Cascade control method of impulse turbine regulating system based on improved crown porcupine algorithm

Abstract

The invention discloses a cascade control method of an impulse turbine regulating system based on an improved crown porcupine algorithm, which considers mechanical time lag of a hydraulic actuating mechanism and establishes a mathematical model of the impulse turbine regulating system under small fluctuation. According to the DMC-FOPID cascade control method for the impulse turbine regulating system, FOPID control is adopted as inner loop control, DMC (dynamic matrix control) is introduced as outer loop control, and the DMC-FOPID cascade control method for the impulse turbine regulating system is provided. According to the method, a Created Porcupine Optimization (CPO) algorithm is improved in combination with tent chaotic mapping and a fractional order longhorn beetle search mechanism, and the improved ICPO algorithm is provided, so that the optimization performance of the CPO is improved, and therefore, the optimal performance of the CPO is improved, and the optimal performance of the Created Porcupine Optimization (ICPO) is improved, and the optimal performance of the Created Porcupine Optimization (ICPO) is improved, and the optimal performance of the Created Porcupine Optimization (ICPO) is improved. And FOPID parameters are set and optimized through ICPO, and control simulation is carried out based on Simulink. The result shows that the cascade control method can effectively improve the control performance of the impulse turbine adjusting system.

Description

Technical Field

[0001] The present invention relates to the field of new energy technology, in particular to a cascade control method for an impulse turbine regulating system based on an improved crown porcupine algorithm. Background Art

[0002] Hydropower stations undertake comprehensive tasks such as power generation, water supply, and flood control. They are not only a crucial support for the construction of new power systems under the dual carbon goals, but also a reliable guarantee for the efficient use of water resources in river basins. With the rapid development of new energy sources in various provinces and regions and increasingly sophisticated and stringent management requirements for river basin water resources, hydropower stations are facing more intense and frequent grid peak and frequency regulation tasks. Southwest my country is rich in water resources and boasts a large number of Pelton hydropower stations. These stations offer advantages such as strong adaptability to high head drops and high operational efficiency. Pelton turbines are the core of Pelton hydropower stations, and their stable operation significantly impacts their profitability. Pelton turbines are the core of Pelton turbine units, and their performance depends primarily on the regulation of water flow and the stability of the water impact. Therefore, precise regulating devices are required to control the inflow of water and the rotational speed of the turbine. In current engineering practice, traditional PID control is often used. However, the actual working conditions are complex and changeable, and have extremely strong nonlinear characteristics. Conventional PID, as a linear structure, cannot meet the control requirements of the regulation system under complex working conditions, resulting in the generator speed being difficult to quickly reach stability, which to a certain extent affects the power generation capacity of the impact hydropower station.

[0003] To achieve better and faster control of the regulation system and ensure the stable operation of hydropower station units, industry experts have proposed new controllers such as sliding mode controllers, fuzzy controllers, and active disturbance rejection controllers to address complex and changing operating conditions. In recent years, they have also introduced more mature algorithms such as genetic algorithms, particle swarm algorithms, and ant colony algorithms to optimize controller parameters. However, the use of new controllers and optimization algorithms alone still has many drawbacks and limitations, such as a single solution and inaccurate optimization results. These limitations make it difficult to cope with various complex operating conditions, and new strategies are urgently needed to ensure the stable operation of hydropower units. The key to ensuring the efficient operation of hydropower stations is to better integrate the application of new controllers and optimization algorithms to further maximize the benefits of hydropower stations and reduce the time units operate under adverse conditions. Summary of the Invention

[0004] The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

[0005] The present invention proposes a cascade control method for a Pelton turbine regulating system based on an improved Crested Porcupine algorithm, controls the Pelton turbine regulating system based on a DMC-FOPID collaborative control strategy, introduces the concept of fractional order and the Beetle Antennae Search (BAS) search mechanism into the Crested Porcupine Optimizer (CPO), proposes an improved Crested Porcupine Optimizer (ICPO) based on the fusion of the fractional order strategy and the BAS search mechanism, optimizes and solves the fractional order PID control parameters, and obtains a reasonable control scheme for the Pelton turbine regulating system.

