CN115562008A - Power system chaos layered sliding mode control method based on improved fixed time - Google Patents
Power system chaos layered sliding mode control method based on improved fixed time Download PDFInfo
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Abstract
The invention discloses a hierarchical sliding mode control method of a chaos phenomenon of an electric power system based on improved fixed time, which comprises the following steps: carrying out chaos phenomenon analysis on the nine-order power system model by using a chaos analysis tool; the method is characterized in that the defects of the traditional fixed time sliding mode control are improved, the singularity problem is avoided, fixed time nonsingular terminal sliding mode control is combined with a self-adaptive technology, then a layered sliding mode is combined with the fixed time nonsingular self-adaptive terminal sliding mode to reduce the number of designed controllers, and a hyperbolic approximation law is added to reduce the buffeting phenomenon existing in the sliding mode control; and finally, in order to shorten the searching time of the control parameters, optimizing the control parameters by utilizing an improved ant lion algorithm on the basis of constructing a new objective function, and the research result has a reference function for controlling the actual chaos phenomenon of the power system.
Description
Technical Field
The invention belongs to the technical field of power system control, and particularly relates to a power system chaos phenomenon layered sliding mode control method based on improved fixed time.
Background
Modern electric power systems, as a complex power system of high nonlinearity, exhibit rich nonlinear dynamic behavior. Oscillation is a typical nonlinear dynamic behavior in the transmission process of the power system. In addition to the periodic oscillation during normal operation, the power system may sometimes suddenly, irregularly and aperiodically oscillate, and with the progress of research, many scholars find that the irregular oscillation presented by the power system is closely related to the chaotic operation behavior thereof. Although the irregular oscillation does not always damage the overall stability of the system, the potential destructive power of the irregular oscillation on the system safety is huge, once the system continuously generates the irregular oscillation, the system is likely to be disconnected, even crashed, and further large-area power failure accidents occur, and under the condition, in order to ensure the safe and stable operation of the power system, advanced control theories, technologies and methods need to be continuously researched.
Disclosure of Invention
The invention aims to provide a layered sliding mode control method of a chaos phenomenon of an electric power system based on improved fixed time, and the invention designs a new fixed time nonsingular self-adaptive terminal layered sliding mode control method based on a traditional fixed time sliding mode surface, solves the singularity problem existing in the traditional fixed time sliding mode control by adding a saturation function and utilizing the idea of a piecewise function, estimates uncertain parameters in the system by utilizing a self-adaptive method, weakens the buffeting phenomenon by utilizing a hyperbolic approximation law, combines the layered sliding mode control with the designed sliding mode surface so as to reduce the number of controllers, and finally seeks time for reducing control parameters by utilizing an improved ant algorithm on the basis of constructing a new target function.
The purpose of the invention is realized by adopting the following technical scheme:
a layered sliding mode control method for a chaos phenomenon of an electric power system based on improved fixed time comprises the following steps:
step 1: analyzing a power system chaos model, and analyzing a chaos phenomenon by using a chaos analysis method;
and 2, step: aiming at the defects of the traditional fixed time sliding mode control method, the method is improved from different aspects, and a layered sliding mode control method for improving fixed time is established;
and step 3: in order to shorten the control parameter searching time, a new objective function is designed, and the ant lion algorithm is improved for optimizing the control parameters.
Further, step 1 specifically comprises: the nine-order power system model is analyzed, and the existence of the chaos phenomenon is explained through analyzing four aspects of each state timing diagram, a system bifurcation diagram, a system power spectrum diagram and a system phase diagram.
And (3) system model:
in the formula, delta v Is the power angle of the generator, s v Is the engine slip; e d ' and E d "transient electromotive force and sub-transient electromotive force for the d-axis of the generator; e q ' and E q "transient electromotive force and sub-transient electromotive force for q-axis of the generator; e fd Is the excitation electromotive force of the generator; delta L And V L The phase angle and the amplitude of the load bus voltage are shown; d v External periodic interference for the generator side; u. of v ，u L1 And u L2 Is a control input to the system. Of the variables of the controlled system expression, P g 、I d 、I q 、V t P, Q is a function of each state variable.
