CN113890019A - Stability-constrained intermittent power system self-adaptive CGPC-PI control method - Google Patents

Stability-constrained intermittent power system self-adaptive CGPC-PI control method Download PDF

Info

Publication number
CN113890019A
CN113890019A CN202111138149.2A CN202111138149A CN113890019A CN 113890019 A CN113890019 A CN 113890019A CN 202111138149 A CN202111138149 A CN 202111138149A CN 113890019 A CN113890019 A CN 113890019A
Authority
CN
China
Prior art keywords
cgpc
control
equation
stability
output
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202111138149.2A
Other languages
Chinese (zh)
Inventor
邓文生
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Individual filed Critical Individual
Priority to CN202111138149.2A priority Critical patent/CN113890019A/en
Publication of CN113890019A publication Critical patent/CN113890019A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a stability-constrained intermittent power system self-adaptive CGPC-PI control method, which aims to calculate the track of PI control parameters and optimize the future output y, firstly obtains the stable region of a load frequency control LFC system, and then converts the independent variable of a constrained generalized predictive control CGPC into a K in an upper-layer control systemPAnd KiFinally, a shorter time lag and a smaller overshoot are obtained by adding an anti-saturation scheme in a lower control level, thereby further optimizing KpAnd KiThe method has the advantages that the CGPC-PI has better control performance than PI and CGPC, the CGPC-PI has more obvious superiority when processing change disturbance which is large enough to trigger an anti-saturation scheme, and the CGPC-PI can improve the frequency regulation performance of an intermittent power penetration system.