[0006] To achieve the above-mentioned object, the present invention proposes, on one hand, a cascade control method for a pulse turbine regulating system using an improved crown porcupine algorithm, comprising:

[0007] Inner loop FOPID control: A Pelton turbine regulating system model consisting of a Pelton turbine mathematical model, a microcomputer regulator, a hydraulic actuator, a water diversion system, and a generator is established, and FOPID is used for control.

[0008] Outer-loop DMC control: The impulse turbine regulation system model controlled by FOPID is regarded as a generalized object, and DMC is introduced externally for control to perform DMC-FOPID coordinated cascade control of the impulse turbine regulation system; among them, the crested porcupine optimization algorithm CPO is improved based on tent chaos mapping and fractional-order longicorn beetle whisker search mechanism to obtain the improved crested porcupine optimization algorithm ICPO, and the FOPID parameters are optimized through ICPO tuning for control simulation.

[0009] The control strategy of the crested porcupine optimization algorithm based on the fusion of multiple strategies in the embodiment of the present invention comprises the following specific steps:

[0010] Step S101: input the objective function and related parameters;

[0011] Step S102: Calculate the initial fitness value and find the initial optimal solution;

[0012] Step S103: Update the initial value, generate a random number, and determine whether the random number meets the exploration requirements; if so, generate two new random numbers and execute step S104; otherwise, only generate one random number and execute step S105;

[0013] Step S104: determining whether the generated random number meets the conditions of the odor defense mechanism of the crested porcupine optimization algorithm CPO; if so, executing the odor defense mechanism; if not, executing the physical defense mechanism;

[0014] Step S105: Determine whether the two generated random numbers meet the conditions of the visual defense mechanism. If so, execute the visual defense mechanism. If not, proceed to step S106.

[0015] Step 106: determine whether the number of iterations is greater than 3, if so, execute the fractional order beetle whisker search mechanism, if not, execute the beetle whisker search mechanism;

[0016] Step S107: Determine the stopping condition; set the stopping condition. If the stopping condition is met, output the optimal parameters; otherwise, return to step S102.

[0017] The improved crown porcupine algorithm cascade control method for the impulse turbine regulation system of the embodiment of the present invention adopts FOPID control as the inner loop control, introduces dynamic matrix predictive control (DMC) as the outer loop control, and proposes a DMC-FOPID cascade control method for the impulse turbine regulation system, which can effectively improve the control performance of the impulse turbine regulation system.

[0018] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0020] Figure 1 This is a schematic structural diagram of the FOPID controlled impulse turbine regulation system provided by the present invention;

[0021] Figure 2 This is a structural diagram of the DMC-FOPID collaborative control impulse turbine regulation system provided by the present invention;

[0022] Figure 3 This is a flow chart of the algorithm for adjusting FOPID parameters by integrating the multi-strategy crested porcupine optimization algorithm provided by the present invention;

[0023] Figures 4 to 7 These are the performance graphs of the improved crested porcupine optimization algorithm for the test function test;

[0024] Figure 8 、 Figure 9 These are the results of simulation experiments for the six different cases of the designed BAS-FOPID, CPO-FOPID, ICPO-FOPID, DMC-BAS-FOPID, DMC-CPO-FOPID, and DMC-ICPO-FOPID under disturbances of 5% and 10%. DETAILED DESCRIPTION

[0025] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0026] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0027] The following describes a cascade control method for an impulse turbine regulating system using an improved crested porcupine algorithm according to an embodiment of the present invention with reference to the accompanying drawings.

[0028] Specifically, the cascade control method of the impulse turbine regulating system using the improved crown porcupine algorithm of the present invention includes:

[0029] Inner loop FOPID control: A Pelton turbine regulating system model consisting of a Pelton turbine mathematical model, a microcomputer regulator, a hydraulic actuator, a water diversion system, and a generator is established, and FOPID is used for control.

[0030] Outer-loop DMC control: The impulse turbine regulation system model controlled by FOPID is regarded as a generalized object, and DMC is introduced externally for control to perform DMC-FOPID coordinated cascade control of the impulse turbine regulation system; among them, the crested porcupine optimization algorithm CPO is improved based on tent chaos mapping and fractional-order longicorn beetle whisker search mechanism to obtain the improved crested porcupine optimization algorithm ICPO, and the FOPID parameters are optimized through ICPO tuning for control simulation.

