CN110262223B - Water turbine comprehensive model modeling method based on fractional PID speed regulation system - Google Patents
Water turbine comprehensive model modeling method based on fractional PID speed regulation system Download PDFInfo
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Abstract
The invention provides a water turbine comprehensive model modeling method of a self-adaptive fractional order PID speed regulating system, which comprises the following steps: step 1: establishing a water turbine speed regulator simulation analysis mathematical model based on a fractional order PID speed regulating system, and optimizing a target function based on the fractional order PID speed regulating system by using a hybrid algorithm; step 2: establishing a mechanical hydraulic system and a diversion system mathematical model of a water turbine speed regulating system; and step 3: establishing a water turbine generator model; according to the invention, MATLAB simulation modeling is utilized, a classical PID speed regulating system is improved on the basis of the previous research, a comprehensive model capable of reflecting various parameters of a water turbine speed regulating system and a generator system is established according to example analysis, and the comprehensive model has good reaction on the operation condition of an actual water turbine set in practical application and in the face of the change of various parameters of the water turbine during load fluctuation, so that guarantee is provided for accident prediction and system safe operation.
Description
The technical field is as follows:
the invention relates to hydropower station mechanics and a water turbine speed regulating system principle, in particular to a water turbine comprehensive model modeling method based on a fractional PID speed regulating system.
Background
Traditional hydraulic turbine governing system control structure generally adopts classic hydraulic turbine governing system, and PID governing system control that connects in parallel promptly has advantages such as simple easy operation, along with electric power system's development, also constantly improves to hydroelectric generating set's stability requirement, however, the hydraulic turbine system of the control of PID governing system that connects in parallel has following problem:
1. the stability is slow during starting;
2. the stability is poor when the system load fluctuates, and the problem that the self-regulation capability of the power system is insufficient in case of an emergency occurs.
In order to overcome the defects of the classical water turbine speed regulating system, a large number of scholars provide advanced intelligent control modes, such as fuzzy PID control, BP neural network control, chaotic particle group control and the like, and the researches further optimize the water turbine speed regulating system so as to obviously improve the speed regulating performance of the water turbine.
Considering that the domestic water turbine control mode mostly adopts a regulation mode based on the control of a parallel PID speed regulation system, in order to quickly respond to the system requirements and bring less impact to a power system as much as possible, the optimization of the speed regulation system of the water turbine is very important.
The simulation modeling aspect has made great progress on the nonlinear mechanism modeling research of the water turbine, but the influence of load fluctuation on a speed regulating system of the water turbine is not deeply analyzed; at present, a load model and a generator model are generally equivalent to a first-order transfer function, the limitation of reflected practical problems is large, and the influence on a water turbine speed regulating system when the characteristics of a water turbine generator, a dynamic load model and a power system are in failure is to be further analyzed on the basis of reflecting the speed regulating performance of the water turbine.
Disclosure of Invention
The invention provides a water turbine comprehensive model modeling method based on a fractional order PID speed regulation system, aiming at solving the problem that various important parameters of a water turbine cannot be changed when dynamic load cannot be reflected in nonlinear mechanism modeling of the water turbine.
In order to achieve the purpose, the invention adopts the following technical scheme:
a water turbine comprehensive model modeling method of a self-adaptive fractional order PID speed regulation system comprises the following steps:
step 1: establishing a water turbine speed regulator simulation analysis mathematical model based on a fractional order PID speed regulating system, and optimizing a target function based on the fractional order PID speed regulating system by using a hybrid algorithm;
and 2, step: establishing a mechanical hydraulic system and a diversion system mathematical model of a water turbine speed regulating system;
and 3, step 3: establishing a water turbine generator model, expanding the traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model;
the step 1 specifically comprises the following steps:
step 1.1: the fractional order PID speed regulation system is obtained by a classical PID speed regulation system, and the specific method comprises the following steps:
the differential expression of the classical PID speed regulation system is as follows:
u(t)＝k p e(t)+k i De(t)+k d De(t)；
wherein kp represents a proportional parameter, and the setting range is 0.5-20; ki represents an integral parameter, the setting range is 0.05s < -1 > to 10s < -1 >, kd represents a differential parameter, and the setting range is 0 to 5s;
respectively replacing three adjusting parameters of kp, ki and kd with a transient slip coefficient bt, a buffering time constant Td and an acceleration time constant Tn, specifically:
the transfer function of a classical PID speed regulation system is:
wherein bt is transient slip coefficient, and is 0-1.0; td is a buffer time constant, a setting range is 2 s-20s, tn is an acceleration time constant, a setting range is 0-2s, pc and P are set unit power and set unit power respectively, y is c Y is guide vane opening degree given and guide vane degree, fc and f are frequency given and unit frequency, delta f is frequency difference, delta f' is passing frequency dead zone e f The latter frequency deviation;
and transforming the differential expression of the classical PID speed regulation system into a differential expression of a fractional order PID speed regulation system through Laplace:
u(t)＝k p e(t)+k i D α e(t)+k d D μ e(t)； (4)
wherein α, μ >0, α is an integration order and μ is a differentiation order;
the transfer function of the fractional order PID speed regulation system is as follows:
step 1.2: the method for defining the objective function of the fractional order PID speed regulation system comprises the following steps:
using double error integral as the objective function of the fractional order PID speed regulation system in step 1.1:
where e (t) represents the deviation of the actual output from the desired output, t is time, I SE Represents the squared deviation integral;
step 1.3: and (3) optimizing the objective function based on the fractional order PID speed regulation system in the step 1.2 by using a hybrid algorithm, wherein the specific method comprises the following steps:
will k p 、k i 、k d Alpha and mu parameters form an initial drosophila position, so that the drosophila is optimized according to taste concentration, and the deep search characteristic of the BP neural network is utilized to search k p 、k i 、k d And the optimization solution of the five parameters of alpha and mu specifically comprises the following steps:
step 1.3.1: initializing the fruit fly population size groupsize (400) and the maximum iteration number maxnum (400), and randomly generating the fruit fly population position (X) axis ，Y axis ) The iterative step value R is defined as (0.85-1);
step 1.3.2: randomizing the position and direction of the fruit fly population according to the distance D between the position and the origin of the fruit fly population Dist Determining Drosophila population taste concentration value S i ；
Step 1.3.3: calculating the taste concentration of individual fruit flies, and comparing the taste concentration value S of the fruit fly population i Substituted taste concentration determination function F function Finding individuals with optimal taste concentration from each drosophila population;
retaining the optimum taste concentration b bestsmell To (X) of i ，Y i ) Location, drosophila population S smell Flying to the coordinate, b best indes Expressing the optimal fruit fly position;
step 1.3.4: the position coordinates (X) of the fruit flies obtained in the step 1.3.3 i ，Y i ) Hidden layer n of input BP neural network net (2) (k) Defining input and output;
wherein i =1,2, \ 8230and Q, n, Q value and Z are defined according to the complexity of the controlled object j (2) To optimize the post-drosophila population (X) i ，Y i ) Position, w ij (2) Weighting coefficients, Z, for the hidden layer i (k) (2) Taking a Sigmoid function of an activation function;
step 1.3.5: defining BP neural network output layer n net (3) (k) Updating individual fruit fly, selecting E (k) as performance error index, and keeping position coordinate (X) of fruit fly individual with most concentrated taste i ，Y i )；
Step 1.3.6: by judging the performance index calculated in the last step, the optimal parameter k is output when the maximum iteration number is reached p ,k i ,k d α, μ, end of the process,otherwise, the step 1.3.2 is carried out, and the optimal parameter k is output until the maximum iteration times are reached p ,k i ,k d α, μ, end the process.
The step 2 specifically comprises the following steps:
step 2.1: establishing a mathematical model of a mechanical hydraulic system of a water turbine speed regulating system, and specifically adopting the following method:
the mechanical hydraulic system is used for converting and amplifying an electrical signal into a mechanical displacement signal with certain operating force; because of the response time constant T of the secondary servomotor y1 Is far less than the response time constant T of the main servomotor y The method is generally simplified into an inertia link in modeling, wherein y is an output signal of a mechanical hydraulic system and can also represent the relative size of the opening of a guide vane, a frequency dead zone and a saturation limiting link are added according to the regulation characteristic of a water turbine, and the transfer function of a linear part of a main distributing valve and a servomotor is as follows:
step 2.2: a mathematical model of a water diversion system of a water turbine speed regulating system is established, and the following method is specifically adopted:
according to different lengths of the diversion pressure pipelines, in terms of simulation modeling, a rigid water hammer model is adopted below 700m, an elastic water hammer is adopted when the length is more than 700m, and the water flow pressure change process in the diversion system is described by the following equation:
equation of motion:
h is a water head, Q is water flow, S is the cross-sectional area of a water pipeline, t is time, and g is gravity acceleration;
the flow equation:
wherein a is the water flow acceleration;
and (3) expanding a water hammer equation in the pressure water conduit by Taylor series to obtain n =0 and n =1 terms to obtain the rigid water hammer G A1 And elastic water hammer G A2 Transfer function:
wherein T is W Is rigid water hammer time constant, tr =2L/V is elastic water hammer time constant, L is the length of pressure water conduit, V is water flow wave velocity, H 0 Is the head, Q 0 Is the flow rate, V 0 Is the base speed of water flow.