Description

Stability-constrained intermittent power system self-adaptive CGPC-PI control method
Technical Field
The invention relates to the field of power systems, in particular to a stability-constrained intermittent power system self-adaptive CGPC-PI control method.
Background
The increasing demand for reduction of fossil fuel consumption and development of environmentally friendly energy sources requires a more powerful power system to cope with the attendant intermittent problems. The ever-increasing popularity of renewable energy sources will present the following challenges: (1) inertia will be reduced because more and more electronic inverters separate the power supply from the load and output variations will be more active due to atmospheric volatility. Therefore, maintaining frequency, power angle, and voltage stability is more challenging.
In consideration of the decoupling characteristic of the system, the frequency stability of the system can be researched by using a linear frequency modulation method under the condition of small interference. The load frequency control LFC mainly aims to maintain stability of local frequency and tie line switching power, and may be divided into a centralized load frequency control LFC, a distributed load frequency control LFC, and a distributed load frequency control LFC. The centralized load frequency control LFC measures all system outputs using a single controller and calculates the control variables for all actuators in the system, which is computationally and geographically difficult to implement. Therefore, the distributed load frequency control LFC and the distributed load frequency control LFC are more widely used in large-scale power grids.
With the increasing popularity of renewable energy sources, modern power systems face greater challenges in maintaining frequency stability, which can be studied by load frequency control LFC, but traditional Proportional Integral (PI) controllers cannot meet the increasing robustness requirement.
Disclosure of Invention
In order to overcome the defects and shortcomings in the prior art, the invention provides a stability-constrained intermittent power system self-adaptive CGPC-PI control method.
The method adopts the technical scheme that the method aims at calculating the track of PI control parameters and optimizing future output y, firstly, a stable region of a load frequency control LFC system is obtained, and then, the independent variable of a constraint generalized predictive control CGPC is converted into K in an upper-layer control systemPAnd KiFinally, a shorter time lag and a smaller overshoot are obtained by adding an anti-saturation scheme in a lower control level, thereby further optimizing KpAnd Ki。
In the present invention, the stability region and the stability constraint of the system are determined by the simple structure of the actual implementation device PI, the stability boundary of the system is determined by the time series obtained from historical or experimental data, and three steps are required to achieve the goal:
step 1: given a scalar time series
Figure BDA0003283037430000021
The system can use xt＝f(xt-L，xt-2L，...，xt-mL) By a form fit of the expressionThe feedforward neural network approximates any non-linear function with a suitably chosen set of parameters, which is expressed as equation (1) below:
Figure BDA0003283037430000022
wherein α 0, α 1,. alpha.j, α j and β 0, β 1, 1,. beta.m，qTwo sets of parameters, [ m, q, L ], representing the need for training]The complexity of the fitting process and the accuracy of the results are determined and set to [5, 6, 5 ]]；
Step 2: then, the jacobian matrix is calculated according to the formula in step 1, as shown in the following formula (2):
Figure BDA0003283037430000023
step 2: the maximum lyapunov coefficient is obtained by the following formula (3):
Figure BDA0003283037430000031
wherein M ═ (length (X) -M L)2/3，
Figure BDA0003283037430000032
And v1Max (eig (Tm' × Tm)), if the maximum lyapunov coefficient is not greater than 0, the system is proved to be stable;
calculating the maximum Lyapunov coefficient of the linear frequency modulation system under different PI control parameters through an exhaustive algorithm to obtain the boundary of a stable domain, wherein the calculation logic is based on equations (1) - (2), starting from Kp ═ 0 and Ki ═ 0, and a time sequence { x } t ═ 1 can be collected through simulationTBy applying a feed-forward neural network to { x } t ═ 1TEquation (1) can be derived, then, from equations (2) and (3), the maximum lyapunov coefficient can be calculated, then Kp and Ki can be iteratively increased until λ is greater than 0, and finally, by separating the regions where (Kp, Ki) is consistent or inconsistent with the stability criterion, a stable region is foundThe boundary of (2).
In the present invention, the upper control structure of the CGPC-PI controller restricts the argument of the CGPC controller for the generalized predictive control to be modified to the control parameter of the PI controller, adds the stability restriction using the result of claim 2, and for the following formula, "(k)" indicates that the value of a certain state variable is obtained at the k-th step. "| k" denotes the kth step in the prediction horizon;
the prediction model, GPC, was designed based on the CARIMA model and is described by the formula:
A(z-1)y(k)＝z-dB(z-1)u(k)+C(z-1)ξ(k)/Δ (4)，
where u (k) is a manipulated variable, the input variable, y (k) is a process output, ζ (k) represents a white noise sequence, d represents a time delay, Δ is a differential operator, and is expressed as Δ ═ 1-z-1，A(z-1)、B(z-1) And C (z)-1) Expressed by equation (5).
Figure BDA0003283037430000041
When d is equal to 1, we can perform a difference operation on both sides, and finally obtain equation (6),
Figure BDA0003283037430000042
in the formula
Figure BDA0003283037430000043
Figure BDA0003283037430000044
Figure BDA0003283037430000045
Figure BDA0003283037430000046
And 0. ltoreq. i.ltoreq.na
Formula (6) shows a fitting formula of the input and output sequences, and on the basis of the fitting formula, a prediction model in an optimization window is established;
and (3) performing multi-step prediction for GPC by using a charpy equation, wherein the expression is formula (7):
Figure BDA0003283037430000047
wherein Ej, Gj, Fj should satisfy formula (8):
Figure BDA0003283037430000048
