A sliding mode control method for MMC-HVDC based on extended state observer

Abstract

This invention provides a sliding mode control method for MMC-HVDC based on an extended state observer, belonging to the field of DC transmission technology for power systems. It can at least partially solve the problems of parameter uncertainty, external disturbances, and chattering in existing MMC-HVDC systems. The invention includes: establishing a mathematical model of the MMC in a synchronous rotating coordinate system; establishing an interval state-space model based on interval theory, transforming parameter uncertainty into lumped disturbance terms; designing a multi-channel coupled extended state observer to estimate state variables and lumped disturbances in real time; constructing a non-singular terminal sliding surface based on the estimates, and designing a sliding mode controller by combining equivalent control laws and switching control laws; and applying the sliding mode controller to inner-loop current control and circulating current suppression control. This invention effectively suppresses chattering through state-disturbance collaborative estimation and feedforward compensation, improving the robustness and dynamic response quality of the system.

Description

Technical Field

[0001] This invention belongs to the field of DC power transmission technology in power systems, and specifically relates to an MMC-HVDC sliding mode control method based on an extended state observer. Background Technology

[0002] Modular multilevel converters (MMCs), as core equipment in flexible high-voltage direct current (HVDC) transmission systems, have become a key technology for achieving large-scale renewable energy grid integration, long-distance high-capacity power transmission, and asynchronous grid interconnection due to their significant technical advantages, such as modular cascaded structure, excellent output power quality, low switching losses, and strong fault ride-through capability. As flexible HVDC transmission technology develops towards higher voltage and larger capacity, the control performance of MMC converter stations directly determines the safe and stable operation capability of the entire transmission system. Especially when dealing with complex operating conditions such as fluctuations in renewable energy output, AC grid faults, drastic switching of operating conditions, and time-varying parameters, extremely stringent requirements are placed on the robustness, dynamic response speed, and anti-interference capability of the control system.

[0003] The MMC-HVDC system is essentially a high-order, strongly coupled, multi-input multi-output nonlinear complex system. In actual engineering operation, converter stations not only face parameter uncertainties such as temperature rise drift of bridge arm reactor parameters and aging of power devices, but also suffer from external disturbances such as AC side voltage sag, frequency fluctuations, and harmonic injection. More importantly, the system contains unmodeled dynamics such as multi-timescale coupling between outer and inner loop control, sampling delay, dead-zone nonlinearity, and high-frequency parasitic parameters, and sensor measurement signals inevitably contain noise interference. These factors intertwine to form lumped disturbances, seriously affecting current tracking accuracy and power control quality, and even inducing system oscillations, threatening equipment safety.

[0004] Existing MMC control methods mainly include linear control strategies based on PI controllers and nonlinear control methods based on disturbance observers.

[0005] In terms of linear control strategies, PI control relies on the linearized model of the system at a specific operating point. When the operating conditions deviate from the design point or the parameters drift, problems such as tracking overshoot, increased steady-state error, or even instability of the control system may occur, making it difficult to guarantee control quality over a wide operating range.

[0006] In terms of conventional sliding mode control, although sliding mode control has strong robustness to matched disturbances, its discontinuous switching characteristics can cause chattering, which can excite unmodeled high-frequency dynamics. It is also sensitive to unmatched disturbances and measurement noise, making it difficult to achieve high-precision control in strongly coupled systems.

[0007] In terms of traditional disturbance observers, they mainly estimate and compensate for external disturbances, lacking the ability to comprehensively process the strong coupling characteristics, unmodeled dynamics, and measurement noise within the system. Furthermore, they often adopt a single-input single-output design architecture, which is difficult to adapt to the multivariable coupling characteristics of MMC systems.

[0008] Therefore, how to design a control method suitable for the strong coupling characteristics of multiple inputs and multiple outputs in MMC-HVDC systems, effectively estimate and compensate for lumped disturbances while suppressing chattering in sliding mode control, and improve the robust control performance and dynamic quality of the system under complex disturbance environments, is a technical problem that urgently needs to be solved in the field of flexible DC transmission control. Summary of the Invention

[0009] The present invention aims to at least solve one of the technical problems existing in the prior art, and to provide an MMC-HVDC sliding mode control method based on an extended state observer.

[0010] To achieve the above objectives, this invention provides an MMC-HVDC sliding mode control method based on an extended state observer, comprising: A mathematical model of a modular multilevel converter in a synchronous rotating coordinate system is established, the mathematical model including an AC loop model and a DC loop model; Based on interval theory, interval state-space models are established for the AC loop model and the DC loop model respectively, and the parameter uncertainty and external disturbance of the modular multilevel converter are uniformly transformed into lumped disturbance terms. A multi-channel coupled extended state observer is designed for the aforementioned interval state-space model. This extended state observer monitors the system state variables and the lumped disturbance term in real time, and the error of the extended state observer is converged using a pole placement method. A non-singular terminal sliding surface is constructed based on the estimated values ​​of the extended state observer. A sliding mode controller is designed by combining the equivalent control law and the switching control law. The equivalent control law compensates for system dynamics based on the state values ​​and disturbance values ​​observed by the extended state observer. The switching control law compensates for observation errors and disturbance residuals. The sliding mode controller is applied to the inner loop current control and circulating current suppression control of the modular multilevel converter to achieve output current tracking and circulating current second harmonic component suppression.