In order to inhibit the chaotic oscillation phenomenon, three control input pairs are designed to respectively correspond to delta according to the dynamic mathematical characteristics of the power system v ,s v ,δ L ,V L Control is carried out, namely the system is divided into three subsystems, and the expression of each subsystem is as follows:
subsystem (one):
subsystem (b):
subsystem (b):
in the above formula delta Lin And V Lin Is the integral of the phase angle and amplitude of the load bus voltage, u L1 、u L2 、u v The controller is designed. According to the expression of the system dynamics equation, when the states of the three subsystems tend to be stable, E d ′,E q ′,E d ″,E q ″,E fd It will tend to stabilize. Therefore, only three control inputs are needed to control the whole system, and the expected value of the system is set to be delta vd ,s vd ,δ Ld ,V Ld ]＝[0,0,0.78,1]The system error is:
further, step 2 improves the conventional fixed time sliding mode, and is combined with a layered sliding mode: the improved method comprises the following steps:
by a systematic error e 1 For example, the conventional fixed-time fast sliding mode surfaces are:
the traditional fixed-time fast sliding mode surface can enable the system state to be converged in fixed time, but has the problem of singularity, and the control process generates a buffeting phenomenon due to the discontinuous characteristic of the symbolic function. In order to further accelerate the convergence speed of the fixed-time rapid sliding mode surface and solve the buffeting phenomenon existing in the traditional sliding mode surface, the improved fixed-time rapid sliding mode surface is as follows:
in the formula alpha 1 、α 2 、β 1 、β2、ψ 1 、
k are all positive constants greater than zero, coefficient psi 1 、
The size of k determines the convergence speed of the whole sliding mode surface, alpha 1 、α 2 、β 1 、β 2 Is related to the system stability, sat is a saturation function, and the expression is as follows:
in the formula, p is a constant larger than zero, the buffeting phenomenon existing in the control process can be weakened by replacing a sign function with a saturation function, the sliding mode surface is divided into two parts, and when the system state is smaller than k, namely when the system state is close to a balance point, the convergence speed of the sliding mode surface (a) is high; when the system state is larger than k, namely when the system state is far away from the balance point, the sliding mode surface (b) can accelerate the convergence speed of the system. It follows that the system convergence speed can be further increased when using an improved fixed time fast sliding surface, whether the system conditions are far away or near the equilibrium point. Thus, the improved slip surface attenuates the buffeting problem associated with conventional fixed time slip surfaces and improves the time to reach the equilibrium point of the system.
Pair formula s 1 The derivation is carried out to obtain:
according to the above formula, when e 1 Equal to 0, due to a 1 Less than 1, so singular points may occur. For an improved fixed-time slip-form face, when the slip-form face approaches the origin, one can obtain:
for improved sliding form surfaces, when psi 1 When greater than 0, e 1 When the sliding mode surface is equal to 0, no singular point can occur, and the improved sliding mode surface can solve the singularity problem existing in the traditional fixed time sliding mode surface. In order to carry out better adaptive law design on the improved sliding mode surface, the improved fixed-time sliding mode surface is improved, and a new sliding mode surface with p = a is:
after a sliding mode surface shown in the formula is obtained, a sliding mode approximation law is designed, a hyperbolic function is selected as the approximation law, the hyperbolic approximation law can realize quick convergence of sliding mode control and buffeting reduction, and the expression is as follows:
in the above formula, s is a designed sliding mode surface, q is a positive odd number, and lambda 1 ,λ 2 ,r 1 ,r 2 The parameters are positive parameters respectively, and tanh and asinh are hyperbolic tangent functions and inverse hyperbolic sine functions, and the values of the hyperbolic tangent functions and derivatives thereof are in a range from-1 to 1, and the hyperbolic tangent functions change slowly, so that the hyperbolic tangent functions have similar linear characteristics when the sliding mode surface approaches to 0. The characteristics of the hyperbolic function are the same, and the buffeting phenomenon is reduced or even eliminated due to the linear characteristic.
In an actual power system, damping coefficient d in constant value parameters of system equation and electromagnetic power P of generator m For better control, an adaptive law is designed for the two uncertain parameters to estimate:
the above equation is the derivative of the estimated value of the parameter d; tau is 1 For designed adaptive parameters, s v And H is the inertia time constant of the generator. The control precision can be adjusted by adjusting tau according to the difference of the change size of the constant parameter.