in the invention, the CARIMA model is introduced by using a loss map equation, and the output prediction is obtained through a formula (9):
Y＝F1ΔU+F2ΔU(k)+G′Yk+E′ξ (9)
in equation (9), the parameters may be interpreted as follows:
Figure BDA0003283037430000049
Figure BDA0003283037430000051
Figure BDA0003283037430000052
Figure BDA0003283037430000053
Figure BDA0003283037430000054
wherein N is1And N respectively represents the predicted view NpInitial and final values of (2), NuRepresents a control range;
the output prediction Y is divided into two parts, F1Δ U represents the variable influence from the future control increment, F2ΔU(k)+G’Yk+ E' ζ represents a fixed contribution from the past, and the increment of the manipulated value directly determines the variables (9) and (10) of the output predictions in the equation.
In the present invention, the scrolling is optimized by controlling the FOV NuThe optimal delta U sequence is found, the cost function can be minimized, and compared with the CGPC controlled by the constraint generalized prediction, two special processes are carried out: first, the cost function and constraints are rewritten to meet continuity and stability requirements, and second, Δ u is converted to PI (K)pAnd Ki) The control parameter of (2);
smoothing of said first reference output trajectory, which should be set to a first order process, as shown in equation (11), ensures a smooth transition of the output y (k) from the original value to the setpoint ω,
Figure BDA0003283037430000055
in the formula (11), j represents the prediction horizon NpA is a smoothing factor.
In the present invention, the second objective function treats;
from the definition of the reference output trajectory, the cost function can be written as equation (12):
J＝min{[Y-Yr]T[Y-Yr]+ΔUTΓ1ΔU+[K(k)-K(k-1)]Tr2[K(k)-K(k-1)]} (12)，
wherein Y isr＝[yr(k+N1|k)；yr(k+N1+1|k)；...；yr(k+Np|k)]，Γ1And Γ2Are respectively made of gamma1＝γ1INu×Nu，Γ2＝γ2INu×NuIs represented by two diagonal matrices, where γ1And gamma2Is an adjustable weighting parameter, K is a matrix of the form of equation (13)：
Figure BDA0003283037430000061
The cost function is to track the set output track, reduce the control cost and ensure the continuity of the control parameters;
since practical operating constraints can reduce performance, a set of inequalities is taken as a feasible solution range of CGPC-PI as shown in formula (14):
Figure BDA0003283037430000062
wherein Δ uminAnd Δ umaxIs a constraint on the incremental change of the control variable, uminAnd umaxIs a constraint controlling the amplitude of the variable, likewise, yminAnd ymaxLimiting the amplitude of the output variable, KminAnd KmaxAre approximate limits obtained by the stable region, respectively denoted as [ Kpmin，Kimin]And [ K ]pmax，Kimax]Avoiding over-compressing the feasible solution range, application e1、e2And e3To ensure that the constraints only affect the control variables in the current step, representing [1, 0]1×Nu、[1，0，...，0]1×NpAnd [1, 1; 0, 0; ...; 0,0]Nu×2；
Subsequently, the previous adjustable variable needs to be converted into k (k) (12) and (14) in the equation.
In the invention, the characteristics of the discrete time PI control strategy can be used for deducing the CGPC-PI controller, and the increment of the PI manipulation value can be expanded as shown in a formula (15):
Figure BDA0003283037430000071
in the formula (15), i is within [1, 2.. N ]u-1]At represents the time step, e represents the error between the setpoint and the predicted output,
Figure BDA0003283037430000075
equation (15) needs to be expanded to matrix form to describe the relationship between Δ U (k) and k (k), to resolve the contradiction between predicting output y (k) requiring Δ U (k) and calculating Δ U (k) requiring y (k), a trade-off is being made, and by reviewing the final objective of this step, i.e., finding equivalent transitions for Δ U (k) and k (k), it is assumed that if γ 2 is sufficiently small, Δ U '(k) calculated by GPC is almost equal to Δ U (k) calculated by CGPC-PI, and Δ U' (k) and the output prediction can be calculated in equations (16) and (17), respectively.
Figure BDA0003283037430000072
Y′(k|k)＝F1ΔU′+F2dU(k)+GYk (17)，
In the present invention, the equations (15) to (17) are equivalent transformation equations as shown in the following equation (18):
ΔU(k)＝E(k)S(k)K(k) (18)，
where e (k), s (k), k (k) are matrices corresponding to the form given in equation (19).
Figure BDA0003283037430000073
Figure BDA0003283037430000074
In the present invention, J is expressed as a standard quadratic programming form by applying equations (12) to (18), and k (k) is a decision variable.
Figure BDA0003283037430000081
In equation (20), H and F yield from the following equations:
Figure BDA0003283037430000082
constraint processing, the constraint quantity in equation (14) may be rewritten into a linear form, the argument is k (k), the incremental change of the control variable may be directly replaced by Δ U (k) ═ e (k) s (k) k (k), and the control variable U (k) may be replaced by U (k) ═ U (k-1) + e (k) s (k) k (k), and by combining equations (9) and (18), the relationship between the output variables y (k) and k (k) is obtained, and the constraint on the control parameter does not need further processing, and in conclusion, the modified constraint is as follows:
Figure BDA0003283037430000083
the output of the upper control hierarchy, K (k), is computed (29) - (31) by solving a quadratic programming problem composed of equations and only the first column of K (k), namely [ Kp (k | k), Ki (k | k) ], is implemented.
In the invention, the lower control level of the CGPC-PI controller adopts an anti-saturation scheme to shorten time lag and reduce overshoot, as shown in the following formula (22):
Figure BDA0003283037430000084
as shown in equation (22), Δ u (k) is described using a piecewise function. If u (k-1) exceeds the preset limit um, only a negative error can be added in the integration of the k-th step. Vice versa, if u (k-1) < -um, only positive errors can be added.
The method has the advantages that the CGPC-PI has better control performance than PI and CGPC, the CGPC-PI has more obvious superiority when processing the change disturbance which is large enough to trigger the anti-saturation scheme, and the CGPC-PI can improve the frequency regulation performance of the intermittent power penetration system.
Drawings
FIG. 1 is a flow chart of a stabilization zone determination process of the present invention;