[0011] Furthermore, the AC loop model is established as follows: Kirchhoff's voltage law equations are written for each phase upper and lower bridge arm of the modular multilevel converter, and the AC loop equations in the synchronous rotating coordinate system are obtained by Park transformation: ; ; in, and These represent the AC side currents respectively. shaft and Axial components, and These represent the differential mode voltages. shaft and Axial components, and These represent the AC side voltages respectively. shaft and Axial components, Represents the angular frequency of the power system. and These represent the equivalent resistance and equivalent inductance after conversion, respectively.

[0012] Furthermore, the DC loop model is established as follows: Kirchhoff's voltage law equations are written for each phase of the modular multilevel converter's upper and lower arms, and the DC loop equations in the synchronous rotating coordinate system are obtained through Park transformation: ; ; in, and These represent the second harmonic components of the circulating current. shaft and Axial components, and These represent the common-mode voltages respectively. shaft and Axial components, and These represent the equivalent loss resistance and inductance of the bridge arm reactor, respectively.

[0013] Furthermore, the method for establishing the interval state-space model of the AC loop model based on interval theory is as follows: According to the interval operation rules, the ratio of equivalent resistance to equivalent inductance and the reciprocal of equivalent inductance are decomposed into intervals to obtain the nominal value and the uncertainty, respectively. Define the state variables of the AC loop and and virtual control variables and ; The AC loop model is transformed into the following interval state-space model: ; ; in, This is the nominal value of the ratio of equivalent resistance to equivalent inductance. and The lumped disturbance term includes internal and external disturbances caused by parameter uncertainties.

[0014] Furthermore, the structure of the extended state observer designed for the AC loop is as follows: ; ; ; ; in, and Representing state variables respectively and The estimated value, and Represent the lumped disturbance terms respectively and The estimated value, and This is the positive gain of the extended state observer. , ; The positive gain of the extended state observer is selected by the pole placement method so that the eigenvalues ​​corresponding to the error dynamic characteristic equation of the extended state observer are located in the left half of the s-plane.

[0015] Furthermore, the non-singular terminal sliding surface is constructed as follows: Define the sliding surface function: , ; in, This represents the state estimate of the extended state observer. Compared with reference value deviation, , ; The equivalent control law is calculated as follows: the derivative of the sliding surface function is taken and set to zero, and the equivalent control law is obtained by combining the estimated value of the extended state observer. The switching control law is calculated as follows: ; in, and To switch the control law gain, , .

[0016] Furthermore, the inner loop current control Axis control law and The axis control laws are as follows: ; ; in, and They represent shaft and The derivative of the shaft current reference value; The Axis control law and the aforementioned The differential voltage reference value is obtained by inverse transformation of the output of the axis control law. and .

[0017] Furthermore, the circulating flow suppression control method is as follows: A second extended state observer is designed for the interval state-space model of the DC loop. The second extended state observer estimates the circulating state variables and the corresponding lumped disturbance terms in real time. Based on the estimates from the second extended state observer, a non-singular terminal sliding surface for circulating current suppression is constructed. Combining the equivalent control law and switching control law for circulating current suppression, a common-mode voltage reference value is output. and ; The objective of the circulating current suppression control is to reduce the second harmonic component of the circulating current. shaft and The axis component is controlled to zero.

[0018] Furthermore, it also includes outer loop control steps: In DC voltage and reactive power control mode, the outer loop employs a proportional-integral controller, using the deviation between the DC voltage reference value and the actual DC voltage, and the deviation between the reactive power reference value and the actual reactive power, as inputs, to output the inner loop current control. Shaft current reference value and Shaft current reference value; In both active and reactive power control modes, the outer loop employs a proportional-integral controller, using the deviations between the active power reference value and the actual active power, and the deviations between the reactive power reference value and the actual reactive power, as inputs to output the inner loop current control. Shaft current reference value and Shaft current reference value.

[0019] Furthermore, the convergence verification method of the extended state observer is as follows: Constructing Lyapunov functions ,in Let be the observer error vector. To meet A symmetric positive definite matrix, For positive integers, It is the identity matrix; The derivative of the Lyapunov function satisfies: ; in, For the input matrix, This is the upper bound of the derivative of the lumped perturbation term; The error of the extended state observer is uniformly bounded, and its boundary is: .

[0020] The beneficial effects of this invention are as follows: This invention establishes an interval state-space model of MMC, which unifies system parameter uncertainties, unmodeled dynamics, and external disturbances into lumped disturbance terms, providing a unified mathematical framework for subsequent disturbance estimation and compensation.

[0021] The multi-channel coupled extended state observer designed in this invention addresses the strong coupling characteristics of MMC systems with multiple inputs and multiple outputs. It achieves real-time online estimation of state variables and lumped disturbances through a multi-channel collaborative observation mechanism, significantly reducing the dependence on precise mathematical models.

