Inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator

Abstract

The invention discloses an adaptive virtual inertia control method for an inverter based on an Andronov-Hopf oscillator, and relates to the technical field of network-forming inverter control. The invention aims to solve the problem that the stability and reliability of a power system can be damaged by control based on an oscillator. According to the invention, the difference between the output current of the inverter and the reference current is obtained, and the difference passes through an inertia link to obtain an input current error signal of the oscillator; the difference between the active power reference value and the actual value of the inverter is obtained, and the difference is subjected to active-frequency control with self-adaptive virtual inertia to obtain the angular frequency of the oscillator; the reactive power reference value and the actual value of the inverter are subtracted, and the difference value is subjected to reactive-voltage control with a PI controller to obtain the voltage amplitude of an oscillator; the voltage generated by the Andronov-Hopf oscillator is calculated through the Andronov-Hopf oscillator, the voltage passes through the integrator to obtain SVPWM reference voltage, the three-phase voltage source inverter is modulated, and grid-connected control is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of grid-type inverter control. Background Art

[0002] Virtual oscillator control (VOC) is an emerging grid-forming inverter control that simulates the near-sinusoidal oscillation response of a weakly nonlinear limit cycle oscillator. VOC can spontaneously generate periodic voltage, provide voltage support, and achieve communication-free synchronization and power sharing. Within an AC cycle, the average dynamics of the VOC output voltage and frequency have an embedded nonlinear droop law, providing grid-forming control capabilities. Compared with droop control, VOC operates in the time domain and has faster dynamic response and lower harmonic content.

[0003] Inspired by the consensus of multi-agent networks, various oscillator-based controllers have been proposed, such as the Andronov-Hopf oscillator, which is a network control based on instantaneous current feedback and provides almost global synchronization and dispatchability. However, the oscillator-based control is an inertia-free first-order controller that is easily affected by load or frequency disturbances. Inertia plays a vital role in maintaining the frequency stability of the power system. Insufficient inertia will deteriorate the frequency minimum point and undermine the stability and reliability of the power system. Summary of the invention

[0004] The present invention aims to solve the problem that the control based on the oscillator is a first-order controller without inertia, and the insufficient inertia will deteriorate the lowest frequency point and destroy the stability and reliability of the power system. An inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator is provided.

[0005] The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator includes:

[0006] The output current of the inverter is subtracted from the reference current, and the difference is passed through the inertia link to obtain the oscillator input current error signal;

[0007] The active power reference value of the inverter is subtracted from the actual value, and the difference is used to obtain the oscillator angular frequency through active-frequency control with adaptive virtual inertia;

[0008] The reactive power reference value of the inverter is subtracted from the actual value, and the obtained difference is used to obtain the oscillator voltage amplitude through reactive-voltage control with a PI controller;

[0009] The oscillator input current error signal, oscillator angular frequency and oscillator voltage amplitude are passed through an Andronov-Hopf oscillator to calculate the voltage generated by the Andronov-Hopf oscillator, and the voltage is then passed through an integrator to obtain an SVPWM reference voltage, which is used to modulate a three-phase voltage source inverter to achieve grid-connected control.

[0010] Furthermore, the above-mentioned subtracting the output current of the inverter from the reference current and obtaining the oscillator input current error signal through the inertia link includes:

[0011]

[0012] Among them, i eα and i eβ are the α-axis and β-axis components of the oscillator input current error signal, i α and i β They are the α-axis and β-axis components of the inverter output current, and are the α-axis and β-axis components of the inverter reference current, T is the inertia time constant, and s is the complex parameter of the Laplace transform.

[0013] Furthermore, the expressions of the α-axis and β-axis components of the inverter reference current in the stationary α-β reference frame are as follows:

[0014]

[0015] Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, P * and Q * They are the active power and reactive power reference values ​​of the inverter respectively.

