STATCOM parameter optimization method based on D segmentation method

Abstract

The invention discloses an STATCOM (Static Synchronous Compensator) parameter optimization method based on a D segmentation method. The method comprises the following steps: firstly, deducing a dynamic mathematical model of an STATCOM control system, and obtaining a transfer function of a current inner loop control structure; secondly, obtaining a stability domain of a PI parameter of the controller by using a D segmentation method principle, and setting the PI parameter of the controller based on an expected control loop stability margin and bandwidth; next, the PI parameter setting domains under different expected levels are superposed, and a universal PI parameter domain is obtained; and finally, performing simulation test on the stability domain obtained based on the D segmentation method and the set controller parameter domain. According to the parameter optimization method based on the D segmentation method, the PI parameter stability domain of the STATCOM inner loop control system simultaneously meeting multiple performance indexes such as the phase margin, the amplitude margin, the current loop bandwidth and the short circuit ratio can be obtained, and the PI parameter stability domain is visually shown through a graph, so that the PI parameters under the weak power grid are rapidly and accurately obtained. And powerful support is provided for the PI parameter optimization problem analysis of the control system of the STATCOM.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a STATCOM parameter optimization method based on a D-segmentation method. Background Art

[0002] In STATCOM, the PI regulator is the key link to achieve zero-static-error tracking of the dq axis current, and determines the system control performance of STATCOM constant DC voltage and constant AC voltage. In addition, the complex operating conditions of STATCOM will cause system parameter changes, reduce the current loop control performance, and even cause instability. Therefore, when designing PI parameters, there will be contradictions between multiple dynamic and steady-state performance indicators, as well as uncertainty in parameter changes. It often requires repeated trials and skilled operation skills to achieve relatively satisfactory results. Therefore, it is urgent to study a flexible and simple PI parameter design method that can take into account multiple performance index requirements.

[0003] Existing PI parameter design methods can be divided into two categories: model-free method and parameter model method. Typical model-free methods include Ziegler-Nichols method, but the PI parameters designed by it often have large overshoot or long adjustment time, which makes it difficult to meet multiple performance index requirements. Parameter model methods are further divided into analytical method and visualization method. Common analytical methods include typical system tuning, zero-pole cancellation, Routh criterion method and frequency domain response method, as well as methods for directly calculating PI parameters based on performance index relationship, but it takes repeated trial and error to meet multiple performance index constraints. In fact, there are direct contradictions and trade-offs between multiple performance indicators in the system, and direct calculation is difficult to coordinate multiple performance index relationships at the same time. Compared with analytical methods, visualization methods have the advantages of intuitiveness and convenience. They show the quantitative relationship between performance indicators and parameters in a graphical way. Common methods include root locus method, Bode plot method and Nyquist plot method. These methods can obtain parameter regions that meet the requirements of steady-state error and stability margin at the same time. However, it is difficult to take into account multiple performance index constraints in the time domain and frequency domain by only considering unilateral performance indicators in the time domain or frequency domain.

[0004] In addition, the complex operating conditions of STATCOM cause parameter changes. If the PI parameter design does not take into account the parameter uncertainty requirements, the system stability cannot be guaranteed when the parameters change, and in severe cases, it will cause overcurrent and shutdown. Internal model control, inversion controller, robust predictive current control, fuzzy adaptive PI control, anti-disturbance control and resonant controller can solve the parameter uncertainty problem. However, these control strategies are much more complex than PI control, and engineering implementation is more difficult.

[0005] In view of the difficulty in taking into account multiple performance indicators in the time domain and frequency domain and the uncertainty of system parameters when designing PI parameters, it is urgent to further study systematic tuning methods with strong theoretical basis. The D-partition method establishes a direct connection between the polar plane and the controller parameter space. By mapping the boundary of the polar plane stability domain to the parameter space, the D-partition boundary in the parameter space is constructed, so that the stable region of the controller parameters can be quickly determined.

[0006] On the basis of the above research, the present invention proposes a STATCOM parameter optimization method based on the D-segmentation method. The continuous domain mathematical model of the STATCOM system is established by considering the digital control delay. The continuous domain D-segmentation method is used to obtain the PI parameter stability domain, analyze the relationship between the time domain and frequency domain performance indicators and the PI parameters, and propose a continuous domain PI parameter design method that takes into account the time domain and frequency domain performance indicators. On this basis, the visual domain of the time domain and frequency domain performance indicators (phase margin, amplitude margin, bandwidth) changing with the PI parameters is obtained. Summary of the invention

[0007] The technical problem to be solved by the present invention is to propose a STATCOM parameter optimization method based on the D-segmentation method to solve the problem that it is difficult to take into account multiple performance indicators in the time domain and frequency domain and the uncertainty of system parameters in the existing PI parameter design.