FIG. 2 is a flow chart of the CGPC-PI method of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments can be combined with each other without conflict, and the present application will be further described in detail with reference to the drawings and specific embodiments.
As shown in figure 1, the self-adaptive CGPC-PI control method of the intermittent power system with stability constraint has the overall aim of calculating the track of PI control parameters and optimizing future output y, firstly, a stable region of a load frequency control LFC system is obtained, and then, the independent variable of the constraint generalized predictive control CGPC is converted into K in an upper-layer control systemPAnd KiFinally, a shorter time lag and a smaller overshoot are obtained by adding an anti-saturation scheme in a lower control level, thereby further optimizing KpAnd Ki。
In the present invention, the stability region and the stability constraint of the system are determined by the simple structure of the actual implementation device PI, the stability boundary of the system is determined by the time series obtained from historical or experimental data, and three steps are required to achieve the goal:
step 1: given a scalar time series
Figure BDA0003283037430000101
The system can use xt＝f(xt-L，xt-2L，...，xt-mL) Approximating any non-linear function by a feed-forward neural network with a set of suitably selected parameters, as shown in equation (1) below:
Figure BDA0003283037430000102
wherein α 0, α 1,. alpha.j, α j and β 0, β 1, 1,. beta.m，qTwo sets of parameters, [ m, q, L ], representing the need for training]The complexity of the fitting process and the accuracy of the results are determined and set to [5, 6, 5 ]]；
Step 2: then, the jacobian matrix is calculated according to the formula in step 1, as shown in the following formula (2):
Figure BDA0003283037430000103
step 2: the maximum lyapunov coefficient is obtained by the following formula (3):
Figure BDA0003283037430000104
wherein M ═ (length (X) -M L)2/3，
Figure BDA0003283037430000105
And v1Max (eig (Tm' × Tm)), if the maximum lyapunov coefficient is not greater than 0, the system proves to be stable:
calculating the maximum Lyapunov coefficient of the linear frequency modulation system under different PI control parameters through an exhaustive algorithm to obtain the boundary of a stable domain, wherein the calculation logic is based on equations (1) - (2), starting from Kp ═ 0 and Ki ═ 0, and a time sequence { x } t ═ 1 can be collected through simulationTBy applying a feed-forward neural network to { x } t ═ 1TEquation (1) can be derived, then, from equations (2) and (3), the maximum lyapunov coefficient can be calculated, then Kp and Ki can be iteratively increased until λ is greater than 0, and finally, the boundary of the stable region is found by separating the regions where (Kp, Ki) is consistent or inconsistent with the stability criterion.
As can be seen from the flow chart in fig. 1, the proposed stability criterion is easy to implement and is highly dependent on the operating parameters of the system compared to the conventional method of adding equal or equal internal constraints, since the stability region changes when the operating conditions are switched, and therefore, in engineering practice, it is preferable to use the conservative stability region result when determining the search boundary of the PI parameter.
In the present invention, the upper control structure of the CGPC-PI controller restricts the argument of the CGPC controller for the generalized predictive control to be modified to the control parameter of the PI controller, adds the stability restriction using the result of claim 2, and for the following formula, "(k)" indicates that the value of a certain state variable is obtained at the k-th step. "| k" denotes the kth step in the prediction horizon;
the prediction model, GPC, was designed based on the CARIMA model and is described by the formula:
A(z-1)y(k)＝z-dB(z-1)u(k)+C(z-1)ξ(k)/Δ (4)，
where u (k) is a manipulated variable, the input variable, y (k) is a process output, ζ (k) represents a white noise sequence, d represents a time delay, Δ is a differential operator, and is expressed as Δ ═ 1-z-1，A(z-1)、B(z-1) And C (z)-1) Expressed by equation (5).
Figure BDA0003283037430000111
When d is equal to 1, we can perform a difference operation on both sides, and finally obtain equation (6),
Figure BDA0003283037430000116
in the formula
Figure BDA0003283037430000112
Figure BDA0003283037430000113
Figure BDA0003283037430000114
Figure BDA0003283037430000115
And 0. ltoreq. i.ltoreq.na
Formula (6) shows a fitting formula of the input and output sequences, and on the basis of the fitting formula, a prediction model in an optimization window is established;
and (3) performing multi-step prediction for GPC by using a charpy equation, wherein the expression is formula (7):
Figure BDA0003283037430000121
wherein Ej, Gj, Fj should satisfy formula (8):
Figure BDA0003283037430000122
in the invention, the CARIMA model is introduced by using a loss map equation, and the output prediction is obtained through a formula (9):
Y＝F1ΔU+F2ΔU(k)+G′Yk+E′ξ (9)
in equation (9), the parameters may be interpreted as follows:
Figure BDA0003283037430000123
Figure BDA0003283037430000131
Figure BDA0003283037430000132
Figure BDA0003283037430000133
Figure BDA0003283037430000134
wherein N is1And N respectively represents the predicted view NpInitial and final values of (2), NuRepresents a control range;
the output prediction Y is divided into two parts, F1Δ U represents the variable influence from the future control increment, F2ΔU(k)+G’Yk+ E' zeta represents a fixed influence from the past, and the increment of the manipulated value directly determines the variables (9) and (1) of the output prediction in the equation0)。
In the present invention, the scrolling is optimized by controlling the FOV NuThe optimal delta U sequence is found, the cost function can be minimized, and compared with the CGPC controlled by the constraint generalized prediction, two special processes are carried out: first, the cost function and constraints are rewritten to meet continuity and stability requirements, and second, Δ u is converted to PI (K)pAnd Ki) The control parameter of (2);
smoothing of said first reference output trajectory, which should be set to a first order process, as shown in equation (11), ensures a smooth transition of the output y (k) from the original value to the setpoint ω,