[0022] This invention employs a non-singular terminal sliding surface design, which avoids the singularity problem at the origin of conventional terminal sliding surfaces, ensuring that the system state on the sliding surface converges to the equilibrium point within a finite time, thereby improving steady-state control performance.

[0023] This invention effectively reduces the chattering phenomenon of traditional sliding mode control by using an extended state observer for real-time estimation and feedforward compensation of lumped disturbances, thereby improving the system's disturbance rejection capability and current tracking accuracy.

[0024] The circulating current suppression controller designed in this invention can effectively suppress the second harmonic component in the circulating current inside the MMC, reduce the operating loss and voltage ripple of the submodule, and improve the overall operating efficiency of the system. Attached Figure Description

[0025] Figure 1 This is a flowchart of the MMC-HVDC sliding mode control method based on an extended state observer according to an embodiment of the present invention; Figure 2 This is a structural diagram of a single-sided converter station system according to an embodiment of the present invention; Figure 3 This is a control structure diagram of the MMC converter station according to an embodiment of the present invention; Figure 4 This is a block diagram of a constant DC voltage and constant reactive power controller according to an embodiment of the present invention; Figure 5This is a block diagram of a constant active power and constant reactive power controller according to an embodiment of the present invention; Figure 6 This is a block diagram of the circulating current suppression controller according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and beneficial effects of this application clearer, the following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates this application. It should be understood that the specific embodiments described in this specification are merely for explaining this application and are not intended to limit it.

[0027] The MMC-HVDC sliding mode control method based on an extended state observer of the present invention is implemented in a flexible high-voltage direct current transmission system. The flexible high-voltage direct current transmission system adopts a modular multilevel converter as the core equipment. Each MMC consists of 6 bridge arms. The upper and lower bridge arms of each phase are collectively referred to as a phase unit. Each bridge arm is connected in series with N sub-modules.

[0028] See Figure 2 A single-sided converter station system consists of two parts: a DC side and an AC side. The DC side is connected via DC cables or overhead lines, while the AC side is connected to the AC power grid via a connecting transformer. The core equipment of the converter station is the MMC (Multi-Mechanical Control Unit), among which... and These represent the equivalent loss resistance and inductance of each bridge arm reactor, respectively. and These represent the leakage resistance and leakage inductance of the connecting transformer referred to the valve side of the connecting transformer, respectively. This is the DC side current. This represents the DC-side inter-electrode voltage.

[0029] See Figure 3 The MMC converter station control structure consists of two parts: differential-mode dual-loop control and common-mode control. The differential-mode dual-loop control comprises an outer loop controller and an inner loop current controller. The outer loop controller receives power reference values, DC voltage reference values, and actual measured values, and outputs... shaft and The shaft current reference value is used; the inner loop current controller employs a sliding mode controller based on an extended state observer, outputting a differential-mode voltage reference value. Common-mode control consists of a circulating current suppression controller, also employing a sliding mode controller based on an extended state observer, outputting a common-mode voltage reference value. The differential-mode voltage reference value is... arrive After transformation, it is compared with the common-mode voltage reference value. arrive The transformation results are superimposed to obtain the voltage reference values ​​of the upper and lower arms of the converter station.

[0030] Example 1 This embodiment uses the sending-end converter station control of a dual-end MMC-HVDC DC transmission system as an application scenario. The sending-end converter station adopts a constant active power and constant reactive power control mode, responsible for controlling the active power transmitted to the DC system and the reactive power on the AC side. The rated DC voltage of the DC transmission system is 400kV, the rated transmission power is 1000MW, and each bridge arm of the converter station has 200 sub-modules connected in series.

[0031] See Figure 1 The sliding mode control method in this embodiment includes the following steps: Step S1: Establish the mathematical model of MMC in the synchronous rotating coordinate system.

[0032] See Figure 2 ,for The phase of the upper bridge arm starts from the DC positive terminal, passes through the upper bridge arm, and reaches the AC side. At the point, write Kirchhoff's voltage law equation. For Phase lower bridge arm, from the AC side Starting from point A, passing through the lower bridge arm to reach the DC negative terminal, Kirchhoff's voltage law equations are written. By performing appropriate addition and subtraction operations on the equations of the upper and lower bridge arms, mathematical models of the AC and DC sides of the MMC can be obtained respectively.

[0033] definition The differential mode voltage of the upper and lower bridge arms is The common-mode voltage is , The circulation of the phase is ,in and These are the currents of the upper and lower bridge arms, respectively. and These are the voltages synthesized by the cascading of submodules in the upper and lower bridge arms, respectively. The equivalent inductance is defined. and equivalent resistance .

[0034] The difference between the equations of the upper and lower bridge arms yields the MMC AC loop equation: ; Adding the equations for the upper and lower bridge arms yields the MMC DC loop equation: ; Applying the Park transform to the above AC loop equations, we obtain the MMC in... Mathematical model of AC loop in coordinate system: ; ; in, Represents the angular frequency of the power system. and These represent the AC side voltages respectively. shaft and Axial components, and These represent the AC side currents respectively. shaft and Axial components, and These represent the differential mode voltages. shaft and Axial components.