[0008] The present invention is achieved by adopting the following technical solutions:

[0009] A STATCOM parameter optimization method based on D-partition method. First, the mathematical model of the STATCOM control system is established to obtain the current inner loop transfer function. Then, the stability domain of the controller PI parameters is obtained based on the D-partition method, and the PI parameters are adjusted based on the desired control system phase margin, amplitude margin and bandwidth. Finally, based on the visible domain of the PI parameters, the PI parameters that meet the requirements are obtained.

[0010] As a preferred embodiment of the present invention, the scheme comprises the following steps:

[0011] Step A1: Establish the response transfer function according to the dynamic mathematical model of the STATCOM control system.

[0012] Step A2: Use the D-segmentation method to obtain the critical stability curve of the system.

[0013] Step A3: Use a phase-gain margin tester to obtain the desired margin area. You can select a value within a certain margin range and further evaluate the PI parameters in combination with the current loop bandwidth.

[0014] The specific strategy of establishing the dynamic mathematical model of the STATCOM control system and deriving the transfer function described in step A1 is as follows:

[0015] The current inner loop in the STATCOM control system is controlled in the dq coordinate system, that is, the detection value i of the grid-connected inverter output current a ,i b ,i c , after the coordinate transformation of abc / αβ / dq, it is converted into the DC quantity i in the synchronous rotating dq coordinate system d ,i q Compare it with the current reference value i of the inner current loop d * ,i q * Compare and control the corresponding PI regulators to achieve the d ,i q After the output signal of the current inner loop PI regulator is inversely transformed by dq / αβ, the corresponding switch drive signal S of the grid-connected inverter can be obtained through SPWM. a , S b , S c .

[0016] If the grid disturbance is not considered, when the feedforward decoupling control of the dq coordinate system is adopted and the delay of the digital control system is considered, the i d Current inner loop control structure q The q-axis current loop is used as an example for modeling and analysis, and the d-axis current loop is the same. When the switching frequency is high enough, the amplification characteristics of the inverter bridge can be expressed by the proportional gain K PWM Approximately expressed. Considering the DC side voltage disturbance of the grid-connected inverter system, the Vdc decoupling link 1 / Vdc is added to the control system, so the equivalent gain K of the grid-connected inverter is PWM is 1.

[0017] G d (s) Calculate the delay of one-beat control when the duty cycle is delayed. The expression is:

[0018]

[0019] Where, T s is the sampling period.

[0020] G h (s) represents the zero-order holder delay, reflecting the PWM modulation delay, and the expression is:

[0021]

[0022] Then the open-loop transfer function of the system can be expressed as:

[0023] G Io (s) = GPI,I (s)G o1 (s) (3)

[0024] Open loop transfer function G Io (s) is obtained by multiplying the transfer functions of the PI link and the modulation link, and its expression is as follows:

[0025]

[0026] In the formula, K p,I and K i,I are the proportional and integral coefficients of the constant current controller respectively.

[0027] The D-segmentation method described in step A2 is used to obtain the critical stability curve of the system. The specific strategy is:

[0028] The unit negative feedback control system equation with PI controller is shown in equation (5), G PI(s) and G 0(s) They are the transfer functions of the PI link and the modulation link in the open-loop transfer function, respectively, and their expressions are shown in formula (5).

[0029]

[0030] Where: K p and K i are the proportional and integral coefficients of the PI controller respectively; a n , a n-1 , …, a1, a0 and b m , b m-1 ,…,b1,b0 are the denominator and numerator polynomial coefficients of G0(s) respectively. The closed-loop characteristic equation of the system can be expressed as:

[0031] δ(s,K)=s(a n s n +…a1s 1 +a0)+(sK p +K i )(b m s m +…b1s 1 +b0)=0 (6)

[0032] Then the D segmentation boundary can be composed of δ(0, K) = 0, δ(∞, K) = 0 and δ(±jω, K) = 0:

[0033]

[0034] Where: K is the parameter (K p , K i ) is the function parameter domain. From D0 and D1, we can get two singular boundaries:

[0035]

[0036] a n = 0 and b0 = 0 do not constitute the boundary constraints of the parameter stability region, K i = 0. The constraint relationship holds. Therefore, the boundary obtained is:

[0037] K i =0 (9)

[0038] The frequency response of G0(s) can be written as G0(jω)=a(ω)+jb(ω). Substituting G0(jω) into D2 and simplifying it, we can get:

[0039]

[0040] By solving equation (10), we can obtain equation (11), where ω∈(0,∞). Therefore, the boundary of the D-partition method is given by K i =0 and formula (11).