The step 3 specifically comprises the following steps:
establishing a water turbine generator model, expanding the traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model; the specific method comprises the following steps:
step 3.1: the first order model used by the conventional turbine generator model is:
wherein f is the unit frequency, p is the unit input power difference, tn is the unit inertia time constant, and T is general n Is 3s to 12s, e n For the unit static frequency self-regulation coefficient, e n Taking 0.5-2.0 s;
the first-order model cannot reflect actual parameters of the hydraulic turbine generator and parameters of an excitation system, a synchronous motor model of a five-order space state equation is established through an MATLAB/Simulink simulation platform to be equivalent to the hydraulic turbine generator model, basic parameter characteristics of a hydraulic turbine are defined, dynamic characteristics of stator and rotor magnetic fields and damping windings are considered, and an equivalent circuit of the model is expressed in a rotor reference system (dq frame).
Wherein the stator voltage equation is:
wherein U is d For stator d-axis voltage, U q Is the stator q-axis voltage, phi d And phi q Representing dp-axis flux linkage, i d And i q Is the current in the equivalent dq coordinate system, r a The dq axis sub-transient electromotive force is E ″, which is an equivalent resistance d And E ″) q ，X” d And X' q Is dq times transient reactance;
the voltage equation of the f winding and the dq winding of the rotor and the motion equation of the rotor are as follows:
wherein the d-axis and q-axis time constants (all in units of s), the d-axis open transient (Tdo ') or short circuit (Td') time constants, the d-axis sub-open transient (Tdo ") or short circuit (Td") time constants, the q-axis open transient (Tqo ') or short circuit (Tq') time constants (for a round rotor only), and the q-axis sub-open transient (Tqo ") or short circuit (Tq") time constants. E' q Is a transient electromotive force, E e Is dq winding electromotive force, X' d Is d-axis transient reactance, X d And X q Is the dq-axis reactance, W is the mechanical angular velocity of the rotor, T j Is the inertia time constant, T, of the generator set m Is the mechanical torque of the prime mover,
is an unbalanced torque acting on the rotor shaft.
The invention has the beneficial effects that:
the invention establishes a water turbine speed regulator simulation analysis mathematical model based on a fractional order PID speed regulation system, utilizes MATLAB simulation modeling, improves the classical PID speed regulation system on the basis of the prior research, establishes a comprehensive model capable of reflecting various parameters of the water turbine speed regulation system and a generator system according to example analysis, can specifically analyze the capacity, the frequency, the rotor winding, the stator winding, the excitation winding, the magnetic pole pair number, the output voltage and current condition, the excitation voltage condition and the load change condition of a water turbine unit, can simulate the transient steady state change of various hydropower stations in actual operation to a great extent, and makes up the defects of the traditional water turbine modeling; in practical application, the change of various parameters of the water turbine has good response to the running condition of the actual water turbine set when the load fluctuates, and the accident prediction and the safe running of the system are guaranteed.
Description of the drawings:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a flow chart of a method for establishing a mathematical model for simulation analysis of a hydro governor based on a fractional order PID governing system and optimizing a target function based on the fractional order PID governing system by using a hybrid algorithm according to the present invention;
FIG. 3 is a flow chart of a method for optimizing the objective function of the fractional order PID speed regulation system using a hybrid algorithm according to the invention;
FIG. 4 is a schematic diagram showing the comparison of the control results of a classical PID speed control system and a fractional order PID speed control system during load disturbance;
FIG. 5 is a schematic diagram showing the comparison of the control results of the FOA-PID speed control system and the BP-PID speed control system during load disturbance;
FIG. 6 is a schematic diagram showing the comparison of control results of a BP-PID speed control system and a BPFOA-FOPID speed control system during load disturbance;
FIG. 7 shows changes in turbine excitation voltage, active power, and rotational speed during load switching;
FIG. 8 shows the three-phase current variation when a load is put in;
FIG. 9 is a graph of three phase current change with load partially cut away;
FIG. 10 is a schematic diagram showing a comparison of BPFOA-PID dual-target optimization control results;
FIG. 11 is a diagram showing the result of BPFOA-FOPID adaptive optimization.