[0035] Applying the Park transform to the DC loop equations yields the MMC in... Mathematical model of DC loop in coordinate system: ; ; in, and For the second harmonic component of the internal circulating current of MMC shaft and Axial components, and These represent common-mode voltages respectively. shaft and Axial components.

[0036] In this embodiment, the converter station parameters are set as follows: bridge arm reactor inductance. The nominal value is 50mH, and the equivalent loss resistance of the bridge arm reactor is... The nominal value is 0.5 Leakage inductance of the connecting transformer The nominal value is 60mH, and the leakage resistance of the connecting transformer is... The nominal value is 0.3 System angular frequency rad / s.

[0037] Step S2: Establish the interval state space model.

[0038] Considering that in actual engineering, the resistance and inductance parameters of the converter station will fluctuate within a certain range due to factors such as temperature changes and device aging, interval theory is used to model the parameter uncertainty.

[0039] The mathematical model of an AC loop can be written in the following state equation form: ; in, and For state variables, and To control the variable, the control objective is to let and Track its target value and .

[0040] According to the interval division rules in interval theory, for We can conclude that: ; Define variables: ; ; therefore: ; for We can conclude that: ; Define variables: ; ; Define the state variables as follows: ; Define virtual control variables and for: ; ; Based on the above variable definitions, the interval state-space model of the MMC AC loop can be derived as follows: ; ; in, and For the lumped disturbance term: ; ; in, and Represents external disturbances and satisfies , .

[0041] If the virtual control variables are calculated through subsequent controller design and Then the actual control variable and It can be obtained through the following formula: ; ; Due to aggregate disturbance and It is composed of a combination of bounded, time-varying external variables and internal uncertainties, and these uncertainties stem from the variations in output current and system parameters within a limited range. Therefore, the disturbance and its first derivative both exhibit extreme values. , ; , ; For the mathematical model of the DC loop, interval theory is also used for modeling. We can conclude that: ; Define variables: ; ; for We can conclude that: ; Define variables: ; ; Define the state variables as follows: ; Define virtual control variables and for: ; ; Based on the above variable definitions, the interval state-space model of the MMC DC loop can be derived as follows: ; ; in, and For the lumped disturbance term: ; ; in, and Represents external disturbances and satisfies , .

[0042] If the virtual control variables are calculated through subsequent controller design and Then the actual control variable and It can be obtained through the following formula: ; ; In this embodiment, the parameter at its nominal value is considered. Fluctuations within a certain range. Equivalent inductance. mH, nominal value mH, the range of variation is mH. Equivalent resistance nominal value The range of variation is Therefore, it can be calculated that... , , , .

[0043] Step S3: Design the extended state observer.

[0044] To effectively eliminate uncertain disturbances, a first extended state observer is designed to estimate the state variables of the inner loop current controller. , With lumped disturbance term , .

[0045] Considering the AC circuit of the MMC system shaft and Based on the coupling characteristics between axes, a first extended state observer with multi-channel coupling is designed, and its structure is as follows: ; ; ; ; in, and State variables and The estimated value, and Representing lumped disturbances and The estimated value and , and This is the positive gain of the observer.

[0046] Based on the interval state-space model and the extended state observer equation, the dynamic characteristic equation of the observer error can be obtained. The state estimation error is defined. , and disturbance estimation error , The dynamic characteristic equation of the observer error is: ; ; ; ; The above error equation can be expressed in matrix form as follows: ; in: ; ; ; The system can be viewed as having the input as Status is The system. The characteristic equation of the system is: ; The pole placement method is used to select the observer gain. and The characteristic roots of the system's characteristic equation are located at The left half of the plane contains eigenvalues ​​with negative real parts, thus ensuring the convergence of the observer error. At this point, the matrix... It is a Hurwitz matrix.

[0047] The convergence of the first extended state observer is further analyzed using Lyapunov's theorem. Based on Lyapunov stability analysis, the matrix... It is a Hurwitz matrix, therefore there exists a symmetric positive definite matrix. satisfy: ; in, For positive integers, It is an identity matrix.

[0048] Define the Lyapunov function for the first extended state observer. for: ; but The derivative satisfies the following inequality: ; in, .

[0049] Therefore, the estimation error of the first extended state observer is uniformly bounded, meaning that the estimation error is bounded over a finite time, and its boundary is: ; in: ; The above analysis shows that, In the case of increasing, This will decrease, thereby expanding the observation error of the state observer. It will decrease. The larger the value, the faster the observer error converges. This can be seen from the Lyapunov equation. Increase Without changing the matrix The absolute value needs to be increased, thus increasing the observer gain. and The gain needs to be increased. Therefore, in practical applications, while ensuring the stability of the extended state observer, the gain of the observer needs to be increased as much as possible.

[0050] In this embodiment, the gain parameter of the first extended state observer is set as follows: , , , , , , , It has been verified that, under this set of gain parameters, the matrix... All eigenvalues ​​are located at In the left half-plane of the plane, the observer is stable and the convergence speed meets the bandwidth requirements of the inner loop current control.

