CN110262223A - A kind of comprehensive model modelling approach of hydraulic turbine based on Fractional Order PID speed-regulating system - Google Patents

Abstract

The invention provides a comprehensive model modeling method for a hydraulic turbine of an adaptive fractional-order PID speed control system, comprising the following steps: Step 1: establishing a simulation analysis mathematical model of the hydraulic turbine speed governor based on the fractional-order PID speed control system; And use the hybrid algorithm to optimize the objective function based on the fractional-order PID speed control system; Step 2: Establish the mathematical model of the mechanical hydraulic system and the water diversion system of the turbine speed control system; Step 3: Establish the turbine generator model; The present invention uses MATLAB Simulation modeling, on the basis of previous research, the classic PID speed control system has been improved. According to the analysis of examples, a comprehensive model that can reflect the parameters of the turbine speed control system and the generator system is established. The actual operation of the hydro turbine unit has a good response to the changes of various parameters of the hydro turbine when the load fluctuates, which provides a guarantee for the accident prediction and the safe operation of the system.

Description

A comprehensive model modeling method of hydraulic turbine based on fractional-order PID speed control system

Technical field:

The invention relates to the mechanics of hydropower stations and the principle of a water turbine speed regulating system, in particular to a hydraulic turbine comprehensive model modeling method based on a fractional-order PID speed regulating system.

Background technique

The control structure of the traditional hydraulic turbine speed control system generally adopts the classic hydraulic turbine speed control system, that is, the parallel PID speed control system control, which has the advantages of being simple and easy to operate. However, the turbine system controlled by the parallel PID speed control system has the following problems:

1. Stable and slow at startup;

2. The stability is poor when the system load fluctuates, and the self-regulation ability is insufficient in the face of emergencies in the power system.

Facing the shortcomings of the classical hydraulic turbine speed control system, a large number of scholars have proposed advanced intelligent control methods, such as fuzzy PID control, BP neural network control, chaotic particle swarm control, etc. The speed control performance has been significantly improved.

Considering that the control methods of domestic water turbines mostly use the control method based on the parallel PID speed control system control, in order to respond quickly to the system requirements and bring as little impact to the power system as possible, the optimization of the speed control system of the water turbine is carried out. becomes crucial.

In terms of simulation modeling, great progress has been made in modeling the nonlinear mechanism of hydraulic turbines, but the impact of load fluctuations on the speed control system of hydraulic turbines has not been thoroughly analyzed. At present, the load and generator models are generally equivalent to first-order transfer functions. , the actual problems reflected are relatively limited, and on the basis of reflecting the speed regulation performance of the turbine, the influence of the turbine generator characteristics, the dynamic load model and the power system failure on the turbine speed regulation system needs to be further analyzed.

SUMMARY OF THE INVENTION

In order to solve the problem that the nonlinear mechanism modeling of the hydraulic turbine cannot reflect the changes of various important parameters of the hydraulic turbine under dynamic load, the invention proposes a comprehensive model modeling method of the hydraulic turbine based on the fractional-order PID speed regulating system.

To achieve the above object, the present invention adopts the following technical solutions:

A hydraulic turbine comprehensive model modeling method for an adaptive fractional-order PID speed control system, comprising the following steps:

Step 1: establish a simulation analysis mathematical model of the turbine governor based on the fractional-order PID speed control system, and use a hybrid algorithm to optimize the objective function based on the fractional-order PID speed control system;

Step 2: Establish the mathematical model of the mechanical hydraulic system and the water diversion system of the turbine speed control system;

Step 3: establish a turbine generator model, extend the traditional first-order turbine generator model to a fifth-order turbine model, and introduce the exciter model and the dynamic load model from this;

The step 1 specifically includes the following steps:

Step 1.1: Obtain the fractional-order PID speed control system from the classical PID speed control system. The specific method is:

The differential expression of the classical PID speed control system is:

u(t)=k _p e(t)+ _ki De(t)+k _d De(t);

Among them, kp represents the proportional parameter, the setting range is 0.5～20; ki is the integral parameter, the setting range is 0.05s-1～10s-1, kd is the differential parameter, the setting range is 0～5s;

Replace the three adjustment parameters kp, ki, and kd with transient slip coefficient bt, buffer time constant Td, and acceleration time constant Tn, respectively. Specifically:

The transfer function of the classic PID speed control system is:

Among them, bt is the transient slip coefficient, taking 0 to 1.0; Td is the buffer time constant, the setting range is 2s～20s, Tn is the acceleration time constant, the setting range is 0～2s, pc and P are the unit power given respectively and unit power, y _c and y are the guide vane opening and guide vane degrees, respectively, fc and f are the frequency setting and unit frequency, respectively, Δf is the frequency difference, and Δf' is the frequency after passing through the frequency dead zone e _f deviation;