[0016] Furthermore, the above-mentioned difference between the active power reference value of the inverter and the actual value is made, and the obtained difference is used to obtain the oscillator angular frequency through active-frequency control with adaptive virtual inertia, including:

[0017] ω=ω * +ω s =ω * +∫f(ω s ,P rsrv )dt,

[0018] Where, ω is the oscillator angular frequency, ω * is the rated angular frequency of the oscillator, ω s is the angular frequency offset, P rsrv is the reserved power and Prsrv=P*-P, P *and P are the active power reference value and actual value of the inverter respectively, f(ω s ,P rsrv ) represents ω s The first derivative of .

[0019] Furthermore, the above ω s The first-order derivative expression of is as follows:

[0020]

[0021] Among them, J0 is the nominal constant inertia of the adaptive virtual inertia mathematical equation, k is the positive inertia compensation coefficient, D m is the nominal damping coefficient.

[0022] Furthermore, the expression of the actual value P of the active power of the above inverter is as follows:

[0023]

[0024] Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, respectively, i α and i β They are the α-axis and β-axis components of the inverter output current respectively.

[0025] Furthermore, the reactive power reference value of the inverter is subtracted from the actual value, and the obtained difference is used to obtain the oscillator voltage amplitude through reactive-voltage control with a PI controller, including:

[0026]

[0027] Among them, V h is the oscillator voltage amplitude, V * is the voltage amplitude reference value, k p and k i are the proportional and integral coefficients of the PI controller, s is the complex parameter of the Laplace transform, Q * and Q are the reactive power reference value and actual value of the inverter respectively.

[0028] Furthermore, the expression of the actual value Q of reactive power of the above inverter is as follows:

[0029]

[0030] Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, respectively, i α and i β They are the α-axis and β-axis components of the inverter output current respectively.

[0031] Furthermore, the above-mentioned passing the oscillator input current error signal, the oscillator angular frequency and the oscillator voltage amplitude through the Andronov-Hopf oscillator to calculate the voltage generated by the Andronov-Hopf oscillator includes:

[0032]

[0033] Among them, μ is the oscillator convergence speed control coefficient, K i is the current error amplification factor, V h is the oscillator voltage amplitude, i eα and i eβ are the α-axis and β-axis components of the oscillator input current error signal, ω is the oscillator angular frequency, V α and V β They are the α-axis and β-axis components of the oscillator voltage respectively.

[0034] Based on comprehensive consideration of the rate of change of frequency (ROCOF) and power oscillation requirements, the present invention proposes an adaptive virtual inertia control method for inverters based on an Andronov-Hopf oscillator, which provides virtual inertia for frequency response, so as to better adapt to the large-scale access requirements of new energy sources in modern power systems. The improved Andronov-Hopf controller can effectively provide the power system with a suitable inertia ratio and damping ratio, and provides sufficient inertia to mitigate the frequency change rate of the power system, while having a smaller power overshoot. When the inverter output power or current changes suddenly, the system's ROCOF can be alleviated. Improving frequency stability issues under large-scale access of inverters to power systems BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 To improve the structure of the three-phase inverter based on Andronov-Hopf oscillator by using adaptive virtual inertia, V dc is the DC voltage, V g is the three-phase grid voltage, L f is the inverter side inductance, L g is the grid-side inductance, R g is the grid side resistance, i abc The inverter outputs three-phase current, P * and Q * are the reference values ​​of active power and reactive power respectively, ω * is the rated angular frequency of the AC side;

[0036] Figure 2 It is the inverter power output curve diagram when the inverter is connected to the grid;

[0037] Figure 3It is the inverter angular frequency output curve diagram when the inverter is connected to the grid;

[0038] Figure 4 It is the three-phase line voltage output curve diagram of the inverter when the inverter is connected to the grid;

[0039] Figure 5 This is the inverter three-phase current output curve when the inverter is running in grid connection. DETAILED DESCRIPTION

[0040] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0041] The nonlinear droop characteristics embedded in the Andronov-Hopf dynamic response cannot provide inertia for the power system. In order to expand the application scope of Andronov-Hopf, it is necessary to add appropriate inertial response to the traditional Andronov-Hopf oscillator. The details are as follows:

[0042] The inverter adaptive virtual inertia control method based on the Andronov-Hopf oscillator described in this embodiment includes the following steps:

[0043] Step 1: Set the inverter output current (i α with i β ) and the reference current ( and ) is used to make a difference, and the difference is obtained through the inertia link to obtain the oscillator input current error signal (i eα and i eβ ), so that the inverter based on Andronov-Hopf oscillator has adjustable inertial damping.

