GRID FORMING VECTOR CURRENT CONTROL

Abstract

The present disclosure provides a grid forming vector current control system configured to emulate a virtual synchronous machine (VSM). The disclosed system comprises a droop control unit, a current control unit, a virtual admittance unit and a phase locked loop (PLL) unit. The virtual admittance unit and the PLL unit are configured to emulate an inertia of the VSM. A virtual current source is connected in parallel to the VSM.

Claims

1. A grid forming vector current control system configured to emulate a virtual synchronous machine (VSM), the system comprising: a droop control unit; a current control unit; a virtual admittance unit; and a phase locked loop (PLL) unit, wherein the virtual admittance unit and the PLL unit are configured to emulate an inertia of the VSM, and wherein a virtual current source is connected in parallel to the VSM.

2. The system according to claim 1, wherein an output signal of the droop control unit is connected to the virtual current source in order to emulate a speed governor.

3. The system according to claim 1, wherein an output signal of the droop control unit is connected to the PLL unit in order to emulate a virtual mechanical speed governor.

4. The system according to claim 1, further comprising an active voltage regulator (AVR) unit.

5. The system according to claim 1, wherein the system is deployed in at least one of a micro grid converter, a photovoltaic (PV) inverter, an uninterruptable power supply (UPS), a grid intertie converter, a railway grid intertie converter, a high voltage direct current (HVDC) converter, or a battery energy storage system (BESS).

6. The system according to claim 1, wherein a factor k.sub.VSM is configured to change one or more characteristics of the system continuously from voltage source to current source by proportionally scaling output signals of the virtual admittance unit with the factor k.sub.VSM.

7. The system according to claim 6, wherein the factor k.sub.VSM is fed into at least one of the droop control unit, the virtual admittance unit, or the PLL unit in order to increase or decrease an inertial response of the system to disturbances in a main grid.

8. The system according to claim 7, wherein the system is deployed in at least one of a micro grid converter, a photovoltaic (PV) inverter, an uninterruptable power supply (UPS), a grid intertie converter, a railway grid intertie converter, a high voltage direct current (HVDC) converter, or a battery energy storage system (BESS), and wherein the at least one of the micro grid converter, the PV inverter, the UPS, the grid intertie converter, the railway grid intertie converter, the HVDC converter, or the BESS is connected to the main grid.

9. The system according to claim 7, wherein the system is deployed in at least one of a micro grid converter, a photovoltaic (PV) inverter, or an uninterruptable power supply (UPS), and wherein the at least one of the micro grid converter, the PV inverter, or the UPS is connected to the main grid.

10. The system according to claim 6, wherein the factor k.sub.VSM scales a nominal power of the VSM by proportionally scaling the output signals of the virtual admittance unit with the factor k.sub.VSM, inversely proportionally scaling a proportional gain of the PLL unit with the factor k.sub.VSM, and/or proportionally scaling a droop constant with the factor k.sub.VSM.

11. The system according to claim 6, wherein the factor k.sub.VSM scales at least one of a spinning wheel factor or a transient power or the inertia.

12. The system according to claim 1, wherein the droop control unit comprises a fast current source.

13. The system according to claim 4, wherein the AVR unit is configured to keep a magnitude of a voltage, at a Point of Common Coupling (PCC), constant.

14. The system according to claim 1, wherein the PLL unit is configured to measure a voltage at a Point of Common Coupling (PCC).

15. A method for controlling a grid forming vector current control emulating a Virtual Synchronous Machine (VSM), the method comprising: providing a droop control unit, providing a current control unit, providing a virtual admittance unit, and providing a phase locked loop (PLL) unit, emulating an inertia of the VSM, and controlling a virtual current source connected in parallel to the VSM.

16. The method according to claim 15, wherein an output signal of the droop control unit is connected to the virtual current source in order to emulate a speed governor.

17. The method according to claim 15, wherein an output signal of the droop control unit is connected to the PLL unit in order to emulate a virtual mechanical speed governor.