The differential expression of the above classical PID speed control system is transformed into the differential expression of the fractional order PID speed control system through Laplace:

u(t)=k _p e(t)+ _ki D ^α e(t)+k _d D ^μ e(t); (4)

Where α, μ>0, α is the integral order, μ is the differential order;

The transfer function of fractional order PID speed control system is:

Step 1.2: Define the objective function of the fractional-order PID speed control system, the specific method is:

Use the double error integral as the objective function of the fractional-order PID speed control system described in step 1.1:

Among them, e(t) represents the deviation between the actual output and the expected output, t is the time, and I _SE represents the square deviation integral;

Step 1.3: Use the hybrid algorithm to optimize the objective function of the fractional-order PID speed control system described in Step 1.2. The specific method is:

Five parameters of _{k p} , _ki , _{k d} , α and μ are used to form the initial fruit fly position, so that the fruit fly can be optimized according to the taste concentration _. The five parameters of α and μ are optimized and solved, including the following steps:

Step 1.3.1: Initialize the fruit fly population size groupsize(400) and the maximum number of iterations maxnum(400), randomly generate the fruit fly population position (X _axis , Y _axis ), and the iteration step value R is defined as (0.85-1);

Step 1.3.2: Randomize the position and direction of the fruit fly population, and determine the taste concentration value S _i of the fruit fly population according to the distance D _Dist between the fruit fly population position and the origin;

Step 1.3.3: Calculate the taste concentration of individual fruit flies, substitute the taste concentration value S _i of the fruit fly population into the taste concentration determination function F _function , and find the optimal individual of taste concentration from each fruit fly population;

Retain the optimal taste concentration b _bestsmell and the corresponding (X _i , Y _i ) position, the fruit fly population S _smell flies to this coordinate, and b _{best indes} represents the optimal fruit fly position;

Step 1.3.4: Input the position coordinates (X _i , Y _i ) of the fruit fly obtained in step 1.3.3 into the hidden layer n _net ⁽²⁾ (k) of the BP neural network to define the input and output;

Among them, i=1,2,...,Q, the value of n and Q is defined according to the complexity of the controlled object, Z _j ⁽²⁾ is the optimal position of the fruit fly population (X _i , Y _i ), w _ij ⁽²⁾ is the hidden Layer weighting coefficient, Z _i (k) ⁽²⁾ Take the activation function Sigmoid function;

Step 1.3.5: Define the output layer n _net ⁽³⁾ (k) of the BP neural network, update the individual fruit fly, select E(k) as the performance error index, and keep the position coordinates (X _i , Y _i );

Step 1.3.6: By judging the performance index calculated in the previous step, when the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process, otherwise, go to step 1.3.2, until When the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process.

The step 2 specifically includes the following steps:

Step 2.1: Establish the mathematical model of the mechanical hydraulic system of the turbine speed control system, specifically using the following methods:

The function of the mechanical hydraulic system is to convert and amplify the electrical signal into a mechanical displacement signal with a certain operating force; since the response time constant T _y1 of the secondary relay is much smaller than the response time constant T _y of the main relay, it is usually used in modeling. Simplified as an inertia link, where y is the output signal of the mechanical hydraulic system, and can also represent the relative size of the guide vane opening. According to the adjustment characteristics of the turbine, the frequency dead zone and saturation limit links are added, and the main pressure distribution valve and the servomotor linear part The transfer function is:

Step 2.2: Establish the mathematical model of the water diversion system of the turbine speed control system, using the following methods:

According to the length of the water diversion pressure pipeline, in the simulation modeling, the rigid water hammer model is used below 700 m, and the elastic water hammer is used when it is greater than 700 m. The hydraulic change process of the water flow in the water diversion system is described by the following equation:

Equation of motion:

Where H is the water head, Q is the water flow, S is the cross-sectional area of the water pipe, t is the time, and g is the acceleration of gravity;

Flow equation:

where a is the water flow acceleration;

The transfer functions of rigid water hammer G _A1 and elastic water hammer G _A2 are obtained by expanding the water hammer equation in the pressure diversion pipeline through Taylor series and taking the terms n=0 and n=1:

where T _W is the rigid water hammer time constant, Tr=2L/V is the elastic water hammer time constant, L is the length of the pressure diversion pipeline, V is the water flow wave velocity, H ₀ is the water head, Q ₀ is the flow rate, and V ₀ is the flow base speed.