[0044] Specifically, the reference current expression in the stationary α-β reference frame is as follows:

[0045]

[0046] In the formula, and are the α-axis and β-axis components of the inverter reference current, V α and V β are the α-axis and β-axis components of the oscillator voltage, P * and Q *They are the active power and reactive power reference values ​​of the inverter respectively.

[0047] The expression of inertia link G(s) is:

[0048]

[0049] Where T is the inertia time constant and s is the complex parameter of Laplace transform.

[0050] The oscillator input current error signal i is obtained eα and i eβ :

[0051]

[0052] In the formula, i eα and i eβ are the α-axis and β-axis components of the oscillator input current error signal, i α and i β They are the α-axis and β-axis components of the inverter output current respectively.

[0053] The oscillator input current error signal is obtained through the inertia link, and the inverter based on the Andronov-Hopf oscillator has adjustable inertia damping.

[0054] Step 2: Set the inverter active power reference value P * The actual value of active power P is subtracted and the oscillator angular frequency signal is obtained through active power-frequency control with adaptive virtual inertia.

[0055] Specifically, the active power P output by the inverter is expressed as follows:

[0056]

[0057] In order to provide an equivalent inertial response, the Andronov-Hopf reference power can be directly adjusted by the PD controller to compensate for the difference between the desired frequency and the actual frequency. However, the additional differential loop amplifies the noise generated by the frequency calculation and causes unexpected instability. To overcome the above shortcomings, this embodiment proposes an adaptive virtual inertia method to support frequency stability, specifically:

[0058] When the frequency deviates from the nominal reference, the system responds slowly, so a larger inertia should be used; when the frequency returns to the nominal frequency, a smaller inertia should be used to accelerate the system dynamics. This method combines the advantages of large inertia and small inertia to improve the frequency regulation performance. To this end, a concise and unified adaptive virtual inertia mathematical equation is constructed:

[0059]

[0060] From formula (7), we can see that the construction inertia consists of two terms: the first term J0 is the nominal constant inertia, and the second term is the adaptive compensation inertia. ω and ω * are the actual angular frequency and rated angular frequency of the oscillator respectively. k is the positive inertia compensation coefficient, which can dynamically adjust the frequency response speed. In fact, the total moment of inertia J is calculated based on the relative angular frequency ω-ω * and its rate of change In particular, in the nominal steady state ω = ω * In this case, the adaptive compensation inertia is 0 and the total inertia J is equal to J0.

[0061] In formula (7), it is worth noting that since the frequency derivative is sensitive to measurement noise, if the adaptive inertia value is directly calculated, it will be inaccurate. Therefore, the constructed formula (7) is combined with the steady-state active power-frequency droop characteristics of the oscillator with inertia link to obtain:

[0062]

[0063] Where D m is the nominal damping coefficient, ω s is the angular frequency offset, and:

[0064] ω s =ω-ω * (9).

[0065] Rewrite equation (8):

[0066]

[0067] In the formula, ω s The first derivative of rsrv is the reserved power, and there are:

[0068] P rsrv =P * -P (11).

[0069] Obviously, formula (10) is the variable The quadratic equation is . According to Vieta's theorem, the two roots are solved as:

[0070]

[0071] because and In formula (8), they may exist simultaneously, so only one root of formula (12) is valid, which is derived as follows:

[0072]

[0073] In order to avoid singularities (ω s =0), rewrite equation (13) by rationalizing the denominator:

[0074]

[0075] Then, combining equation (8) and equation (14), we can get the improved angular frequency ω based on the adaptive virtual inertia algorithm:

[0076] ω=ω * +ω s =ω * +∫f(ω s ,P rsrv )dt (15).

