute, hydraulic turbine mechanical output is by electromagnetic power approximate substitution;

3) determine self-adaptation chaos and differential evolution particle cluster algorithm fitness function, fitness function value is set to normatron tool power and actual hydraulic turbine mechanical output sum of square of deviations;

4) self-adaptation chaos and differential evolution particle cluster algorithm basic parameter are set: basic parameter comprises: the number N of particle, the maximal rate v of particle _max, inertial factor ω, accelerator coefficient c ₁and c ₂, algorithm maximum iteration time T; In given range by the position x of N particle of logistic chaotic maps initialization _iwith its speed v _i, and make t=1; Chaos initialization formula is:

\{\begin{matrix} x_{i} (1) = {αx}_{(i - 1)} (1) (1 - x_{(i - 1)} (1)) \\ v_{i} (1) = {αv}_{(i - 1)} (1) (1 - v_{(i - 1)} (1)) \end{matrix}

Wherein, α is controlling elements, i=1, and 2 ... N, x ₀(1), v ₀(1) be the random number between (0,1);

5) calculate the fitness function value of particle in colony, calculate the individual extreme value pbest of particle and the global extremum gbest of colony, and more speed and the position of new particle, its more new formula be:

\{\begin{matrix} v_{i} (t + 1) = {ωv}_{i} (t) + c_{1} r_{1} [{pbest}_{i} (t) - x_{i} (t)] + c_{2} r_{2} [gbest (t) - x_{i} (t)] \\ x_{i} (t + 1) = x_{i} (t) + v_{i} (t + 1) \end{matrix}

Wherein, r ₁and r ₂for the random number between (0,1);

6) calculate Colony fitness variance σ ²carry out the precocious judgement of particle, if fitness variances sigma ²be less than a certain threshold value, judge its precocity;

σ^{2} = \frac{1}{N} Σ_{i = 1}^{N} {(\frac{f_{i} - f_{avg}}{f})}^{2}

F _iit is the fitness of i particle; f _avgit is population fitness average, f is fitness function value normalized factor, if be absorbed in earliness, the diversity that shows population is poor, utilizes differential evolution algorithm to carry out variation, intersect and select operation particle, realizes the evolution of particle, improve the diversity of population, the ability of searching optimum that strengthens population, prevents that algorithm is absorbed in local optimum, and differential evolution algorithm formula is as follows:

A _i(t+1)＝x _i(t)+λ×(gbest(t)-x _i(t))+F×(x _j(t)-x _k(t))

B_{i} (t + 1) = \{\begin{matrix} A_{i} (t + 1) & rand (0,1) \leq CR \\ x_{i} (t) & rand (0,1) > CR \end{matrix}

x_{i} (t + 1) = \{\begin{matrix} B_{i} (t + 1), f (B_{i} (t + 1)) \leq f (x_{i} (t)) \\ x_{i} (t), f (B_{i} (t + 1)) > f (x_{i} (t)) \end{matrix}

Wherein, j, k is random integers, represents individual sequence number in population, and i ≠ j ≠ k; λ, F are mutagenic factor, and CR is for intersecting the factor, and rand (0,1) is the random number between (0,1), and f (x) is variable x fitness function;

7) whether check algorithm meets end condition, if t>T stops iteration, and output optimum solution, i.e. the water hammer time constant T that identification obtains _w; Otherwise inertial factor ω adaptive change, re-executes step 5-7, and makes t=t+1.Inertial factor adaptive change formula:

ω = ω_{\max} - \frac{t \times (ω_{\max} - ω_{\min})}{T}

ω _max, ω _minbe respectively inertial factor maximal value and minimum value.

Tool of the present invention has the following advantages:

Conventional particle cluster algorithm random initializtion particle position and speed, the present invention adopts chaos method initialization particle position and speed, can effectively improve the diversity of primary.Chaos algorithm initialization can avoid to greatest extent algorithm to be absorbed in local optimum together with differential evolution operation.Self-adaptation inertial factor can improve convergence of algorithm speed in calculating early stage, and the later stage is improved algorithm convergence precision, makes whole efficiency of algorithm higher.In addition, because the present invention adopts nonlinear model, therefore water wheels function meaning aperture in office is tested, and effectively reduces experimentation cost.

Brief description of the drawings

Fig. 1 is Nonlinear hydraulic turbine model block diagram.

Wherein y is aperture, and q is flow, and h is head, P _mfor mechanical output, T _wfor water hammer time constant.

The comparison diagram of hydraulic turbine real response curve and model response curve when Fig. 2 is frequency step.

Wherein, real response curve is actual measurement hydraulic turbine output mechanical power curve, and model response curve is that identification obtains water hammer time constant T _wbring the simulation curve that Fig. 1 institute representation model obtains into.

Fig. 3 is turbine parameter identification process flow diagram.