The specific implementation mode is as follows:
as shown in fig. 1: the invention relates to a water turbine comprehensive model modeling method of a self-adaptive fractional order PID speed regulation system, which is characterized by comprising the following steps of:
step 1: establishing a water turbine speed regulator simulation analysis mathematical model based on a fractional order PID speed regulating system, and optimizing a target function based on the fractional order PID speed regulating system by using a hybrid algorithm;
and 2, step: establishing a mechanical hydraulic system and a diversion system mathematical model of a water turbine speed regulating system;
and step 3: establishing a water turbine generator model, expanding the traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model;
as shown in fig. 2: the step 1 specifically comprises the following steps:
step 1.1: the fractional order PID speed regulation system is obtained by a classical PID speed regulation system, and the specific method comprises the following steps:
the differential expression of the classical PID speed regulation system is as follows:
u(t)＝k p e(t)+k i De(t)+k d De(t)； (1)
wherein kp represents a proportional parameter, and the setting range is 0.5-20; ki represents an integral parameter, and the setting range is 0.05s < -1 > to 10s < -1 >; kd represents a differential parameter, and the setting range is 0-5 s;
then k is added p 、k i 、k d Three adjusting parameters are respectively replaced by transient slip coefficients b t Buffer time constant T d Acceleration time constant T n Specifically, the method comprises the following steps:
the transfer function of a classical PID speed regulation system is:
wherein bt is transient slip coefficient, and 0-1.0 is selected; td is a buffering time constant, and the setting range is 2-20 s; tn is the acceleration time constantThe fixed range is 0-2 s; pc and P are the set power setting and set power (for power regulation mode), respectively; y is c And y is guide vane opening degree setting and guide vane degree respectively; a frequency adjustment mode and an opening adjustment mode; fc and f are respectively frequency given and unit (or power grid) frequency; Δ f is the frequency difference; Δ f' is the passing frequency dead zone e f The latter frequency deviation;
the differential expression (formula (1)) of the classical PID speed regulating system is a differential expression of a fractional order PID speed regulating system after Laplace transformation, and the differential expression is as follows:
u(t)＝k p e(t)+k i D α e(t)+k d D μ e(t)； (4)
wherein alpha, mu is more than 0, alpha is an integral order, mu is a differential order, when the values of alpha and mu are both 1, the expression (4) is changed into a classical PID speed regulating system (expression (1)), and the introduction of fractional calculus enables the traditional PID regulation to have more applicability and flexibility;
the transfer function of the fractional order PID speed regulation system is as follows:
step 1.2: the method for defining the objective function of the fractional order PID speed regulation system comprises the following steps:
in order to optimize the governing performance of the controlled water turbine system, double error integrals are used as the objective function of the fractional order PID governing system in the step 1.1:
where e (t) represents the deviation of the actual output from the desired output, t is time, I SE The integral of the square deviation is expressed, and the smaller the value of the integral of the square deviation is, the faster the response speed of the system is; I.C. A TAE The integral of time and square deviation is adopted, and the smaller the value is, the better the system stability is reflected;
as shown in fig. 3: step 1.3: and (3) optimizing the objective function based on the fractional order PID speed regulation system in the step 1.2 by using a hybrid algorithm, wherein the specific method comprises the following steps:
will k is p 、k i 、k d Alpha and mu parameters form an initial drosophila position, so that the drosophila is optimized according to taste concentration, and the deep search characteristic of the BP neural network is utilized to search k p 、k i 、k d And the optimization solution of the five parameters of alpha and mu specifically comprises the following steps:
step 1.3.1: initializing the fruit fly population size groupsize (400) and the maximum iteration number maxnum (400), and randomly generating the fruit fly population position (X) axis ，Y axis ) The iteration step value R is defined as (0.85-1);
step 1.3.2: randomizing the position and direction of the fruit fly population according to the distance D between the position and the origin of the fruit fly population Dist Determining Drosophila population taste concentration value S i ；
Step 1.3.3: calculating the taste concentration of individual fruit flies, and comparing the taste concentration value S of the fruit fly population i Substituting taste concentration determination function F function Finding individuals with optimal taste concentration from each drosophila population;
retaining the optimum taste concentration b bestsmell To (X) of i ，Y i ) Location, drosophila population S smell Flying to the coordinate, b best indes Representing the optimal fruit fly position;
step 1.3.4: the position coordinate (X) of the fruit fly obtained in the step 1.3.3 i ，Y i ) Hidden layer n of input BP neural network net (2) (k) Defining input and output;
wherein i =1,2, \ 8230and Q, n, Q value and Z are defined according to the complexity of the controlled object j (2) To optimize the post-drosophila population (X) i ，Y i ) Position, w ij (2) Weighting coefficients for hidden layers, Z i (k) (2) Taking a Sigmoid function of an activation function;
step 1.3.5: defining BP neural network output layer n net (3) (k) Updating individual fruit fly, selecting E (k) as performance error index, and keeping position coordinate (X) of fruit fly individual with most concentrated taste i ，Y i )；
Step 1.3.6: by judging the performance index calculated in the last step, the optimal parameter k is output when the maximum iteration number is reached p ,k i ,k d And alpha and mu, ending the process, otherwise, turning to the step 1.3.2, and outputting the optimal parameter k until the maximum iteration times are reached p ,k i ,k d α, μ, end the process.