The above equation is the derivative of the estimated value of the parameter Pm; τ 2 is a designed adaptive parameter as is τ 1.
Layering sliding mode:
the system equations of the subsystem (II) and the subsystem (III) can be closely related by observing the subsystem (II) and the subsystem (III), in order to reduce the design number of controllers, the concept of layered sliding mode control is added into the system, and one control input is designed to simultaneously make the subsystem (II) and the subsystem (III) converge, namely u in the system L1 ＝u L2 ＝u eq 。
Subsystem s 32 And s 33 In the second layer, the two sliding surfaces are linearly combined into:
s 4 ＝ms 32 +ns 33
according to the design process of the sliding mode theory, the total control law comprises the equivalent control laws of the two subsystems and the switching control law of the sliding mode surface approach law, and then the total control law is designed as follows:
u eq ＝u L2 +u L3 +u sw
the selection of the approximation law is based on a constant-scaled approximation law, and the expression of the approximation law is as follows:
the switching control law u can be obtained by the above formula sw Comprises the following steps:
in the formula G 1 And G 2 For the control law coefficient, the expression is:
further, aiming at the defects existing in the initialization of the ant lion algorithm, the ant lion algorithm is improved, and a new objective function is designed according to the required control effect to optimize the parameters of the controller, and the specific contents are as follows:
in the traditional ant lion algorithm, a random function is used for initialization, in order to improve the randomness of an initial population and enable the population to be uniformly distributed in an optimized area, the method adopts an improved initialization method, namely, the initialization is divided into a plurality of areas, and a Logistic mapping model is used for initializing the population in each sub-area, so that the population can be more randomly distributed in a parameter range.
For an optimized objective function, the invention selects the absolute error of integration time as a performance standard for an accurate index according to the starting point of 'stable', 'quasi' and 'fast' of a control requirement, selects overshoot, rise time, transition time and peak time as performance indexes for the stable and fast performance indexes, and provides the following objective functions:
OF＝(1-e -θ )(M p +ITAE)+e -θ (t s +t r +t p )
in the formula, M p For overshoot, ITAE is the absolute error of integration time, t s As transition time of the system, t p Is the peak time of the system, t r And theta is a weighting factor for the rise time of the system, and the requirements of designers on different performance indexes can be met by adjusting the weighting factor.
Compared with the prior art, the invention has the beneficial effects that:
on the basis of fixed time sliding mode control, the method designs an improved fixed time nonsingular self-adaptive sliding mode surface in consideration of the singularity problem, so that the system state can be stabilized within fixed time; in order to eliminate the influence brought by interference such as parameter disturbance and the like, a self-adaptive law is designed for variable parameters, and meanwhile, the inherent buffeting phenomenon of sliding mode control is weakened by utilizing the characteristics of a saturation function and a hyperbolic function, simulation results show that the performance of the sliding mode surface is better compared with that of the sliding mode surface provided by the traditional fixed time sliding mode surface, the hierarchical sliding mode control is combined with the fixed time nonsingular self-adaptive sliding mode surface improved and improved by design to control the chaos phenomenon of a system, the number of controllers can be reduced, the optimized ant algorithm is utilized to optimize the parameters of the control method, and a new control objective function is constructed according to the requirement of the control performance so as to optimize the control parameters towards better control performance.