[0031] In one embodiment of the present invention, a model of a Pelton turbine regulating system is established:

[0032] Mathematical model of impulse turbine:

[0033] The flow rate of the Pelton turbine is independent of the turbine speed, and the flow rate of the nozzle is similar to the orifice outflow:

[0034]

[0035] Where Q is the nozzle flow rate; is the flow coefficient (generally taken as 0.97); g is the acceleration of gravity; H is the working water head of the turbine; d0 is the nozzle jet diameter.

[0036] The needle jet is controlled by the stroke S, and the jet diameter is generally nonlinearly related to the needle stroke size:

[0037]

[0038] Where k q k is the coefficient reflecting the nonlinear relationship between flow rate and needle stroke. For different needle strokes, k q Take different values.

[0039] The water flow out of the nozzle is also affected by the deflector. During the adjustment process, the effect coefficient of the deflector is taken as 1.

[0040] At this time, the work P done by the water flow on the runner is:

[0041] P=9.81QHη (3)

[0042] Where η is the turbine efficiency, which is related to the nozzle relay stroke, turbine speed, and turbine head. Nonlinear flow models and power models can be used to numerically analyze the transient process of the Pelton turbine. Linearization at the stable operating point is:

[0043]

[0044] M t =P / ω (6)

[0045] Where M t is the turbine torque; ω is the angular velocity of the turbine runner.

[0046] Taking the relative value:

[0047] q=e qy y+e qh h (7)

[0048] m t =e y y+e h h+e x x (8)

[0049] Where x, y, h, q, and m are t are the relative values of speed, servo stroke, water head, flow rate and torque deviation respectively; e qx 、e qh is the transfer coefficient related to flow rate; e y 、e h 、e h The transfer coefficients related to the torque respectively.

[0050] The microcomputer regulator adopts fractional order PID controller (FOPID) and its transfer function can be expressed as:

[0051]

[0052] Where K p , K i , K d are the proportional, integral and differential coefficients respectively, λ and μ are the fractional orders of integration and differentiation respectively, and s is the La-place operator.

[0053] The hydraulic actuator consists of an auxiliary servomotor and a main servomotor. The transfer functions of the two parts are:

[0054] G f (s)=1 / (1+T y1 s) (10)

[0055] G z (s)=1 / (T y s) (11)

[0056] Where, T y is the auxiliary relay reaction time constant, T y1 is the reaction time constant of the main relay, and s is the La-place operator.

[0057] The water diversion system adopts the second-order approximate elastic water hammer model to describe the characteristics of the water diversion system:

[0058]

[0059] Where h is the working head, q is the flow rate, T r is the water hammer phase of the diversion system, f is the head loss coefficient, h w The characteristic length of the pipeline, s is the La-place operator.

[0060] The generator adopts the equivalent torque model, which is:

[0061] T ae dx / dt=m te -m g (13)

[0062]

[0063] m g =m g0 +e g x;k i =P ri / P s (15)

[0064] Where, T ae is the equivalent inertia time constant of the parallel units; T aeis the equivalent active torque of the parallel units;

[0065] m g is the total load torque of the power grid; k i is the proportion of each unit's rated output to the grid capacity; m g0 is the initial load deviation value; e g is the self-regulation coefficient of the load in the isolated grid.

[0066] In one embodiment of the present invention, the DMC-FOPID coordinated impulse turbine regulation system cascade control includes: a prediction model

[0067] The prediction model is obtained by measuring the unit step response of the system

[0068] y m (k)=y0(k)+AΔu(k) (16)

[0069] y m (k)=[y m (k+1|k),…,y m (k+P|k)] T (17)

[0070] y0(k)=[y0(k+1|k),…,y0(k+P|k)] T (18)

[0071] Δu(k)=[Δu(k|k),…,Δu(k+M-1|k)] T (19)

[0072]

[0073] In formula (16)-(19), y m (k) is the model prediction value at time k; Δu(k) is the control variable at time k; y0(k) is the initial output value; P is the prediction time domain; M is the control time domain; A is the matrix composed of prediction vectors obtained from the unit step response; (k+1|k) is the prediction of time k+1 based on time k.

[0074] Scrolling optimization

[0075] The purpose of rolling optimization is to make the future predicted output value of the control system approach the set expected value. That is, the optimization is performed within a certain range of the time domain at each sampling moment k. The optimization performance index at moment k is as shown in formula (21):

[0076]

[0077] where q i With r j All are weighting coefficients.

