A passive control method of transformer with virtual inertia and damping simulation function

Abstract

The application discloses a passive control method of a converter with virtual inertia and damping simulation function, which comprises the following steps: constructing a mathematical model of a virtual direct-current motor, combining passive control and virtual direct-current motor compensation to design a controller satisfying various unknown disturbances for a direct-direct converter system, and modulating a pulse for controlling on-off of a switch tube in the direct-direct converter by using the designed controller. The application combines the virtual direct-current motor compensation with the steady-state error problem of the passive controller and provides additional inertia and damping, thereby enhancing the stability of the controller when facing unknown disturbances. Moreover, the passive control method of the converter with virtual inertia and damping simulation function can realize fast response for constant power load, thereby guaranteeing global stability and strong robustness of the system.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and in particular to a passive control method for a DC-DC converter. Background Technology

[0002] To meet today's demand for efficient, clean, and continuous electricity, control system theory and power electronics technology have been developing rapidly. DC-DC converter technology is also playing a significant role in distributed energy generation, aerospace, and shipbuilding, and its importance to my country's economic and technological development has grown considerably. Microgrids can be classified into DC microgrids and AC microgrids based on the type of bus they connect to. DC microgrids fundamentally eliminate the problems of harmonic power balance, reactive power compensation, and the need for reactive power compensation capacitors. Compared to AC microgrids, DC microgrids are simpler to design and less expensive. Therefore, researching the clean, green, and reliable power supply of DC microgrids is of great significance and application value. On the one hand, as more and more electrical loads are converted to power electronic converter-powered loads and servo motor drive systems, their constant power load characteristics result in negative input impedance for load increments, which easily weakens system damping, causes source-load interaction, and induces severe oscillation problems. On the other hand, with a high proportion of new energy sources, new energy storage, and new electrical loads connected to DC microgrids, the characteristics of diversified system entities, complex grid configurations, and diverse operating modes are becoming increasingly apparent. Therefore, linearized control strategies based on steady-state operating points are insufficient to guarantee global system stability. There is an urgent need for a nonlinear control method suitable for DC-DC converters to achieve global system stability.

[0003] Currently, in order to overcome the above-mentioned difficulties, many academic papers and patents have been published and proposed corresponding solutions, such as:

[0004] 1. In the patent application CN202410050273.0 entitled "A DC / DC converter and a control method for a DC / DC converter", Liu Yunlong et al. optimized PID parameters based on the sampled voltage output at both ends of the load and controlled the voltage regulation circuit to control multiple switching transistors and energy storage inductors according to the optimized PID parameters so that the system can achieve stability. However, this method can only guarantee local stability and cannot guarantee global stability.

[0005] 2. In the article entitled "Nonlinear Control of Power Converter Based on Energy Shaping", the author Tian Wei established the Hamiltonian model of DC / DC converter, and used the energy shaping method of interconnection and damping configuration to give the feedback stabilization principle of DC / DC converter, thereby realizing the stability of the system. He also verified that this control method has good robustness and dynamic performance. However, this method cannot eliminate steady-state error when the system is subjected to large disturbances.

[0006] 3. Karanakos P et al. published "Direct Voltage Control of DC–DC Boost Converters Using Enumeration-Based Model Predictive Control" in IEEE Transactions on Power Electronics, 2014, 29(2):968-978. This article derives a discrete-time switching nonlinear (hybrid) model for Boost converters. This model can simultaneously capture continuous and discontinuous conduction modes, achieving optimal control by minimizing the objective function under the dynamic constraints of the model. However, in general, this method uses model predictive control, which has drawbacks such as high computational cost and sensitivity to model parameters. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a passive control method for converters with virtual inertia and damping simulation functions, so as to solve the technical problems that the strong nonlinearity of DC-DC converters themselves and the negative damping characteristics of constant power loads (CPL) in DC microgrids can easily induce severe system oscillations, as well as the difficulty of existing control algorithms in achieving global system stability.

[0008] The present invention provides a passive control method for converters with virtual inertia and damping simulation capabilities, characterized in that it includes:

[0009] 1) The equations for the virtual DC motor armature circuit are established as follows:

[0010]

[0011] Among them, E a =C T Φω, C T Φ is the product of the torque coefficient and magnetic flux of the virtual DC motor, ω is the mechanical angular velocity of the virtual DC motor, U is the terminal voltage of the virtual DC motor, and i a L represents the armature current of the virtual DC motor. a R is the armature inductance of a virtual DC motor. a This is the equivalent resistance of the armature circuit;

[0012] The mechanical equations for the virtual DC motor are as follows:

[0013]

[0014] In the formula, T m T eThe mechanical torque and electromagnetic torque of the virtual DC motor are respectively defined, where J is the moment of inertia, D is the damping coefficient, and ω0 is the rated mechanical angular velocity of the virtual DC motor.