The step 2 specifically comprises the following steps:
step 2.1: establishing a mathematical model of a mechanical hydraulic system of the water turbine speed regulating system, and specifically adopting the following method:
the mechanical hydraulic system is used for converting and amplifying an electrical signal into a mechanical displacement signal with certain operating force; due to the response time constant T of the secondary servomotor y1 Is far less than the response time constant T of the main servomotor y The method is generally simplified into an inertia link in modeling, wherein y is an output signal of a mechanical hydraulic system and can also represent the relative size of the opening of a guide vane, a frequency dead zone and a saturation limiting link are added according to the regulation characteristic of a water turbine, and the transfer function of a linear part of a main distributing valve and a servomotor is as follows:
step 2.2: a mathematical model of a water diversion system of a water turbine speed regulating system is established, and the following method is specifically adopted:
the mathematical model of the diversion system of the water turbine speed regulating system is established, according to the difference of the lengths of diversion pressure pipelines, a rigid water hammer model is generally adopted below 700m in simulation modeling, an elastic water hammer is generally adopted for the precision consideration when the length is more than 700m, and the water flow pressure change process in the diversion system is described by the following equation:
equation of motion:
h is a water head, Q is water flow, S is the cross-sectional area of a water pipeline, t is time, and g is gravity acceleration;
the flow equation:
wherein a is the water flow acceleration;
and (3) expanding a water hammer equation in the pressure water conduit by Taylor series to obtain n =0 and n =1 terms to obtain the rigid water hammer G A1 And elastic water hammer G A2 Transfer function:
wherein T is W Is rigid water hammer time constant, tr =2L/V is elastic water hammer time constant, L is pressure water conduit pipe length, V is water flow wave velocity, H 0 Is the head, Q 0 Is the flow rate, V 0 Is the base speed of water flow.
The step 3 specifically comprises the following steps:
establishing a water turbine generator model, expanding the traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model;
the specific method comprises the following steps: conventional turbine generator models typically use a first order model:
f is the unit frequency; p is the difference value of the input power of the unit; tn is a unit (load) inertia time constant (dynamic frequency characteristic time constant), and is generally 3 s-12 s; en is a self-adjusting (characteristic) coefficient of the static frequency of the unit (load), is different along with different load properties, and is generally 0.5-2.0 s;
the first-order model cannot reflect actual parameters of the hydraulic turbine generator and parameters of an excitation system, a synchronous motor model of a five-order space state equation is established through an MATLAB/Simulink simulation platform to be equivalent to the hydraulic turbine generator model, basic parameter characteristics of a hydraulic turbine are defined, dynamic characteristics of stator and rotor magnetic fields and damping windings are considered, and an equivalent circuit of the model is expressed in a rotor reference system (dq frame).
Wherein the stator voltage equation is:
wherein U is d For stator d-axis voltage, U q Is the stator q-axis voltage, phi d And phi q Representing dp-axis flux linkage, i d And i q Is the current in an equivalent dq coordinate system, r a The dq axis sub-transient electromotive force is E ″, which is an equivalent resistance d And E ″) q ，X” d And X ″) q Is dq times transient reactance;
the voltage equation of the f winding and the dq winding of the rotor and the motion equation of the rotor are as follows:
wherein the d-axis and q-axis time constants (all in units of s), the d-axis open transient (Tdo ') or short circuit (Td') time constants, the d-axis sub-open transient (Tdo ") or short circuit (Td") time constants, the q-axis open transient (Tqo ') or short circuit (Tq') time constants (for a round rotor only), and the q-axis sub-open transient (Tqo ") or short circuit (Tq") time constants. E' q Is a transient electromotive force, E e Is dq winding electromotive force, X' d Is d-axis transient reactance, X d And X q Is dq-axis reactance, W is rotor mechanical angular velocity, T j Is the inertia time constant, T, of the generator set m Is the mechanical torque of the prime mover,
is an unbalanced torque acting on the rotor shaft;
the excitation system adopts an IEEE typical direct current exciter; when the load of the power system is suddenly increased or decreased, the generator is forcibly excited and demagnetized so as to improve the stability of the power system.
According to the comprehensive model modeling method of the water turbine based on the fractional order PID speed regulating system, according to example analysis, an MATLAB platform simulation experiment is utilized, transmission parameters (see table 1) of the water turbine speed regulating system are taken as a simulation example, a dead zone with the rotating speed of +/-0.001 (pu) is set for the speed regulating system due to the rotating speed characteristic of a water turbine set, and partial parameters of a water turbine generator are shown in table 2.