Drawings
FIG. 1 is a control flow block diagram of the method of the present invention;
FIG. 2 is a timing diagram of various states of the system; (a) The state variable delta v A timing diagram; (b) State variable s v A timing diagram; (c) The state variable delta L A timing diagram; (d) State variable V L A timing diagram; (e) State variable E q ' timing diagram; (f) State variable E d ' timing diagram; (g) State variable E d "timing diagram; (h) State variable E q "timing diagram; (i) State variable E fd Time sequence;
FIG. 3 is a diagram of a system fork; (a) State variable s v A bifurcation diagram; (b) State variable E d ' bifurcation map;
FIG. 4 is a functional diagram of the system;
FIG. 5 is a system phase diagram; (a) a system phase diagram; (b) strange attractors for the presence of the system;
FIG. 6 is a layered slip form construction;
FIG. 7 is a diagram of system state variables after control;
FIG. 8 is a system phase diagram after control;
FIG. 9 is a state diagram of the system after control; (a) Delta v A timing diagram; (b) s v A timing diagram; (c) Delta L A timing diagram; (d) V L A timing diagram;
FIG. 10 is a controller output value; (a) Control u v Outputting the value; (b) Control u eq Outputting the value;
fig. 11 is a comparison graph of the presence or absence of adaptive parameters.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
Aiming at the chaos phenomenon of an electric power system, the invention provides a novel fixed-time nonsingular self-adaptive terminal layered sliding mode control, firstly, the traditional fixed-time terminal sliding mode surface is improved, and the singularity problem is avoided; secondly, in order to solve the challenge brought by external interference such as system parameters to system control, the fixed-time nonsingular terminal sliding mode control is combined with the self-adaptive technology, a novel fixed-time nonsingular self-adaptive terminal sliding mode control is provided, then the layered sliding mode and the fixed-time nonsingular self-adaptive terminal sliding mode are combined to reduce the number of design controllers, and a hyperbolic approximation law is added to reduce the buffeting phenomenon in the sliding mode control. In order to shorten the control parameter searching time, the control parameters are optimized by using the improved ant lion algorithm on the basis of constructing a new objective function, and the result shows that the proposed control method has good control performance. The control flow diagram of the method of the invention is shown in figure 1, and comprises the following steps:
step 1: analyzing a power system chaotic model, and analyzing a chaotic phenomenon by using a chaotic analysis method; and (3) system model:
in the formula, delta v Is the power angle of the generator, s v Is the engine slip; e d ' and E d "transient electromotive force and sub-transient electromotive force for the d-axis of the generator; e q ' and E q "transient electromotive force and sub-transient electromotive force for q-axis of the generator; e fd Is the excitation electromotive force of the generator; delta L And V L The phase angle and the amplitude of the load bus voltage are shown; d v External periodic interference for the generator side; u. of v ，u L1 And u L2 Is a control input to the system. Of the variables of the controlled system expression, P g 、I d 、I q 、V t P, Q is a function of each state variable.
In order to inhibit the chaotic oscillation phenomenon, three control input pairs are designed to respectively correspond to delta according to the dynamic mathematical characteristics of the power system v ,s v ,δ L ,V L Control is carried out, namely the system is divided into three subsystems, and the expression of each subsystem is as follows:
subsystem (one):
subsystem (b):
subsystem (b):
in the above formula delta Lin And V Lin Is the integral of the phase angle and amplitude of the load bus voltage, u L1 、u L2 、u v The controller is designed. According to the expression of the system dynamics equation, when the states of the three subsystems tend to be stable, E d ′,E q ′,E d ″,E q ″,E fd It will tend to stabilize. Therefore, only three control inputs are needed to control the whole system, and the expected value of the system is set to be delta vd ,s vd ,δ Ld ,V Ld ]＝[0,0,0.78,1]The system error is:
in order to analyze the chaos phenomenon, the chaos analysis tool is used to analyze the core of the model of the power system, fig. 2 to 5 are analysis results, wherein fig. 2 is a system timing diagram showing that the system is in a disordered state, and fig. 3 is a system variable s v And E d ' bifurcation diagram with increasing electromagnetic power, as can be seen from FIG. 3, the system starts to be in a normal state with increasing electromagnetic power, and s is when the electromagnetic power increases to 1.24 v And E d ' continuous period forking begins to occur, and as the forking parameter increases, the system has 4 times period and 8 times period. When the electromagnetic power reaches 1.360, the system is in a disordered chaotic state, so that chaos occurs, and then when the electromagnetic power is 1.394, the system returns to a double-cycle state from the chaotic state. To further demonstrate the electromagnetic power P m The chaotic state of 1.361 can be seen by the power spectrum and the phase diagram of the system, i.e. fig. 4 and 5.