[0015] Establish the mechanical power P of the DC motor m and electromagnetic power P e for:

[0016]

[0017] 2) Design a virtual DC motor compensation controller for the DC-DC converter using virtual DC motor compensation control:

[0018] I Lref =ΔI Lref +P o / v i (4)

[0019] Among them, I Lref P represents the expected current required for passive control after compensation. o For the load-side output power of the DC-DC converter, v i ΔI is the input current of the DC-DC converter. Lref This is the dynamic compensation value for the desired current required for passive control;

[0020]

[0021] Among them, v o This refers to the output voltage of the DC-DC converter.

[0022] 3) Design a passive controller for the DC-DC converter:

[0023] When the DC-DC converter is a single-phase Boost converter, the duty cycle control law of the Boost converter switching transistor is:

[0024]

[0025] Where, r a1 i is the damping coefficient; Lref This represents the expected value of the inductor current after dynamic compensation by the virtual DC motor.

[0026] When the DC-DC converter is a two-phase interleaved parallel Boost converter, the duty cycle control law of the Boost converter switching transistors is:

[0027]

[0028] Where, r a1 r a2 i is the damping coefficient. L1 For the current through the first inductor, iL2 The current flowing through the second inductor;

[0029] 4) Acquire the input current v of the DC-DC converter. i Output voltage v o and output current i o , let v o =U, i o =i a Substitute it into equations (1) to (5) to calculate the expected current value I. Lref The collected DC-DC converter input current, output voltage, inductor current and the calculated current expectation value are input into equation (6) or (7) to calculate the duty cycle control law d. The pulse of switching on and off in the Boost converter is modulated according to the duty cycle control law d.

[0030] The beneficial effects of this invention are:

[0031] This invention presents a passive converter control method with virtual inertia and damping simulation capabilities. By designing a passive controller through damping injection, it achieves output voltage stability under large-scale system disturbances. Furthermore, it dynamically compensates for the desired current required for passive control by designing a virtual DC motor, providing additional inertia and damping, thus eliminating the steady-state error problem inherent in passive controllers and further improving system robustness. Moreover, this passive converter control method with virtual inertia and damping simulation capabilities enables rapid response to constant power loads (CPL), ensuring the global stability of the system. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating a passive control method for a converter with virtual inertia and damping simulation capabilities. The diagram shows the structure of a two-phase interleaved parallel Boost converter, which includes a first inductor L1, a second inductor L2, a first switch Q1, a second switch Q2, a first diode S1, a second diode S2, and an output capacitor C. o The collector of the first switching transistor Q1 is connected to the anode of the first diode S1, and the emitter of the first switching transistor Q1 is connected to the cathode of the DC power supply. The two ends of the first inductor L1 are connected to the anode of the DC power supply and the anode of the first diode S1, respectively. The collector of the second switching transistor Q2 is connected to the anode of the second diode S2, and the emitter of the second switching transistor Q2 is connected to the cathode of the DC power supply. The two ends of the second inductor L2 are connected to the anode of the DC power supply and the anode of the second diode S2, respectively. The cathodes of the first diode S1 and the second diode S2 are connected to the output capacitor C. o The terminals are connected, and the emitter of the first switching transistor Q1 and the emitter of the second switching transistor Q2 are connected to the output capacitor C. oThe other terminal is connected. The pulse signals controlling the first switch Q1 and the second switch Q2 are respectively input to their bases.

[0033] Figure 2 This is a block diagram of virtual DC motor compensation.

[0034] Figure 3 To bring the Boost converter port fully loaded with CPL(P) CPL =3KW), when the input voltage changes sequentially at intervals of 0.01s from 100V, 110V, 120V, 110V, and 100V, the input voltage v i Output voltage v o Inductor current i L1 i L2 Total input current i i Waveform diagram.

[0035] Figure 4 To enable a step change CPL at the Boost converter port, the input rated voltage v i =110V, total load power P CPL The total load power P varies sequentially with values ​​of 1000W, 1500W, 3000W, 1500W, and 1000W at 0.01s intervals. CPL Output voltage v o and inductor current i L1 i L2 Total input current i i Waveform diagram. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] The mathematical model of a unidirectional Boost converter is as follows:

[0038]

[0039] Where L is the inductance of the Boost converter, C is the capacitance of the Boost converter, and i L For the inductor current of the Boost converter, v o v is the output voltage of the Boost converter. i d is the input voltage of the Boost converter, d is the duty cycle of the Boost converter's switching transistor, and p is the constant power load of the Boost converter.