1, set up model and be written into data, 2, parameters initialization, 3, calculate fitness function, 4, upgrade particle position and speed, 5, precocious judgement, 6, differential evolution operation, 7, finish judgement, 8, inertial factor adaptive change, 9, Output rusults.

When Fig. 4 is turbine parameter identification, fitness function is with iterations change curve.

Embodiment

Below by embodiment, the present invention is specifically described; be necessary to be pointed out that at this present embodiment is only used to further illustrate the present invention; but can not be interpreted as limiting the scope of the invention, the person skilled in the art in this field can make according to the content of the invention described above improvement and the adjustment of some non-intrinsically safes to the present invention.

Embodiment 1

The present invention utilizes self-adaptation chaos and differential evolution particle cluster algorithm to carry out identification to hydraulic turbine water hammer time constant.From non-linear Mathematical Model for Hydraulic Turbine, after water hammer time constant is determined, just can determine the acting characteristic of the hydraulic turbine.By discrimination method, can determine a water hammer time constant value, make the hydraulic turbine motion state that emulation obtains approach real hydraulic turbine motion state.In identification process, first test and obtain one group of guide vanes of water turbine aperture and output mechanical power sampled data by frequency step, and then utilize self-adaptation chaos and differential evolution particle cluster algorithm to determine water hammer time constant value in non-linear hydraulic turbine model, make in same guide vane opening situation nonlinear model calculating machine power and actual hydraulic turbine output mechanical power deviation minimum.

1) determine Nonlinear hydraulic turbine model and parameter to be identified.Mathematical Model for Hydraulic Turbine is:

\{\begin{matrix} P_{m} = qh \\ q = y \sqrt{h} \\ - T_{w} \frac{dq}{dt} = 1 - h \end{matrix}

Comprising aperture y, flow q, head h, mechanical output P _m4 variablees, think that the hydraulic turbine is taking aperture y as input, mechanical output P _mfor the nonlinear function of output, water hammer time constant T _wfor parameter to be identified.Hydraulic turbine model block diagram as shown in Figure 1;

2) hydraulic turbine is carried out to frequency step test, measure guide vanes of water turbine aperture and mechanical output, because guide vanes of water turbine aperture is difficult to direct measurement, adopt servomotor stroke to substitute, hydraulic turbine mechanical output is by electromagnetic power approximate substitution; When certain hydraulic turbine frequency step increases 0.2Hz, hydraulic turbine output mechanical power curve is as shown in Fig. 2 solid line part.

3) determine self-adaptation chaos and differential evolution particle cluster algorithm fitness function.Fitness function value is set to model and calculates output power and actual hydraulic turbine output power sum of square of deviations.

4) press process flow diagram shown in Fig. 3 by self-adaptation chaos and differential evolution particle cluster algorithm identification water hammer time constant T _w, process flow diagram the 1st step is the sampled data of setting up model and being written into the hydraulic turbine while test; The 2nd step arranges position and the speed of self-adaptation chaos and differential evolution particle cluster algorithm basic parameter and chaos initialization particle; The 3rd step is calculated each particle fitness function, finds out individual extreme value and global extremum; The 4th step is position and the speed of new particle more; The 5th step is carried out the precocious judgement of particle, if the precocity of being judged as enters the 6th step, particle is carried out to differential evolution operation, then enters the 7th step; If judge, particle does not have precocity, directly enters the 7th step; Whether the 7th step evaluation algorithm meets termination condition, if meet, calculates and finishes, output optimum solution, i.e. the water hammer time constant that identification obtains; If do not meet termination condition, enter the 8th step, inertial factor adaptive change, and proceed to the 3rd step.

Identification algorithm basic parameter is set to:

Population size N=100, inertial factor ω=0.6, accelerator coefficient c ₁=1.3, c ₂=1.7, the mutagenic factor of differential evolution operation is λ=F=0.8, intersection factor CR=0.6, Colony fitness variance threshold value σ ²=0.001, controlling elements α=4, total iterations T=100 of algorithm.

5) when Fig. 4 is for application identification turbine parameter of the present invention, fitness function is with iterations change curve.From figure, can find out that the present invention's discrimination method fast convergence rate used, convergence precision are high.Final identification obtains water hammer time constant T _w=2.3, carry it in the model shown in Fig. 1, obtain hydraulic turbine model response curve as shown in Fig. 2 dotted line, model response curve and real response curve error are little, illustrate that the present invention's discrimination method used is accurately and reliably.