The step 3 specifically includes the following steps:

The turbine generator model is established, the traditional first-order turbine generator model is extended to the fifth-order turbine model, and the exciter model and dynamic load model are introduced from this; the specific methods are as follows:

Step 3.1: The first-order model used by the traditional hydro-turbine generator model is:

Among them, f is the frequency of the unit, p is the input power difference of the unit, Tn is the inertia time constant of the unit, generally T _n is 3s ~ 12s, e _n is the static frequency self-adjustment coefficient of the unit, and e _n is 0.5 ~ 2.0s;

The above first-order model cannot reflect the actual parameters of the hydro-generator and excitation system. In this paper, the synchronous motor model of the fifth-order space state equation established by the MATLAB/Simulink simulation platform is equivalent to the hydro-generator model, which defines the basic parameters of the hydro-turbine. Parametric characteristics, considering the dynamic characteristics of stator and rotor magnetic fields and damping windings, the equivalent circuit of the model is represented in the rotor reference frame (dq frame).

Among them, the stator voltage equation is:

where U _d is the stator d-axis voltage, U _q is the stator q-axis voltage, φ _d and φ _q represent the _dp -axis flux linkage, id and _{i q} are the currents in the equivalent dq coordinate system, ra is the equivalent resistance, dq The axial sub-transient electromotive force is E″ _d and E″ _q , X” _d and X” _q are dq sub-transient reactance;

The rotor f winding, dq winding voltage equation and rotor motion equation are:

where d-axis and q-axis time constants (all in s), d-axis transient open (Tdo') or short-circuit (Td') time constants, and d-axis sub-transient open (Tdo") or short-circuit (Td") time constants Time constant, q-axis transient open (Tqo') or short-circuit (Tq') time constant (round rotor only), q-axis sub-transient open (Tqo") or short-circuit (Tq") time constant. E' _q is the transient electromotive force, E _e is the dq winding electromotive force, X' _d is the d-axis transient reactance, X _d and X _q are the dq-axis reactance, W is the rotor mechanical angular velocity, and T _j is the inertia time constant of the generator set , T _m is the mechanical torque of the prime mover, is the unbalanced torque acting on the rotor shaft.

The beneficial effects of the present invention are:

The mathematical model of the simulation analysis of the hydraulic turbine governor based on the fractional-order PID speed control system is established, and the MATLAB simulation model is used to improve the classical PID speed control system on the basis of the previous research. According to the analysis of examples, A comprehensive model that can reflect various parameters of the turbine speed control system and generator system has been established. For the turbine unit capacity, frequency, rotor winding, stator winding, excitation winding, number of pole pairs, output voltage and current, excitation voltage, load The change situation can be analyzed in detail, and to a large extent, it can simulate the temporary steady state changes in the actual operation of various hydropower stations, making up for the shortcomings of traditional turbine modeling; in practical applications, the operation of the actual turbine unit is faced with load fluctuations. The change of various parameters of the turbine has a good response, which provides a guarantee for the accident prediction and the safe operation of the system.

Description of drawings:

Fig. 1 is the method flow chart of the present invention;

Fig. 2 is the establishment of the hydraulic turbine governor simulation analysis mathematical model based on fractional-order PID speed control system according to the present invention, and utilizes hybrid algorithm to optimize the method flow chart of the objective function based on fractional-order PID speed control system;

Fig. 3 is the method flow chart of utilizing the hybrid algorithm to optimize the described objective function based on fractional order PID speed regulation system of the present invention;

Figure 4 is a schematic diagram of the comparison of the control results between the classical PID speed control system and the fractional-order PID speed control system when the load is disturbed;

Figure 5 is a schematic diagram of the comparison of the control results of the FOA-PID speed control system and the BP-PID speed control system when the load is disturbed;

Figure 6 is a schematic diagram of the comparison of the control results between the BP-PID speed control system and the BPFOA-FOPID speed control system when the load is disturbed;

Figure 7. Turbine excitation voltage, active power, and rotational speed changes during load switching;

Figure 8 shows the three-phase current changes when the load is turned on;

Figure 9 shows the three-phase current changes when the load is partially cut off;

Figure 10 is a schematic diagram showing the comparison of BPFOA-PID dual-objective optimization control results;

Figure 11 is a schematic diagram of the BPFOA-FOPID adaptive optimization result.

