Control method for transducers with virtual inertia

Abstract

The present disclosure relates to a method for controlling a power converter coupled to an electric grid. The method includes: acquiring an output power of the power converter, an electrical parameter of the power converter, and an electrical parameter of the electric grid; determining a power control error based on the output power of the power converter and a reference power; determining a rotational frequency of the inertial model based on an inertial model that uses the power control error as an input, the inertial model being a mathematical model of the inertia of the machine; determining a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter according to at least one control path different from the control path including the inertial model, the phase angle being a target angle between the electrical parameter of the power converter and the electrical parameter of the electric grid; and determining a coupling impedance, the coupling impedance being a preset value determined before operation of the power converter and determined based on a differential phase angle in two iterations and a differential output power of the power converter in two iterations, and / or determined based on the determined phase angle and a reference expected phase angle; and controlling the power converter based on the phase angle and the coupling impedance. The present disclosure also relates to a corresponding apparatus and a computer-readable medium.

Description

[Technical Field]

[0001] Technical Field The present disclosure relates to methods, apparatus, computer-readable media, and systems for controlling power converters coupled to an electrical grid. [Background technology]

[0002] background Historically, the electrical grid was primarily equipped with synchronous generators (SGs), but now includes an increasing number of new renewable energy sources, such as photovoltaic (PV) solar panels and wind turbines, connected to the grid by power electronic inverters. However, the characteristics of inverter-based resources (IBRs) differ from those of synchronous generators, e.g., with inertia and high fault currents, which impacts the operation of the electrical grid, especially under the assumption that SGs are dominant within the grid. In particular, the behavior of high-speed inverters has led to large frequency fluctuations, instability, and power grid outages.

[0003] Figure 1 shows a conventional synchronous generator and its corresponding control system. SGs are rotating machines typically driven by turbines (steam, gas, or hydro) or engines (diesel or heavy oil), and therefore have inherent inertia. With additional control of speed and voltage, the generators passively share and balance power generation among themselves, maintaining grid frequency within a fixed band without communication. SGs also provide a large fault current capability that allows protection systems to operate quickly and reliably. Furthermore, SGs have several inherent attributes that make them compliant, as shown in Figure 2. The system in Figure 2 includes parallel-connected generators, each with its own regulator, inertia, and output impedance. When there is a load change, the initial portion of the load change carried by the SG is determined by how strongly the SG is coupled to that load change. SGs with higher impedance from stator and transformer leakage and line impedance pick up less of the load change than those with lower impedance coupling. Inertia affects the subsequent dynamic behavior of load sharing, with larger pickups being carried by generators with higher inertia. Following the inertial response, the frequency controller strength and frequency droop coefficient determine how much the generator contributes to grid disturbances, and the frequency droop determines the steady-state portion of the load that is shared (if secondary / tertiary control is not used).

[0004] Figure 3 shows a typical three-phase, two-level power electronic inverter and its controller. In contrast to the inherent characteristics of SGs, IBRs exhibit limited energy storage in either the DC bus capacitor (used only to smooth DC ripple) or the output filter (low-value inductors and capacitors are used), and are inherently unable to provide grid inertia. Furthermore, they also provide low fault currents. Typically, IBRs are controlled to follow the grid, which does not require additional energy storage capacity, but this requires a relatively rigid grid to operate, and SGs provide grid stiffness and fault current.

[0005] Inverters can be controlled to act like voltage sources, forming so-called grid-forming inverters (GFMIs). Using GFMIs in a grid can increase grid stiffness and reduce instabilities within the grid, but such inverters are often too stiff. As a result, transient load fluctuations in the grid are picked up by the GFMIs, which shield these fluctuations from other slow-response generators, such as SGs. Furthermore, normal grid transients, such as phase jumps, can generate large transient currents in the rigid GFMIs.

[0006] The inertia of the SG can be virtually mimicked by the IBR using a control method. A Virtual Synchronous Machine (VSM) controller is used with an energy storage unit to add an SG-based response, thereby mimicking the response of the SG. Figure 4 shows a Virtual Synchronous Machine (VSM) control system with five components. VSM in this specification refers to an electrical machine that mimics at least one behavior, particularly the physical behavior, more specifically the inertia, of a synchronous machine, by a control system designed to generate at least one parameter used for the mimicry. The first component is a virtual impedance R v +jX v and has a response similar to the impedance at the output of the SG. This virtual impedance is the key to creating a GFMI that can be in parallel with other GFMIs, SGs and the grid. v vs. R vThe ratio allows the VSM to have a strong coupling between active power and phase angle, a strong coupling between reactive power and voltage magnitude, and a decoupling of these two relationships. The rotor flux model and automatic voltage regulator (AVR) make the reactive power / voltage magnitude dynamics like those of an SG, so there is a significant degree of commonality between transient and regulatable dynamics. Similarly, the inertia model and frequency governor make the VSM have active power / frequency dynamics like an SG.

[0007] Figure 5a) is a voltage source (V A ) to the grid (represented by V G Figure 5b) shows the electrical equivalent circuit network of the power system, which is coupled to the voltage source V by a coupling impedance R+jX. Figure 5b) shows the phasor diagram with parameters of the electrical equivalent circuit network of the power system shown in Figure 5a). Equations (1) and (2) describe the complete equations for the active and reactive power flows between them. A represents the internal voltage within the GFMI. The active and reactive power flows from the GFMI voltage source are given by:

[0008]

number

[0009]

number

[0010] For a predominantly inductive grid, the above two equations can be simplified to:

[0011]

number

[0012]

number

[0013] For small δ, equation (3) can be further simplified as follows:

[0014]

number

[0015] In most grids, X is fixed and V A &V G is usually constant, so equation (5) can be simplified to:

[0016]

number

[0017] The power transferred to the grid from GFMIs, including those with VSM control, is approximately proportional to the power angle. Set may be used to set the VSM power.