[0078] Convert equation (21) into vector form:

[0079]

[0080] In formula (22), w p (k) = [w(k+1)...w(k+P)] is the expected output; Q = diag(q1,...,q P ) and R=diag(r1,...,r M ) are the error weighting matrix and the control weighting matrix respectively. In order to obtain the optimal control effect, J(k) must be the minimum value, that is, dJ(k) / dΔu M (k) = 0, we can get:

[0081]

[0082] where d T =c T (A T QA+R) -1 A T Q=[d1…d P ], c T =[10…0].

[0083] Feedback correction

[0084] In order to obtain better control effect and improve the robustness of the system, it is necessary to correct the predicted value at the future moment online. The online feedback correction is achieved by comparing the actual output y(k+1) of the control system with the predicted value y at the next moment. m (k+1|k) is subtracted to get the error e(k+1), that is:

[0085] e(k+1)=y(k+1)-y m (k+1|k) (24)

[0086] By adding the correction vector h = [h1...h N ] T To correct the predicted value at future time:

[0087] y P (k+1)=y m (k+1)+he(k+1) (25)

[0088] where y P (k+1) is the output prediction value after correction, which is then converted into the initial value predicted at the next moment through the softening coefficient matrix s:

[0089] y P0 (k+2)=s×yP (k+1) (26)

[0090]

[0091] The sampling period of the present invention is T=2s; the time domain length of the prediction model is N=50; the prediction time domain is P=8; and the control time domain is M=2.

[0092] DMC is combined with the impulse turbine unit regulation system, that is, DMC is introduced as the outer loop control on the basis of the original FOPID control of the regulation system as the inner loop control. For the impulse turbine regulation system, the FOPID controller is first optimized by the optimization algorithm to make the system achieve preliminary stability, and then the optimized FOPID control system is treated as a generalized object and controlled by the DMC algorithm, forming a cascade control strategy for the impulse turbine regulation system.

[0093] Furthermore, the improved crested porcupine optimization algorithm includes:

[0094] The crested porcupine optimization algorithm, CPO, simulates the various defensive behaviors of the crested porcupine. The four defense strategies of the crested porcupine are visual, sound, smell, and physical attack.

[0095] (1) Visual defense mechanism:

[0096] When the CP becomes aware of a predator, it begins to lift and fan its quills, creating a deeper impression. This type of behavior can be expressed mathematically as:

[0097]

[0098] is the vector generated between the current crested porcupine and a randomly selected crested porcupine in the population, Used to indicate the position of the predator in the iteration, represents the position of the crested porcupine during the iteration process, τ1 is a random number based on the normal distribution, and τ2 is a random value between [0,1]. The generated mathematical formula is as follows:

[0099]

[0100] Where r is a random number between [1, N].

[0101] (2) Sound defense mechanism:

[0102] In this strategy, crested porcupines use vocalizations to create noise and intimidate predators. To mathematically model this behavior, the following formula was proposed:

[0103]

[0104] Where r1 and r2 are two random integers between [1, N], and τ3 is a random value generated between 0 and 1.

[0105] (3) Odor defense mechanism:

[0106] When the predator gets closer to the crested porcupine, the crested porcupine will secrete a foul odor and spread it in the surrounding area. To mathematically simulate this behavior, the following formula is proposed:

[0107]

[0108] Where r3 is a random number between [1, N]. is a parameter used to control the search direction, defined by formula (22), γ t is the defense factor defined using Eq. τ3 is a random value in the interval [0,1], is the odor diffusion factor defined using equation (23).

[0109]

[0110]

[0111] in, represents the objective function value of the i-th individual at iteration t, ε is a small value to avoid division by zero, rand is a vector of randomly generated numbers between 0 and 1, rand is a variable containing randomly generated numbers between 1 and 0, N is the population size, t is the current iteration number, t max is the maximum number of iterations. Three possible situations that may occur in this strategy are simulated:

[0112] When U1 is equal to 0, the crested porcupine will stop spreading its scent; when U1 is equal to 1, it will emit scent significantly; when U1 is a combination of 0 and 1, there is no need to release its scent widely.