18. The method according to claim 15, wherein a factor k.sub.VSM changes one or more characteristics of a system, comprising the droop control unit, current control unit, virtual admittance unit, and PLL unit, continuously from voltage source to current source by proportionally scaling output signals of the virtual admittance unit with the factor k.sub.VSM.

19. The method according to claim 18, further comprising feeding the factor k.sub.VSM into at least one of the droop control unit, the virtual admittance unit, or the PLL unit in order to increase or decrease an inertial response of the system to disturbances in a main grid.

20. The method according to claim 15, further comprising scaling a nominal power of the VSM by one or more of: proportionally scaling output signals of the virtual admittance unit with a factor k.sub.VSM; inversely proportionally scaling a proportional gain of the PLL unit with the factor k.sub.VSM; or proportionally scaling a droop constant with the factor k.sub.VSM.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0040] Embodiments will be described with reference to the appended figures, in which

[0041] FIGS. 1a and 1b show schematic diagrams according to the prior art,

[0042] FIGS. 2a and 2b show schematic diagrams according to the present disclosure,

[0043] FIGS. 3a and 3b show schematic block diagrams according to an embodiment of the present disclosure,

[0044] FIG. 4 shows the basic structure of the proposed grid supporting scheme,

[0045] FIGS. 5a to 5c show virtual machine variants,

[0046] FIGS. 6a and 6b show equivalent models of the proposed control scheme,

[0047] FIG. 7 depicts a vector diagram for a transient situation,

[0048] FIG. 8 is a block diagram showing the usage of a factor k.sub.VSM to adjust an amount of grid support,

[0049] FIGS. 9 and 10 are diagrams showing the response of the system to a fault and the clearing thereof with different settings,

[0050] FIGS. 11a and 11b show schematic block diagrams according to another embodiment of the present disclosure,

[0051] FIG. 12 shows an alternative implementation of the proposed control concept,

[0052] FIG. 13 is an equivalent circuit of the control concept with an optional active damper in parallel to the current source,

[0053] FIG. 14 shows an implementation of an active damper branch according to FIG. 13, and

[0054] FIG. 15 shows a block diagram according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

[0055] FIG. 1a shows a scheme of a control system according to the prior art. It employs a virtual impedance and a VSM. The outputs of both the VSM and the virtual impedance are fed into a cascaded voltage and current control. FIG. 1b is a more detailed view of the virtual generator control approach. As can be seen from the schematic, it is a rather complex structure with many parameters that have to be tuned and adapted to each other.

[0056] In the following, the terms block and unit may be used interchangeably and are not meant to be exclusive.

[0057] FIG. 2 schematically depicts the vector current control system according to the present disclosure. In particular, FIG. 2a shows a virtual synchronous machine (VSM) with a current source connected in parallel, while FIG. 2b shows the equivalent circuit diagram thereof. The system emulates the combined effect of a virtual machine, whose nominal power and amount of grid support can be scaled independently and online with a single input/parameter and a parallel connected current source. Thus, the system may be controlled remotely. For certain aspects, e.g. fault handling, it may be preferable to change the nominal power and amount of grid support within the application code.

[0058] In more detail, the disclosed system according to an exemplary embodiment uses control blocks as shown in FIG. 3 to emulate the proposed behaviour. The calculation thereof will be discussed below. FIG. 3a comprises a phase locked loop (PLL) block fed by a voltage at a point of common coupling (PCC) V.sub.pcc as well as a speed control block having a reference frequency f.sub.ref as an input. The output of the PLL is provided to a virtual admittance block together with V.sub.pcc and a voltage of the virtual synchronous machine V.sub.vsm. The speed control output, the virtual admittance output as well as a reference current I.sub.ref are then processed in a current control block which outputs a voltage V.sub.out.

[0059] FIG. 3b additionally comprises the parameter k.sub.VSM as an input to at least one of the PLL, speed control and current control blocks. Thereby, an amount of grid support of a main grid may be controlled. k.sub.VSM may also be used to smoothly change the characteristics of the control scheme from voltage source to current source, also supporting a mix of both characteristics. A smooth changeover to stiff current control can be beneficial during grid faults to keep synchronism with the grid. The control mode does not have to be changed.