TABLE 1 Water turbine governing System parameters
Wherein E qy The transmission coefficient of the relative value of the flow deviation to the relative value of the stroke deviation of the servomotor E qh As a transfer coefficient of the relative value of the flow deviation to the relative value of the head deviation, E y The transmission coefficient of the torque deviation relative value of the water turbine to the stroke deviation relative value of the servomotor, E h Relative torque deviation of water turbineAnd (4) the transmission coefficient of the value to the relative value of the water head deviation.
TABLE 2 Water turbine Generator parameters
Wherein P is n At rated power, V n To rated line voltage, F n For the rated frequency, P is the pole pair number, H is the inertia coefficient, d-axis synchronous reactance Xd, transient reactance Xd 'and sub-transient reactance Xd', q-axis synchronous reactance Xq, transient reactance Xq '(only for circular rotors) and sub-transient reactance Xq', and finally leakage reactance X1, W ref At a rated speed, V ref A nominal excitation voltage.
From the comparison of tables 1 and 2, it can be seen that: the invention improves the speed regulating system of the water turbine on the basis of the current research state, and compared with the current mainstream speed regulating system, the speed regulating result is shown in figures 4-6; the load part is subjected to simulation analysis according to the operating characteristics of the water turbine under the conditions of charging and cutting under the load of 40% and 75%, and various simulation results of the water turbine are shown in figures 7-9.
Compared with a classical water turbine speed regulating system, the fractional order PID speed regulating system-based water turbine comprehensive model modeling method is superior to the classical water turbine speed regulating system in both regulating time and overshoot because of the increase of controllable parameters; the speed regulation time and overshoot of the self-adaptive PID control adopting the FOA algorithm and the BP neural network algorithm compared with the PID and the FOPID control are obviously reduced, but the four controls have the defect of more system oscillation times; the traditional speed regulation mode is stable only when the system vibrates for more than 4 times, the dual-target FOPID optimization controller controlled by a mixed fruit fly algorithm (BP-FOA) further reduces the regulation time and the overshoot, meanwhile, the vibration times are greatly reduced, the system is stable only by 2 times, and the specific speed regulation optimization is shown in figure 10.
As shown in fig. 11: by carrying out self-adaptive optimization parameter analysis on the FOA algorithm, the BP neural network algorithm and the BP-FOA algorithm designed in the text, the global optimization capability of the drosophila algorithm is enhanced due to the set high iteration step value, but the iteration times are many, and the optimization time is long; the BP neural network algorithm has strong optimizing capability and high convergence speed, but is easy to fall into local optimization, and has an unstable phenomenon when running in the face of load fluctuation; the BP-FOA algorithm further reduces the self-adaptive adjustment time by utilizing the rapid convergence of the BP neural network on the basis of strong global optimization capability, improves the self-adaptive adjustment time by 24.58 percent, and shows stronger adaptability and stability in the face of load fluctuation.
As can be seen from comparison of the tables 3 and 4, the mixed drosophila algorithm dual-target FOPID regulator has obvious advantages in the aspects of speed regulation optimizing time and control overshoot, 46.86% of overshoot delta is reduced on the basis of the current mainstream BP neural network control algorithm, and the regulation time T is shortened by 36.59% s Wherein T is r For rise time, T p Is the peak time.
TABLE 3 comparison of simulation results of different controller indexes under load disturbance
TABLE 4 comparison of optimized parameters of different controllers under load disturbance
The BPFOA-FOPID double-target optimized turbine model is tested to carry 40% of load initially, 35% of load is added at 30s, and 35% of load is cut off at 60 s. The fluctuation of the rotating speed is +/-2% when the load is switched for 30s and 60s, and is stable when the load is switched for 3.9s, so that the stability of the system is greatly improved; because the adopted direct-current exciter adopts strong excitation and reduced excitation on the generator when the load is increased or decreased, the running condition of the exciter can be basically reflected; the output force and the output current of the generator basically keep stable when the load fluctuates, and good output performance is reflected.
The modeling analysis compares four mainstream single-target control methods including PID, FOPID, FOA algorithm and BP neural network control on the basis of establishing a comprehensive water turbine model, provides a mixed algorithm BPFOA-FOPID double-target function control mode, and tests the quick action and stability of the control of the water turbine speed regulating system in the face of load fluctuation. Simulation results show that the adjustment time and the overshoot of the water turbine are obviously reduced in the BPFOA-FOPID dual-target control mode, and the robustness and the adaptability are stronger compared with those of the conventional control mode.