[0113] (4) Physical attack mechanism:

[0114] When a predator gets very close to it, the crested porcupine will resort to physical attack. In order to express its physical attack behavior with a mathematical formula, the following formula is proposed:

[0115]

[0116] α is the convergence speed factor of the parameter setting part, τ4 is a random value in the interval [0,1], F i t is the average force affecting the CP of the i-th predator. It is given by the law of inelastic collision and defined by equation (36):

[0117]

[0118] Among them,

[0119] where m i is the mass of the i-th individual (predator) at iteration t, is the final velocity of the i-th individual at the next iteration t + 1, and is assigned based on randomly selecting a solution from the current population, is the initial velocity of the i-th individual at iteration t, and τ6 is a vector including random values generated between 0 and 1.

[0120] Improve the CPO optimization algorithm, including:

[0121] (1) Tent chaos mapping

[0122] The Tent chaos mapping is a common one-dimensional chaos mapping, also known as the tent mapping, which is a simple but non-linear dynamic system showing complex behaviors. Its mathematical expression is:

[0123]

[0124] When a = 0.5, the system presents a short-period state. When the initial value of the system is the same as a, the system will evolve into a periodic system.

[0125] (2) Fractional-order strategy

[0126] Fractional-order calculus refers to integration and differentiation with fractional orders, which is an extension of traditional calculus. Due to its memory property, it has wide applications in fields such as digital image processing and digital signal processing. There are various definitions of fractional-order calculus, and here the commonly used G-L (Grumwald-Letniko) definition is adopted. Assume that there is a continuously differentiable function f(x) in the interval [a, b] (a < b, a ∈ R, b ∈ R), then the first derivative of f(x) is:

[0127]

[0128] where δ is the increment on the interval [a, b]. Further derivation from the above formula gives the n-th derivative of the function as:

[0129]

[0130] where n ∈ N. Extend the order in the above formula from integer order to fractional order. When the order υ > 0, the υ-th order fractional-order expression defined by G-L is:

[0131]

[0132] In the above formula, is the Gamma function.

[0133] According to formula (40), the approximate differential expression of the υ-order integral of the signal f(x) defined by GL can be obtained:

[0134]

[0135] (3) Longicorn beard optimization algorithm search mechanism

[0136] In the BAS algorithm, the beetle uses the two whiskers on its head to detect the food odor concentration (fitness value) on both sides every time it moves, and then chooses to move to the side with a higher food odor concentration (better fitness value). The beetle's position update is as follows:

[0137]

[0138] Among them, δ is the step size factor, satisfying δ i+1 =0.95δ i ; b is the direction vector after the longicorn moves to the next step; sign is the sign function, f(·) is the fitness function; Xr i With Xl i are the positions of the right and left whiskers of the longicorn at the i-th iteration.

[0139] The tent mapping is introduced during the initialization phase. It exhibits distinct chaotic properties: small changes in initial values can lead to significantly different iteration results, effectively demonstrating the "butterfly effect" of chaotic systems. Due to its strong chaotic behavior, the tent mapping is also very useful for generating pseudo-random numbers, producing highly unpredictable numerical sequences and exhibiting excellent randomness. Compared to traditional pseudo-random number generation methods, the random numbers generated using the tent mapping exhibit greater complexity and unpredictability.

[0140] In order to improve the global search capability, the fractional order strategy and the search step mechanism in BAS are combined and introduced into the CPO algorithm. This algorithm replaces the position iteration update mechanism of the two strategies with the position update formula of the sound defense mechanism of the CPO algorithm, and uses the heredity and memory of fractional order calculus and the search step mechanism of searching for the best fitness value in the BAS algorithm to ensure that it does not move randomly in each iteration, but moves to the side with better fitness value, overcomes the search blindness problem, improves the problem that the original CPO algorithm is prone to falling into local optimality, and can effectively improve the convergence speed of the CPO algorithm. The crown porcupine algorithm that integrates the fractional order and BAS algorithm mechanisms is replaced by the sound defense strategy position iteration formula (30) as follows:

[0141]

[0142] Numerical simulation analysis:

[0143] In order to verify the effectiveness of the DMC-ICPO-FOPID strategy proposed in the present invention for the control of impulse turbine units. First, the ICPO is tested with a test function and compared with (particle swarm algorithm) PSO, (sparrow algorithm) SSA, and CPO. The initial population size is set to 30, and the maximum number of iterations is set to 500. In order to avoid the randomness and systematic errors of the algorithm, 20 experiments are conducted and the average is taken as the experimental result. Then, a simulation experiment is carried out on simulink, and BAS-FOPID, CPO-FOPID, ICPO-FOPID, DMC-BAS-FOPID, DMC-CPO-FOPID, and DMC-ICPO-FOPID are designed. The above six different situations are compared and analyzed under the conditions of 5% and 10% disturbance. Among them, the BAS algorithm group size of the present invention is set to 30, the number of iterations is 200 times, the dimension dim is 5, the search step step=1, δ=1, and the FOPID parameters optimized by the BAS algorithm are K p , K i , K d , λ, and μ are 6.1252, 1.9667, 2.8533, 1.0326, and 0.34553, respectively. The CPO algorithm group size is set to 50, the number of iterations is 200, the dimension dim is 5, T=2, α=0.2, and Tf=0.8. The FOPID parameters optimized by the CPO algorithm are K p , K i , K d , λ, and μ are 6.0086, 1.65093, 0.81143, 1.0027, and 0.47746 respectively. The ICPO algorithm group size is set to 50, the number of iterations is 200, the dimension dim is 5, T=2, α=0.2, and Tf=0.8. The FOPID parameters optimized by the ICPO algorithm are K p , K i , K d , λ, and μ are 7.2887, 1.2571, 1.1532, 1.0309, and 1.2037, respectively. In this study, the time domain length of the DMC prediction model is N = 50, the prediction time domain is P = 8, the control time domain is M = 2, and the sampling period is T = 2s.

[0144] The parameters of the impulse turbine unit of a hydropower station are shown in Table 1:

[0145] Table 1

[0146]

[0147]

[0148] Experimental simulation is carried out based on the parameters of the above hydropower station.

[0149] Simulation effect analysis:

[0150] The results of testing ICPO using the test function are as follows Figures 4 to 7 As can be seen from the graph, ICPO performs better in terms of convergence speed than PSO, SSA, and CPO. Therefore, it can be concluded that ICPO has improved performance in finding the optimal solution to some practical engineering problems.

[0151] The above six different cases of BAS-FOPID, CPO-FOPID, ICPO-FOPID, DMC-BAS-FOPID, DMC-CPO-FOPID and DMC-ICPO-FOPID were designed and simulation experiments were carried out under the conditions of 5% and 10% disturbance. The simulation results are shown as follows: Figure 8 、 Figure 9 The simulation results show that compared with BAS-FOPID control, CPO-FOPID control, ICPO-FOPID control, DMC-BAS-FOPID control, and DMC-CPO-FOPID control, the designed DMC-ICPO-FOPID cascade controller has obvious advantages in control performance when the Pelton turbine unit regulation system is subjected to 5% and 10% no-load frequency disturbances. This can effectively improve the control quality and provide new ideas for the design of Pelton turbine unit regulation system controllers.

[0152] According to an embodiment of the present invention, a cascade control method for a pulse turbine regulating system based on an improved crested porcupine algorithm adopts FOPID control as the inner loop control and introduces dynamic matrix predictive control as the outer loop control, thereby proposing a DMC-FOPID cascade control method for a pulse turbine regulating system. The crested porcupine optimization algorithm is improved by combining tent chaos mapping and fractional-order longhorn beetle whisker search mechanisms, and an improved crested porcupine optimization algorithm is proposed to improve the optimization performance of CPO. By optimizing the FOPID parameters through ICPO tuning and performing control simulation based on Simulink, the control performance of the pulse turbine regulating system can be effectively improved.

[0153] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0154] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

Claims

1. A cascade control method for an impulse turbine regulating system based on an improved crown porcupine algorithm, characterized in that: include: Inner loop FOPID control: A Pelton turbine regulating system model consisting of a Pelton turbine mathematical model, a microcomputer regulator, a hydraulic actuator, a water diversion system, and a generator is established, and FOPID is used for control. Outer-loop DMC control: The impulse turbine regulation system model controlled by FOPID is regarded as a generalized object, and DMC is introduced externally for control to perform DMC-FOPID coordinated cascade control of the impulse turbine regulation system; among them, the crested porcupine optimization algorithm CPO is improved based on tent chaos mapping and fractional-order longicorn beetle whisker search mechanism to obtain the improved crested porcupine optimization algorithm ICPO, and the FOPID parameters are optimized through ICPO tuning for control simulation.