Detailed ways:

As shown in Figure 1 : a hydraulic turbine comprehensive model modeling method of an adaptive fractional-order PID speed control system according to the present invention is characterized in that, comprising the following steps:

Step 1: establish a simulation analysis mathematical model of the turbine governor based on the fractional-order PID speed control system, and use a hybrid algorithm to optimize the objective function based on the fractional-order PID speed control system;

Step 2: Establish the mathematical model of the mechanical hydraulic system and the water diversion system of the turbine speed control system;

Step 3: establish a turbine generator model, extend the traditional first-order turbine generator model to a fifth-order turbine model, and introduce the exciter model and the dynamic load model from this;

As shown in Figure 2, the step 1 specifically includes the following steps:

Step 1.1: Obtain the fractional-order PID speed control system from the classical PID speed control system. The specific method is:

The differential expression of the classical PID speed control system is:

u(t)=k _p e(t)+ _ki De(t)+k _d De(t); (1)

Among them, kp represents the proportional parameter, and the setting range is 0.5～20; ki represents the integral parameter, and the setting range is 0.05s-1～10s-1; kd represents the differential parameter, and the setting range is 0～5s;

Then replace the three adjustment parameters k _p , k _i and k _d with transient slip coefficient b _t , buffer time constant T _d , acceleration time constant T _n , specifically:

The transfer function of the classic PID speed control system is:

Among them, bt is the transient slip coefficient, taking 0 to 1.0; Td is the buffer time constant, and the setting range is 2s to 20s; Tn is the acceleration time constant, and the setting range is 0 to 2s; pc and P are the unit power given respectively. and unit power (for power regulation mode); y _c and y are the guide vane opening and guide vane degree, respectively; frequency regulation mode and opening regulation mode; fc and f are the frequency reference and unit (or grid), respectively ) frequency; Δf is the frequency difference; Δf' is the frequency deviation after passing through the frequency dead zone _ef ;

The differential expression of the classical PID speed control system (formula (1)) is transformed into the differential expression of the fractional order PID speed control system after Laplace transformation as:

u(t)=k _p e(t)+ _ki D ^α e(t)+k _d D ^μ e(t); (4)

Where α, μ>0, α is the integral order, μ is the differential order, when the values of α and μ are both 1, then the formula (4) becomes the classic PID speed control system (formula (1)), the fraction The introduction of first-order calculus makes the traditional PID adjustment more applicable and flexible;

The transfer function of fractional order PID speed control system is:

Step 1.2: Define the objective function of the fractional-order PID speed control system, the specific method is:

In order to optimize the speed regulation performance of the controlled hydraulic turbine system, the double error integral is used as the objective function of the fractional-order PID speed regulation system described in step 1.1:

Among them, e(t) represents the deviation between the actual output and the expected output, t is the time, I _SE represents the square deviation integral, the smaller the value, the faster the response of the system; I _TAE is the time and the square deviation integral, its value The smaller the value, the better the stability of the system;

As shown in Figure 3: Step 1.3: Use the hybrid algorithm to optimize the objective function of the fractional-order PID speed control system described in Step 1.2. The specific method is:

Five parameters of _{k p} , _ki , _{k d} , α and μ are used to form the initial fruit fly position, so that the fruit fly can be optimized according to the taste concentration _. The five parameters of α and μ are optimized and solved, including the following steps:

Step 1.3.1: Initialize the fruit fly population size groupsize(400) and the maximum number of iterations maxnum(400), randomly generate the fruit fly population position (X _axis , Y _axis ), and the iteration step value R is defined as (0.85-1);

Step 1.3.2: Randomize the position and direction of the fruit fly population, and determine the taste concentration value S _i of the fruit fly population according to the distance D _Dist between the fruit fly population position and the origin;

Step 1.3.3: Calculate the taste concentration of individual fruit flies, substitute the taste concentration value S _i of the fruit fly population into the taste concentration determination function F _function , and find the optimal individual of taste concentration from each fruit fly population;

Retain the optimal taste concentration b _bestsmell and the corresponding (X _i , Y _i ) position, the fruit fly population S _smell flies to this coordinate, and b _{best indes} represents the optimal fruit fly position;

Step 1.3.4: Input the position coordinates (X _i , Y _i ) of the fruit fly obtained in step 1.3.3 into the hidden layer n _net ⁽²⁾ (k) of the BP neural network to define the input and output;

Among them, i=1,2,...,Q, the value of n and Q is defined according to the complexity of the controlled object, Z _j ⁽²⁾ is the optimal position of the fruit fly population (X _i , Y _i ), w _ij ⁽²⁾ is the hidden Layer weighting coefficient, Z _i (k) ⁽²⁾ Take the activation function Sigmoid function;

Step 1.3.5: Define the output layer n _net ⁽³⁾ (k) of the BP neural network, update the individual fruit fly, select E(k) as the performance error index, and keep the position coordinates (X _i , Y _i );

Step 1.3.6: By judging the performance index calculated in the previous step, when the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process, otherwise, go to step 1.3.2, until When the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process.