[0060] The system may also comprise an active voltage regulator (AVR). The system according to the exemplary embodiment emulates the combined effects of virtual inertia, damper winding, virtual stator impedance, AVR and droop governor. Virtual inertia and damper winding are emulated using the standard PLL block.

[0061] Opposite to conventional virtual machine implementations, the active power setpoint tracking and the droop governor are conceptually implemented with a fast current source. Therefore, there is no performance degradation in strong grids which can be often observed when using VSM control. Thus, a good performance in weak and in strong grids is achieved. The method supports unplanned islanding and islanded operation.

[0062] The complexity of the control scheme and the related commissioning effort is very low. Due to the removal of a cascaded voltage control loop and by reusing the PLL to emulate inertia and damping, the number of parameters can be reduced from more than 15 in conventional approaches to only 7 parameters with clear meaning and less interactions. Therefore, the system may also be tuned more easily.

[0063] Further advantages of the proposed concept are the possibility to configure the amount of grid support with a single parameter to simplify offering of grid supporting features in applications with low energy storage such as UPS in data centers, PV with low or no storage, EV charging with buffer battery, insensitive loads etc. as well as a smooth transition in and out of operation with maximum current without losing synchronism, thus improving the fault handling capability.

[0064] The system provides an explicit current control and current limitation and an explicit PLL for synchronization with the grid before closing an MCB and for preventing loss of synchronism during faults. The PLL together with the virtual admittance acts as a virtual swing equation, obviating synchronization using power balance.

[0065] FIGS. 4 to 6b show a more detailed overview of the proposed grid supporting control scheme and respective equivalent circuits.

[0066] The control scheme of FIG. 4 is conceptually depicted in FIGS. 2a and 2b. The control scheme of FIG. 2a can be separated into two functional parts being a VSM without any governor, i.e. a spinning wheel or inertia, respectively, as shown by the dotted line and a current source connected in parallel at the terminals of the virtual synchronous machine. The behaviour of the virtual synchronous machine is emulated with the PLL. The current source is working in parallel. It acts simultaneously as a fast power setpoint tracker and as a governor, because it ensures steady-state power balance between the grid and the spinning wheel. The inertial response with respect to the active power is ensured by the virtual admittance. In the steady state, the complete power flowing to the grid is injected by the current source. The spinning wheel injects power only during transients.

[0067] FIG. 4 shows a system according to an embodiment having a droop control unit 1, a current control unit 2, a virtual admittance unit 3 and a phase locked loop (PLL) unit 4. The virtual admittance unit 3 and the PLL unit 4 are configured to emulate an inertia of the VSM and a virtual current source 5 is connected in parallel to the VSM. In this embodiment, an output signal of the droop control unit 1 is connected to the virtual current source 5 in order to emulate a speed governor.

[0068] The system according to a preferred embodiment will now be described in more detail. The simplest form of traditional state-of-the-art implementations of a virtual synchronous machine are based on the swing equation. The goal of virtual synchronous machine control is to make the behaviour of the converter at the point of common coupling (PCC) equal to the behaviour of a synchronous machine.

[0069] FIGS. 5a to 5c are equivalent circuits of respective components, i.e. state-of-the-art virtual machine variants, depicted in FIGS. 1a and 1b. In particular, FIG. 5a shows a converter, FIG. 5b shows a VSM without virtual inductance and FIG. 5c shows a VSM with virtual inductance.

[0070] The following derivations are based on a converter with an inductive output filter for simplicity reasons. However, the control method proposed herein is suitable for converters with any type of output filter structure, such as L, LC or LCL.