[0077] From equation (15), we can see that the angular frequency is a function of the output active power, the control input is the real-time active power, and the control output is the angular frequency reference value. The control algorithm with adaptive virtual inertia is added, which avoids the frequency derivative term. Therefore, the proposed control scheme is simple and practical.

[0078] Step 3: Set the reactive power reference value Q * The voltage amplitude signal of the oscillator is obtained by subtracting the reactive power Q output by the inverter through reactive-voltage control with a PI controller.

[0079] Specifically, the reactive power Q output by the inverter is expressed as follows:

[0080]

[0081] Due to the strong nonlinear dynamics of Andronov-Hopf with respect to amplitude, an additional PI controller is used to track reactive power using the QV droop relationship. A dual-channel controller corresponding to P and Q is designed according to the power reference. The PI controller based on the droop relationship converts the reactive error into an amplitude voltage reference error. Since reactive power is independently controlled, to simplify the calculation, Q in formula (1) can be * Therefore, the Andronov-Hopf oscillator with current feedback and amplitude regulation can generate a reference voltage while being synchronized with the input signal.

[0082] The reactive power reference value Q * The difference between the reactive power Q output by the inverter and the reference value of the oscillator voltage deviation is obtained through the PI controller, which is compared with the voltage amplitude reference value V * The sum is the Andronov-Hopf oscillator voltage amplitude V h ;

[0083]

[0084] In the formula, kp and k i are the proportional and integral coefficients of the PI controller, respectively, which can be optimized using the Ziegler-Nichols method.

[0085] Step 4: Generate the voltage derivative value in the stationary α-β reference frame through the Andronov-Hopf oscillator as follows:

[0086]

[0087] Where μ is the oscillator convergence speed control coefficient, K i is the current error amplification factor;

[0088] The Andronov-Hopf oscillator acts as a synchronous current error and subsequent voltage reference in the α-β framework. Therefore, the amplitude regulation and phasor are integrated into a second-order differential equation. In terms of phasor, the reference current and As an external period input, the Andronov-Hopf oscillator controller has the ability to synchronize with current feedback.

[0089] The Andronov-Hopf oscillator output voltage (V α With V β ) The SVPWM reference voltage is obtained through the integrator, and the three-phase voltage source inverter is modulated by SVPWM to achieve grid-connected control.

[0090] In order to prove the effectiveness of the inverter adaptive virtual inertia control method based on the Andronov-Hopf oscillator described in this embodiment, a three-phase grid-connected inverter structure is used to test its virtual inertia effect and frequency regulation capability. The details are as follows:

[0091] The initial active power reference value is 2000W. After a period of time, the active power reference value is increased to 4000W, and the reactive power reference value is always 0 to prove the frequency regulation capability of this implementation. Figure 1 The parameters of the components of the three-phase inverter are shown in Table 1:

[0092] Table 1 Three-phase inverter parameters

[0093]

[0094] from Figure 2 It can be seen that the inverter output active power can accurately follow the given active power reference value with a small power overshoot, and the inverter output reactive power can also be accurately kept near 0.

[0095] from Figure 3It can be seen that when the active power reference value changes suddenly, the inverter output angular frequency changes very little. It can be seen that the frequency regulation strategy proposed in this embodiment can effectively provide a suitable inertia ratio and damping ratio for the power system, and provide sufficient inertia to alleviate the frequency change rate of the power system. When the inverter output power changes suddenly, the ROCOF of the system can be effectively alleviated.

[0096] from Figure 4 and Figure 5 It can be seen that the three-phase line voltage output by the inverter will be stably maintained at around 380V, and the three-phase current output by the inverter will be adjusted accordingly with the change of the active power reference value, outputting the same amount of active power, providing network control capability.

