Novel self-adaptive oscillation suppression method

Abstract

The invention discloses a novel self-adaptive oscillation suppression method, which comprises the following steps of: enabling a system to be controlled to be equivalent to a single-input single-output discrete time nonlinear system, and converting the system to be controlled into a partial format dynamic linearization data model of which the sliding time window length is L; calculating a pseudo partial derivative estimated value # imgabs0 # by using input and output data of a to-be-controlled system, and setting different constraint conditions and initial values for different items in a pseudo partial derivative vector; two different input criterion functions are comprehensively considered, and a control algorithm which simultaneously considers the input variable quantity and the input quantity expectation is 0 is provided; sequentially sampling all input information in the sliding time window according to a certain interval, and reforming a sparse new input information vector with the length of m (m is smaller than or equal to L); the influence of historical input signals except the m sampling signals on the system is ignored, and a new pseudo-partial derivative estimation algorithm and control algorithm are obtained. Compared with the prior art, the oscillation suppression effect is better, and the calculation amount and the storage burden are greatly reduced on the premise that the control effect is guaranteed.

Description

Technical Field

[0001] The invention belongs to the field of electric power technology, relates to an oscillation suppression technology, and in particular to a novel model-free adaptive oscillation suppression method based on partial format linear dynamicization. Background Art

[0002] In modern control theory, the design of the controller is usually based on the mathematical model of the controlled system. This model-driven control method has unmodeled dynamics and other uncertainties, and even a small modeling error may lead to control instability. With the introduction of model-free adaptive control theory proposed by Professor Hou Zhongsheng, this data-driven control method that does not require system modeling has quickly verified its correctness and usability in various fields.

[0003] In the dynamic linearization process of model-free adaptive control, there are three methods: compact format dynamic linearization, partial format dynamic linearization, and full format dynamic linearization, depending on the length of the required historical input data. Among them, the model-free adaptive scheme based on compact format and partial format can ensure the monotonic convergence of the closed-loop system tracking error and bounded input-output stability. The compact format dynamic linearization method only requires the historical data of the previous moment, and the method is the easiest to implement, but it is difficult to guarantee the accuracy of the data model; the partial format dynamic linearization method is based on multiple historical input data, which can better capture the complex dynamics existing in the original system. As the number of historical data used increases, the description of the system becomes more accurate, and the complexity of each component in the control process will also decrease, but it greatly increases the requirements for calculation and storage.

[0004] At the same time, the input criterion function commonly used in model-free adaptive control theory considers the stability between each step of the control algorithm more from the perspective of the input change |u(k)-u(k-1)|, and ignores the problem of directly solving the energy consumption and the actual effect of the controller from the perspective of the input quantity |u(k)|; at the same time, under the model-free adaptive control theory based on partial linear dynamic linearization, the existing methods use the same input criterion function for all input data, which is simple to implement, but may not be able to give full play to the optimal effect of the controller.

[0005] In the prior art, although some scholars have successfully explored oscillation suppression using model-free adaptive control methods, they have not analyzed and solved the above-mentioned problems.

[0006] Purpose of the Invention

[0007] The purpose of the present invention is to solve the deficiencies of the prior art. The present invention proposes a novel adaptive oscillation suppression method, which has a better control effect than the prior art and does not require high computing and storage capabilities. Summary of the invention

[0008] According to a first aspect of the present application, a novel model-free adaptive oscillation suppression method based on partial format dynamic linearization is provided, which may include the following steps:

[0009] Step 1: Convert the system to be controlled into a partial format dynamic linearized data model;

[0010] (1) The controlled system is equivalent to a single-input single-output discrete-time nonlinear system. Generally, the single-input single-output discrete-time nonlinear system is expressed as follows:

[0011] y(k+1)=f(y(k),…,y(kn y ),u(k),…,u(kn u )) (1)

[0012] Among them, u(k)∈R and y(k)∈R represent the input and output of the system at time k, respectively, and n u 、n y is the dimension of the system input and output, f(…) is the unknown nonlinear function that characterizes the system;