This patent utilizes MATLAB simulation modeling, improved hydraulic turbine speed control system on the basis of the research of the predecessor, according to the example analysis, the comprehensive model that can reflect hydraulic turbine speed control system and each item parameter of generator system has been established, to hydraulic turbine unit capacity, the frequency, rotor winding, stator winding, excitation winding, the magnetic pole is to the number, the output voltage current condition, the excitation voltage condition, the load change condition can concrete analysis, can simulate the transient state change of all kinds of hydropower station actual operation at to a great extent, the defect of traditional hydraulic turbine modeling has been remedied. In practical application, the change of various parameters of the water turbine has good response to the running condition of the actual water turbine set when the load fluctuates, and the accident prediction and the safe running of the system are guaranteed.
Claims (3)
1. A water turbine comprehensive model modeling method based on a fractional PID speed regulation system is characterized by comprising the following steps:
step 1: establishing a water turbine speed regulator simulation analysis mathematical model based on a fractional order PID speed regulating system, and optimizing a target function based on the fractional order PID speed regulating system by using a hybrid algorithm;
the step 1 specifically comprises the following steps:
step 1.1: the fractional order PID speed regulating system is obtained by a classical PID speed regulating system, and the specific method comprises the following steps:
the differential expression of the classical PID speed regulation system is as follows:
u(t)＝k p e(t)+k i De(t)+k d De(t)；
wherein kp represents a proportional parameter, and the setting range is 0.5-20; ki represents an integral parameter, the setting range is 0.05s < -1 > to 10s < -1 >, kd represents a differential parameter, and the setting range is 0 to 5s;
will k p 、k i 、k d Three adjusting parameters are respectively replaced by transient slip coefficients b t Buffer time constant T d Acceleration time constant T n Specifically, the method comprises the following steps:
the transfer function of a classical PID speed regulation system is:
wherein bt is transient slip coefficient, and is 0-1.0; td is a buffer time constant, the setting range is 2 s-20s, tn is an acceleration time constant, the setting range is 0-2s, pc and P are respectively set unit power and unit power, y is c Y is guide vane opening degree given and guide vane degree, fc and f are frequency given and unit frequency, delta f is frequency difference, delta f' is passing frequency dead zone e f The latter frequency deviation;
transforming the differential expression of the classical PID speed regulation system into a differential expression of a fractional order PID speed regulation system through Laplace:
u(t)＝k p e(t)+k i D α e(t)+k d D μ e(t)； (4)
wherein α, μ >0, α is an integration order and μ is a differentiation order;
the transfer function of the fractional order PID speed regulating system is as follows:
step 1.2: the method for defining the objective function of the fractional order PID speed regulation system comprises the following specific steps:
using double error integral as the objective function of the fractional order PID speed regulation system in step 1.1:
where e (t) represents the deviation of the actual output from the desired output, t is time, I SE Represents the squared deviation integral;
step 1.3: and (3) optimizing the objective function based on the fractional order PID speed regulation system in the step 1.2 by using a hybrid algorithm, wherein the specific method comprises the following steps:
will k is p 、k i 、k d Alpha and mu parameters form an initial fruit fly position to optimize the fruit fly according to the taste concentration, and the deep search characteristic of the BP neural network is utilized to search k p 、k i 、k d And the optimization solution of the five parameters of alpha and mu specifically comprises the following steps:
step 1.3.1: initializing fruit fly population size group (400) and maximum iteration number maxnum (400), and randomly generating fruit fly population position (X) axis ，Y axis ) The iterative step value R is defined as (0.85-1);
step 1.3.2: randomizing the position and direction of the fruit fly population according to the distance D between the position and the origin of the fruit fly population Dist Determining Drosophila population taste concentration value S i ；
Step 1.3.3: calculating the taste concentration of individual fruit flies, and comparing the taste concentration value S of the fruit fly population i Substituting taste concentration determination function F function Finding individuals with optimal taste concentration from each drosophila population;
retaining optimum taste concentrationb bestsmell To (X) of i ，Y i ) Location, drosophila population S smell Flight direction coordinate, b bestindes Representing the optimal fruit fly position;
step 1.3.4: the position coordinate (X) of the fruit fly obtained in the step 1.3.3 i ，Y i ) Hidden layer n of input BP neural network net (2) (k) Defining input and output;
wherein i =1,2, \ 8230and Q, n, Q value and Z are defined according to the complexity of the controlled object j (2) To optimize the post-drosophila population (X) i ，Y i ) Position, w ij (2) Weighting coefficients for hidden layers, Z i (k) (2) Taking a Sigmoid function of an activation function;
step 1.3.5: defining BP neural network output layer n net (3) (k) Updating individual fruit fly, selecting E (k) as performance error index, and keeping position coordinate (X) of fruit fly individual with most concentrated taste i ，Y i )；
Step 1.3.6: outputting an optimal parameter k when the maximum iteration times is reached by judging the performance index calculated in the previous step p ,k i ,k d And alpha and mu, ending the process, otherwise, turning to the step 1.3.2, and outputting the optimal parameter k until the maximum iteration times are reached p ,k i ,k d α, μ, end of the process;
and 2, step: establishing a mechanical hydraulic system and a diversion system mathematical model of a water turbine speed regulating system;
and step 3: and establishing a water turbine generator model, expanding the traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model.