Step 2: aiming at the defects of the traditional fixed time sliding mode control method, the method is improved from different aspects, and a layered sliding mode control method for improving the fixed time is established;
by a systematic error e 1 For example, the conventional fixed-time fast sliding mode surfaces are:
the traditional fixed-time fast sliding mode surface can enable the system state to be converged in fixed time, but has the problem of singularity, and the control process generates a buffeting phenomenon due to the discontinuous characteristic of the symbolic function. In order to further accelerate the convergence speed of the fixed-time rapid sliding mode surface and solve the buffeting phenomenon existing in the traditional sliding mode surface, the improved fixed-time rapid sliding mode surface is as follows:
in the formula of alpha 1 、α 2 、β 1 、β2、ψ 1 、
k are all positive constants greater than zero, coefficient psi 1 、
The size of k determines the convergence speed of the whole sliding mode surface, alpha 1 、α 2 、β 1 、β 2 Is related to the system stability, sat is a saturation function, and the expression is as follows:
in the formula, p is a constant larger than zero, the buffeting phenomenon existing in the control process can be weakened by replacing a sign function with a saturation function, the sliding mode surface is divided into two parts, and when the system state is smaller than k, namely when the system state is close to a balance point, the convergence speed of the sliding mode surface (a) is high; when the system state is larger than k, namely when the system state is far away from the balance point, the sliding mode surface (b) can accelerate the convergence speed of the system. It follows that the system convergence speed can be further increased when using an improved fixed time fast sliding surface, whether the system conditions are far away or near the equilibrium point. Thus, the improved slip surface reduces the buffeting problem of conventional fixed time fast slip surfaces and improves the time for the system to reach the equilibrium point.
Pair formula s 1 The derivation is carried out to obtain:
according to the above formula, when e 1 Equal to 0, due to a 1 Less than 1, so singular points may occur. For an improved fixed-time slip-form face, when the slip-form face approaches the origin, one can obtain:
for improved sliding form surfaces, when psi 1 When greater than 0, e 1 When the sliding mode surface is equal to 0, no singular point can be generated, and the improved sliding mode surface can solve the singularity problem existing in the traditional fixed time sliding mode surface. In order to carry out better adaptive law design on the improved sliding mode surface, the improved fixed-time sliding mode surface is improved, and a new sliding mode surface with p = a is:
after a sliding mode surface shown in the formula is obtained, a sliding mode approximation law is designed, a hyperbolic function is selected as the approximation law, the hyperbolic approximation law can realize quick convergence of sliding mode control and buffeting reduction, and the expression is as follows:
in the above formula, s is a designed sliding mode surface, q is a positive odd number, and lambda 1 ,λ 2 ,r 1 ,r 2 The parameters are positive parameters respectively, and tanh and asinh are hyperbolic tangent functions and inverse hyperbolic sine functions, and the values of the hyperbolic tangent functions and derivatives thereof are in a range from-1 to 1, and the hyperbolic tangent functions change slowly, so that the hyperbolic tangent functions have similar linear characteristics when the sliding mode surface approaches to 0. The characteristics of the hyperbolic function are the same, and the buffeting phenomenon is reduced or even eliminated due to the linear characteristic.
In an actual power system, damping coefficient d in constant value parameters of system equation and electromagnetic power P of generator m For better control, an adaptive law is designed for the two uncertain parameters to estimate:
the above equation is the derivative of the estimated value of the parameter d; tau. 1 For designed adaptive parameters, s v And H is the inertia time constant of the generator. The control precision can be adjusted by adjusting tau according to the difference of the change size of the constant parameter.
The above equation is the derivative of the estimated value of the parameter Pm; τ 2 is a designed adaptive parameter as is τ 1.
Layering sliding mode:
the system equations of the subsystem (II) and the subsystem (III) can be closely related by observing the subsystem (II) and the subsystem (III), in order to reduce the design number of controllers, the concept of layered sliding mode control is added into the system, and one control input is designed to simultaneously make the subsystem (II) and the subsystem (III) converge, namely u in the system L1 ＝u L2 ＝u eq The hierarchical structure of the slip plane of the system is shown in fig. 6.
Subsystem s 32 And s 33 In the second layer, the two sliding surfaces are linearly combined into:
s 4 ＝ms 32 +ns 33
according to the design process of the sliding mode theory, the total control law comprises the equivalent control laws of the two subsystems and the switching control law of the sliding mode surface approach law, and then the total control law is designed as follows:
u eq ＝u L2 +u L3 +u sw
the selection of the approximation law is based on a constant-scaled approximation law, and the expression of the approximation law is as follows:
the switching control law u can be obtained by the above formula sw Comprises the following steps:
in the formula G 1 And G 2 For the control law coefficient, the expression is:
and step 3: in order to shorten the control parameter searching time, a new objective function is designed, and the ant lion algorithm is improved for optimizing the control parameters.