[0018] Figure 6a) shows the control block diagram, or equivalently the State Block Diagram (SBD), of a VSM connected to a power system. The control scheme in Figure 6a calculates the output power P of the power converter given the voltage of the power converter and the voltage electrical parameters of the electrical grid. Act The relationship between the reference power P Set is used to determine the power control error. Act The inertia model of the SG is expressed in a control block containing (1 / 2H) and (1 / s). The damping parameter K d The control path is also shown, including a damping model including the grid frequency F grid is a mathematical construct to aid in the analysis and is therefore shown for completeness, but may be omitted from the control system analysis as is done in the calculations disclosed herein. SetVarying the value of P changes the input to the inertia and damping block, indirectly affecting the power angle δ. Since the system is closed loop, P Set The new value of δ required to achieve ≡ ...

[0019]

number

[0020] This is a second-order system with the following resonant frequencies:

[0021]

number

[0022] The damping coefficient is

[0023]

number

[0024] and the critical damping is

[0025]

number

[0026] Figure 6b) shows the pole-zero map of the control loop shown in Figure 6a), and Figure 6c) shows the case where the inertia is set to 1.5 seconds and the effective inductive coupling is damped by K d Figure 6a) shows the response of the system set to 0.1 pu for various values ​​of the SBD and the effective inductive coupling L in the above equation. gNote that is a combination of the virtual inductance and the Thévenin equivalent inductance of the grid. In particular, Figure 6b) shows the pole-zero map for various values ​​of damping, and Figure 6c) shows the step response for the same set of damping values. For this particular system, the critical is K d,o = 0.365. The step response is slow, about 0.5 seconds due to inertia.

[0027] Figure 7 shows measurements of a system implementing the control block of Figure 6a. The system uses a fast active power injection scheme called System Integrity Protection Scheme (SIPS) to increase network reliability and support power system operation with high wind penetration in conditions. SIPS works by requesting fast power injection from assets during contingencies that result in power shortages. A Battery Energy Storage System (BESS) with VSM functionality is installed and participates in the SIPS. An activation signal is sent to the BESS, which directly Set Maximum power output is triggered by setting the input to the BESS rated power value. The SIPS trigger is sent from the centralized control center at 6:09 PM. After a 40 ms communication delay to the microgrid, followed by a further 40 ms communication delay within the microgrid, the power command is given to the BESS. The output power is then increased at a maximum rate limited by the BESS inertia, for an inertial system where full power is reached in 300 ms. A faster step response is desired.

[0028] Therefore, there is a need for improved methods, apparatus, computer-readable media, and systems for controlling power converters coupled to an electrical grid, particularly by modifying control system building blocks to improve their step response. Summary of the Invention [Means for solving the problem]

[0029] overview The present disclosure relates to a method for controlling a power converter coupled to an electrical grid, the method including: obtaining an output power of the power converter, an electrical parameter of the power converter, and an electrical parameter of the electrical grid; determining a power control error based on the output power of the power converter and a reference power; determining a rotational frequency of the inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of inertia of the machine; determining a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter according to at least one control path different from the control path including the inertial model, the phase angle being a target angle between the electrical parameter of the power converter and the electrical parameter of the electrical grid; and controlling the power converter based on the phase angle.

[0030] The present disclosure also relates to a method for controlling a power converter coupled to an electric grid, the method including: obtaining an output power of the power converter, an electrical parameter of the power converter, and an electrical parameter of the electric grid; determining a power control error based on the output power of the power converter and a reference power; determining a rotational frequency of the inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of inertia of the machine; determining a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter according to at least one control path different from the control path including the inertial model, the phase angle being a target angle between the electrical parameter of the power converter and the electrical parameter of the electric grid; determining a coupling impedance, the coupling impedance being a preset value determined before operation of the power converter, and determined based on a differential phase angle at two iterations and a differential output power of the power converter at two iterations, and / or determined based on the determined phase angle and a reference expected phase angle; and controlling the power converter based on the phase angle and the coupling impedance.

[0031] In one embodiment, at least one control path different from the control path including the inertial model is a feedforward path including a feedforward control block.

[0032] In one embodiment, the method further includes obtaining the output power of the power converter based on a coupled model that takes the phase angle as an input.

[0033] In one embodiment, the coupling model is a mathematical model of the electrical coupling of the power converter to the electrical grid.

[0034] In one embodiment, the coupling model includes a coupling term expressed in terms of a coupling impedance that includes the impedance at the output of the power converter and the impedance at the coupling port of the electrical grid.

[0035] In one embodiment, the method further includes controlling the power converter based on the obtained output power of the power converter.

[0036] In one embodiment, the feedforward control block includes a feedforward parameter that is determined based on the combined parameter.

[0037] In one embodiment, prior to operation of the power converter, the output power of the power converter is a preset value or modeled output of a closed feedback control loop that receives the reference power as an input.

[0038] In one embodiment, during operation of the power converter, the output power of the power converter is updated based, among other things, on the output power of the power converter measured during operation of the power converter.

[0039] In one embodiment, the coupling impedance is a preset value determined prior to operation of the power converter.

[0040] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the differential phase angle over two iterations and the differential output power of the power converter over two iterations, particularly during operation of the power converter.

[0041] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the determined phase angle and a reference expected phase angle, particularly during operation of the power converter.

[0042] In one embodiment, the method further comprises updating, particularly iteratively, the coupling parameters based on the coupling impedance.

[0043] In one embodiment, the method further comprises updating, particularly iteratively, the feedforward control block based on the coupling parameters.

[0044] In one embodiment, the further control path, distinct from the at least one control path, includes a damping model having the power control error as an input, the damping model being a mathematical model of the damping of the machine, and the rotational frequency being determined further based on an output of the damping model.

[0045] In one embodiment, the electrical parameter of the power converter is the voltage or current of the power converter.

[0046] In one embodiment, the electrical parameter of the electrical grid is the voltage or current of the electrical grid.

[0047] In one embodiment, the at least one parameter is one of a power control error, an output power of the power converter, or a reference power.

[0048] In one embodiment, the phase angle is a combination, in particular a linear combination, of the integral of the rotation frequency of the inertial model and at least one control signal.