[0051] Step S4: Design an inner-loop current sliding mode controller based on an extended state observer.

[0052] Based on the first extended state observer, a sliding mode controller for the inner loop current is constructed. The sliding surface is a crucial element in designing the sliding mode controller. To reduce chattering and improve the steady-state control performance of the MMC, a non-singular terminal sliding surface is adopted, whose sliding surface function is expressed as: ; in, It corresponds to Inner loop current and The sliding surface switching function of the target for inner loop current control. represent Its reference value deviation, , .

[0053] The state values ​​estimated by the extended state observer Substituting the above sliding surface function, we get: ; in, represent Its reference value The deviation.

[0054] Differentiating with respect to the sliding surface and estimating the value using an extended state observer, we obtain: ; make Ignoring estimation errors, the equivalent control law is obtained as follows: ; Considering the estimation error and disturbance residual, the switching control law is designed as follows: ; Among them, the switching control law gain , .

[0055] Therefore, the sliding mode controller design combining the first extended state observer is obtained as follows: ; Substituting the specific expressions of the equivalent control law and the switching control law, we obtain the inner-loop current controller. Axis control law: ; Axis control law: ; The convergence and stability of the inner-loop current controller are verified as follows. The standard form of the Lyapunov function is defined as: ; By combining the dynamic equations and control laws of the interval state-space model, it can be derived that... The derivative satisfies: ; in, and These are the bounded quantities of system function estimation error and disturbance estimation error, respectively.

[0056] The switching gain must satisfy: ; available: ; Therefore, it can be known that when hour, According to Lyapunov stability theory, Uniformly bounded and stable, its convergence bound is: ; If the observer gain is large enough, then... ,thereby , .

[0057] From the sliding surface function, we can see that and Since both terms have the same sign, therefore: ; Therefore, the upper bound of the tracking error is: ; This upper bound can be reduced. or increase To reduce it arbitrarily, thus having .

[0058] In this embodiment, the parameters of the inner loop current sliding mode controller are set as follows: , , , The above parameters ensure that shaft and The shaft currents can track their reference values ​​within a limited time, and the chattering amplitude is controlled within an acceptable range.

[0059] Step S5: Design a circulation suppression controller based on an extended state observer.

[0060] The circulating current suppression controller is structurally similar to the inner-loop current controller. A second extended state observer is designed to estimate the circulating current state variables. , With lumped disturbance term , .

[0061] The structure of the second extended state observer is as follows: ; ; ; ; in, and State variables and The estimated value, and Representing lumped disturbances and The estimated value and , and For the observer's positive gain, , .

[0062] Based on the interval state-space model of the DC loop and the second extended state observer equation, the dynamic characteristic equation of the observer error is obtained. The state estimation error is defined. , and disturbance estimation error , The dynamic characteristic equation of the observer error is: ; ; ; ; The above equation can be written in matrix form as follows: ; Similarly, the pole placement method is used, by selecting the observer gain. and , make the matrix It is a Hurwitz matrix, therefore the second extended state observer is stable, i.e., the observer error... It is convergent.

[0063] Analysis using Lyapunov's theorem reveals a symmetric positive definite matrix. satisfy: ; in This is a positive constant. The estimation error of the second extended state observer is bounded in finite time, and its boundary is: ; Using a non-singular terminal sliding surface, its sliding surface function is expressed as: ; Combining the equivalent control law and the switching control law, the circulating current suppression controller is obtained. Axis control law: ; Axis control law: ; The control objective of the circulating current suppression controller is to reduce the second harmonic component of the circulating current. shaft and The axis component is controlled to zero, that is... .

[0064] In this embodiment, the gain parameter of the second extended state observer is set as follows: , , , , , , , The parameter settings for the circulating current suppression sliding mode controller are as follows: , , , .

[0065] Step S6: Design the outer loop controller.

[0066] See Figure 5 In this embodiment, the sending-end converter station adopts a constant active power and constant reactive power control mode. Both the outer loop active power controller and the reactive power controller are proportional-integral controllers.

[0067] The output of the active outer loop proportional-integral controller is Shaft current reference value: ; The output of the reactive power outer loop proportional-integral controller is Shaft current reference value: ; in, and These are the proportional and integral coefficients of the active power outer-loop proportional-integral controller. and These are the proportional and integral coefficients of the reactive power outer-loop proportional-integral controller. and These are the reference values ​​for active power and reactive power, respectively. and These are the actual active power and reactive power, respectively.

[0068] In this embodiment, the parameters of the active power outer loop proportional-integral controller are set as follows: , The parameter settings for the reactive power outer loop proportional-integral controller are as follows: , .

[0069] Step S7: Model deployment and simulation verification.

[0070] The inner loop current controller will use the current reference value output from the outer loop. and As a tracking target, the system state and lumped disturbance are estimated in real time through the first extended state observer, and combined with the non-singular terminal sliding mode control law, the differential mode voltage reference value is output. and The actual control variables can be transformed by inverse Parker transformation to obtain the three-phase output voltage of the AC side of the converter station. Then, the number of sub-modules that should be put into operation on the upper and lower arms of the corresponding converter station can be calculated by the nearest level modulation strategy.