The step 2 specifically includes the following steps:

Step 2.1: Establish the mathematical model of the mechanical hydraulic system of the turbine speed control system, specifically using the following methods:

The function of the mechanical hydraulic system is to convert and amplify the electrical signal into a mechanical displacement signal with a certain operating force; since the response time constant T _y1 of the secondary relay is much smaller than the response time constant T _y of the main relay, it is usually used in modeling. Simplified as an inertia link, where y is the output signal of the mechanical hydraulic system, and can also represent the relative size of the guide vane opening. According to the adjustment characteristics of the turbine, the frequency dead zone and saturation limit links are added, and the main pressure distribution valve and the servomotor linear part The transfer function is:

Step 2.2: Establish the mathematical model of the water diversion system of the turbine speed control system, using the following methods:

The mathematical model of the water diversion system of the turbine speed control system is established. According to the length of the water diversion pressure pipeline, the rigid water hammer model is generally used for simulation modeling below 700 m, and the elastic water hammer is generally used for accuracy considerations when it is greater than 700 m. The hydraulic change process of water flow in the system is described by the following equation:

Equation of motion:

Where H is the water head, Q is the water flow, S is the cross-sectional area of the water pipe, t is the time, and g is the acceleration of gravity;

Flow equation:

where a is the water flow acceleration;

The transfer functions of rigid water hammer G _A1 and elastic water hammer G _A2 are obtained by expanding the water hammer equation in the pressure diversion pipeline through Taylor series and taking the terms n=0 and n=1:

where T _W is the rigid water hammer time constant, Tr=2L/V is the elastic water hammer time constant, L is the length of the pressure diversion pipeline, V is the water flow wave velocity, H ₀ is the water head, Q ₀ is the flow rate, and V ₀ is the flow base speed.

The step 3 specifically includes the following steps:

Establish a turbine generator model, extend the traditional first-order turbine generator model to a fifth-order turbine model, and introduce the exciter model and dynamic load model from this;

The specific method is: the traditional hydro-turbine generator model usually uses a first-order model:

f is the unit frequency; p is the unit input power difference; Tn is the unit (load) inertia time constant (dynamic frequency characteristic time constant), generally Tn is 3s ~ 12s; en is the unit (load) static frequency self-adjustment (characteristic) The coefficient varies with the nature of the load. Generally, en is taken as 0.5 to 2.0s;

The above first-order model cannot reflect the actual parameters of the hydro-generator and excitation system. In this paper, the synchronous motor model of the fifth-order space state equation established by the MATLAB/Simulink simulation platform is equivalent to the hydro-generator model, which defines the basic parameters of the hydro-turbine. Parametric characteristics, considering the dynamic characteristics of stator and rotor magnetic fields and damping windings, the equivalent circuit of the model is represented in the rotor reference frame (dq frame).

Among them, the stator voltage equation is:

where U _d is the stator d-axis voltage, U _q is the stator q-axis voltage, φ _d and φ _q represent the _dp -axis flux linkage, id and _{i q} are the currents in the equivalent dq coordinate system, ra is the equivalent resistance, dq Axial sub-transient electromotive force is E″ _d and E″ _q , X″ _d and X″ _q are dq sub-transient reactance;

The rotor f winding, dq winding voltage equation and rotor motion equation are:

where d-axis and q-axis time constants (all in s), d-axis transient open (Tdo') or short-circuit (Td') time constants, and d-axis sub-transient open (Tdo") or short-circuit (Td") time constants Time constant, q-axis transient open (Tqo') or short-circuit (Tq') time constant (round rotor only), q-axis sub-transient open (Tqo") or short-circuit (Tq") time constant. E' _q is the transient electromotive force, E _e is the dq winding electromotive force, X' _d is the d-axis transient reactance, X _d and X _q are the dq-axis reactance, W is the rotor mechanical angular velocity, and T _j is the inertia time constant of the generator set , T _m is the mechanical torque of the prime mover, is the unbalanced torque acting on the rotor shaft;

The excitation system adopts the IEEE typical DC exciter; when the load of the power system increases or decreases suddenly, the generator is forcibly excited and demagnetized to improve the stability of the power system.

A comprehensive model modeling method of a hydraulic turbine based on a fractional-order PID speed control system proposed by the present invention, according to the analysis of the example, using the MATLAB platform simulation experiment, taking the transmission parameters of the hydraulic turbine speed control system (see Table 1) as a simulation example, because For the speed characteristics of the hydraulic turbine unit, a dead zone of ±0.001 (pu) is set for the speed control system, and some parameters of the hydraulic turbine generator are shown in Table 2.