[0049] In one embodiment, the machine is a synchronous generator. In one embodiment, the inertia model is a mathematical model of the inertia of a synchronous generator.

[0050] In one embodiment, the virtual synchronous machine VSM is or includes an inertial model, and the power converter is controlled based on the VSM.

[0051] The present disclosure relates to an apparatus for controlling a power converter coupled to an electric grid, the apparatus comprising: a processor configured to acquire an output power of the power converter, electrical parameters of the power converter, and electrical parameters of the electric grid; determine a power control error based on the output power of the power converter and a reference power; determine a rotational frequency of the inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of the inertia of a machine; determine a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter according to at least one control path different from the control path including the inertial model; the phase angle being a target angle between the electrical parameters of the power converter and the electrical parameters of the electric grid; and control the power converter based on the phase angle.

[0052] The present disclosure also relates to an apparatus for controlling a power converter coupled to an electric grid, the apparatus comprising: a processor configured to: acquire an output power of the power converter, an electrical parameter of the power converter, and an electrical parameter of the electric grid; determine a power control error based on the output power of the power converter and a reference power; determine a rotational frequency of the inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of inertia of the machine; determine a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter according to at least one control path different from the control path including the inertial model, the phase angle being a target angle between the electrical parameter of the power converter and the electrical parameter of the electric grid; determine a coupling impedance, the coupling impedance being a preset value determined before operation of the power converter, and determined based on a differential phase angle at two iterations and a differential output power of the power converter at two iterations, and / or determined based on the determined phase angle and a reference expected phase angle; and control the power converter based on the phase angle and the coupling impedance.

[0053] In one embodiment, at least one control path different from the control path including the inertial model is a feedforward path including a feedforward control block.

[0054] In one embodiment, the processor is further configured to obtain an output power of the power converter based on a coupled model that takes the phase angle as an input.

[0055] In one embodiment, the coupling model is a mathematical model of the electrical coupling of the power converter to the electrical grid.

[0056] In one embodiment, the coupling model includes a coupling term expressed in terms of a coupling impedance that includes the impedance at the output of the power converter and the impedance at the coupling port of the electrical grid.

[0057] In one embodiment, the processor is configured to control the power converter based on the obtained output power of the power converter.

[0058] In one embodiment, the feedforward control block includes a feedforward parameter that is determined based on the combined parameter.

[0059] In one embodiment, prior to operation of the power converter, the output power of the power converter is a preset value or modeled output of a closed feedback control loop that receives the reference power as an input.

[0060] In one embodiment, during operation of the power converter, the output power of the power converter is updated based, among other things, on the output power of the power converter measured during operation of the power converter.

[0061] In one embodiment, the processor is configured to determine and / or update the output power of the power converter before, during, and / or after operation of the power converter.

[0062] In one embodiment, the coupling impedance is a preset value determined prior to operation of the power converter.

[0063] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the differential phase angle over two iterations and the differential output power of the power converter over two iterations, particularly during operation of the power converter.

[0064] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the determined phase angle and a reference expected phase angle, particularly during operation of the power converter.

[0065] In one embodiment, the method further comprises updating, particularly iteratively, the coupling parameters based on the coupling impedance.

[0066] In one embodiment, the processor is configured to determine and / or update the coupling impedance before, during, and / or after operation of the power converter.

[0067] In one embodiment, the method further comprises updating, particularly iteratively, the feedforward control block based on the coupling parameters.

[0068] In one embodiment, the processor is configured to update the feedforward control block.

[0069] In one embodiment, the inertial model further includes a damping model that has the power control error as an input, the damping model being a mathematical model of the damping of the machine, and the rotational frequency is determined further based on an output of the damping model.

[0070] In one embodiment, the electrical parameter of the power converter is the voltage or current of the power converter.

[0071] In one embodiment, the electrical parameter of the electrical grid is the voltage or current of the electrical grid.

[0072] In one embodiment, the at least one parameter is one of a power control error, an output power of the power converter, or a reference power.

[0073] In one embodiment, the phase angle is a combination, in particular a linear combination, of the integral of the rotation frequency of the inertial model and at least one control signal.

[0074] In one embodiment, the machine is a synchronous generator. In one embodiment, the inertia model is a mathematical model of the inertia of a synchronous generator.

[0075] In one embodiment, the virtual synchronous machine VSM is or includes an inertial model, and the power converter is controlled based on the VSM.

[0076] The following items refer to specific embodiments of the present disclosure: 1. A method for controlling a power converter coupled to an electrical grid, comprising: obtaining an output power of the power converter, electrical parameters of the power converter, and electrical parameters of the electrical grid; determining a power control error based on an output power of the power converter and a reference power; determining a rotational frequency of an inertial model based on an inertial model having the power control error as an input, the inertial model being a mathematical model of the inertia of the machine; determining a phase angle based on a rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from the control path including the inertial model; determining a phase angle, the phase angle being a target angle between an electrical parameter of the power converter and an electrical parameter of the electrical grid; controlling the power converter based on the phase angle; A method comprising:

[0077] 2. The method according to item 1, wherein at least one control path different from the control path including the inertial model is a feedforward path including a feedforward control block.

[0078] 3. Obtaining the output power of the power converter based on a coupled model with a phase angle as an input, The coupling model is a mathematical model of the electrical coupling of the power converter to the electrical grid, obtaining a coupling model including a coupling term expressed in terms of a coupling impedance including an impedance at an output of the power converter and an impedance at a coupling port of the electrical grid; controlling the power converter based on the obtained output power of the power converter; 3. The method according to item 1 or 2, further comprising:

[0079] 4. The method according to item 3, wherein the feedforward control block includes a feedforward parameter determined based on the combined parameter.

[0080] 5. The method according to item 3 or 4, wherein, before operation of the power converter, the output power of the power converter is a preset value or a modeled output of a closed feedback control loop that receives the reference power as an input, and during operation of the power converter, the output power of the power converter is updated, particularly based on the output power of the power converter measured during operation of the power converter.