[0041]

[0042] From formula (4), we can get the D2 boundary of the D segmentation method as:

[0043]

[0044] According to the corresponding parameters of STATCOM, the corresponding K can be obtained by traversing the ω value p,I and K i,I The D segmentation boundary can be obtained by using the value.

[0045] The area of ​​the desired margin obtained by using the phase-gain margin tester in step A3 can select a value within a certain margin range, and further evaluate the PI parameters in combination with the current loop bandwidth. The specific strategy is:

[0046] The D-division boundary curve obtained by equation (12) corresponds to the constant current control loop being in a critical stable state. When the current inner loop controller PI parameter combination (K p，I , K i，I ) is taken as the parameter combination corresponding to the critical curve, the constant current control loop is closed-loop stable, otherwise the closed-loop is unstable. In order to allow the STATCOM control system to have a certain gain margin (gain margin, G M ) and phase margin (P M), so it is necessary to further adjust the controller parameter stability domain shown in the figure. By introducing the gain-phase margin tester into the current inner loop control loop, it is easy to obtain the D-division boundary that meets the expected gain margin and phase margin, as shown in the figure, where: M is the magnification corresponding to the expected gain margin; is the angle corresponding to the desired phase margin.

[0047] At this time, the D division boundary of the constant current controller PI parameter is

[0048]

[0049] Let M = 1, The obtained curve is the one that satisfies the phase margin of θ; let M = A, The resulting curve is one that satisfies the amplitude margin A.

[0050] In order to maximize the bandwidth, the bandwidth in the stable domain should be matched with the margin at the same time, and the bandwidth needs to be calculated. Io (s) can be written as G in the frequency domain Io (jω)=A1+jB1, and K is derived p,I , K i,I and loop bandwidth ω b1 The direct relationship is:

[0051]

[0052] In formula (13), ω b1 =2πf b1 Given different f b1 K p,I and K i,I Therefore, by setting different sizes of f b1 , we can obtain the corresponding stable domain.

[0053] The beneficial effects of the present invention are as follows: First, the dynamic mathematical model of the STATCOM control system is derived, and the transfer function of the current inner loop control structure is obtained. Secondly, the stability domain of the controller PI parameters is obtained by using the D-segmentation principle, and the controller PI parameters are adjusted based on the desired control loop stability margin and bandwidth; next, the PI parameter adjustment domains under different desired levels are superimposed to obtain a universal PI parameter domain; finally, the stability domain obtained based on the D-segmentation method and the adjusted controller parameter domain are simulated and tested to verify the effectiveness of the controller parameter adjustment method proposed by the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A control flow chart of a STATCOM parameter optimization method based on a D-segmentation method provided by the present invention.

[0055] Figure 2 This is the control block diagram of the unit negative feedback system in the D-partitioning principle.

[0056] Figure 3 is the current i in the STATCOM control system d Inner loop control structure

[0057] Figure 4 In a STATCOM control system, after the D-splitting method of the present invention is adopted, when the phase margin and the amplitude margin are set to zero, the PI parameters are in a critical stability region.

[0058] Figure 5 This is the control block diagram of the unit negative feedback system after adding the phase angle and amplitude margin tester to the D-division method principle.

[0059] Figure 6 In a STATCOM control system, after the D-splitting method of the present invention is adopted, when the phase angle margin is set to P M =30° and P M =45° amplitude margin is set to G M =5 and G M =10, the obtained value satisfies 30° <P M <45°, 5dB <G M <10dB D-split boundary.

[0060] Figure 7 In a STATCOM control system, after the D-division method of the present invention is adopted, when the current loop bandwidth is set to f b =800hz, f b =1000 Hz and f b =1200hz to get the D division boundary.

[0061] Figure 8 is the current at the STATCOM grid connection point. DETAILED DESCRIPTION

[0062] The present invention provides a STATCOM parameter optimization method based on the D-segmentation method. In order to make the purpose, technical solution and effect of the present invention clearer, the specific implementation scheme of the present invention is described in detail below in conjunction with the accompanying drawings and examples. The specific examples described in the present invention are only used to explain the present invention and are not used to limit the present invention.

[0063] 1. Introduction to the specific embodiments of the invention

[0064] Figure 1 A control flow chart of a STATCOM parameter optimization method based on the D-segmentation method provided by the present invention. Figure 1The present invention describes a STATCOM parameter optimization method based on the D-segmentation method, which includes:

[0065] A1: Establish the response transfer function based on the dynamic mathematical model of the STATCOM control system.