Further, aiming at the defects existing in the initialization of the ant lion algorithm, the ant lion algorithm is improved, and a new objective function is designed according to the required control effect to be used for optimizing the parameters of the controller, wherein the specific contents are as follows: ,
in the traditional ant lion algorithm, a random function is used for initialization, in order to improve the randomness of an initial population and enable the population to be uniformly distributed in an optimized area, the invention adopts an improved initialization method, namely, the initialization is divided into a plurality of areas, and a Logistic mapping model is used for initializing the population in each sub-area, so that the population can be more randomly distributed in a parameter range
For an optimized objective function, the invention selects the absolute error of integration time as a performance standard for an accurate index according to the starting point of 'stable', 'quasi' and 'fast' of a control requirement, selects overshoot, rise time, transition time and peak time as performance indexes for the stable and fast performance indexes, and provides the following objective functions:
OF＝(1-e -θ )(M p +ITAE)+e -θ (t s +t r +t p )
in the formula, M p For overshoot, ITAE is the absolute error of integration time, t s As transition time of the system, t p Is the peak time of the system, t r And theta is a weighting factor for the rise time of the system, and the requirements of designers on different performance indexes can be met by adjusting the weighting factor.
The steps are programmed and simulated by a matlab2018b platform. The state diagram of part of the system obtained through simulation is shown in fig. 7, and as can be seen from fig. 7, after the controller is added, the state variables of the system except the controlled state can change the chaotic oscillation state of the system into expected values within 1s, the system smoothly recovers to a stable state, the chaotic state of the system is restrained, and the effectiveness of designing the controller is demonstrated. Fig. 8 is a phase diagram of the system after control, in which the initial state of the system is shown, and the steady state of the system is shown. In fig. 8, the strange chaotic attractors have disappeared as compared to the phase diagram shown in fig. 5, and the strange attractors in the phase diagram have evolved into equilibrium motionless points. To illustrate that the designed sliding mode surface is superior to the traditional fixed-time sliding mode surface, the comparison result between the designed sliding mode surface and the traditional fixed-time sliding mode surface is shown in fig. 9, and it can be seen from fig. 9 that the improved sliding mode surface tracks the signal faster than the traditional sliding mode surface in terms of convergence time, and the improved sliding mode surface has better performance in terms of system overshoot. In terms of reducing buffeting, the same control input is designed for two subsystems by utilizing layered sliding mode control, wherein the system is divided into two layers and a discontinuous function exists in the second layer, and unexpected buffeting is brought to system control. As shown in fig. 9 (c) and 9 (d), the conventional fixed time slip surface does not eliminate the chatter, while the improved slip surface is better at eliminating chatter, and is better at coping with chatter. To further demonstrate the advantage of improved fixed-time sliding-mode control, a conventional fixed-time sliding-mode is compared with an improved fixed-time sliding-mode control output, such as that shown in FIG. 10. As can be clearly seen from fig. 10, the conventional fixed-time sliding mode has the phenomenon of buffeting, but the fixed time after the improvement of the invention has almost no buffeting, which indicates a certain practical significance of the designed controller. To prove the effectiveness of the adaptive parameters, periodic interference is added to the generator side of the system, and the result is shown in fig. 11 by taking the power angle of the generator as an example. As can be seen from fig. 11, the controller with adaptive parameters can better cope with the influence of the external interference on the system, which indicates that the controller designed by the present invention has good robustness.
The foregoing merely illustrates preferred embodiments of the invention and is therefore to be understood as illustrative and not restrictive. It should be noted that, for those skilled in the art, various changes, modifications and substitutions can be made without departing from the spirit of the present invention, and these are all within the scope of the present invention.
Claims (4)
1. A hierarchical sliding mode control method for a chaos phenomenon of an electric power system based on improved fixed time is characterized by comprising the following steps:
step 1, analyzing a power system chaotic model, and analyzing a chaotic phenomenon by using a chaotic analysis method;
step 2, improving the traditional fixed time sliding mode control method, and establishing a layered sliding mode control method for improving fixed time;
and 3, designing a new objective function for shortening the control parameter searching time, and improving the ant lion algorithm for optimizing the control parameters.