[0081] 6. The coupling impedance is a preset value determined prior to operation of the power converter; adaptively and / or iteratively determined, in particular during operation of the power converter, based on the differential phase angle over the two iterations and the differential output power of the power converter over the two iterations; and / or 6. The method according to any one of items 3 to 5, wherein the reference expected phase angle is adaptively and / or iteratively determined based on the determined phase angle and the reference expected phase angle, in particular during operation of the power converter.

[0082] 7. The method according to item 6, further comprising updating, particularly iteratively, the coupling parameters based on the coupling impedance.

[0083] 8. The method according to item 7, further comprising updating, particularly iteratively, the feedforward control block based on the coupling parameters.

[0084] 9. The method of any one of items 1 to 8, wherein the further control path, different from the at least one control path, includes a damping model having the power control error as an input, the damping model being a mathematical model of the damping of the machine, and the rotation frequency is determined further based on an output of the damping model.

[0085] 10. The electrical parameters of a power converter are the voltage or current of the power converter, The electrical parameters of the electrical grid are the voltage or current of the electrical grid, and / or 10. The method according to any one of items 1 to 9, wherein the at least one parameter is one of a power control error, an output power of the power converter, or a reference power.

[0086] 11. The method according to any one of items 1 to 10, wherein the phase angle is a combination, in particular a linear combination, of the integral of the rotation frequency of the inertial model and at least one control signal.

[0087] 12. The method according to any one of items 1 to 11, wherein the machine is a synchronous generator and the inertia model is a mathematical model of the inertia of the synchronous generator.

[0088] 13. The method according to item 12, wherein the virtual synchronous machine VSM is or includes an inertial model, and the power converter is controlled based on the VSM.

[0089] 14. An apparatus for controlling a power converter coupled to an electric grid, comprising: obtaining an output power of the power converter, electrical parameters of the power converter, and electrical parameters of the electrical grid; determining a power control error based on the output power of the power converter and a reference power; determining a rotation frequency of the inertia model based on the inertia model having the power control error as an input, the inertia model being a mathematical model of the inertia of the machine; determining a phase angle based on a rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from the control path including the inertial model; The phase angle is the target angle between the electrical parameter of the power converter and the electrical parameter of the electrical grid; Controlling a power converter based on a phase angle 11. An apparatus comprising: a processor configured to:

[0090] 15. A computer-readable medium for controlling a power converter coupled to an electrical grid, the computer-readable medium carrying instructions for performing the method of any one of items 1 to 13.

[0091] The present disclosure also relates to a computer-readable medium carrying instructions for performing the method of any one of the above-mentioned embodiments for controlling a power converter coupled to an electrical grid.

[0092] The present disclosure further relates to a system for controlling a power converter coupled to an electrical grid, comprising the power converter, the electrical grid, and the apparatus and / or computer-readable medium of any one of the above-described embodiments.

[0093] Various exemplary embodiments of the present disclosure are directed to providing features that will become readily apparent by reference to the following description in conjunction with the accompanying drawings. In accordance with various embodiments, exemplary systems, methods, and apparatuses are disclosed herein. It is understood, however, that these embodiments are presented by way of example and not limitation, and it will be apparent to those skilled in the art upon reading this disclosure that various modifications to the disclosed embodiments may be made while remaining within the scope of the present disclosure.

[0094] Thus, the present disclosure is not limited to the example embodiments and applications described and illustrated herein. Additionally, the specific order and / or hierarchy of steps in the methods disclosed herein is merely example approaches. Based on design preferences, the specific order or hierarchy of steps in a disclosed method or process can be rearranged while remaining within the scope of the present disclosure. Thus, those skilled in the art will understand that the methods and techniques disclosed herein present various steps or operations in a sample order, and that the present disclosure is not limited to the specific order or hierarchy presented, unless otherwise stated.

[0095] Hereinafter, exemplary embodiments of the present disclosure will be described. It should be noted that some aspects of any one of the described embodiments may also be found in some other embodiments unless otherwise specified or obvious. However, in order to improve understanding, each aspect will be described in detail only when first mentioned, and repeated descriptions of the same aspects will be omitted.

[0096] These and other aspects and implementations thereof are described in more detail in the drawings, description, and claims. [Brief explanation of the drawings]

[0097] [Figure 1] A synchronous generator and control system are shown. [Figure 2] 1 illustrates load sharing in parallel-connected generators. [Figure 3] 1 shows a three-phase power electronic inverter with a controller. [Figure 4] 1 shows a virtual synchronous machine control system. [Figure 5a)] 1 illustrates an equivalent model of a power system according to one embodiment of the present disclosure. [Figure 5b] 1A and 1B show respective phasor diagrams according to one embodiment of the present disclosure. [Figure 6a)] 1 shows a control block diagram of a virtual synchronous machine connected to a power system. [Figure 6b] 1 shows a pole-zero map of the control loop shown in the control block diagram. [Figure 6c] 1 shows a step response of the control loop shown in the control block diagram. [Figure 7] Measurements of a system implementing the control block of Figure 6a) are shown. [Figure 8a)] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 8b] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 9a)] FIG. 1 illustrates a control block diagram for a power system according to one embodiment of the present disclosure. [Figure 9b] FIG. 1 illustrates a control block diagram for a power system according to one embodiment of the present disclosure. [Figure 9c)] FIG. 1 illustrates a control block diagram for a power system according to one embodiment of the present disclosure. [Figure 10a)] 9a)-9c) with various control parameters according to one embodiment of the present disclosure. [Figure 10b] 9a)-9c) with various control parameters according to one embodiment of the present disclosure. [Figure 10c)] 9a)-9c) with various control parameters according to one embodiment of the present disclosure. [Figure 11a)] 9a)-9c) with their respective pole-zero maps as shown in FIGS. 10a)-10c). [Figure 11b)] 9a)-9c) with their respective pole-zero maps as shown in FIGS. 10a)-10c). [Figure 11c)] 9a)-9c) with their respective pole-zero maps as shown in FIGS. 10a)-10c). [Figure 12a)] 1 shows an apparatus according to one embodiment of the present disclosure. [Figure 12b)] 1 illustrates a system according to one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0098] Detailed Description of Disclosure FIG. 8a) shows a flowchart of a method according to one embodiment of the present disclosure. In S801, an output power of a power converter, an electrical parameter of the power converter, and an electrical parameter of an electrical grid are acquired. The term “acquire” may have the same meaning as, and thus may be used interchangeably with, terms such as “receive” and “measure,” but is not limited to such. In one embodiment, the electrical parameter of the power converter is a voltage or a current of the power converter. In one embodiment, the electrical parameter of the electrical grid is a voltage or a current of the electrical grid. In one embodiment, the at least one parameter is one of a power control error, an output power of the power converter, or a reference power. In S802, a power control error is determined based on the output power of the power converter and the reference power. In S803, a rotational frequency of the inertial model is determined based on an inertial model that uses the power control error as an input, where the inertial model is a mathematical model of the inertia of the machine. At S804, a phase angle is determined based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from the control path including the inertial model, the phase angle being a target angle between an electrical parameter of the power converter and an electrical parameter of the electrical grid. At S805, the power converter is controlled based on the phase angle.