2. The method according to claim 1, characterized in that The control strategy of the crown porcupine optimization algorithm based on the fusion of multiple strategies has the following specific steps: Step S101: input the objective function and related parameters; Step S102: Calculate the initial fitness value and find the initial optimal solution; Step S103: Update the initial value, generate a random number, and determine whether the random number meets the exploration requirements; if so, generate two new random numbers and execute step S104; otherwise, only generate one random number and execute step S105; Step S104: determining whether the generated random number meets the conditions of the odor defense mechanism of the crested porcupine optimization algorithm CPO; if so, executing the odor defense mechanism; if not, executing the physical defense mechanism; Step S105: Determine whether the two generated random numbers meet the conditions of the visual defense mechanism. If so, execute the visual defense mechanism. If not, proceed to step S106. Step S106: determining whether the number of iterations is greater than 3, if so, executing the fractional order beetle whisker search mechanism, if not, executing the beetle whisker search mechanism; Step S107: Determine the stopping condition; set the stopping condition. If the stopping condition is met, output the optimal parameters; otherwise, return to step S102.

3. The method according to claim 1, characterized in that The flow rate of the Pelton turbine is independent of the turbine speed, and the flow rate of the nozzle is similar to the orifice outflow: Where Q is the nozzle flow rate; is the discharge coefficient; g is the acceleration of gravity; H is the working water head of the turbine; d0 is the nozzle jet diameter; The needle jet is controlled by the stroke S, and the jet diameter has a nonlinear relationship with the needle stroke size: Where k q It is the coefficient reflecting the nonlinear relationship between flow rate and needle stroke; The water flow from the nozzle is also affected by the deflector, and the work P done by the water flow on the runner is: P=9.81QHη (3) Where η is the turbine efficiency, and the linearization process at the stable operating point is: M t =P / ω (6) Where M t is the turbine torque; ω is the turbine runner rotation angular velocity; Taking the relative value: q=e qy y+e qh h (7) m t =e y y+e h h+e x x (8) Where x, y, h, q, and m are t are the relative values of speed, servo stroke, water head, flow rate and torque deviation respectively; e qx 、e qh is the transfer coefficient related to flow rate; e y 、e h 、e h The transfer coefficients related to the torque respectively.

4. The method according to claim 1, wherein The microcomputer regulator adopts fractional-order PID controller transfer function as follows: Where K p , K i , K d are the proportional, integral and differential coefficients respectively, λ and μ are the fractional orders of integral and differential respectively, and s is the La-place operator; The hydraulic actuator consists of an auxiliary servomotor and a main servomotor. The transfer functions of the two parts are: G f (s)=1 / (1+T y1 s) (10) G z (s)=1 / (T y s) (11) Where, T y is the auxiliary relay reaction time constant, T y1 is the main relay reaction time constant, s is the La-place operator; The water diversion system adopts the second-order approximate elastic water hammer model to describe the characteristics of the water diversion system: Where h is the working head, q is the flow rate, T r is the water hammer phase of the diversion system, f is the head loss coefficient, h w Characteristic length of pipe, The generator adopts the equivalent torque model, which is: T ae dx / dt=m te -m g (13) m g =m g0 +e g x;k i =P ri / P s (15) Where, T ae is the equivalent inertia time constant of the parallel units; T ae is the equivalent active torque of the parallel units; m g is the total load torque of the power grid; k i is the proportion of each unit's rated output to the grid capacity; m g0 is the initial load deviation value; e g is the self-regulation coefficient of the load in the isolated grid.