[0013] (2) It is assumed that the output change of the system at the next moment is related to the changes of several control inputs at the previous moment. Considering the impact of all input changes within a fixed-length sliding time window at the current moment on the system, define U L (k)=[u(k),…,u(k-L+1)] T is all control input vectors within a sliding time window [k-L+1,k];

[0014] (3) The output change between two adjacent time periods is recorded as Δy(k)=y(k)-y(k-1), and the input change ΔU L (k) = U L (k)-U L (k-1);

[0015] (4) According to the partial format dynamic linearization method theory, for the case where constraints 1 are satisfied: f(…) with respect to the (nth y +2) to (n y +L+1) variables have continuous partial derivatives, Constraint 2: The system (1) that satisfies the generalized Lipschitz condition can be transformed into a partial format dynamic linearized data model as follows (2), and for any time k, φ p,L (k)=[φ1(k),…,φ L (k)] T is bounded:

[0016]

[0017] It should be noted that during the partial format dynamic linearization process, L≤n u and L is a positive integer; when L = 1, the partial format dynamic data model of formula (1) becomes a compact format dynamic data model; reasonable selection of L can improve the flexibility of the dynamic linearization data model in equivalently describing the original nonlinear system;

[0018] Step 2: Calculate pseudo-partial derivative estimates

[0019] (1) Due to the pseudo partial derivative φ p,L (k) is a time-varying parameter, and its exact true value is difficult to obtain. Therefore, it is necessary to design a pseudo partial derivative estimate using the input and output data of the controlled system. So as to carry out the subsequent control algorithm design;

[0020] (2) The pseudo partial derivative estimation algorithm at time k is:

[0021]

[0022] Among them, η∈(0,2], μ>0;

[0023] (3) When or ||ΔU L (k-1)||≤ε or Added reset algorithm:

[0024]

[0025] in, for The initial value of , ε is a small positive number;

[0026] (4) Consideration Different constraints are set for different items in Execute steps (1) and (2) and take the initial value is positive; Only execute step (1) and take the initial value All are 0;

[0027] Step 3: Obtain the control algorithm according to the input criterion function;

[0028] (1) Consider that the output change Δy(k+1) of the system at time k+1 is proportional to the input change ΔU in the sliding time window [k-L+1,k] L (k) Sensitivity; input change ΔU L (k) = U L (k)-U L (k-1), then the output change Δy(k+1) of the system at time k+1 is proportional to the input U in the sliding time window [k-L+1, k]L (k) also sensitive;

[0029] (2) For discrete-time systems, the control algorithm obtained by minimizing the one-step-ahead prediction error criterion function may produce excessive control input, while the control algorithm obtained by minimizing the weighted one-step-ahead prediction error criterion function may produce steady-state tracking errors. Therefore, in order to keep the system as stable as possible and make the input change |u(k)-u(k-1)| expected to be 0, the model-free adaptive control input criterion function is generally taken as:

[0030] J(u(k))=|y * (k+1)-y(k+1)| 2 +λ|u(k)-u(k-1)| 2 (5)

[0031] Among them, λ>0 is a weight factor, y * (k+1) is the desired output signal; Substitute equation (2) into the criterion function (5), take the derivative of u(k) and set it to 0. The general control algorithm is:

[0032]

[0033] Among them, the step factor ρ i ∈(0,1], i=1,2,…,L;

[0034] (3) Considering that the application object of this control algorithm is a controller for suppressing oscillation in actual engineering, the control output signal u(k) should tend to 0 after the system recovers to stability, so as to avoid interference with other control loops of the system and reduce the energy input for control. Therefore, the input criterion function whose input quantity |u(k)| is expected to be 0 is considered:

[0035] J(u(k))=|y * (k+1)-y(k+1)| 2 +λ|u(k)| 2 (7)

[0036] (4) Comprehensively considering the input criterion functions (5) and (7), a control algorithm is proposed that comprehensively considers the input variation and the input expectation is 0:

[0037]

[0038] Among them, each item is configured with a step factor ρ i ∈(0,1], i=0,1,2,…,L, the step size factor ρ0 of the u(k-1) term is to ensure that the control algorithm has better convergence and stability.