[0099] FIG. 8b) shows a flowchart of a method according to one embodiment of the present disclosure. In S801′, an output power of a power converter, an electrical parameter of the power converter, and an electrical parameter of an electrical grid are acquired. The term “acquire” may have the same meaning as, and therefore may be used interchangeably with, terms such as “receive” and “measure,” but is not limited to such. In one embodiment, the electrical parameter of the power converter is a voltage or a current of the power converter. In one embodiment, the electrical parameter of the electrical grid is a voltage or a current of the electrical grid. In one embodiment, the at least one parameter is one of a power control error, an output power of the power converter, or a reference power. In S802′, a power control error is determined based on the output power of the power converter and the reference power. In S803′, a rotational frequency of the inertial model is determined based on an inertial model that uses the power control error as an input, where the inertial model is a mathematical model of the inertia of the machine. In S804', a phase angle is determined based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from the control path including the inertial model, where the phase angle is a target angle between an electrical parameter of the power converter and an electrical parameter of the electrical grid. In S805', a coupling impedance is determined, where the coupling impedance is a preset value determined before operation of the power converter and is determined based on a differential phase angle in two iterations and a differential output power of the power converter in two iterations, and / or is determined based on the determined phase angle and a reference expected phase angle. In S806', the power converter is controlled based on the phase angle and the coupling impedance.

[0100] 9a)-9c) illustrate control block diagrams for a power system according to one embodiment of the present disclosure. For example, the power system may be the modeled power system shown in FIG. 5a) with relationships of electrical parameters of the system according to FIG. 5b). 9a)-9c) illustrate non-limiting variations of methods for controlling a power converter. That is, FIG. 9a) illustrates a control block diagram for a power system according to one embodiment of the present disclosure. FIG. 9b) illustrates another control block diagram for a power system according to one embodiment of the present disclosure. FIG. 9c) illustrates yet another control block diagram for a power system according to one embodiment of the present disclosure.

[0101] The control method in Fig. 9a) is to control the output power P Act , the voltage of the power converter and the voltage of an electrical parameter of the electrical grid. The acquired voltage of the power converter and / or the electrical grid may be any other electrical parameter, e.g., a current, and / or may be a vector quantity. Set is used to determine the power control error. Act It is also used with P Set follows a feedforward path different from the control path including the inertial model of the machine, i.e., in this embodiment, at least one parameter following at least one path different from the control path including the inertial model is the reference power P Set This is shown in Figure 9a), where P Set Command feedforward gain K f is shown. The inertial model of the machine is represented by a control block including (1 / 2H) and (1 / s). Those skilled in the art will understand that the inertial model may be modeled differently, and therefore the control loop in FIG. 9a), particularly the control block relating to the inertia of the machine, may be implemented differently. The machine may be a synchronous generator, and therefore the inertial model may be a mathematical model of the inertia of a synchronous generator. The virtual synchronous machine VSM may be or include the inertial model, and the power converter may be controlled based on the VSM. As will be apparent from the disclosure herein, the added command feedforward path may be PSet bypassing the inertial model of the machine, which in turn varies the power angle δ directly and immediately. Such a feature advantageously reduces the command response, i.e., the controlled parameter P Act faster than the control loop without the added feedforward path. Set The resulting feedforward command may be a control signal generated by at least one parameter following at least one control path different from the control path including the inertial model. In an embodiment, the damping parameter K d The control path is shown with a damping model including the grid frequency F grid is a mathematical construct to aid in the analysis and is therefore shown for completeness, but may be omitted from the control system analysis, as is done in the calculations disclosed herein. Mathematically, the transfer function of the SBD in Figure 9a) is as follows:

[0102]

number

[0103] The characteristic equation is

[0104]

number

[0105] and the resonant frequency is

[0106]

number

[0107] The damping coefficient is

[0108]

number

[0109] and the critical damping is equal to

[0110]

number

[0111] Comparing equation (7) with equation (11), the feedforward gain K f This indicates that the addition of a quadratic term is added to the numerator. Therefore, in particular, the feedforward gain K f L g A desired transfer function can be achieved by adjusting the f L g Based on, as a ratio to, or in relation to, K f =αL g where α is a rational number, particularly between 0 and 2, more particularly 1. f =L g , a closed-loop forward gain of unity is achieved, and as a result, the controlled parameter P Act The instantaneous response to a step input of P Set Furthermore, since the feedforward path is outside the closed loop, i.e., δ converges to K f The power control error following the control path containing K f P following a control path containing Set The disturbance response is invariant because it is determined by K d Such a disturbance response may be desirable for grid-forming inverters during the grid transition to net-zero emissions.