Figure BDA0003283037430000135
in the formula (11), j represents the prediction horizon NpA is a smoothing factor.
In the present invention, the second objective function treats;
from the definition of the reference output trajectory, the cost function can be written as equation (12):
J＝min{[Y-Yr]T[Y-Yr]+ΔUTΓ1ΔU+[K(k)-K(k-1)]Tr2[K(k)-K(k-1)]} (12)，
wherein Y isr＝[yr(k+N1|k)；yr(k+N1+1|k)；...；yr(k+Np|k)]，Γ1And Γ2Are respectively made of gamma1＝γ1INu×Nu，Γ2＝γ2INu×NuIs represented by two diagonal matrices, where γ1And gamma2Is an adjustable weighting parameter, K is a matrix of the form of equation (13):
Figure BDA0003283037430000141
the cost function is to track the set output track, reduce the control cost and ensure the continuity of the control parameters;
since practical operating constraints can reduce performance, a set of inequalities is taken as a feasible solution range of CGPC-PI as shown in formula (14):
Figure BDA0003283037430000142
wherein Δ uminAnd Δ umaxIs a constraint on the incremental change of the control variable, uminAnd umaxIs a constraint controlling the amplitude of the variable, likewise, yminAnd ymaxLimiting the amplitude of the output variable, KminAnd KmaxAre approximate limits obtained by the stable region, respectively denoted as [ Kpmin，Kimin]And [ K ]pmax，Kimax]Avoiding over-compressing the feasible solution range, application e1、e2And e3To ensure that the constraints only affect the control variables in the current step, representing [1, 0]1×Nu、[1，0，...，0]1×NpAnd [1, 1; 0, 0; ...; 0,0]Nu×2；
Subsequently, the previous adjustable variable needs to be converted into k (k) (12) and (14) in the equation.
In the invention, the characteristics of the discrete time PI control strategy can be used for deducing the CGPC-PI controller, and the increment of the PI manipulation value can be expanded as shown in a formula (15):
Figure BDA0003283037430000151
in the formula (15), i is within [1, 2.. N ]u-1]At represents the time step, e represents the error between the setpoint and the predicted output,
Figure BDA0003283037430000152
equation (15) needs to be expanded to matrix form to describe the relationship between Δ U (k) and k (k), to resolve the contradiction between predicting output y (k) requiring Δ U (k) and calculating Δ U (k) requiring y (k), a trade-off is being made, and by reviewing the final objective of this step, i.e., finding equivalent transitions for Δ U (k) and k (k), it is assumed that if γ 2 is sufficiently small, Δ U '(k) calculated by GPC is almost equal to Δ U (k) calculated by CGPC-PI, and Δ U' (k) and the output prediction can be calculated in equations (16) and (17), respectively.
Figure BDA0003283037430000153
Y′(k|k)＝F1ΔU′+F2dU(k)+GYk (17)，
In the present invention, the equations (15) to (17) are equivalent transformation equations as shown in the following equation (18):
ΔU(k)＝E(k)S(k)K(k) (18)，
where e (k), s (k), k (k) are matrices corresponding to the form given in equation (19).
Figure BDA0003283037430000154
Figure BDA0003283037430000155
In the present invention, J is expressed as a standard quadratic programming form by applying equations (12) to (18), and k (k) is a decision variable.
Figure BDA0003283037430000161
In equation (20), H and F yield from the following equations:
Figure BDA0003283037430000162
constraint processing, the constraint quantity in equation (14) may be rewritten into a linear form, the argument is k (k), the incremental change of the control variable may be directly replaced by Δ U (k) ═ e (k) s (k) k (k), and the control variable U (k) may be replaced by U (k) ═ U (k-1) + e (k) s (k) k (k), and by combining equations (9) and (18), the relationship between the output variables y (k) and k (k) is obtained, and the constraint on the control parameter does not need further processing, and in conclusion, the modified constraint is as follows:
Figure BDA0003283037430000163
the output of the upper control hierarchy, K (k), is computed (29) - (31) by solving a quadratic programming problem composed of equations and only the first column of K (k), namely [ Kp (k | k), Ki (k | k) ], is implemented.
Feedback correction, common knowledge, is impossible to establish an absolutely accurate model for a practical system, the uncertainty of the prediction can be caused by the introduction of nonlinearity, time-varying characteristics and interference, and online identification can process a relatively inaccurate model, so that the superiority of the CGPC is ensured.
The PI controller introduces an integrating element into the system, providing a pole-zero that contributes to stability. However, due to integration, the control outputs may also add when faced with errors of the same sign, even into the saturation region, when an inverse error is introduced, a slower response will be obtained since the system must first exit the saturation region, and therefore an anti-saturation scheme is employed to reduce skew and overshoot, as shown in equation (22):
Figure BDA0003283037430000171
as shown in equation (22), Δ u (k) is described using a piecewise function. If u (k-1) exceeds the preset limit um, only a negative error can be added in the integration of the k-th step. Vice versa, if u (k-1) < -um, only positive errors can be added.
To apply equation (22), two methods may be employed. First, the increment of the GPC control variable may be rewritten in the form of equation (22). Then, the cost function and the constraint condition under different conditions are respectively deduced. Or we can simply modify the lower hierarchy of CGPC-PI to the form of equation (22). This demonstrates one of the advantages of CGPC-PI, which can be used directly with advanced PI control theory without further modification of the GPC algorithm, and thus can achieve control performance by a simpler approach.
In summary, the flow chart of the CGPC-PI control strategy for each sampling step is shown in fig. 2.
The method has the advantages that the CGPC-PI has better control performance than PI and CGPC, the CGPC-PI has more obvious superiority when processing the change disturbance which is large enough to trigger the anti-saturation scheme, and the CGPC-PI can improve the frequency regulation performance of the intermittent power penetration system.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made herein without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims (10)