[0066] A2: Use the D-partition method to obtain the critical stability curve of the system.

[0067] A3: Optimize PI parameters to meet phase angle, amplitude margin and bandwidth

[0068] Further, the following specific steps are included:

[0069] A1: Establish the dynamic mathematical model of STATCOM control system and derive the transfer function

[0070] A11: Construct the coupling relationship between each control link of the current inner loop.

[0071] Without considering the grid disturbance, the delay of the PWM digital control system is replaced by the transfer function. The switching frequency is high enough, and the amplification characteristics of the inverter bridge can be expressed by the proportional gain K PWM Approximately expressed. Considering the DC side voltage disturbance of the grid-connected inverter system, the Vdc decoupling link 1 / Vdc is added to the control system, so the equivalent gain K of the grid-connected inverter is PWM is 1.

[0072] A12: Derive the model transfer function based on the control structure.

[0073] G d (s) Calculate the delay of one-beat control when the duty cycle is delayed. The expression is:

[0074]

[0075] Where, T s is the sampling period.

[0076] G h (s) represents the zero-order holder delay, reflecting the PWM modulation delay, and the expression is:

[0077]

[0078] Then the open-loop transfer function of the system can be expressed as:

[0079] G Io (s) = G PI,I (s)G o1 (s) (17)

[0080] Open loop transfer function G Io(s) is obtained by multiplying the transfer functions of the PI link and the modulation link, and its expression is as follows:

[0081]

[0082] In the formula, K p,I and K i,I are the proportional and integral coefficients of the constant current controller respectively.

[0083] A2: According to the D-division method, the critical stability curve of the system is obtained

[0084] A21: Based on the principle of D-segmentation method, the boundary curve is obtained. The construction process is as follows:

[0085] The boundary of the D segmentation method is determined by K i =0 and formula (19).

[0086]

[0087] A21: Substitute the transfer function obtained in step A1 into the boundary curve of the D-division method to obtain the critical stability region boundary curve of the STATCOM current inner loop PI parameter:

[0088] From formula (19), we can get the D2 boundary of the D segmentation method as:

[0089]

[0090] A3: Optimize PI parameters to meet phase angle, amplitude margin and bandwidth.

[0091] A31: In order to allow the STATCOM control system to have a certain gain margin (G M ) and phase margin (P M ).

[0092] The D-division boundary curve obtained by equation (12) corresponds to the constant current control loop being in a critical stable state. When the current inner loop controller PI parameter combination (K p，I , K i，I ) is taken as the parameter combination corresponding to the critical curve, the constant current control loop is closed-loop stable, otherwise the closed-loop is unstable. Therefore, it is necessary to further adjust the controller parameter stability domain shown in the figure. By introducing the gain-phase margin tester into the current inner loop control loop, it is easy to obtain the D-division boundary that meets the expected gain margin and phase margin, as shown in the figure, where: M is the amplification factor corresponding to the expected gain margin; is the angle corresponding to the desired phase margin.

[0093] At this time, the D division boundary of the constant current controller PI parameter is

[0094]

[0095] Let M = 1, The obtained curve is the one that satisfies the phase margin of θ; let M = A, The resulting curve is one that satisfies the amplitude margin A.

[0096] A32: In order to maximize the bandwidth, the bandwidth in the stable region should be matched with the margin at the same time, and the bandwidth needs to be calculated. Io (s) can be written as G in the frequency domain Io (jω)=A1+jB1, and K is derived p,I , K i,I and loop bandwidth ω b1 The direct relationship is:

[0097]

[0098] In formula (13), ω b1 =2πf b1 Given different f b1 K p,I and K i,I Therefore, by setting different sizes of f b1 , we can obtain the corresponding stable domain.

[0099] A33: Use the phase-gain margin tester to obtain the area of ​​the desired margin, and combine it with the current loop bandwidth to further evaluate the PI parameters.

[0100] 2. Technical feasibility verification of the present invention

[0101] The simulation results are as follows Figure 4 , Figure 6 , Figure 7 and Figure 8 As shown, the effectiveness of the present invention is verified.

[0102] Figure 4 is the critical stability curve of the PI parameter of the current inner loop of the STATCOM control system obtained by the D-division method. By traversing the ω value, the corresponding K p,I and K i,I The area surrounded by the D segmentation boundary is the PI parameter stability domain. Figure 4 It can be seen that K p,I and K i,I Both parameters will affect the system stability. p,I The value will correspond to different K i,I Optional range, different K i,I The value will also correspond to different K p,I Optional range. When K i When K is 0, p,IThe maximum value is 0.0307; when K p,I When K is 0.018, i,I The maximum value can be 58.87. The PI parameter selection must be within the PI parameter stability domain, otherwise the system will be in an unstable state.