[0071] The swing equation couples the change of frequency of the voltage source V.sub.C with the active power flowing out or into the machine. In the case of a VSM without virtual inductance, the converter voltage V.sub.C is equal to the back electromotive force (back-emf) of the virtual machine. The converter filter inductance L.sub.C is equal to the stator inductance of the virtual machine and the PCC voltage V.sub.pcc is equal to the stator voltage of the virtual machine. The converter voltage V.sub.C (virtual back-emf) has the rotational frequency ω.sub.r to highlight its equivalency with the virtual rotor frequency. The PCC voltage (virtual stator voltage) has the rotational frequency ω.sub.pcc. The swing equation looks as follows:

[00001]$\begin{array}{cc}M.Math.\frac{d{\omega }_r}{dt}=-P_{\mathrm{out}}+\stackrel{\mathrm{setpoint}}{\overbrace{P_{\mathrm{set}}}}-\stackrel{\mathrm{governor}}{\overbrace{K_g\left({\omega }_r-{\omega }_{\mathrm{set}}\right)}}-\stackrel{\mathrm{damper}\mathrm{winding}}{\overbrace{K_f\left({\omega }_r-{\omega }_{\mathrm{pcc}}\right)}}& \left(1\right)\end{array}$$\begin{array}{cc}\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r& \left(2\right)\end{array}$

[0072] In quasi steady-state, the power flow is given by the angle difference between the virtual back-emf V.sub.C and the PCC voltage V.sub.pcc across the converter filter reactance X.sub.C=ω.sub.N*L.sub.C.

[00002]$\begin{array}{cc}{P}_{\mathrm{out}}=\frac{V_C{V}_{\mathrm{pcc}}}{X_C}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(3\right)\end{array}$

[0073] There is a direct dependency of the power flow, the reactances and the angle differences across parts of the transmission line, i.e.

[00003]$\begin{array}{cc}{P}_{\mathrm{out}}=\frac{V_C{V}_{\mathrm{pcc}}}{X_c}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)=\frac{V_{\mathrm{pcc}}{V}_g}{X_g}\sin \left({\theta }_{\mathrm{pcc}}-{\theta }_g\right)=\frac{V_C{V}_g}{X_C+X_g}\sin \left({\theta }_r-{\theta }_g\right)& \left(4\right)\end{array}$

[0074] The swing equation thus becomes

[00004]$\begin{array}{cc}\frac{d{\omega }_r}{\mathrm{dt}}=-\frac{V_C{V}_{\mathrm{pcc}}}{{\mathrm{MX}}_C}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)+\frac{1}{M}\stackrel{\mathrm{setpoint}}{\overbrace{P_{\mathrm{set}}}}-\frac{1}{M}\stackrel{\mathrm{governor}}{\overbrace{K_g\left({\omega }_r-{\omega }_{\mathrm{set}}\right)}}-\frac{1}{M}\stackrel{\mathrm{damper}\mathrm{winding}}{\overbrace{K_f\left({\omega }_r-{\omega }_{\mathrm{pcc}}\right)}}& \left(5\right)\end{array}$$\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r$

[0075] In a second step, state-of-art VSM implementations have introduced a virtual reactance X.sub.vs=ω.sub.N*L.sub.vs according to FIG. 5c. The virtual reactance changes the equations slightly. The converter voltage V.sub.C in phasor notation is calculated according to

V.sub.C=V.sub.v−jX.sub.vs.Math.I.sub.c  (6)

[0076] The virtual back-emf of the machine is designated as V.sub.v (with rotational frequency (or and angle θ.sub.r) and has moved behind the virtual reactance X.sub.vs. Regarding the behaviour at the PCC, the virtual machine has now a total virtual stator reactance of X.sub.v=X.sub.c+X.sub.vs and the power flow equation changes to