1. A stability-constrained intermittent power system self-adaptive CGPC-PI control method is characterized in that the method is used for calculating the track of PI control parameters and optimizing future output y, firstly, a stable region of a load frequency control LFC system is obtained, and then, the independent variable of the constrained generalized predictive control CGPC is converted into K in an upper-layer control systemPAnd KiFinally, K is further optimized by adding an anti-saturation scheme in a lower control level to obtain shorter time lag and smaller overshootpAnd Ki。
2. The intermittent power system adaptive CGPC-PI control method of the stability constraint is characterized in that a stable area of the system, the stability constraint utilizes a simple structure of an actual implementation device PI, a stable boundary of the system is determined by a time sequence obtained by historical or experimental data, and three steps are needed to achieve the aim:
step 1: given a scalar time series
Figure FDA0003283037420000011
The system can use xt＝f(xt-L，xt-2L，...，xt-mL) Approximating any non-linear function by a feed-forward neural network with a set of suitably selected parameters, as shown in equation (1) below:
Figure FDA0003283037420000012
wherein α 0, α 1,. alpha.j, α j and β 0, β 1, 1,. beta.m，qTwo sets of parameters, [ m, q, L ], representing the need for training]The complexity of the fitting process and the accuracy of the results are determined and set to [5, 6, 5 ]]；
Step 2: then, the jacobian matrix is calculated according to the formula in step 1, as shown in the following formula (2):
Figure FDA0003283037420000013
step 2: the maximum lyapunov coefficient is obtained by the following formula (3):
Figure FDA0003283037420000021
wherein M ═ (length (X) -M L)2/3，
Figure FDA0003283037420000022
And v1Max (eig (Tm' × Tm)), if the maximum lyapunov coefficient is not greater than 0, the system is proved to be stable;
calculating the maximum Lyapunov coefficient of the linear frequency modulation system under different PI control parameters through an exhaustive algorithm to obtain the boundary of a stable domain, wherein the calculation logic is based on equations (1) - (2), starting from Kp ═ 0 and Ki ═ 0, and a time sequence { x } t ═ 1 can be collected through simulationTBy applying a feed-forward neural network to { x } t ═ 1TEquation (1) can be derived, then, from equations (2) and (3), the maximum lyapunov coefficient can be calculated, then Kp and Ki can be iteratively increased until λ is greater than 0, and finally, the boundary of the stable region is found by separating the regions where (Kp, Ki) is consistent or inconsistent with the stability criterion.
3. The stability-constrained intermittent power system adaptive CGPC-PI control method of claim 2, wherein an upper-layer control structure of the CGPC-PI controller restricts an argument of a generalized predictive control CGPC controller to be modified into a control parameter of the PI controller, adds stability constraint using a result of claim 2, and for the following formula, "(k)" indicates that a value of a certain state variable is obtained at a kth step, and "| k" indicates the kth step in a predictive view;
the prediction model, GPC, was designed based on the CARIMA model and is described by the formula:
A(z-1)y(k)＝z-dB(z-1)u(k)+C(z-1)ξ(k)/Δ (4)，
where u (k) is a manipulated variable, the input variable, y (k) is a process output, ζ (k) represents a white noise sequence, d represents a time delay, Δ is a differential operator, and is expressed as Δ ═ 1-z-1，A(z-1)、B(z-1) And C (z)-1) Expressed by equation (5).
Figure FDA0003283037420000031
When d is equal to 1, we can perform a difference operation on both sides, and finally obtain equation (6),
Figure FDA0003283037420000032
in the formula
Figure FDA0003283037420000033
Figure FDA0003283037420000034
And 0. ltoreq. i.ltoreq.na
Formula (6) shows a fitting formula of the input and output sequences, and on the basis of the fitting formula, a prediction model in an optimization window is established;
and (3) performing multi-step prediction for GPC by using a charpy equation, wherein the expression is formula (7):
Figure FDA0003283037420000035
wherein Ej, Gj, Fj should satisfy formula (8):
Figure FDA0003283037420000036
4. the stability-constrained intermittent power system adaptive CGPC-PI control method of claim 3, wherein the CARIMA model is introduced using a charpy equation to obtain an output prediction by equation (9):
Y＝F1ΔU+F2ΔU(k)+G′Yk+E′ξ (9)
in equation (9), the parameters may be interpreted as follows:
Figure FDA0003283037420000037
Figure FDA0003283037420000041
Figure FDA0003283037420000042
Figure FDA0003283037420000043
Figure FDA0003283037420000044
wherein N is1And N respectively represents the predicted view NpInitial and final values of (2), NuRepresents a control range;
the output prediction Y is divided into two parts, F1Δ U represents the variable influence from the future control increment, F2ΔU(k)+G’Yk+ E' ζ represents a fixed contribution from the past, and the increment of the manipulated value directly determines the variables (9) and (10) of the output predictions in the equation.
5. The stability-constrained intermittent power system adaptive CGPC-PI control method of claim 4, wherein said rolling optimization is performed by controlling FOV NuThe optimal delta U sequence is found, the cost function can be minimized, and compared with the CGPC controlled by the constraint generalized prediction, two special processes are carried out: first, the cost function and constraints are rewritten to meet continuity and stability requirements, and second, Δ u is converted to PI (K)pAnd Ki) The control parameter of (2);