Table 1 Parameters of turbine speed control system

Where E _qy is the transfer coefficient of the relative value of flow deviation to the relative value of the stroke deviation of the cooperator, E _qh is the transmission coefficient of the relative value of the flow deviation to the relative value of the head deviation, E _y is the relative value of the torque deviation of the turbine to the stroke deviation of the cooperator E _h is the transfer coefficient of the relative value of the turbine torque deviation to the relative value of the head deviation.

Table 2 Turbine generator parameters

where P _n is rated power, V _n is rated line voltage, F _n is rated frequency, P is the number of pole pairs, H is inertia coefficient, d-axis synchronous reactance Xd, transient reactance Xd' and sub-transient reactance Xd", The q-axis synchronous reactance Xq, the transient reactance Xq' (only when the rotor is round) and the sub-transient reactance Xq", and finally the leakage reactance X1, W _ref is the rated speed, and V _ref is the rated excitation voltage.

It can be seen from the comparison between Table 1 and Table 2: the present invention improves the speed regulation system of the turbine on the basis of the current research state, and the speed regulation results of the current mainstream speed regulation system are shown in Figure 4-Figure 6; the load part is based on the operation of the turbine. The characteristics are simulated and analyzed according to the input and cut conditions under two load conditions, 40% and 75%. The simulation results of the turbine are shown in Figures 7-9.

Compared with the classical hydraulic turbine speed control system, a hydraulic turbine comprehensive model modeling method based on the fractional-order PID speed control system proposed by the present invention is based on the fractional-order PID speed control system due to the increase of controllable parameters. Compared with the PID and FOPID control, the adaptive PID control using the FOA algorithm and the BP neural network algorithm has significantly reduced speed regulation time and overshoot, but the above four kinds of control all have the advantages of The defect of many system oscillations; the traditional speed regulation method oscillates more than 4 times before the system begins to stabilize. The dual-objective FOPID optimization controller controlled by the hybrid fruit fly algorithm (BP-FOA) further reduces the adjustment time and overshoot At the same time, the number of oscillations is greatly reduced, and the system is stable after only 2 times. The specific speed regulation optimization is shown in Figure 10.

As shown in Figure 11: By analyzing the adaptive optimization parameters of the FOA algorithm, the BP neural network algorithm and the BP-FOA algorithm designed in this paper, due to the high iterative step value set, the global optimization ability of the fruit fly algorithm is enhanced. However, the number of iterations is large, and the optimization time is long; the BP neural network algorithm has strong optimization ability and fast convergence speed, but it is easy to fall into local optimum, and it will appear unstable when running in the face of load fluctuations; BP-FOA algorithm in the global search On the basis of strong optimization ability, the rapid convergence of BP neural network further reduces the self-adaptive adjustment time by 24.58%, and shows stronger adaptability and stability in the face of load fluctuations.

Through the comparison of Table 3 and Table 4, it can be seen that the dual-objective control FOPID regulator with the mixed fruit fly algorithm has obvious advantages in optimizing the speed regulation time and control overshoot. On the basis of the current mainstream BP neural network control algorithm, the 46.86% overshoot δ, shortening the adjustment time T _s by _36.59 %, where Tr is the rise time and T _p is the peak time.

Table 3 Comparison of simulation results of different controller indicators under load disturbance

Table 4 Comparison of optimization parameters of different controllers under load disturbance

The hydraulic turbine model optimized by BPFOA-FOPID dual objective is tested with 40% load initially, 35% load is put in at 30s, and 35% load is cut off at 60s. The speed fluctuation is ±2% when the load is switched on and off at 30s and 60s, and it is stable at 3.9s, which greatly improves the stability of the system; due to the DC exciter used, the generator is strongly excited and reduced when the load is increased or decreased. It can basically reflect the operating conditions of the exciter; the output output and output current of the generator are basically stable when the load fluctuates, reflecting good output performance.

This modeling analysis compares the four mainstream single-objective control methods of PID, FOPID, FOA algorithm and BP neural network control on the basis of establishing a comprehensive turbine model, and proposes a hybrid algorithm BPFOA-FOPID dual-objective function control method. In the face of load fluctuations, the speed and stability of the control of the turbine speed control system are improved. The simulation results show that under the BPFOA-FOPID dual-objective control method, the adjustment time and overshoot of the turbine are significantly reduced. Compared with the conventional control method, it shows stronger robustness and adaptability.