[00005]$\begin{array}{cc}{P}_{\mathrm{out}}=\frac{V_v{V}_{\mathrm{pcc}}}{X_{\mathrm{vs}}+X_c}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)=\frac{V_v{V}_{\mathrm{pcc}}}{X_v}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(7\right)\end{array}$

and the swing equation becomes

[00006]$\begin{array}{cc}\frac{d{\omega }_r}{\mathrm{dt}}=-\frac{V_v{V}_{\mathrm{pcc}}}{{\mathrm{MX}}_v}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)+\frac{1}{M}\stackrel{\underset{︷}{\mathrm{setpoint}}}{P_{\mathrm{set}}}-\frac{1}{M}\stackrel{\underset{︷}{\mathrm{governor}}}{K_g\left({\omega }_r-{\omega }_{\mathrm{set}}\right)}-\frac{1}{M}\stackrel{\underset{︷}{\mathrm{damper}\mathrm{winding}}}{K_f\left({\omega }_r-{\omega }_{\mathrm{pcc}}\right)}& \left(8\right)\end{array}$$\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r$

[0077] It should be noted that the virtual inductance L.sub.vs is in series to the converter filter inductance L.sub.C and therefore adds to the total virtual stator inductance of the virtual machine seen from the PCC.

[0078] FIGS. 6a and 6b show an equivalent model of a control scheme according to an exemplary embodiment. Therein, the swing equation is not directly implemented as in traditional approaches. Moreover, the effect of the PLL together with the virtual admittance is compared to the swing equation. The angle θ.sub.r is no longer computed by the swing equation, but it is the output of the PLL according to the PLL equations:

[00007]$\begin{array}{cc}{\omega }_r=\left(K_{\mathrm{pll},p}+\frac{K_{\mathrm{pll},i}}{s}\right).Math.V_{\mathrm{pccq}}=-\left(K_{\mathrm{pllp}}+\frac{K_{\mathrm{plli}}}{s}\right).Math.V_{\mathrm{pcc}}.Math.\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(9\right)\end{array}$$\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r$

[0079] Calculating the derivative of equation (9) yields:

[00008]$\begin{array}{cc}\frac{d{\omega }_r}{\mathrm{dt}}=-\left(s.Math.K_{\mathrm{pll},p}+K_{\mathrm{pll},i}\right).Math.V_{\mathrm{pcc}}.Math.\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(10\right)\end{array}$$\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r$

[0080] For small angle differences (which is the case for reasonable PLL tuning), the sine function can be approximated as sin(θ.sub.r−θ.sub.pcc)≈(θ.sub.r−θ.sub.pcc) and the derivative thereof becomes s.Math.sin(θ.sub.r−θ.sub.pcc)≈ω.sub.r−ω.sub.pcc.

[0081] The equation set may thus also be formulated as follows:

[00009]$\begin{array}{cc}\frac{d{\omega }_r}{\mathrm{dt}}=-K_{\mathrm{pll},i}.Math.V_{\mathrm{pcc}}.Math.\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)-K_{\mathrm{pll},p}.Math.V_{\mathrm{pcc}}.Math.\left({\omega }_r-{\omega }_{\mathrm{pcc}}\right)& \left(11\right)\end{array}$$\frac{d{\theta }_r}{\mathrm{dt}}={\omega }_r$

[0082] By comparing equation (11) with the original swing equation (1), the PLL gains for formal equivalence of the two equations may be

[00010]$\begin{array}{cc}{K}_{\mathrm{pll},p}=\frac{K_f}{{\mathrm{MV}}_{\mathrm{pcc}}},K_{\mathrm{pll},i}=\frac{V_v}{{\mathrm{MX}}_v}& \left(12\right)\end{array}$

[0083] The governor power will be replaced with the parallel current source in a later step below. The proportional gain of the PLL therefore emulates the damper winding effect and the integral gain couples the angle difference with an increase/decrease of frequency, emulating the self-synchronization principle of synchronous machines.

[0084] Opposite to the swing equation, the PLL does not implicitly couple power flow with the angle difference, because it describes only the evolution of the internal PLL angle θ.sub.r. Coupling of power flow and angle difference has to be ensured explicitly with an additional current reference for the current controller. The reference is created with a virtual admittance being equivalent to the inverse of the virtual stator impedance, i.e.