[0112] FIG. 9b) shows another embodiment of the SBD. Referring to FIG. 9b), two parameters are used to control two different feedforward paths: the feedforward gain K f A power control error P Set -P Actand the feedforward gain K f The power control error P Act and . Nevertheless, mathematically, the SBD of FIG. 9b) yields the same transfer function as the SBD of FIG. 9a), i.e., equation (11). It is therefore clear that any other non-limiting SBD variant with the transfer function of equation (11) may be implemented.

[0113] Figure 9c) shows multiple P Set , i.e., the first power reference P Set_fast and a second power reference P Set_slow 1 illustrates another embodiment of an SBD including: The number of power reference terms and / or the number of power control errors determined therefrom may not be limited to two. The power control error may be determined by the output power P Act and the first power reference P Set_fast and a second power reference P Set_slow The first power reference P Set_fast is the feedforward gain K f The control block diagram in Figure 9a follows a feedforward path that includes a feedforward block containing P Set_slow It is clear that this is mathematically equivalent to the control block diagram in Figure 9c) where =0.

[0114] 10a)-10c) illustrate pole-zero maps of the control block of any one of FIGS. 9a)-9c) with various control parameters according to one embodiment of the present disclosure. In particular, FIG. 10a) illustrates the pole-zero map of the control block diagram shown in any one of FIGS. 9a), 9b), or 9c) with the feedforward gain set to 100% of the coupled value. FIG. 10b) illustrates the pole-zero map of the control block diagram shown in any one of FIGS. 9a), 9b), or 9c) with the feedforward gain set to 90% of the coupled value. FIG. 10a) illustrates the pole-zero map of the control block diagram shown in any one of FIGS. 9a), 9b), or 9c) with the feedforward gain set to 110% of the coupled value. In particular, a system with inertia set to 1.5 seconds and effective inductive coupling set to 0.1 pu is illustrated with a damping parameter K d Various values ​​of K were analyzed. As discussed above, including a feedforward path, as shown in the exemplary embodiment of Figures 9a)-9c), introduces a second-order term, i.e., a set of zeros, into the transfer function. For the case shown in Figure 10a), the feedforward gain was set to 100% of the combined value, i.e., K f =L g Therefore, the damping parameter K d Regardless of the value of , the numerator zero completely cancels with the pole from the denominator, achieving unity gain in the transfer function. The cancellation of the zero and pole is shown in Figure 10a) and is shown for the damping parameter K d For various values ​​of K, the pole and zero locations overlap perfectly. f =0.9×L g , i.e., the undercompensated feedforward gain and damping parameter K d The pole-zero maps are shown for various values ​​of K. Note that the poles no longer overlap with the zeros. The proximity of the pole-zero pair locations is f and L g Figure 10c) corresponds to the closeness of agreement between K f = 1.1 x L g, i.e., shows a pole-zero map with an over-compensated feedforward gain, where again each pole has a corresponding nearby zero that partially cancels its effect. Figure 11 shows the step response of the control block of Figure 9 with various control parameters in accordance with one embodiment of the present disclosure. Specifically, Figures 11a)-11c) show the step response of any one of the control blocks of Figures 9a)-9c) with their respective pole-zero maps as shown in Figures 10a)-10c).

[0115] Figure 11a) shows the damping parameter K d Figure 10a) shows the step response of the system with perfect pole-zero cancellation for various values ​​of P at t = 0s. Since all poles of the system are cancelled by their corresponding zeros, there is a perfect response without transients, i.e., P at t = 0s. Set For an instantaneous step change in the power converter output P Act is immediately P Set However, the power converter output P Act Note that K is a control parameter, and that the change in the actual output of the power converter may be limited by physical and electrical constraints, such as limitations on the rate of change of current at the output of the power converter, particularly for transient behavior on the order of half the fundamental frequency of the system frequency. For example, the transient behavior may include a rise or settling time of 10 ms for a 50 Hz system. In comparison, the method without a feedforward path of the present disclosure achieves a rise or settling time of 500 ms. Figure 11b) shows the damping parameter K d Figure 10b) shows the step response of the undercompensated system shown in Figure 10b) for various values ​​of K. In this case, the initial step is 90% compensated, so the instantaneous response is 90% of the final value. Eventually, the system reaches the expected steady-state value, and the transient response for the missing 10% has the same characteristics as the uncompensated system. Figure 11c) shows the step response of the undercompensated system for various values ​​of K. dFigure 10c) shows the step response of the overcompensated system for various values ​​of 1101. In this case, the instantaneous response is 110% of the setpoint, and an excess of 10% has a similar transient behavior to the previous case. Note that in all three cases shown in Figures 11a-11c, the correct steady-state value is reached, and the initial response error is only as large as the compensation error. In other words, the compensation does not need to be perfect to achieve the desired result of faster response.

[0116] The transient performance of the system depends on the coupling parameter L in the coupled model. g (also called the coupling term), the feedforward gain K f It is particularly clear from the embodiments shown in Figures 10a)-10c) and 11a)-11c) that the coupling model depends on the value of X. The coupling model is a mathematical model of the electrical coupling of the power converter to the electrical grid. The coupling term may be expressed in terms of a coupling impedance, including the impedance at the output of the power converter and the impedance at the coupling port of the electrical grid. For example, the impedance R+jX in Figure 5a) may be an equivalent impedance to the impedance at the output of the power converter and the impedance at the coupling port of the electrical grid. The impedance at the output of the power converter may be a VSM virtual inductance, and the impedance at the coupling port of the electrical grid may be the Thévenin equivalent inductance of the electrical grid. The grid inductance may include any combination of the following: coupling transformer leakage, transmission line impedance, stator leakage of an online synchronous generator, and other online power generation sources. Thus, the value of X may change over time.