This patent uses MATLAB simulation modeling to improve the hydraulic turbine speed control system on the basis of previous research. The unit capacity, frequency, rotor winding, stator winding, excitation winding, number of pole pairs, output voltage and current, excitation voltage, and load changes can be analyzed in detail, and to a large extent can simulate the temporary stability of various hydropower stations during actual operation. The state change makes up for the defects of traditional turbine modeling. In practical application, it has a good response to the operation of the actual hydraulic turbine unit and the changes of various parameters of the hydraulic turbine when the load fluctuates, which provides a guarantee for accident prediction and safe operation of the system.

Claims (4)

1. a hydraulic turbine comprehensive model modeling method of an adaptive fractional-order PID speed control system, is characterized in that, comprises the following steps: Step 1: establish a simulation analysis mathematical model of the turbine governor based on the fractional-order PID speed control system, and use a hybrid algorithm to optimize the objective function based on the fractional-order PID speed control system; Step 2: Establish the mathematical model of the mechanical hydraulic system and the water diversion system of the turbine speed control system; Step 3: Establish a turbine generator model, extend the traditional first-order turbine generator model to a fifth-order turbine model, and introduce the exciter model and dynamic load model from this. 2. the hydraulic turbine comprehensive model modeling method of a kind of adaptive fractional-order PID speed control system according to claim 1, is characterized in that, described step 1 specifically comprises the following steps: Step 1.1: Obtain the fractional-order PID speed control system from the classical PID speed control system. The specific method is: The differential expression of the classic PID speed control system is: u(t)=k _p e(t)+ _ki De(t)+k _d De(t); Among them, kp represents the proportional parameter, the setting range is 0.5～20; ki is the integral parameter, the setting range is 0.05s-1～10s-1, kd is the differential parameter, the setting range is 0～5s; Replace the three adjustment parameters k _p , k _i , k _d with transient slip coefficient b _t , buffer time constant T _d , acceleration time constant T _n , specifically: The transfer function of the classic PID speed control system is: Among them, bt is the transient slip coefficient, taking 0 to 1.0; Td is the buffer time constant, the setting range is 2s～20s, Tn is the acceleration time constant, the setting range is 0～2s, pc and P are the unit power given respectively and unit power, y _c and y are the guide vane opening and guide vane degrees, respectively, fc and f are the frequency setting and unit frequency, respectively, Δf is the frequency difference, and Δf' is the frequency after passing through the frequency dead zone e _f deviation; The differential expression of the above classical PID speed control system is transformed into the differential expression of the fractional order PID speed control system through Laplace: u(t)=k _p e(t)+ _ki D ^α e(t)+k _d D ^μ e(t); (4) Where α, μ>0, α is the integral order, μ is the differential order; The transfer function of fractional order PID speed control system is: Step 1.2: Define the objective function of the fractional-order PID speed control system, the specific method is: Use the double error integral as the objective function of the fractional-order PID speed control system described in step 1.1: Among them, e(t) represents the deviation between the actual output and the expected output, t is the time, and I _SE represents the square deviation integral; Step 1.3: Use the hybrid algorithm to optimize the objective function of the fractional-order PID speed control system described in Step 1.2. The specific method is: Five parameters of _{k p} , _ki , _{k d} , α and μ are used to form the initial fruit fly position, so that the fruit fly can be optimized according to the taste concentration _. The five parameters of α and μ are optimized and solved, including the following steps: Step 1.3.1: Initialize the fruit fly population size groupsize(400) and the maximum number of iterations maxnum(400), randomly generate the fruit fly population position (X _axis , Y _axis ), and the iteration step value R is defined as (0.85-1); Step 1.3.2: Randomize the position and direction of the fruit fly population, and determine the taste concentration value S _i of the fruit fly population according to the distance D _Dist between the fruit fly population position and the origin; Step 1.3.3: Calculate the taste concentration of individual fruit flies, substitute the taste concentration value S _i of the fruit fly population into the taste concentration determination function F _function , and find the optimal individual of taste concentration from each fruit fly population; Retain the optimal taste concentration b _bestsmell and the corresponding (X _i , Y _i ) position, the fruit fly population S _smell flies to this coordinate, and b _bestindes represents the optimal fruit fly position; Step 1.3.4: Input the position coordinates (X _i , Y _i ) of the fruit fly obtained in step 1.3.3 into the hidden layer n _net ⁽²⁾ (k) of the BP neural network to define the input and output; Among them, i=1,2,...,Q, the value of n and Q is defined according to the complexity of the controlled object, Z _j ⁽²⁾ is the optimal position of the fruit fly population (X _i , Y _i ), w _ij ⁽²⁾ is the hidden Layer weighting coefficient, Z _i (k) ⁽²⁾ Take the activation function Sigmoid function; Step 1.3.5: Define the output layer n _net ⁽³⁾ (k) of the BP neural network, update the individual fruit fly, select E(k) as the performance error index, and keep the position coordinates (X _i , Y _i ); Step 1.3.6: By judging the performance index calculated in the previous step, when the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process, otherwise, go to step 1.3.2, until When the maximum number of iterations is reached, output the optimal parameters k _p , k _i , k _d , α, μ, and end the process. 