Y.sub.v(s)=Z.sub.v(s).sup.−1  (13)

[0085] The stator impedance is assumed to be of RL-type. If the admittance is implemented in dq-reference frame it can be described as follows

[00011]$\begin{array}{cc}{Z}_v=\left[\begin{array}{cc}{R}_v+s.Math.L_v& -{\omega }_N.Math.L_v\\ {\omega }_N.Math.L_v& R_v+s.Math.L_v\end{array}\right]& \left(14\right)\end{array}$$\begin{array}{cc}{Y}_v=\left[\begin{array}{cc}\frac{R_v+s.Math.L_v}{R_v^2+2L_v{R}_{v}s+L_v^2\left(s^2+{\omega }_N^2\right)}& \frac{{\omega }_N{L}_v}{R_v^2+2L_v{R}_{v}s+L_v^2\left(s^2+{\omega }_N^2\right)}\\ \frac{-{\omega }_N{L}_v}{R_v^2+2L_v{R}_{v}s+L_v^2\left(s^2+{\omega }_N^2\right)}& \frac{R_v+s.Math.L_v}{R_v^2+2L_v{R}_{v}s+L_v^2\left(s^2+{\omega }_N^2\right)}\end{array}\right]& \left(15\right)\end{array}$

[0086] The current references i.sub.v,dq are created according to the matrix multiplication of the virtual admittance with the voltage difference between a virtual back-emf voltage V.sub.v aligned to the d-direction of the PLL reference frame (V.sub.v=V.sub.N+j*0) and the PCC voltage V.sub.pcc (this is shown in FIG. 7 depicting a vector diagram for a transient situation).

i.sub.v,d=Y.sub.v,dd(s).Math.(V.sub.pcc,d−V.sub.N)+Y.sub.v,dq(s).Math.V.sub.pcc,q  (16)

i.sub.v,q=Y.sub.v,qd(s).Math.(V.sub.pcc,d−V.sub.N)+Y.sub.v,qq(s).Math.V.sub.pcc,q  (17)

[0087] Alternatively, it is also possible to work with complex numbers and implement the admittance according to

[00012]$\begin{array}{cc}{i}_{v,d}+j.Math.i_{v,q}=\frac{1}{\left(R+s.Math.L_v+j.Math.{\omega }_N{L}_v\right)}.Math.\left(\left(V_{\mathrm{pcc},d}+j.Math.V_{\mathrm{pcc},q}\right)-\left(V_N+j.Math.0\right)\right)& \left(18\right)\end{array}$

[0088] In the steady state and assuming that R.sub.v<<ω.sub.N*L.sub.v, the admittance simplifies to

[00013]$\begin{array}{cc}{Y}_v\approx \left[\begin{array}{cc}0& \frac{1}{w_N{L}_v}\\ -\frac{1}{{\omega }_N{L}_v}& 0\end{array}\right]& \left(19\right)\end{array}$

and thus leads to the following steady-state current references:

[00014]$\begin{array}{cc}{i}_{v,d}=\frac{1}{{\omega }_N{L}_v}.Math.V_{\mathrm{pcc},q}& \left(20\right)\end{array}$$\begin{array}{cc}{i}_{v,q}=-\frac{1}{{\omega }_N{L}_v}.Math.\left(V_{\mathrm{pcc},d}-V_N\right)& \left(21\right)\end{array}$

[0089] If the PCC voltage V.sub.pcc is equal to the nominal voltage V.sub.N, the injected q-axis current can be neglected. Thus, a coupling between q-voltage and active current in d-direction over the virtual stator reactance (X.sub.v=ω*L.sub.V) may be described as

[00015]$\begin{array}{cc}{i}_{v,d}=\frac{1}{X_v}.Math.V_{\mathrm{pcc},q}=-\frac{V_{\mathrm{pcc}}}{X_v}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(22\right)\end{array}$

wherein the related power flow (assuming fast current tracking) is

[00016]$\begin{array}{cc}{P}_{\mathrm{out}}=V_v{i}_{v,d}=-\frac{V_v{V}_{\mathrm{pcc}}}{X_v}\sin \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)& \left(23\right)\end{array}$

[0090] Therefore, according to the present disclosure, an equivalence between the quasi steady-state power flow governed by the swing equation and the power flow created by the PLL+virtual admittance combination is ensured.