[0040] Representing the mathematical model of the Boost converter in matrix form, we obtain the Euler-Lagrange mathematical model of the Boost converter as follows:

[0041]

[0042] in,

[0043]

[0044]

[0045] To address the steady-state error problem inherent in passive control and further suppress output voltage fluctuations of the Boost converter under varying input voltage and load conditions, this embodiment employs a virtual DC motor-compensated DC-DC converter control method with virtual inertia and damping simulation capabilities. Additional virtual inertia and damping are injected into the converter to suppress steady-state errors and fluctuations in the output voltage. The specific method is as follows:

[0046] 1) The equations for the virtual DC motor armature circuit are established as follows:

[0047]

[0048] Among them, E a =C T Φω, C T Φ is the product of the torque coefficient and magnetic flux of the virtual DC motor, ω is the mechanical angular velocity of the virtual DC motor, U is the terminal voltage of the virtual DC motor, and i a L represents the armature current of the virtual DC motor. a R is the armature inductance of a virtual DC motor. a It is the equivalent resistance of the armature circuit.

[0049] The mechanical equations for the virtual DC motor are as follows:

[0050]

[0051] In the formula, T m T e The mechanical torque and electromagnetic torque of the virtual DC motor are respectively defined, where J is the moment of inertia, D is the damping coefficient, and ω0 is the rated mechanical angular velocity of the virtual DC motor.

[0052] Establish the mechanical power P of the DC motor m and electromagnetic power P e for:

[0053]

[0054] 2) Design a virtual DC motor compensation controller for the DC-DC converter using virtual DC motor compensation control:

[0055] according to Figure 2As shown in the block diagram of virtual DC motor compensation, the mechanical power P of the virtual DC motor is obtained by multiplying the output of the PI controller by the expected value of the output voltage. m Furthermore, the virtual mechanical torque T can be obtained. m Based on the above three equations, the control loop for the virtual DC motor is designed to give the Boost converter the same external characteristics as a DC motor, thus obtaining additional damping and inertia. When the CPL power fluctuates, the expected change in the converter current ΔI can be obtained. Lref Therefore, when the CPL fluctuates, the dynamic compensation value of the desired current required for passive control is:

[0056]

[0057] Therefore, the expected current required for passive control after compensation is:

[0058] I Lref =ΔI Lref +P o / v i (5)

[0059] Among them, I Lref P represents the expected current required for passive control after compensation. o For the load-side output power of the DC-DC converter, v i This is the input current of the DC-DC converter.

[0060] Among them, v o This is the output voltage of the DC-DC converter.

[0061] 3) Design a passive controller:

[0062] Let the state error vector be e = xx * The Euler-Lagrange mathematical model of the Boost converter can be expressed as:

[0063]

[0064] Where, x * Let be the expected value of the state variable. For x * The derivative, It is the derivative of e.

[0065] The error energy storage function can be expressed as:

[0066]

[0067] To make H e (x) converges rapidly to zero, requiring damping injection to increase the damping factor. Damping injection r a It can be represented as:

[0068]

[0069] In the formula, r a1 r a2 The damping coefficient;

[0070] The error Euler-Lagrange mathematical model can then be expressed as:

[0071]

[0072] The passive controller u can be represented as:

[0073]

[0074] Therefore, we can conclude that:

[0075]

[0076] H e The derivative of (x) with respect to time can be expressed as:

[0077]

[0078] As shown in the above equation, the error energy storage function can converge to 0, and its convergence rate depends on R. Bo +R a Therefore, the fast convergence condition for the passive controller is R. Bo +R a >0.

[0079] Because x * Since it is a given constant, therefore Then we can obtain:

[0080] The duty cycle control law for the switching transistors of a single-phase Boost converter is:

[0081]

[0082] Where, r a1 i is the damping coefficient; Lref This represents the expected value of the inductor current after dynamic compensation by the virtual DC motor.

[0083] Solving the above equation yields:

[0084]

[0085] It can be seen that using this passive controller enables the inductor current to quickly track the desired current value.

[0086] Considering the complementary cancellation of the two-phase inductor currents and the fact that both can quickly track the reference current, the duty cycle control law for the switching transistors of the two-phase interleaved parallel Boost converter is as follows:

[0087]

[0088] Where, r a1 r a2 i is the damping coefficient. L1 For the current through the first inductor, i L2 This represents the current flowing through the second inductor.

[0089] 4) Acquire the input current v of the DC-DC converter. i Output voltage v o and output current i o , let v o =U, i o =i a Substitute it into equations (1) to (5) to calculate the expected current value I. Lref The collected DC-DC converter input current, output voltage, inductor current and the calculated current expectation value are input into equation (6) or (7) to calculate the duty cycle control law d. The pulse of switching on and off in the Boost converter is modulated according to the duty cycle control law d.

[0090] The passive control method for converters with virtual inertia and damping simulation functions described in this embodiment is used below to... Figure 1 The two-phase interleaved parallel Boost converter shown was simulated and its control verified.