[0103] Based on the principle of automatic control, the desired gain margin G of the current control loop is M And the phase margin P M Meet 30° <P M <45° and 5dB <G M <10dB, then in the current controller PI parameter stability domain, G is calculated according to formula (21). M =10dB, G M =5dB, P M =45° and P M =30°, and the D-division boundary curves and the constant current controller PI parameter domain that meets the above stability margin requirements are obtained. Figure 6 As shown. When (K p,I , K i,I ) is taken as Figure 6 When the parameters corresponding to the shaded part are combined, the constant current control loop can be guaranteed to be closed-loop stable, and the stability margin of the control loop meets 30° <P M <45° and 5dB <G M <10dB requirement.

[0104] Due to the limitation of switching frequency, the current loop control bandwidth is usually 1 / 10 of the switching frequency. Therefore, the present invention sets the lower limit of the desired current control loop bandwidth as f b =800Hz, bandwidth upper limit is f b =1200Hz, let K p,I Change in the range of (4, 8), and calculate the corresponding K according to the formula p,I , and obtain the current controller PI parameter domain that meets the bandwidth limitation requirements, as shown in the green shaded part of the figure. Figure 7 By superimposing the green shaded part in , we can get the constant current controller PI parameter setting domain that meets both the stability margin requirement and the bandwidth limitation requirement. Figure 7 shown.

[0105] Table 1 shows that in the stable domain formed by the D segmentation curve, the parameter optimization method of the present invention is used to optimize the parameters of the STATCOM control system. Figure 7Select parameter performance comparison. As shown in Table 1, points A, B, and C have similar amplitude margins, but their phase margins, overshoots, and adjustment times are quite different. If the system is required to have the smallest possible overshoot, point C should be selected; if the system adjustment time is required to be short, point A should be selected; if the desired phase margin is large, point C should be selected; if the various performance indicators of the system are required to be relatively balanced, point B should be selected.

[0106] Table 1

[0107]

[0108] The above simulation results show that when the D-division boundary established by the STATCOM parameter optimization method of the present invention is regarded as the control system PI parameter stability domain, the D-division boundary can characterize the dynamic characteristics consistent with the stable system and the characteristics between the unstable system. The above simulation results verify the effectiveness and feasibility of the parameter optimization method of the present invention.

[0109] In summary, the parameter optimization based on the D-segmentation method described in the present invention can take into account multiple performance indicators in the time domain and frequency domain as well as the problem of system parameter uncertainty. The D-segmentation method maps the boundary of the polar plane stability domain to the parameter space by establishing a direct connection between the polar plane and the controller parameter space, and constructs the D-segmentation boundary in the parameter space, so that the stable region of the controller parameters can be quickly determined.

[0110] Finally, it should be noted that the above examples of the present invention are merely examples for illustrating the present invention, and are not intended to limit the embodiments of the present invention. Although the applicant has described the present invention in detail with reference to the preferred embodiments, for those of ordinary skill in the art, other different forms of changes and modifications can be made based on the above description. It is impossible to list all the embodiments here. Any obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A STATCOM parameter optimization method based on D-segmentation method, characterized in that: The following steps are involved: S1: Establish the STATCOM current inner loop transfer block diagram; S2: The critical stability curve of the system is obtained by using the D-segmentation method, and the adjustable range of the PI parameters is obtained; S3: Based on the phase-gain margin tester, the desired margin area is obtained, and the value is selected within a certain margin range, and the PI parameters are determined in combination with the current loop bandwidth; For a control system, it is generally required to have a certain gain margin (GM) and phase margin (PM), so the original controller parameter stability domain needs to be further adjusted. Introducing the gain-phase margin tester into the constant current control loop can easily obtain the D-split boundary that meets the expected gain margin and phase margin.

2. A STATCOM parameter optimization method based on D-segmentation method according to claim 1, characterized in that: Step S3 establishes a visualized parameter stability domain based on the phase-gain margin tester and the current loop bandwidth to determine the PI parameters. The specific strategy is: S31: Based on the critical stability curve of the STATCOM current inner loop calculated in step S2, a controller with desired phase and gain margins is added to obtain an adjustable range of the current inner loop PI parameters that satisfies a certain phase margin and gain margin; S32: deriving the current loop bandwidth, and obtaining the constant current controller PI parameter domain that meets the bandwidth limitation requirement by setting different bandwidth frequencies; S33: Visualize the PI parameter domain that meets the gain margin, phase margin and bandwidth requirements, and select appropriate PI parameters using parameter selection principles.

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