2. The method for modeling the comprehensive model of the water turbine based on the fractional order PID speed regulation system according to claim 1, wherein the step 2 specifically comprises the following steps:
step 2.1: establishing a mathematical model of a mechanical hydraulic system of the water turbine speed regulating system, and specifically adopting the following method:
the mechanical hydraulic system is used for converting and amplifying an electric signal into a mechanical displacement signal with an operating force; due to the response time constant T of the secondary servomotor y1 Is smaller than the response time constant T of the main servomotor y The method is simplified into an inertia link in a modeling, wherein y is an output signal of a mechanical hydraulic system and also represents the relative size of the opening of a guide vane, a frequency dead zone and a saturation limiting link are added according to the regulation characteristic of the water turbine, and the transfer function of a linear part of a main distributing valve and a servomotor is as follows:
step 2.2: a mathematical model of a water diversion system of a water turbine speed regulating system is established, and the following method is specifically adopted:
according to different lengths of the diversion pressure pipelines, in terms of simulation modeling, a rigid water hammer model is adopted below 700m, an elastic water hammer is adopted when the length is more than 700m, and the water flow pressure change process in the diversion system is described by the following equation:
equation of motion:
h is a water head, Q is water flow, S is the cross-sectional area of a water pipeline, t is time, and g is gravity acceleration;
the flow equation:
wherein a is the water flow acceleration;
and (3) expanding a water hammer equation in the pressure water conduit by Taylor series to obtain n =0 and n =1 terms to obtain the rigid water hammer G A1 And elastic water hammer G A2 Transfer function:
wherein T is W Is rigid water hammer time constant, tr =2L/V is elastic water hammer time constant, L is pressure water conduit pipe length, V is water flow wave velocity, H 0 Is the head, Q 0 Is the flow rate, V 0 The water flow base speed.
3. The water turbine comprehensive model modeling method based on the fractional order PID speed regulation system according to claim 1, wherein the step 3 specifically comprises the following steps:
establishing a water turbine generator model, expanding a traditional first-order water turbine generator model to a 5-order water turbine model, and introducing an exciter model and a dynamic load model; the specific method comprises the following steps:
step 3.1: the first order model used by the conventional turbine generator model is:
wherein f is the unit frequency, p is the unit input power difference, tn is the unit inertia time constant, T n Is 3s to 12s, e n For the unit static frequency self-regulation coefficient, e n Taking 0.5-2.0 s;
the first-order model cannot reflect actual parameters of the hydraulic generator and excitation system parameters, the synchronous motor model of a five-order space state equation is established through an MATLAB/Simulink simulation platform to be equivalent to the hydraulic generator model, basic parameter characteristics of the hydraulic turbine are defined, dynamic characteristics of stator and rotor magnetic fields and damping windings are considered, and an equivalent circuit of the model is expressed in a rotor reference system dq frame
Wherein the stator voltage equation is:
wherein U is d For stator d-axis voltage, U q Is the stator q-axis voltage, phi d And phi q Representing dp-axis flux linkage, i d And i q Is the current in the equivalent dq coordinate system, r a The dq axis sub-transient electromotive force is E ″, which is an equivalent resistance d And E ″) q ，X” d And X " q Is dq times transient reactance;
the voltage equation of the f winding and the dq winding of the rotor and the motion equation of the rotor are as follows:
wherein d-axis and q-axis time constants are all in units of s, and d-axis transient open circuit T' d0 D-axis sub-transient open circuit T' d0 Q-axis transient open circuit T' q0 Q-axis secondary transient open circuit T ″, limited to circular rotor q0 ；E’ q Is a transient electromotive force, E e Is dq winding electromotive force, X' d Is d-axis transient reactance, X d And X q Is the dq-axis reactance, W is the mechanical angular velocity of the rotor, T j Is the inertia time constant, T, of the generator set m Is the mechanical torque of the prime mover,
is an unbalanced torque acting on the rotor shaft.
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| CN112000017B (en) * | 2020-09-08 | 2022-03-18 | 金陵科技学院 | Global stabilization control method of fractional order water turbine adjusting system |
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