[0091] The virtual admittance may be implemented with the full dynamic model to ensure passivity and damping of high frequency resonances. However, simplified admittance models (neglecting s*L terms) are also possible as are more complex models which permit additional filtering functions. Even asymmetric admittance is possible. The minimal requirement is to implement coupling between q-voltage and active current.

[0092] It has been shown that the combination of special settings for the PLL gains and a virtual admittance allows emulating the effect of inertia, damper winding and stator impedance of a virtual synchronous machine with the conventional control structure used for vector current control.

[0093] In the following, the droop block is further described. Different to the original VSM implementation, the proposed control method just implements a spinning wheel without a governor for the mechanical input power. Therefore, the injected power from the spinning wheel will be zero in steady-state (i.sub.v,d=0) and the angle θ.sub.r aligns with θ.sub.pcc.

[0094] The governor power is replaced by a current source ensuring the steady-state power balance. In addition to the reference coming from the virtual admittance, an active current reference is created according to

[00017]$\begin{array}{cc}{i}_{d,\mathrm{ref}}=\frac{P_{\mathrm{set}}+K_g.Math.\left({\omega }_r-{\omega }_{\mathrm{set}}\right)}{V_{\mathrm{pcc},d}}=\frac{P_{\mathrm{set}}+K_g.Math.\left({\omega }_r-{\omega }_{\mathrm{set}}\right)}{V_{\mathrm{pcc}}.Math.\cos \left({\theta }_r-{\theta }_{\mathrm{pcc}}\right)}& \left(24\right)\end{array}$

which leads to an injected power of

P=V.sub.pcc,d.Math.i.sub.d,ref=V.sub.pcc cos(θ.sub.r−θ.sub.pcc).Math.i.sub.d,ref=P.sub.set+K.sub.g.Math.(ω.sub.r−ω.sub.set)  (25)

[0095] The main difference is that this current reference is directly fed to the current controller, there is no filtering over the swing equation taking place. Set-point changes feed through directly and are followed much faster compared to conventional VSM implementations.

[0096] For reasonable loading conditions and reasonable virtual stator reactance of the spinning wheel, the angle difference θ.sub.r−θ.sub.pcc is small and cos(θ.sub.r−θ.sub.pcc) is close to unity. In that case, the division by V.sub.pcc,d can be replaced with a division by constant V.sub.N.

[0097] Furthermore, an active voltage regulator (AVR) may be added to keep the magnitude of the PCC voltage constant. The AVR block could be of PI, or integrator (I) type, or proportional type (P) only. It creates a q-current reference i.sub.gref which is used to regulate the voltage magnitude.

i.sub.qref=G.sub.avr(s).Math.(|V.sub.pcc|−V.sub.N)  (26)

[0098] However, the AVR block can also be omitted since the virtual admittance already implements a proportional gain AVR effect with

[00018]$\begin{array}{cc}{i}_{v,q}=-\frac{1}{{\omega }_1{L}_v}.Math.\left(V_{\mathrm{pcc},d}-V_N\right)& \left(27\right)\end{array}$

[0099] As has been indicated above, a factor k.sub.VSM may be used. The factor k.sub.VSM may be configured to change the characteristics of the system continuously from voltage source to current source by proportionally scaling the output signals of the virtual admittance with k.sub.VSM.

[0100] The factor k.sub.VSM can be fed into at least one of the droop block, the virtual admittance block or the PLL block as described throughout the specification in order to increase or decrease the inertial response of the system to disturbances in a main grid to which the micro grid converter, PV inverter, UPS or similar is connected. Preferably at least one of the micro grid converter, or the PV inverter, or the UPS, or the grid intertie converter, or the railway grid intertie converter, or the HVDC converter, or the BESS is connected to the main grid. More preferably, the micro grid converter, PV inverter or UPS is connected. Therein, k.sub.VSM may scale a nominal power of the VSM by proportionally scaling the output signals of the virtual admittance with k.sub.VSM, inversely proportionally scaling the proportional gain of the PLL with k.sub.VSM, and/or proportionally scaling a droop constant with k.sub.VSM.