5. The method according to claim 1, wherein The DMC principle is divided into three parts: Prediction model: Obtained by measuring the unit step response of the system: y m (k)=y0(k)+AΔu(k) (16) y m (k)=[y m (k+1|k),…,y m (k+P|k)] T (17) y0(k)=[y0(k+1|k),…,y0(k+P|k)] T (18) Δu(k)=[Δu(k|k),…,Δu(k+M-1|k)] T (19) In formula (16)-(19), y m (k) is the model prediction value at time k; Δu(k) is the control quantity at time k; y0(k) is the initial output value; P is the prediction time domain; M is the control time domain; A is the matrix composed of the prediction vectors obtained from the unit step response; (k+1|k) is the prediction of time k+1 based on time k; Rolling optimization: that is, optimization is performed on the time domain within a certain range at each sampling moment k. The optimization performance index at moment k is as shown in formula (21): where q i With r j All are weighting coefficients; Convert Equation (21) into vector form: In formula (22), w p (k) = [w(k+1)…w(k+P)] is the expected output; Q=diag(q1,…,q P ) and R=diag(r1,…,r M ) are the error weighting matrix and the control weighting matrix respectively. In order to obtain the optimal control effect, J(k) must be the minimum value, that is, dJ(k) / dΔu M (k) = 0, we get: where d T =c T (A T QA+R) -1 A T Q=[d1…d P ], c T =[10…0]; Feedback correction: Online feedback correction is achieved by converting the actual output y(k+1) of the control system to the predicted value y at the next moment. m (k+1|k) is subtracted to get the error e(k+1), that is: e(k+1)=y(k+1)-y m (k+1|k) (24) By adding the correction vector h = [h1...h N ] T To correct the predicted value at future time: y P (k+1)=y m (k+1)+he(k+1) (25) where y P (k+1) is the output prediction value after correction, which is then converted into the initial value predicted at the next moment through the softening coefficient matrix s: y P0 (k+2)=s×y P (k+1) (26) Among them, the sampling period T = 2s; the prediction model time domain length N = 50; the prediction time domain P = 8; the control time domain M = 2.

6. The method according to claim 2, characterized in that The four defense strategies of the crested porcupine are vision, sound, smell, and physical attack; among them, The visual defense mechanism is expressed by the mathematical formula: is the vector generated between the current crested porcupine and a randomly selected crested porcupine in the population, Used to indicate the position of the predator in the iteration, Indicates the position of the crested porcupine during the iteration process, τ1 is a random number based on the normal distribution, and τ2 is a random value between [0,1]. The generated mathematical formula is as follows: where r is a random number between [1, N]; The sound defense mechanism is expressed by the mathematical formula: where r1 and r2 are two random integers between [1, N], and τ3 is a random value generated between 0 and 1; The smell defense mechanism is expressed by the mathematical formula: Where r3 is a random number between [1, N]. is a parameter used to control the search direction, defined by formula (22), γ t is the defense factor defined using the equation, τ3 is a random value in the interval [0,1], is the odor diffusion factor defined using equation (23); in, represents the objective function value of the i-th individual at iteration t, ε is a small value to avoid division by zero, rand is a vector of randomly generated numbers between 0 and 1, rand is a variable containing randomly generated numbers between 1 and 0, N is the population size, t is the current iteration number, t max is the maximum number of iterations; The mathematical expression of the physical attack mechanism is: α is the convergence speed factor of the parameter setting part, τ4 is a random value in the interval [0,1], F i t is the average force affecting the CP of the i-th predator; it is given by the law of inelastic collisions and defined by equation (36): in, where m i is the mass of the i-th individual at iteration t, is the final velocity of the ith individual at the next iteration t+1, and is allocated based on selecting random solutions from the current population, is the initial velocity of the i-th individual at iteration t, and τ6 is a vector of random values generated between 0 and 1.

7. The method according to claim 6, characterized in that The improved crested porcupine optimization algorithm ICPO includes: The mathematical expression of the Tent chaotic mapping is: Fractional-order strategy: Assume that there is a continuously differentiable function f(x) in the interval [a, b] (a < b, a ∈ R, b ∈ R), then the first derivative of f(x) is: Among them, δ is the increment on the interval [a, b]. Further derivation from the above formula gives the nth derivative of the function as: where n ∈ N. Extend the order of the above formula from integer order to fractional order. When the order υ > 0, the υ-order fractional-order expression defined by G-L is: In the above formula, is the Gamma function; According to Equation (40), the approximate differential expression of the υ-order integral of the signal f(x) defined by G-L is obtained: The expression of the search mechanism of the longhorn beetle antenna optimization algorithm is: Among them, δ is the step size factor, satisfying δ i+1 =0.95δ i ; b is the direction vector after the longicorn moves to the next step; sign is the sign function, f(·) is the fitness function; Xr i With Xl i are the positions of the right and left whiskers of the longicorn at the i-th iteration respectively; The position iteration formula (30) of the sound defense strategy in the crested porcupine algorithm that integrates the fractional-order and BAS algorithm mechanisms is replaced by:

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