[0091] Simulation Verification 1: Settings Figure 1 The interleaved parallel Boost converter shown has a full-load power of 3000W and an output voltage reference value of v. oref 270V, rated input voltage v i 110V, input variable voltage range v i 100-120V, switching frequency f s The frequency is 300kHz, the inductance L is 0.1mH, and the capacitance C is 47μF. Figure 3 To bring the Boost converter port fully loaded with CPL(P) CPL =3KW), when the input voltage changes sequentially at intervals of 0.01s from 100V, 110V, 120V, 110V, and 100V, the input voltage v i Output voltage v o Inductor current i L1 i L2 Total input current i i Waveform diagram.

[0092] from Figure 3The output voltage v can be seen in the image. o Dynamic adjustment time t s The duration is approximately 250 μs, the maximum surge voltage is 270.2 V, and the overshoot σ = 0.074%; the minimum instantaneous voltage drop is 269.9 V, the sag rate is 0.037%, and the output voltage v o It exhibits small fluctuations, quickly tracks reference values, has a fast dynamic response, and provides good adjustment performance. Two-phase inductor current i L1 and i L2 Both can effectively track the desired current after dynamic compensation, achieving current sharing, and the complementary cancellation of ripples reduces the total input current i i The ripple is relatively small.

[0093] Simulation Verification 2: The difference from Simulation Verification 1 is that the rated input voltage v of the Boost converter... i =110V, port with step change CPL, P CPL The power levels were changed sequentially at intervals of 0.01 seconds: 1000W, 1500W, 3000W, 1500W, and 1000W. Figure 4 To enable a step change CPL at the Boost converter port, the input rated voltage v i =110V, total load power P CPL The total load power P varies sequentially with values ​​of 1000W, 1500W, 3000W, 1500W, and 1000W at 0.01s intervals. CPL Output voltage v o and inductor current i L1 i L2 Total input current i i Waveform diagram.

[0094] from Figure 3 The output voltage v can be seen in the image. o Maximum dynamic adjustment time t s The time to voltage drop is approximately 330 μs, the maximum surge voltage is 271.8 V, and the overshoot σ = 0.667%; the minimum instantaneous voltage drop is 267.6 V, the drop rate is 0.889%, and the output voltage v o It exhibits minimal fluctuations, quickly tracks reference values, demonstrates rapid dynamic response, and provides excellent regulation. Two-phase inductor current i L1 and i L2 Both can effectively track the desired current after dynamic compensation, achieving current sharing, and the complementary cancellation of ripples reduces the total input current i i The ripple is relatively small.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A passive control method for a converter with virtual inertia and damping simulation functions, characterized in that: include: 1) The equations for the virtual DC motor armature circuit are established as follows: Among them, E a =C T Φω, C T Φ is the product of the torque coefficient and magnetic flux of the virtual DC motor, ω is the mechanical angular velocity of the virtual DC motor, U is the terminal voltage of the virtual DC motor, and i a L represents the armature current of the virtual DC motor. a R is the armature inductance of a virtual DC motor. a The equivalent resistance of the armature circuit; The mechanical equations for the virtual DC motor are as follows: In the formula, T m T e The mechanical torque and electromagnetic torque of the virtual DC motor are respectively defined, where J is the moment of inertia, D is the damping coefficient, and ω0 is the rated mechanical angular velocity of the virtual DC motor. Establish the mechanical power P of the DC motor m and electromagnetic power P e for: 2) Design a virtual DC motor compensation controller for the DC-DC converter using virtual DC motor compensation control: I Lref =ΔI Lref +P o / v i (4) Among them, I Lref P represents the expected current required for passive control after compensation. o For the load-side output power of the DC-DC converter, v i ΔI is the input current of the DC-DC converter. Lref This is the dynamic compensation value for the desired current required for passive control; Among them, v o This refers to the output voltage of the DC-DC converter. 3) Design a passive controller for the DC-DC converter: When the DC-DC converter is a single-phase Boost converter, the duty cycle control law of the Boost converter switching transistor is: Where, r a1 i is the damping coefficient; Lref This represents the expected value of the inductor current after dynamic compensation by the virtual DC motor. When the DC-DC converter is a two-phase interleaved parallel Boost converter, the duty cycle control law of the Boost converter switching transistors is: Where, r a1 r a2 i is the damping coefficient. L1 For the current flowing through the first inductor, i L2 The current flowing through the second inductor; 4) Acquire the input current v of the DC-DC converter. i Output voltage v o and output current i o , let v o =U,i o =i a Substitute it into equations (1) to (5) to calculate the expected current value I. Lref The collected DC-DC converter input current, output voltage, inductor current and the calculated current expectation value are input into equation (6) or (7) to calculate the duty cycle control law d. The pulse of switching on and off in the Boost converter is modulated according to the duty cycle control law d.

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