2. The electric power system chaos phenomenon layered sliding-mode control method based on the improved fixed time according to claim 1, wherein the step 1 specifically comprises: the nine-order power system model is analyzed, and the existence of the chaos phenomenon is explained through analyzing four aspects of each state timing diagram, a system bifurcation diagram, a system power spectrum diagram and a system phase diagram.
3. The electric power system chaos phenomenon layered sliding-mode control method based on the improved fixed time according to claim 2, characterized in that the mathematical model of the improved fixed time layered sliding-mode control method established in step 2 is as follows:
the improved method comprises the following steps:
by a systematic error e 1 For example, the improved fixed-time slip-form surfaces are:
in the formula of alpha 1 、α 2 、β 1 、β2、ψ 1 、
k are all positive constants greater than zero, coefficient psi 1 、
The size of k determines the convergence speed of the whole sliding mode surface, alpha 1 、α 2 、β 1 、β 2 Is related to the system stability, sat is a saturation function, and the expression is as follows:
in the formula, p is a constant larger than zero, a buffeting phenomenon existing in the control process is weakened by replacing a sign function with a saturation function, the sliding mode surface is divided into two parts, and when the system state is smaller than k, namely when the system state is close to a balance point, the convergence speed of the sliding mode surface (a) is accelerated; when the system state is larger than k, namely when the system state is far away from a balance point, the sliding mode surface (b) can accelerate the convergence speed of the system;
for an improved fixed-time slip-form face, when the slip-form face approaches the origin, one can obtain:
for the improved sliding mode surface, when psi 1 When greater than 0, e 1 When 0 is equal, no singular point appears; in order to carry out better adaptive law design on the improved sliding mode surface, the improved fixed-time sliding mode surface is improved, and a new sliding mode surface with p = a is:
after a sliding mode surface shown in the above formula is obtained, a sliding mode approach law is designed, a hyperbolic function is selected as the approach law, the hyperbolic approach law can realize the fast convergence and buffeting reduction of sliding mode control, and the expression is as follows:
in the above formula, s is a designed sliding mode surface, q is a positive odd number, and lambda 1 ,λ 2 ,r 1 ,r 2 The parameters are positive parameters respectively, and tanh and asinh are hyperbolic tangent functions and inverse hyperbolic sine functions, and the values of the hyperbolic tangent functions and derivatives thereof are in a range of-1 to 1, and the hyperbolic tangent functions have similar linear characteristics when the sliding mode surface approaches 0; the characteristics of the hyperbolic function are the same as those of the hyperbolic function, and the buffeting phenomenon is reduced or even eliminated due to the linear characteristic;
in an actual power system, damping coefficient d in constant value parameters of system equation and electromagnetic power P of generator m And designing an adaptive law for the two uncertain parameters to estimate:
the above equation is the derivative of the estimated value of the parameter d; tau is 1 For designed adaptive parameters, s v The engine slip is obtained, and H is an inertia time constant of the generator; regulating by utilizing tau according to different change sizes of constant parameters to regulate the control precision;
the above formula is parameter P m A derivative of the estimated value of (a); τ 2 is a designed adaptive parameter as is τ 1.
4. The improved fixed time-based hierarchical sliding-mode control method for chaos of an electric power system according to claim 3, wherein in step 3, a ant lion algorithm is improved, and a new objective function is designed for optimizing parameters of a controller, and the specific contents are as follows:
in the ant lion algorithm, an improved initialization method is adopted, namely initialization is divided into a plurality of areas, and a Logistic mapping model is adopted in each sub-area to initialize a population, so that the population is more randomly distributed in a parameter range;
for an optimized objective function, stable, quasi and fast according to control requirements are taken as starting points, absolute errors of integral time are taken as performance standards for the quasi indexes, overshoot, rise time, transition time and peak time are taken as performance indexes for the stable and fast performance indexes, and the proposed objective function according to specific content requirements is as follows:
OF＝(1-e -θ )(M p +ITAE)+e -θ (t s +t r +t p )
in the formula, M p For overshoot, ITAE is the absolute error of integration time, t s As transition time of the system, t p Is the peak time of the system, t r Theta is a weighting factor for the rise time of the system, and the weighting factor is adjusted to meet different performance indexes of a designerThe requirements of (1).
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