smoothing of said first reference output trajectory, which should be set to a first order process, as shown in equation (11), ensures a smooth transition of the output y (k) from the original value to the setpoint ω,
Figure FDA0003283037420000051
in the formula (11), j represents the prediction horizon NpA is a smoothing factor.
6. The stability-constrained intermittent power system adaptive CGPC-PI control method of claim 5, wherein the second objective function treats;
from the definition of the reference output trajectory, the cost function can be written as equation (12):
J＝min{[Y-Yr]T[Y-Yr]+ΔUTF1ΔU+[K(k)-K(k-1)]TΓ2[K(k)-K(k-1)]} (12)，
wherein Y isr＝[yr(k+N1|k)；yr(k+N1+1|k)；...；yr(k+Np|k)]，Γ1And Γ2Are respectively made of gamma1＝γ1INu×Nu，Γ2＝γ2INu×NuIs represented by two diagonal matrices, where γ1And gamma2Is an adjustable weighting parameter, K is a matrix of the form of equation (13):
Figure FDA0003283037420000052
the cost function is to track the set output track, reduce the control cost and ensure the continuity of the control parameters;
since practical operating constraints can reduce performance, a set of inequalities is taken as a feasible solution range of CGPC-PI as shown in formula (14):
Figure FDA0003283037420000053
wherein Δ uminAnd Δ umaxIs a constraint on the incremental change of the control variable, uminAnd umaxIs a constraint controlling the amplitude of the variable, likewise, yminAnd ymaxLimiting the amplitude of the output variable, KminAnd KmaxAre approximate limits obtained by the stable region, respectively denoted as [ Kpmin，Kimin]And [ K ]pmax，Kimax]Avoiding over-compressing the feasible solution range, application e1、e2And e3To ensure thatThe constraints only affect the control variables in the current step, representing [1, 0., 0, respectively]1×Nu、[1，0，...，0]1×NpAnd [1, 1; 0, 0; ...; 0,0]Nu×2；
Subsequently, the previous adjustable variable needs to be converted into k (k) (12) and (14) in the equation.
7. A stability-constrained intermittent power system adaptive CGPC-PI control method as claimed in claim 1, wherein the characteristics of the discrete-time PI control strategy can be used to derive a CGPC-PI controller, and the increment of PI manipulated value can be extended as shown in equation (15):
Figure FDA0003283037420000061
in the formula (15), i ∈ [1, 2 … Nu-1]At represents the time step, e represents the error between the setpoint and the predicted output,
Figure FDA0003283037420000062
equation (15) needs to be expanded to matrix form to describe the relationship between Δ U (k) and k (k), to resolve the contradiction between predicting output y (k) requiring Δ U (k) and calculating Δ U (k) requiring y (k), a trade-off is being made, and by reviewing the final objective of this step, i.e., finding equivalent transitions for Δ U (k) and k (k), it is assumed that if γ 2 is sufficiently small, Δ U '(k) calculated by GPC is almost equal to Δ U (k) calculated by CGPC-PI, and Δ U' (k) and the output prediction can be calculated in equations (16) and (17), respectively.
Figure FDA0003283037420000063
Y′(k|k)＝F1ΔU′+F2dU(k)+GYk (17)。
8. A stability-constrained intermittent power system adaptive CGPC-PI control method as claimed in claim 7 wherein said equations (15) - (17), equivalent transformation equation is shown as equation (18):
ΔU(k)＝E(k)s(k)K(k) (18)，
wherein E (k), S (k), k (k) are matrices corresponding to the forms given in equation (19),
Figure FDA0003283037420000071
Figure FDA0003283037420000072
9. the stability-constrained intermittent power system adaptive CGPC-PI control method of claim 8, characterized by: said J is represented as a standard quadratic programming form by applying equations (12) - (18), k (k) is a decision variable,
Figure FDA0003283037420000073
in equation (20), H and F yield from the following equations:
Figure FDA0003283037420000074
constraint processing, the constraint quantity in equation (14) may be rewritten into a linear form, the argument is k (k), the incremental change of the control variable may be directly replaced by Δ U (k) ═ e (k) s (k) k (k), and the control variable U (k) may be replaced by U (k) ═ U (k-1) + e (k) s (k) k (k), and by combining equations (9) and (18), the relationship between the output variables y (k) and k (k) is obtained, and the constraint on the control parameter does not need further processing, and in conclusion, the modified constraint is as follows:
Figure FDA0003283037420000075
the output of the upper control hierarchy, K (k), is computed (29) - (31) by solving a quadratic programming problem composed of equations and only the first column of K (k), namely [ Kp (k | k), Ki (k | k) ], is implemented.
10. The stability-constrained intermittent power system adaptive CGPC-PI control method of claim 1, characterized by: the lower control level of the CGPC-PI controller adopts an anti-saturation scheme to shorten the time lag and reduce overshoot, as shown in the following formula (22):
Figure FDA0003283037420000081
as shown in equation (22), Δ u (k) is described using a piecewise function, which can only add negative errors in the integration at step k if u (k-1) exceeds a preset limit, um, and vice versa, which can only add positive errors if u (k-1) < -um.
CN202111138149.2A 2021-09-27 2021-09-27 Stability-constrained intermittent power system self-adaptive CGPC-PI control method Pending CN113890019A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111138149.2A CN113890019A (en) 2021-09-27 2021-09-27 Stability-constrained intermittent power system self-adaptive CGPC-PI control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111138149.2A CN113890019A (en) 2021-09-27 2021-09-27 Stability-constrained intermittent power system self-adaptive CGPC-PI control method