[0071] The circulating current suppression controller uses zero as the reference value for the second harmonic component of the circulating current. It estimates the circulating current state and the corresponding lumped disturbance in real time through a second extended state observer, and outputs a common-mode voltage reference value by combining a non-singular terminal sliding mode control law. and The common-mode voltage reference value is superimposed onto the voltage reference values ​​of the upper and lower bridge arms after inverse Parker transformation.

[0072] This embodiment was verified on the MATLAB / Simulink simulation platform. The simulation conditions were set as follows: the system operated normally from 0 to 0.5 seconds, transmitting 800MW of active power and 0Mvar of reactive power. At 0.5 seconds, the active power reference value jumped to 1000MW. At 0.8 seconds, a 30% voltage drop occurred on the AC side, which lasted for 0.2 seconds before recovering.

[0073] Simulation results show that under active power step conditions, the inner loop d-axis current completes tracking transition within 0.02 seconds, with overshoot less than 3% and steady-state error less than 0.5%. Under voltage dip conditions, current tracking recovers to stability within 0.03 seconds without significant oscillation. The circulating current suppression controller suppresses the second harmonic component to within 2% of the steady-state value.

[0074] Example 2 This embodiment uses the receiving-end converter station control of a dual-end MMC-HVDC DC transmission system as an application scenario. The receiving-end converter station adopts a constant DC voltage and constant reactive power control mode, responsible for maintaining the voltage stability of the DC system and keeping the reactive power balance of the AC system. The rated DC voltage of the DC transmission system is 400kV, the rated transmission power is 1000MW, and each bridge arm of the converter station has 200 sub-modules connected in series.

[0075] Steps S1 to S5 in this embodiment are the same as in Embodiment 1, and detailed derivation processes for repeated parts are omitted here. The following focuses on describing the outer loop controller design that differs from Embodiment 1.

[0076] Step S6: Design a constant DC voltage and constant reactive power outer loop controller.

[0077] See Figure 4In this embodiment, the receiving-end converter station adopts a constant DC voltage and constant reactive power control mode. Both the outer loop DC voltage controller and the reactive power controller are proportional-integral controllers.

[0078] The output of the outer loop voltage proportional-integral controller is the d-axis current reference value: ; The output of the outer loop reactive power proportional-integral controller is Shaft current reference value: ; in, and These are the proportional and integral coefficients of the DC voltage outer-loop proportional-integral controller. and These are the proportional and integral coefficients of the reactive power outer-loop proportional-integral controller. and These are the reference DC voltage value and the actual DC voltage, respectively.

[0079] In this embodiment, the parameters of the DC voltage outer loop proportional-integral controller are set as follows: , The parameter settings for the reactive power outer loop proportional-integral controller are as follows: , .

[0080] The inner loop current controller also employs a sliding mode controller based on an extended state observer, using the outer loop output current reference value. and As a tracking target, the system state and lumped disturbance are estimated in real time through the first extended state observer, and combined with the non-singular terminal sliding mode control law, the differential mode voltage reference value is output. and The structure and parameters of the circulating current suppression controller are consistent with those of Example 1.

[0081] Step S7: Model deployment and simulation verification.

[0082] This embodiment was verified on the MATLAB / Simulink simulation platform. The simulation conditions were set as follows: the system operates normally from 0 to 0.5 seconds, with a DC voltage reference value of 400kV and a reactive power reference value of 0Mvar. At 0.5 seconds, the active power at the sending end jumps from 800MW to 1000MW, and the receiving end converter station needs to maintain a stable DC voltage. At 0.8 seconds, a 20% voltage drop occurs on the AC side, which recovers after 0.15 seconds. At 1.2 seconds, the parameters of the bridge arm reactors experience a 10% positive drift, simulating parameter changes caused by temperature rise.

[0083] Simulation results show that under the power step condition at the sending end, the maximum deviation of the DC voltage is 1.5% of the rated value, and it recovers to the steady-state value within 0.05 seconds, with a steady-state error of less than 0.2%. Under the voltage sag condition, the maximum deviation of the DC voltage is 3% of the rated value, and it recovers to stability within 0.08 seconds. Under the parameter drift condition, because the extended state observer can estimate the lumped disturbance caused by parameter changes in real time, the current tracking accuracy is not significantly affected, and the steady-state error remains within 0.3%. The circulating current suppression controller can effectively suppress the second harmonic component to within 2.5% of the steady-state value under various operating conditions.

[0084] Compared to traditional PI controllers, the method of this invention reduces the settling time by 40% and the overshoot by 50% under power step conditions. Under voltage dip conditions, the recovery time is reduced by 35%, and no current oscillation occurs. Under parameter drift conditions, the steady-state error of traditional PI controllers increases to 1.5%, while the steady-state error of the method of this invention remains within 0.3%, demonstrating excellent robustness.