Claims

1. The water turbine parameter identification method based on adaptive chaos and differential evolution particle swarm algorithm, is characterized in that the method comprises the following steps:

1) Determine the nonlinear model of the turbine and the parameters to be identified. The mathematical model of the turbine is:

\{\begin{matrix} {P P}_{m m} = = qh qh \\ q q = = y the y \sqrt{h h} \\ - - {T T}_{w w} \frac{dq dq}{dt dt} = = 11 - - h h \end{matrix}

It includes 4 variables of opening y, flow q, water head h, and mechanical power P _m . It is considered that the water turbine is a nonlinear function with opening y as input and mechanical power P _m as output, and water hammer time constant T _w is to be identified parameter;

2) Carry out a frequency step test on the turbine to measure the opening of the guide vane and the mechanical power of the turbine. Since the opening of the guide vane of the turbine is difficult to measure directly, the servomotor stroke is used instead, and the mechanical power of the turbine is approximately replaced by electromagnetic power;

3) Determine the fitness function of the adaptive chaos and differential evolution particle swarm optimization algorithm, and the fitness function value is set to the sum of the squares of the deviation between the model's calculated mechanical power and the actual hydraulic turbine mechanical power;

4) Set the basic parameters of the adaptive chaos and differential evolution particle swarm optimization algorithm. The basic parameters include: the number of particles N, the maximum velocity v _max of the particles, the inertia factor ω, the acceleration coefficients c ₁ and c ₂ , and the maximum number of iterations T of the algorithm ;In a given range, initialize the positions x _i and their velocities v _i of N particles by the logistic chaotic map, and let t=1; the chaos initialization formula is:

\{\begin{matrix} {x x}_{i i} ((11)) = = {αx αx}_{((i i - - 11))} ((11)) ((11 - - {x x}_{((i i - - 11))} ((11)))) \\ {v v}_{i i} ((11)) = = {αv αv}_{((i i - - 11))} ((11)) ((11 - - {v v}_{((i i - - 11))} ((11)))) \end{matrix}

Among them, α is the control factor, i=1,2,...N, x ₀ (1), v ₀ (1) is a random number between (0,1);

5) Calculate the fitness function value of the particles in the population, calculate the individual extremum pbest of the particles and the global extremum gbest of the population, and update the velocity and position of the particles. The update formula is:

\{\begin{matrix} {v v}_{i i} ((t t + + 11)) = = {ωv ωv}_{i i} ((t t)) + + {c c}_{11} {r r}_{11} [[{pbest pbest}_{i i} ((t t)) - - {x x}_{i i} ((t t))]] + + {c c}_{22} {r r}_{22} [[gbest gbest ((t t)) - - {x x}_{i i} ((t t))]] \\ {x x}_{i i} ((t t + + 11)) = = {x x}_{i i} ((t t)) + + {v v}_{i i} ((t t + + 11)) \end{matrix}

Among them, r ₁ and r ₂ are random numbers between (0,1);

6) Calculate the population fitness variance σ ² to judge the prematurity of the particle. If the fitness variance σ ² is less than a certain threshold, it is judged to be premature;

{σ σ}^{22} = = \frac{11}{N N} {Σ Σ}_{i i = = 11}^{N N} {((\frac{{f f}_{i i} - - {f f}_{avg avg}}{f f}))}^{22}

f _i is the fitness of the i-th particle; f _avg is the average fitness value of the particle swarm, and f is the normalization factor of the fitness function value. If it falls into a premature state, it indicates that the diversity of the particle swarm is poor, and the differential evolution algorithm is used Perform mutation, crossover and selection operations on particles to realize the evolution of particles, increase the diversity of the population, enhance the global search ability of the particle swarm, and prevent the algorithm from falling into local optimum. The formula of the differential evolution algorithm is as follows:

A _i (t+1)＝ _xi (t)+λ×(gbest(t) _-xi (t))+F×(x _j (t)-x _k (t))

{B B}_{i i} ((t t + + 11)) = = \{\begin{matrix} {A A}_{i i} ((t t + + 11)) & rand rand ((0,1 0,1)) \leq \leq CR CR \\ {x x}_{i i} ((t t)) & rand rand ((0,1 0,1)) > > CR CR \end{matrix}

{x x}_{i i} ((t t + + 11)) = = \{\begin{matrix} {B B}_{i i} ((t t + + 11)),, f f (({B B}_{i i} ((t t + + 11)))) \leq \leq f f (({x x}_{i i} ((t t)))) \\ {x x}_{i i} ((t t)),, f f (({B B}_{i i} ((t t + + 11)))) > > f f (({x x}_{i i} ((t t)))) \end{matrix}

Among them, j and k are random integers, indicating the serial number of the individual in the population, and i≠j≠k; λ, F are variation factors, CR is cross factor, and rand(0,1) is the relationship between (0,1). Random number, f(x) is variable x fitness function;

7) Check whether the algorithm meets the termination condition. If t>T, stop the iteration and output the optimal solution, that is, the identified water hammer time constant T _w ; otherwise, the inertia factor ω is adaptively changed, and re-execute steps 5-7, and Let t=t+1. Inertia factor adaptive change formula:

ω ω = = {ω ω}_{max max} - - \frac{t t \times \times (({ω ω}_{max max} - - {ω ω}_{min min}))}{T T}

ω _max , ω _min are the maximum and minimum values of the inertia factor respectively.