[0097] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. An inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator, characterized in that: include: The output current of the inverter is subtracted from the reference current, and the difference is passed through the inertia link to obtain the oscillator input current error signal; The active power reference value of the inverter is subtracted from the actual value, and the difference is used to obtain the oscillator angular frequency through active-frequency control with adaptive virtual inertia; The reactive power reference value of the inverter is subtracted from the actual value, and the obtained difference is used to obtain the oscillator voltage amplitude through reactive-voltage control with a PI controller; The oscillator input current error signal, oscillator angular frequency and oscillator voltage amplitude are passed through an Andronov-Hopf oscillator to calculate the voltage generated by the Andronov-Hopf oscillator, and the voltage is then passed through an integrator to obtain an SVPWM reference voltage, which is used to modulate a three-phase voltage source inverter to achieve grid-connected control.

2. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 1, characterized in that: The step of making a difference between the output current of the inverter and the reference current, and obtaining the difference through an inertia link to obtain an oscillator input current error signal includes: Among them, i eα and i eβ are the α-axis and β-axis components of the oscillator input current error signal, i α and i β are the α-axis and β-axis components of the inverter output current, and are the α-axis and β-axis components of the inverter reference current, T is the inertia time constant, and s is the complex parameter of the Laplace transform.

3. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 2 is characterized in that: The expressions of the α-axis and β-axis components of the inverter reference current in the stationary α-β reference frame are as follows: Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, P * and Q * They are the active power and reactive power reference values ​​of the inverter respectively.

4. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 1, characterized in that: The method of subtracting the active power reference value of the inverter from the actual value and obtaining the oscillator angular frequency by active-frequency control with adaptive virtual inertia comprises: oh = oh * +oh s =ω * +∫f(ω s ,P rsrv )dt, Where, ω is the oscillator angular frequency, ω * is the rated angular frequency of the oscillator, ω s is the angular frequency offset, P rsrv is the reserved power and Prsrv=P*-P, P * and P are the active power reference value and actual value of the inverter respectively, f(ω s ,P rsrv ) represents ω s The first derivative of .

5. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 4 is characterized in that: The ω s The first-order derivative expression of is as follows: Among them, J0 is the nominal constant inertia of the adaptive virtual inertia mathematical equation, k is the positive inertia compensation coefficient, D m is the nominal damping coefficient.

6. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 5, characterized in that: The expression of the actual value P of the active power of the inverter is as follows: Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, respectively, i α and i β They are the α-axis and β-axis components of the inverter output current respectively.

7. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 1, characterized in that: The method of subtracting the reactive power reference value of the inverter from the actual value and obtaining the oscillator voltage amplitude by reactive-voltage control with a PI controller comprises: Among them, V h is the oscillator voltage amplitude, V * is the voltage amplitude reference value, k p and k i are the proportional and integral coefficients of the PI controller, s is the complex parameter of the Laplace transform, Q * and Q are the reactive power reference value and actual value of the inverter respectively.

8. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 7, characterized in that: The expression of the actual value Q of reactive power of the inverter is as follows: Among them, V α and V β are the α-axis and β-axis components of the oscillator voltage, respectively, i α and i β They are the α-axis and β-axis components of the inverter output current respectively.

9. The inverter adaptive virtual inertia control method based on Andronov-Hopf oscillator according to claim 1, characterized in that: The step of passing the oscillator input current error signal, the oscillator angular frequency and the oscillator voltage amplitude through an Andronov-Hopf oscillator to calculate the voltage generated by the Andronov-Hopf oscillator comprises: Among them, μ is the oscillator convergence speed control coefficient, K i is the current error amplification factor, V h is the oscillator voltage amplitude, i eα and i eβ are the α-axis and β-axis components of the oscillator input current error signal, ω is the oscillator angular frequency, V α and V β They are the α-axis and β-axis components of the oscillator voltage respectively.

Images