[0117]

number

[0118]

number

[0119] In the formula, PA and V A may be measured locally, i.e., the parameter is that of a GFMI that has an internal voltage source that can be measured, V G , i.e., the Thévenin equivalent grid voltage source, can be estimated based on the reactive power. However, δ may not be measurable. The differential form of equation (17) is:

[0120]

number

[0121] Therefore, X is the ΔP A , V A , and Δδ are measured, and V G In one embodiment, K f is based on the determined X, in particular based on the determined X, as a ratio to it, or in relation to it, K f is determined by adjusting f =βX, where β is a rational number, particularly between 0 and 2, more particularly 1. In one embodiment, K f is adaptively determined to the coupling inductance value X. In one embodiment, the value of the coupling inductance X is adaptively determined to δ, particularly as the Thevenin equivalent line impedance changes.

[0122] In one embodiment, X is calculated while online, i.e., when the GFMI is operating, specifically by calculating the expected value of Δδ and ΔP A The estimate of X is iteratively updated by comparing the actual value of Δδ to the actual value needed to achieve Δδ. In one embodiment, if the actual value of Δδ is higher than expected, the estimate of X is increased. In one embodiment, if the actual value of Δδ is lower than expected, the estimate of X is decreased.

[0123] In one embodiment, the coupling inductance value X is adaptively determined based on any combination of the above embodiments. fis adaptively determined based on any combination of the above embodiments.

[0124] In one embodiment, the feedforward control block includes a feedforward parameter that is determined based on the combined parameter.

[0125] In one embodiment, prior to operation of the power converter, the output power of the power converter is a preset value or modeled output of a closed feedback control loop that receives the reference power as an input.

[0126] In one embodiment, during operation of the power converter, the output power of the power converter is updated based, among other things, on the output power of the power converter measured during operation of the power converter.

[0127] In one embodiment, the coupling impedance is a preset value determined prior to operation of the power converter.

[0128] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the differential phase angle over two iterations and the differential output power of the power converter over two iterations, particularly during operation of the power converter.

[0129] In one embodiment, the coupling impedance is adaptively and / or iteratively determined based on the determined phase angle and a reference expected phase angle, particularly during operation of the power converter.

[0130] In one embodiment, the method further comprises updating, particularly iteratively, the coupling parameters based on the coupling impedance.

[0131] In one embodiment, the method further comprises updating, particularly iteratively, the feedforward control block based on the coupling parameters.

[0132] FIG. 12a) shows an apparatus 1210 for controlling a power converter coupled to an electric grid, the apparatus 1210 comprising a processor 1211 configured to: acquire an output power of a power converter 1230, electrical parameters of the power converter 1230, and electrical parameters of an electric grid 1220; determine a power control error based on the output power of the power converter 1230 and a reference power; determine a rotational frequency of the inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of the inertia of the machine; determine a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter that follows at least one control path different from the control path including the inertial model; the phase angle being a target angle between the electrical parameters of the power converter and the electrical parameters of the electric grid 1220; and control the power converter 1230 based on the phase angle.

[0133] In one embodiment, the apparatus 1210 is an apparatus for controlling a power converter coupled to an electrical grid, the apparatus 1210 acquiring an output power of a power converter 1230, electrical parameters of the power converter 1230, and electrical parameters of an electrical grid 1220, determining a power control error based on the output power of the power converter 1230 and a reference power, determining a rotational frequency of the inertial model based on an inertial model having the power control error as an input, the inertial model being a mathematical model of the inertia of the machine, and controlling the rotational frequency of the inertial model according to at least one parameter following at least one control path different from the control path including the inertial model. and at least one control signal generated by the power converter 1230, where the phase angle is a target angle between an electrical parameter of the power converter and an electrical parameter of the electrical grid 1220; determine a coupling impedance, where the coupling impedance is a preset value determined before operation of the power converter, determined based on a differential phase angle over the two iterations and a differential output power of the power converter over the two iterations, and / or determined based on the determined phase angle and a reference expected phase angle; and control the power converter 1230 based on the phase angle and the coupling impedance.

[0134] 12b) shows a system 1200 for controlling a power converter coupled to an electrical grid, comprising a power converter 1230, an electrical grid 1220, and an apparatus 1210 of any one of the above-described embodiments. In one embodiment, the system comprises a computer-readable medium for controlling a power converter coupled to an electrical grid, the computer-readable medium carrying instructions for performing the method of any one of the above-described embodiments. In one embodiment, the computer-readable medium is or takes the place of the apparatus.

[0135] While various embodiments of the present disclosure have been described above, it should be understood that they are presented by way of example only, and not by way of limitation. Similarly, various figures may depict example architectures or configurations provided to enable those skilled in the art to understand example features and functionality of the present disclosure. However, those skilled in the art will understand that the present disclosure is not limited to the example architectures or configurations shown, but can be implemented using a variety of alternative architectures and configurations. Moreover, as will be understood by those skilled in the art, one or more features of one embodiment can be combined with one or more features of other embodiments described herein. Thus, the breadth and scope of the present disclosure should not be limited by any of the above-described example embodiments.

[0136] It will also be understood that any reference to an element herein using a designation such as "first," "second," etc., generally does not limit the quantity or order of those elements. Rather, these designations may be used herein as a convenient means of distinguishing between two or more elements or instances of an element. Thus, a reference to a first and a second element does not imply that only two elements may be used or that the first element must in any way precede the second element.

[0137] Additionally, those skilled in the art will understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, the data, instructions, commands, information, signals, bits, and symbols that may be referenced in the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0138] Those skilled in the art will further recognize that any of the various illustrative logical blocks, units, processors, means, circuits, methods, and functions described in connection with the aspects disclosed herein may be implemented by electronic hardware (e.g., digital implementations, analog implementations, or a combination of the two), firmware, various forms of program or design code incorporating instructions (which may be referred to herein for convenience as "software" or "software units"), or any combination of these technologies.

[0139] To clearly illustrate this interchangeability of hardware, firmware, and software, various illustrative components, blocks, units, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware, or software, or a combination of these technologies, depends on the particular application and design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in various ways for each particular application, and such implementation decisions do not depart from the scope of the present disclosure. According to various embodiments, a processor, device, component, circuit, structure, machine, unit, etc. may be configured to perform one or more of the functions described herein. The terms "configured to" or "configured for," as used herein with respect to a specified operation or function, refer to a processor, device, component, circuit, structure, machine, unit, etc. that is physically constructed, programmed, and / or arranged to perform the specified operation or function.