[0039] Correspondingly, the pseudo partial derivative estimation algorithm is updated as:

[0040]

[0041] According to a second aspect of the present invention, there is provided a novel adaptive oscillation suppression method including sparse sampling, comprising the following steps:

[0042] Step 1: Record all input information X in the sliding time window L (k)=[x(k),x(k-1),x(k-2),…,x(k-L+1)] T =[Δu(k),u(k-1),u(k-2)…,u(k-L+1)] T , then equation (8) and equation (9) can be simplified as:

[0043]

[0044]

[0045] Among them, the step factor ρ i ∈(0,1], i=0,1,2,…,L; vector X L (k) is of length L. It should be noted that the vector X L In (k), only the first term is the difference between the input signals at two adjacent moments, and the rest are the input signals at that moment.

[0046] Step 2: X L Each element in (k) is sampled in equal or unequal intervals according to the time interval or label interval, and the new vector formed after sampling is denoted as X a (k), vector X a (k) The length is m, m≤L, and m is a positive integer;

[0047] Step 3: For the new vector X a (k) Each element is re-labeled in turn, denoted by X a (k)=[x(k-a0),x(k-a1),x(k-a2),…,x(ka m-1 )] T =[Δu(k),u(k-a1),u(k-a2),…,u(ka m-1 )] T , where a0=0,1≤a i ≤L-1, i=1,2,…,m-1, {a i} is an increasing positive integer sequence;

[0048] Step 4: To ensure the continuity of the input signal and meet the input criteria, fix X aThe first term in (k) is x(k-a0) = Δu(k), X a The last term x(ka m-1 )=u(ka m-1 )=u(k-L+1), for X a Items 2 to m-1 in (k) are sampled sequentially at certain intervals;

[0049] Step 5: Ignore all but the new vector X a The influence of historical input signals other than the m sampling signals in (k) on the system is used to obtain a new pseudo partial derivative estimation algorithm and control algorithm:

[0050]

[0051]

[0052] Among them, the pseudo partial derivative sparse set Step factor ρ i ∈(0,1],i=0,1,2,…,m。 BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A simulation system model for IEEE 39 nodes connected to a doubly-fed wind turbine generator system.

[0054] Figure 2 This is the oscillation of the grid-connected active power of the doubly-fed wind turbine without control. Divergent subsynchronous oscillations begin to occur after 1 second.

[0055] Figure 3 This is an implementation block diagram of the novel adaptive oscillation suppression method.

[0056] Figure 4 The present invention is specifically implemented in a damping controller of a doubly-fed wind turbine generator system.

[0057] Figure 5 It is the model-free adaptive oscillation suppression effect of the traditional partial format dynamic linearization, L=100.

[0058] Figure 6 This is the model-free adaptive oscillation suppression effect based on the novel partial format dynamic linearization in the present invention, and sparse sampling is not considered, L=100.

[0059] Figure 7 The figure shows the effect of the new adaptive oscillation suppression including the sparse algorithm, L=100, and m=12 after sparse sampling.

[0060] Figure 8 It is the model-free adaptive oscillation suppression effect of the traditional partial format dynamic linearization, L=12. DETAILED DESCRIPTION

[0061] The embodiments are described in detail below in conjunction with the accompanying drawings.

[0062] Taking the calculation example of IEEE 39 node access to double-fed wind turbine in PSCAD / EMTDC simulation platform as an example, Figure 1 The wiring diagram of the simulation system model is shown in Figure 2. The double-fed wind turbine generator set is connected to the grid via a series compensation line. The grid-connected active power of the double-fed wind turbine generator set is taken as the observation object. Without additional control, Figure 2 As shown, divergent subsynchronous oscillations begin to occur at 1 second.