[0085] Example 3 This embodiment uses the control of a three-terminal MMC-HVDC DC transmission system as an application scenario to further verify the applicability of the method of the present invention in multi-terminal DC systems. The three-terminal DC system includes two sending-end converter stations and one receiving-end converter station. The receiving-end converter station adopts a constant DC voltage and constant reactive power control mode, while both sending-end converter stations adopt a constant active power and constant reactive power control mode.

[0086] The parameters of the three-terminal DC system are as follows: the rated DC voltage is 500kV, the rated transmission capacity of the receiving-end converter station is 2000MW, the rated transmission capacity of sending-end converter station 1 is 1200MW, and the rated transmission capacity of sending-end converter station 2 is 800MW. Each bridge arm of each converter station has 250 sub-modules connected in series.

[0087] In this embodiment, the methods for establishing the MMC mathematical model, the interval state space model, the extended state observer design, and the inner loop current sliding mode controller design in steps S1 to S4 are the same as in Embodiments 1 and 2. All three converter stations use the sliding mode controller based on the extended state observer proposed in this invention as the inner loop current controller, and are configured with independent circulating current suppression controllers.

[0088] For the receiving-end converter station, the parameters of its interval state-space model are calculated based on the actual equipment parameters of the receiving-end converter station. (Bridge arm reactor inductance) The nominal value is 60mH, and the equivalent loss resistance of the bridge arm reactor is... The nominal value is 0.4 Leakage inductance of the connecting transformer The nominal value is 70mH, and the leakage resistance of the connecting transformer is... The nominal value is 0.25 The equivalent inductance is calculated. mH, equivalent resistance Consider the parameter at its nominal value. Fluctuations within a certain range can be calculated. , , , .

[0089] For both sending-end converter station 1 and sending-end converter station 2, the same calculation process is performed based on their respective equipment parameters. The gain of the extended state observer and the sliding mode controller parameters of each converter station are independently tuned based on their respective system parameters.

[0090] The receiving-end converter station adopts a constant DC voltage and constant reactive power control mode. The parameter settings of the outer loop proportional-integral controller are as follows: , , , The sending-end converter station 1 adopts a constant active power and constant reactive power control mode. The parameter settings of the outer loop proportional-integral controller are as follows: , , , The sending-end converter station 2 adopts a constant active power and constant reactive power control mode. The parameter settings of the outer loop proportional-integral controller are as follows: , , , .

[0091] The three-terminal system was verified on the MATLAB / Simulink simulation platform. The simulation conditions were set as follows: From 0 to 1.0 seconds, the system operated normally, with sending end 1 transmitting 900MW of active power and sending end 2 transmitting 600MW of active power, and the DC voltage reference value was 500kV. At 1.0 second, the active power reference value of sending end 1 jumped to 1200MW. At 1.5 seconds, a 25% voltage drop occurred on the AC side of sending end 2, which recovered after 0.2 seconds. At 2.0 seconds, the parameters of the bridge arm reactor of the receiving end converter station experienced an 8% positive drift.

[0092] Simulation results show that the three-terminal system maintains stable operation under various disturbance conditions. Under the power step condition at the sending end 1, the receiving end converter station maintains stable DC voltage with a maximum deviation of 1.8% of the rated value, recovering to the steady-state value within 0.06 seconds. Under the voltage drop condition at the sending end 2, the current tracking at the sending end 2 recovers to stability within 0.04 seconds, and the maximum deviation of the receiving end DC voltage is 2.5% of the rated value. Under the parameter drift condition at the receiving end, the current tracking errors remain within 0.5%. The circulating current suppression controllers of all three converter stations effectively suppress the second harmonic component to within 3% of the steady-state value.

[0093] In summary, the embodiments of the present invention have at least the following technical effects: This invention establishes an interval state-space model of MMC, which unifies system parameter uncertainties, unmodeled dynamics, and external disturbances into lumped disturbance terms, providing a unified mathematical framework for subsequent disturbance estimation and compensation, and enabling controller design to be independent of precise system parameters.

[0094] The multi-channel coupled extended state observer designed in this invention achieves state-disturbance co-estimation by simultaneously estimating system state variables and lumped disturbances, and proves the uniform eventual boundedness of the observer error through Lyapunov stability analysis.

[0095] This invention effectively reduces the chattering phenomenon of traditional sliding mode control by using an extended state observer to estimate and feedforward compensate for lumped disturbances in real time, thereby improving the system's anti-disturbance capability and current tracking accuracy. It also exhibits excellent dynamic response performance and robustness under complex operating conditions such as power step, voltage drop, and parameter drift.

[0096] The circulating current suppression controller designed in this invention can effectively suppress the second harmonic component in the circulating current inside the MMC, reduce the operating loss and voltage ripple of the submodule, and improve the overall operating efficiency of the system.