[0140] Furthermore, those skilled in the art will understand that the various example methods, logical blocks, units, devices, components, and circuits described herein can be implemented in or performed by an integrated circuit (IC), which can include a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic device, or any combination thereof. The logical blocks, units, and circuits can further include an antenna and / or transceiver for communicating with various components within a network or device. The general-purpose processor can be a microprocessor, although in the alternative, the processor can be any conventional processor, controller, or state machine. A processor can also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other suitable configuration for performing the functions described herein. If implemented in software, the functions can be stored as one or more instructions or code on a computer-readable medium. Thus, the steps of a method or algorithm disclosed herein can be implemented as software stored on a computer-readable medium.

[0141] Computer-readable media includes both computer storage media and communication media, including any medium that can enable a computer program or code to be transferred from one place to another. Storage media can be any available medium that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer.

[0142] Additionally, memory or other storage devices, as well as communication components, may be used in embodiments of the present disclosure. It will be appreciated that, for clarity, the above description has described embodiments of the present disclosure with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units, processing logic elements, or domains may be used without detracting from the present disclosure. For example, functions shown to be performed by separate processing logic elements or controllers may be performed by the same processing logic element or controller. Accordingly, references to specific functional units do not indicate a strict logical or physical structure or organization, but merely to suitable means for providing the described functionality.

[0143] Various modifications to the embodiments described in this disclosure will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the scope of the present disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the novel features and principles disclosed herein, as set forth in the following claims.

Claims

1. 1. A method for controlling a power converter coupled to an electrical grid, comprising: obtaining an output power of the power converter, electrical parameters of the power converter, and electrical parameters of the electrical grid; determining a power control error based on an output power of the power converter and a reference power; determining a rotational frequency of an inertial model based on an inertial model that has the power control error as an input, the inertial model being a mathematical model of the inertia of a machine; determining a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from a control path including the inertial model; determining that the phase angle is a target angle between the electrical parameter of the power converter and the electrical parameter of the electrical grid; determining a coupling impedance, said coupling impedance comprising: a preset value determined prior to operation of the power converter; determined based on a differential phase angle between two iterations and a differential output power of the power converter between the two iterations; and / or is determined based on the determined phase angle and a reference expected phase angle; determining whether to control the power converter based on the phase angle and the coupling impedance; A method comprising:

2. The method of claim 1 , wherein the at least one control path different from the control path including the inertial model is a feedforward path including a feedforward control block.

3. obtaining the output power of the power converter based on a coupled model that uses the phase angle as an input, the coupling model is a mathematical model of the electrical coupling of the power converter to the electrical grid; obtaining the coupled model, the coupled model including a coupling term expressed in terms of the coupled impedance including an impedance at an output of the power converter and an impedance at a coupled port of the electrical grid; controlling the power converter based on the obtained output power of the power converter; 3. The method of claim 1 or 2, further comprising:

4. The method of claim 3 , wherein the feedforward control block includes a feedforward parameter determined based on a coupling parameter.

5. 5. The method of claim 3 or 4, wherein prior to operation of the power converter, the output power of the power converter is a preset value or a modeled output of a closed feedback control loop that receives the reference power as an input, and during the operation of the power converter, the output power of the power converter is updated, in particular based on the output power of the power converter measured during the operation of the power converter.

6. The coupling impedance is adaptively and / or iteratively determined during the operation of the power converter based on the differential phase angle over two iterations and the differential output power of the power converter over the two iterations; and / or The method of any one of claims 1 to 5, wherein the reference expected phase angle is adaptively and / or iteratively determined during the operation of the power converter based on the determined phase angle and the reference expected phase angle.

7. The method of claim 6 , further comprising iteratively updating a coupling parameter based on the coupling impedance.

8. The method of claim 7 , further comprising updating, particularly iteratively, the feedforward control block based on the coupling parameters.

9. 9. The method of claim 1, wherein a further control path distinct from the at least one control path comprises a damping model having as input the power control error, the damping model being a mathematical model of damping of the machine, and wherein the rotational frequency is determined further based on an output of the damping model.

10. the electrical parameter of the power converter is a voltage or a current of the power converter; the electrical parameter of the electrical grid is a voltage or a current of the electrical grid; and / or The method according to any one of claims 1 to 9, wherein the at least one parameter is any one of the power control error, the output power of the power converter, or the reference power.

11. The method according to any one of claims 1 to 10, wherein the phase angle is a combination, in particular a linear combination, of the integral of the rotation frequency of the inertial model and the at least one control signal.

12. The method of any one of claims 1 to 11, wherein the machine is a synchronous generator and the inertial model is a mathematical model of the inertia of the synchronous generator.

13. The method of claim 12 , wherein a virtual synchronous machine VSM is or includes the inertial model, and the power converter is controlled based on the VSM.

14. 1. An apparatus for controlling a power converter coupled to an electrical grid, comprising: obtaining an output power of the power converter, electrical parameters of the power converter, and electrical parameters of the electrical grid; determining a power control error based on the output power of the power converter and a reference power; determining a rotational frequency of an inertia model based on an inertia model that receives the power control error as an input, the inertia model being a mathematical model of the inertia of the machine; determining a phase angle based on the rotational frequency of the inertial model and at least one control signal generated by at least one parameter following at least one control path different from a control path including the inertial model; the phase angle is a target angle between the electrical parameter of the power converter and the electrical parameter of the electrical grid; determining a coupling impedance, said coupling impedance being: a preset value determined prior to operation of the power converter; determined based on a differential phase angle between two iterations and a differential output power of the power converter between the two iterations; and / or is determined based on the determined phase angle and a reference expected phase angle; controlling the power converter based on the phase angle and the coupling impedance; 11. An apparatus comprising: a processor configured to:

15. A computer readable medium for controlling a power converter coupled to an electrical grid, the computer readable medium carrying instructions for performing the method of any one of claims 1 to 13.

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