[0063] Figure 3 The implementation block diagram of the new adaptive oscillation suppression method is given. Figure 4 is a specific implementation method on the damping controller of the doubly-fed wind turbine generator set, taking the difference Δu between the actual value and the reference value of the grid-connected voltage of the doubly-fed wind turbine generator set ds As the system output, the expected output value is 0; the system input Δu obtained by the adaptive oscillation suppression method dMFAC Attached to the d-axis inner ring of the inverter on the rotor side of the doubly-fed wind turbine. The damping controller is put into control at 1.1 seconds.

[0064] In this example, the parameters of the adaptive oscillation suppression controller are: λ = 0.5; μ = 8.665; η = 0.79; ρ0 = 0.5, ρ i =0.9, i=1,2,…,m; ε=0.001;

[0065] When the sliding time window length L is 100 and sparse sampling is not considered, Figure 5 The oscillation suppression effect under the traditional partial format dynamic linearization model-free adaptive oscillation suppression method is given. Figure 6 The oscillation suppression effect of the model-free adaptive oscillation suppression method based on the novel partial format dynamic linearization in the present invention is given. It can be seen that this novel control algorithm achieves oscillation suppression faster and has smaller ripple after suppression.

[0066] When the sliding time window length L is 100, considering sparse sampling, L Each element in (k-1) is uniformly sampled at intervals of 10 numbers, and we get X a (k-1)=[Δu(k-1),u(k-2),u(k-12),…,u(k-82),u(k-92),u(k-100)] T , the length is m=12, and the overall computational complexity is nearly one-tenth of that before sparse sampling. Figure 7 Shown is the effect of the new adaptive oscillation suppression including the sparse algorithm; Figure 8For L=12, the traditional model-free adaptive control effect of sparse sampling is not considered. Figure 7-8 The length of historical data actually required to be calculated in the two control algorithms is equal, and it is believed that the calculation amount of the two is equal; it can be found that the adaptive oscillation effect of the sparse algorithm is significantly faster than that of the traditional algorithm, and sparse sampling does not significantly affect the speed and effect of oscillation suppression.

[0067] In summary, the method of the present invention has better oscillation suppression effect than the traditional partial format model-free adaptive control method, and reduces the computational complexity and storage burden brought by the partial format linear dynamic method while ensuring the control effect.

[0068] The method of the present invention is not only applicable to the suppression of subsynchronous oscillations in the power system in the embodiment, but is also applicable to the control and prevention of oscillations in actual systems in other fields, including but not limited to electromagnetic stable operation, electromechanical stable operation, chemical process, linear motor engineering, injection molding process, automation engineering and all other control fields that need to eliminate or weaken oscillation interference.