[0097] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A sliding mode control method for MMC-HVDC based on an extended state observer, characterized in that, include: A mathematical model of a modular multilevel converter in a synchronous rotating coordinate system is established, the mathematical model including an AC loop model and a DC loop model; Based on interval theory, interval state-space models are established for the AC loop model and the DC loop model respectively, and the parameter uncertainty and external disturbance of the modular multilevel converter are uniformly transformed into lumped disturbance terms. A multi-channel coupled extended state observer is designed for the interval state space model. The extended state observer observes the system state variables and the lumped disturbance term in real time, and the error of the extended state observer is converged by the pole placement method. as well as A non-singular terminal sliding surface is constructed based on the estimated values ​​of the extended state observer. A sliding mode controller is designed by combining the equivalent control law and the switching control law. The equivalent control law compensates for system dynamics based on the state values ​​and disturbance values ​​observed by the extended state observer. The switching control law compensates for observation errors and disturbance residuals. The sliding mode controller is applied to the inner loop current control and circulating current suppression control of the modular multilevel converter to achieve output current tracking and circulating current second harmonic component suppression.

2. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 1, characterized in that, The AC loop model is established as follows: Kirchhoff's voltage law equations are written for each phase upper and lower bridge arm of the modular multilevel converter, and the AC loop equations in the synchronous rotating coordinate system are obtained by Park transformation: ； ； in, and These represent the AC side currents respectively. shaft and Axial components, and These represent the differential mode voltages. shaft and Axial components, and These represent the AC side voltages respectively. shaft and Axial components, Represents the angular frequency of the power system. and These represent the equivalent resistance and equivalent inductance after conversion, respectively.

3. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 1, characterized in that, The DC loop model is established as follows: Kirchhoff's voltage law equations are written for each phase of the modular multilevel converter's upper and lower arms, and the DC loop equations in the synchronous rotating coordinate system are obtained through Park transformation: ； ； in, and These represent the second harmonic components of the circulating current. shaft and Axial components, and These represent the common-mode voltages respectively. shaft and Axial components, and These represent the equivalent loss resistance and inductance of the bridge arm reactor, respectively.

4. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 2, characterized in that, The method for establishing the interval state-space model of the AC loop model based on interval theory is as follows: According to the interval operation rules, the ratio of equivalent resistance to equivalent inductance and the reciprocal of equivalent inductance are decomposed into intervals to obtain the nominal value and the uncertainty, respectively. Define the state variables of the AC loop and and virtual control variables and ; The AC loop model is transformed into the following interval state-space model: ； ； in, This is the nominal value of the ratio of equivalent resistance to equivalent inductance. and The lumped disturbance term includes internal and external disturbances caused by parameter uncertainties.

5. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 4, characterized in that, The structure of the extended state observer designed for the AC loop is as follows: ； ； ； ； in, and Representing state variables respectively and The estimated value, and Represent the lumped disturbance terms respectively and The estimated value, and This is the positive gain of the extended state observer. , ; The positive gain of the extended state observer is selected by the pole placement method so that the eigenvalues ​​corresponding to the error dynamic characteristic equation of the extended state observer are located in the left half of the s-plane.

6. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 5, characterized in that, The non-singular terminal sliding surface is constructed as follows: Define the sliding surface function: ， ； in, This represents the state estimate of the extended state observer. Compared with reference value deviation, , ; The equivalent control law is calculated as follows: the derivative of the sliding surface function is taken and set to zero, and the equivalent control law is obtained by combining the estimated value of the extended state observer. The switching control law is calculated as follows: ； in, and To switch the control law gain, , .

7. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 6, characterized in that, The inner loop current control Axis control law and The axis control laws are as follows: ； ； in, and They represent shaft and The derivative of the shaft current reference value; The Axis control law and the aforementioned The differential voltage reference value is obtained by inverse transformation of the output of the axis control law. and .

8. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 3, characterized in that, The method of circulating flow suppression control is as follows: A second extended state observer is designed for the interval state-space model of the DC loop. The second extended state observer estimates the circulating state variables and the corresponding lumped disturbance terms in real time. Based on the estimates from the second extended state observer, a non-singular terminal sliding surface for circulating current suppression is constructed. Combining the equivalent control law and switching control law for circulating current suppression, a common-mode voltage reference value is output. and ; The objective of the circulating current suppression control is to reduce the second harmonic component of the circulating current. shaft and The axis component is controlled to zero.

9. The MMC-HVDC sliding mode control method based on an extended state observer according to claim 1, characterized in that, It also includes outer loop control steps: In DC voltage and reactive power control mode, the outer loop employs a proportional-integral controller, using the deviation between the DC voltage reference value and the actual DC voltage, and the deviation between the reactive power reference value and the actual reactive power, as inputs, to output the inner loop current control. Shaft current reference value and Shaft current reference value; In both active and reactive power control modes, the outer loop employs a proportional-integral controller, using the deviations between the active power reference value and the actual active power, and the deviations between the reactive power reference value and the actual reactive power, as inputs to output the inner loop current control. Shaft current reference value and Shaft current reference value.

10. The MMC-HVDC sliding mode control method based on an extended state observer according to any one of claims 1 to 9, characterized in that, The convergence verification method for the extended state observer is as follows: Constructing Lyapunov functions ,in Let be the observer error vector. To meet A symmetric positive definite matrix, For positive integers, It is the identity matrix; The derivative of the Lyapunov function satisfies: ； in, For the input matrix, This is the upper bound of the derivative of the lumped perturbation term; The error of the extended state observer is uniformly bounded, and its boundary is: .

Images