3. the hydraulic turbine comprehensive model modeling method of a kind of self-adaptive fractional-order PID speed control system according to claim 1, is characterized in that, described step 2 specifically comprises the following steps: Step 2.1: Establish the mathematical model of the mechanical hydraulic system of the turbine speed control system, specifically using the following methods: The function of the mechanical hydraulic system is to convert and amplify the electrical signal into a mechanical displacement signal with a certain operating force; since the response time constant T _y1 of the secondary relay is much smaller than the response time constant _Ty of the main relay, it is usually used in modeling. Simplified as an inertia link, where y is the output signal of the mechanical hydraulic system, and can also represent the relative size of the guide vane opening. According to the adjustment characteristics of the turbine, the frequency dead zone and saturation limit links are added, and the main pressure distribution valve and the servomotor linear part The transfer function is: Step 2.2: Establish the mathematical model of the water diversion system of the turbine speed control system, using the following methods: According to the length of the water diversion pressure pipeline, in the simulation modeling, the rigid water hammer model is used below 700 m, and the elastic water hammer is used when it is greater than 700 m. The hydraulic change process of the water flow in the water diversion system is described by the following equation: Equation of motion: Where H is the water head, Q is the water flow, S is the cross-sectional area of the water pipe, t is the time, and g is the acceleration of gravity; Flow equation: where a is the water flow acceleration; The transfer functions of rigid water hammer G _A1 and elastic water hammer G _A2 are obtained by expanding the water hammer equation in the pressure diversion pipeline through Taylor series and taking the terms n=0 and n=1: where _TW is the rigid water hammer time constant, Tr=2L/V is the elastic water hammer time constant, L is the length of the pressure diversion pipeline, V is the water flow velocity, H ₀ is the water head, Q ₀ is the flow rate, and V ₀ is the flow base speed. 4. the hydraulic turbine comprehensive model modeling method of a kind of adaptive fractional-order PID speed control system according to claim 1, is characterized in that, described step 3 specifically comprises the following steps: The turbine generator model is established, the traditional first-order turbine generator model is extended to the fifth-order turbine model, and the exciter model and dynamic load model are introduced from this; the specific methods are as follows: Step 3.1: The first-order model used by the traditional hydro-turbine generator model is: Among them, f is the frequency of the unit, p is the input power difference of the unit, Tn is the inertia time constant of the unit, generally T _n is 3s ~ 12s, e _n is the static frequency self-adjustment coefficient of the unit, and e _n is 0.5 ~ 2.0s; The above first-order model cannot reflect the actual parameters of the hydro-generator and excitation system. In this paper, the synchronous motor model of the fifth-order space state equation established by the MATLAB/Simulink simulation platform is equivalent to the hydro-generator model, which defines the basic parameters of the hydro-turbine. Parametric characteristics, considering the dynamic characteristics of stator and rotor magnetic fields and damping windings, the equivalent circuit of the model is represented in the rotor reference frame (dq frame). Among them, the stator voltage equation is: where U _d is the stator d-axis voltage, U _q is the stator q-axis voltage, φ _d and φ _q represent the _dp -axis flux linkage, id and _{i q} are the currents in the equivalent dq coordinate system, ra is the equivalent resistance, dq The axial sub-transient electromotive force is E″ _d and E″ _q , X” _d and X” _q are dq sub-transient reactance; The rotor f winding, dq winding voltage equation and rotor motion equation are: where d-axis and q-axis time constants (all in s), d-axis transient open (Tdo') or short-circuit (Td') time constants, and d-axis sub-transient open (Tdo") or short-circuit (Td") time constants Time constant, q-axis transient open (Tqo') or short-circuit (Tq') time constant (round rotor only), q-axis sub-transient open (Tqo") or short-circuit (Tq") time constant. E' _q is the transient electromotive force, E _e is the dq winding electromotive force, X' _d is the d-axis transient reactance, X _d and X _q are the dq-axis reactance, W is the rotor mechanical angular velocity, and T _j is the inertia time constant of the generator set , T _m is the mechanical torque of the prime mover, is the unbalanced torque acting on the rotor shaft.