[0069] Those skilled in the art should understand that the embodiments of the present invention are only to describe the preferred specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A novel adaptive oscillation suppression method, characterized in that: The following steps are involved: Step 1: Equivalently treat the controlled system as a single-input single-output discrete-time nonlinear system. Considering that the output of the system at time k+1 is sensitive to some inputs in the sliding time window of length L before time k, a partial format dynamic linearization data model of the controlled system is established: Among them, φ p,L (k)=[φ1(k),…,φ L (k)] T ∈R L is an unknown but bounded pseudo-partial derivative, ΔU L (k)=[Δu(k),…,Δu(k-L+1)] T , L is the control input linearization length constant; Step 2: The estimation algorithm of pseudo partial derivative is: Among them, η∈(0,2], μ>0, is the unknown pseudo partial derivative φ p,L (k) estimated value; Step 3: Generally, the control input function criterion is: J(u(k))=y * (k+1)-y(k+1) 2 +λu(k)-u(k-1) 2 (3) Among them, λ>0 is a weight factor, y * (k+1) is the desired output signal; Substitute equation (1) into the criterion function (3), take the derivative of u(k), and set it equal to 0, and we get the control algorithm: Among them, the step factor ρ i ∈(0,1], i=1,2,…,L; Step 4: Consider the sliding time window of length L before time k. Some input quantities and input changes will affect the system. Change the information before time k-1 in the sliding time window to input quantity. Record all input information X in the sliding time window. L (k)=[x(k),x(k-1),x(k-2),…,x(k-L+1)] T =[Δu(k),u(k-1),u(k-2)…,u(k-L+1)] T , based on equation (2) and equation (4), the improved control scheme is obtained: Among them, the step factor ρ i ∈(0,1],i=0,1,2,…,L。 Step 5: For the input signal X in the sliding time window of length L L (k)=[x(k),x(k-1),x(k-2),…,x(k-L+1)] T =[Δu(k),u(k-1),u(k-2)…,u(k-L+1)] T , perform sparse sampling to obtain X a (k)=[x(k-a0),x(k-a1),x(k-a2),…,x(ka m-1 )] T =[Δu(k),u(k-a1),u(k-a2)…,u(ka m-1 )] T , and ignoring the influence of historical input signals other than m sampling signals on the system, a new pseudo partial derivative estimation algorithm and control algorithm are obtained: Among them, the pseudo partial derivative sparse set Step factor ρ i ∈(0,1],i=0,1,2,…,m。 2. The method according to claim 1, characterized in that: According to the general single-input single-output discrete-time nonlinear system, the system is transformed into a partial format dynamic linearization data model, including the following steps: Step 1: Generally, a single-input single-output discrete-time nonlinear system is represented as follows: y(k+1)=f(y(k),…,y(k-n y ),u(k),…,u(k-n u )) (9) Among them, u(k)∈R and y(k)∈R represent the input and output of the system at time k, respectively, and n u 、n y is the dimension of the system input and output, f(…) is the unknown nonlinear function that characterizes the system; Step 2: Assume that the output change of the system at the next moment is related to the changes of several control inputs at the previous moment, consider the impact of all input changes in a fixed-length sliding time window at the current moment on the system, and define U L (k)=[u(k),…,u(k-L+1)] T is all control input vectors within a sliding time window [k-L+1,k]; Step 3: The output change between two adjacent time periods is recorded as Δy(k)=y(k)-y(k-1), and the input change ΔU L (k) = U L (k)-U L (k-1); Step 4: According to the partial format dynamic linearization method theory, for the constraints (1) that are satisfied at the same time: f(…) with respect to the (nth y +2) to (n y +L+1) variables have continuous partial derivatives, constraint (2): The system (9) that satisfies the generalized Lipschitz condition can be transformed into a partial format dynamic linearized data model as shown in formula (1): And for any time k, φ p,L (k)=[φ1(k),…,φ L (k)] T is bounded.

3. The method according to claim 1, characterized in that: The partial format dynamic linearization model determined based on a sliding time window with a fixed length L includes: L≤n u And L is a positive integer; When L = 1, the partial format dynamic data model of formula (1) becomes a compact format dynamic data model; Reasonable selection of L can improve the flexibility of the dynamic linearization data model in equivalently describing the original nonlinear system.

4. The method according to claim 1, characterized in that: With input vector X L (k) represents the pseudo partial derivative The estimation algorithm includes the following steps: Step 1: The pseudo partial derivative estimation algorithm at time k is Among them, η∈(0,2], μ>0; Step 2: When or ||X L (k-1)||≤ε or Added reset algorithm: in, for The initial value of , ε is a small positive number; Step 3: Consider Different constraints are set for different items in Execute steps 1 and 2 and take the initial value is positive; Only execute step 1 and take the initial value Both are 0.