Publications (1)

Publication Number Publication Date
CN113890019A true CN113890019A (en) 2022-01-04

Family

ID=79007051

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111138149.2A Pending CN113890019A (en) 2021-09-27 2021-09-27 Stability-constrained intermittent power system self-adaptive CGPC-PI control method

Country Status (1)

Country Link
CN (1) CN113890019A (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111897211A (en) * 2020-05-31 2020-11-06 吉林大学 Piezoelectric ceramic micro-positioning platform trajectory tracking control method considering constraint conditions

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111897211A (en) * 2020-05-31 2020-11-06 吉林大学 Piezoelectric ceramic micro-positioning platform trajectory tracking control method considering constraint conditions

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
WANYING LIU 等: "An adaptive CGPC based anti-windup PI controller with stability constraints for the intermittent power penetrated system", 《INTERNATIONAL JOURNAL OF ELECTRICAL POWER AND ENERGY SYSTEMS 》, vol. 130, pages 1 - 18 *
张守艮;: "电力系统供电负荷稳定性优化控制研究", 数字通信世界, no. 11, pages 64 *

Similar Documents

Publication Publication Date Title
CN111459051B (en) Discrete terminal sliding mode model-free control method with disturbance observer
Ellis et al. Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems
CN110048606B (en) DC-DC boost converter dynamic sliding mode voltage control method based on interval two-type self-adaptive fuzzy neural network
Sun A Barbalat-like lemma with its application to learning control
Wang et al. Adaptive T–S fuzzy-neural modeling and control for general MIMO unknown nonaffine nonlinear systems using projection update laws
Wang et al. Cascade optimal control for tracking and synchronization of a multimotor driving system
Chi et al. Active disturbance rejection control for nonaffined globally Lipschitz nonlinear discrete-time systems
Jiang et al. Robust adaptive dynamic programming
Khettab et al. Enhanced fractional order indirect fuzzy adaptive synchronization of uncertain fractional chaotic systems based on the variable structure control: robust H∞ design approach
Ye et al. Backstepping design embedded with time-varying command filters
Kögel et al. Cooperative distributed MPC using the alternating direction multiplier method
CN113625573B (en) Fractional order system backstepping sliding mode control method influenced by asymmetric dead zone input
Zandi et al. Voltage control of DC–DC converters through direct control of power switches using reinforcement learning
Zandi et al. Voltage control of a quasi z-source converter under constant power load condition using reinforcement learning
CN114879508A (en) Grinding robot path tracking control method based on model prediction control
Chang et al. Variance and passivity constrained sliding mode fuzzy control for continuous stochastic non-linear systems
Zhao et al. Stabilization of linear systems with time delay and disturbance: A new state prediction approach
Chen et al. Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm
CN111240201B (en) Disturbance suppression control method
CN113890019A (en) Stability-constrained intermittent power system self-adaptive CGPC-PI control method
CN110908286A (en) Design method of indirect self-adaptive fuzzy optimal synchronous controller of uncertain chaotic system
Zhu et al. Stabilization and optimization of discrete-time Markovian jump linear systems via mode feedback control
Cui et al. Adaptive Horizon Seeking for Generalized Predictive Control via Deep Reinforcement Learning With Application to DC/DC Converters
Van Kien et al. Adaptive MIMO fuzzy controller for double coupled tank system optimizing by jaya algorithm
CN110442028B (en) Fuzzy prediction based anti-bifurcation control method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20220104

RJ01 Rejection of invention patent application after publication