5. The method according to claim 1, characterized in that: The control algorithm u(k) at time k is calculated based on all control input vectors in the previous sliding time window [k-L+1,k] with a length of L, including: It is considered that the output change Δy(k+1) of the system at time k+1 is proportional to the input change ΔU in the sliding time window [k-L+1,k] L (k) sensitive; Input change ΔU L (k) = U L (k)-U L (k-1), then the output change Δy(k+1) of the system at time k+1 also affects the input U in the sliding time window [k-L+1, k] L (k) sensitive; For discrete-time systems, the control algorithm obtained by minimizing the one-step-ahead prediction error criterion function may produce excessive control input, while the control algorithm obtained by minimizing the weighted one-step-ahead prediction error criterion function may produce steady-state tracking errors. Therefore, the model-free adaptive control input criterion function is generally taken as: J(u(k))=|y * (k+1)-y(k+1)| 2 +λ|u(k)-u(k-1)| 2 (12) Substitute equation (1) into the criterion function (12), take the derivative of u(k) and set it to 0. The general control algorithm is: For the criterion function of formula (12), in order to keep the system as stable as possible, the input change |u(k)-u(k-1)| is expected to be 0; considering that the application object of this control algorithm is the controller for suppressing oscillation in actual engineering, the control output signal u(k) should tend to 0 after the system recovers stability to avoid interference with other control loops of the system and reduce the energy input for control. Therefore, there is an input criterion function that considers the input quantity |u(k)| to be 0: J(u(k))=y * (k+1)-y(k+1) 2 +λu(k) 2 (14) Taking into account the input criterion functions (12) and (14), a control algorithm that comprehensively considers the input variation and the input expectation of 0 is proposed: Among them, each item is configured with a step factor ρ i ∈(0,1], i=0,1,2,…,L, the step size factor ρ0 of the u(k-1) term is to ensure better convergence and stability of the control algorithm. Formula (15) is a different way of writing the same meaning as formula (6).

6. The method according to claim 1, characterized in that: Sparse sampling of all control inputs within the sliding time window includes the following steps: Step 1: In the sliding time window [k-L+1,k] of length L, the required input signal in the control algorithm of equation (15) [Δu(k),u(k-1),u(k-2)…,u(k-L+1)] T , define vector X L (k)=[x(k),x(k-1),x(k-2),…,x(k-L+1)] T =[Δu(k),u(k-1),u(k-2)…,u(k-L+1)] T , vector X L (k) has a length of L. It should be noted that only the first term in the vector is the difference between the input signals at two adjacent moments, and the rest are the input signals themselves at that moment; Step 2: X L Each element in (k) is sampled in equal or unequal intervals according to the time interval or label interval, and the new vector formed after sampling is denoted as X a (k), vector X a (k) The length is m, m≤L, and m is a positive integer; Step 3: For the new vector X a (k) Each element is re-labeled in turn, denoted by X a (k)=[x(k-a0),x(k-a1),x(k-a2),…,x(ka m-1 )] T =[Δu(k),u(k-a1),u(k-a2),…,u(ka m-1 )] T , where a0=0,1≤a i ≤L-1, i=1,2,…,m-1, {a i } is an increasing positive integer sequence; Step 4: To ensure the continuity of the input signal and meet the input criteria, fix X a The first term in (k) is x(k-a0) = Δu(k), X a The last term x(ka m-1 )=u(ka m-1 )=u(k-L+1), for X a Items 2 to m-1 in (k) are sampled sequentially at certain intervals.

7. The method according to claim 1, characterized in that: The output y of the controlled system will gradually approach the expected output value y under control. * ,include: y * (k+1) is the given bounded expected output signal; y * (k+1) can be a constant to keep the system output constant; y * (k+1) can also take a bounded time-varying function that changes with time, so that the system output tracks the function; the output actual value y(k+1) and the expected value y * The tracking error between (k+1) will converge to zero asymptotically.

8. The method according to claim 1, characterized in that: All control parameters included in this adaptive oscillation suppression scheme include: λ>0;μ>0;η∈(0,2];ρ i ∈(0,1], i=0,1,2,…,m; ε is a small positive number; The values ​​of various parameters can be adjusted according to the control requirements, and the size constraints of the control parameters can also be appropriately changed, thereby improving the adjustable freedom of the control method and greater design flexibility.

9. The method according to claim 1, characterized in that: Adaptive control methods used in oscillation suppression include: The small disturbance stability control and protection of the power system (such as suppression of low-frequency oscillation, sub-synchronous oscillation, wide-band oscillation, etc.) is also applicable to the control and prevention of oscillations in actual systems in other fields, including but not limited to electromagnetic stable operation, electromechanical stable operation, chemical processes, linear motor engineering, injection molding processes, automation engineering and all other control fields that require elimination or reduction of oscillation interference.

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