[0101] k.sub.VSM may also be used to adjust or scale the amount of grid support. Preferably, the factor k.sub.VSM is continuous and ranges from 0 to 1. With this factor it is possible to scale the nominal power of the virtual machine that can be thought to operate in parallel to the current source with a single factor. The connections and inputs of k.sub.VSM are shown in FIG. 3b. The equations are as follows:

[00019]$\begin{array}{cc}{Y}_{\mathrm{virt}}=k_{\mathrm{VSM}}.Math.Y_{\mathrm{virt},N}& \left(28\right)\end{array}$$\begin{array}{cc}M=k_{\mathrm{VSM}}.Math.M_N& \left(29\right)\end{array}$$\begin{array}{cc}{K}_g=k_{\mathrm{VSM}}.Math.K_{g,N}& \left(30\right)\end{array}$$\begin{array}{cc}{K}_{\mathrm{pll},i}=\frac{3}{2}.Math.\frac{V_N}{k_{\mathrm{VSM}}.Math.M_N\frac{1}{k_{\mathrm{VSM}}.Math.Y_{\mathrm{virt},N}}}=\frac{3}{2}.Math.\frac{V_N}{M_N.Math.Z_{\mathrm{virt},N}}=K_{\mathrm{pll},i,N}& \left(31\right)\end{array}$$\begin{array}{cc}{K}_{\mathrm{pll},p}=K_f.Math.\frac{1}{k_{\mathrm{VSM}}.Math.M_N\frac{3}{2}{V}_N}=\frac{1}{k_{\mathrm{VSM}}}.Math.K_{\mathrm{pll},p,N}& \left(32\right)\end{array}$

[0102] With reference to FIG. 4, the modified block diagrams of the droop block, the virtual admittance block and the PLL block are shown in FIG. 8.

[0103] It is important to saturate the inverse of k.sub.VSM used in the PLL block to a maximum value to keep the PLL loop stable. A too high proportional gain of the PLL loop can lead to instability, a well-known effect of standard vector current control with PLL.

[0104] It should be noted that adjusting the amount of grid support by scaling the nominal power of the VSM is a unique feature of the control structure of the present disclosure. The nominal power of the parallel current source is not affected, and the control structure can therefore continue to operate with conventional current control and with maximum power capability, even if k.sub.VSM is set to zero.

[0105] This feature may not be realised with conventional VSM implementations. With a standard VSM, the power transfer capability is linked to the nominal power of the VSM. The power flow is controlled by advancing the angle of the virtual back-emf in VSM and the voltage difference is applied over the virtual stator reactance. Reducing the nominal power of the VSM leads to an increase of the reactance and consequently, an increased angle difference is required to transfer the same amount of power. Because the maximum angle difference is limited to 90°, the power transfer capability reduces with the nominal power of the VSM. Consequently, the nominal power of the VSM cannot be independently adjusted in conventional control approaches. Other applications than the ones disclosed herein may also be feasible.

[0106] A possible application during a fault event and subsequent resynchronization after clearance of the fault is shown in FIG. 9. Without reducing the k.sub.VSM factor (similar to standard VSM behaviour), heavy oscillations are triggered after clearance of the fault because the synchronization between the grid and the VSM has been lost while the PCC voltage was close to zero.

[0107] In contrast, if the k.sub.VSM factor is reduced to zero during the LVRT event, smooth resynchronization is achieved and no oscillations in between the converter and the grid after fault clearance is observed. This can be seen from the graphs in FIG. 10 showing the behaviour of the proposed control system. Due to the temporary reduction of k.sub.VSM, the control characteristics has turned into a conventional stiff current control scheme with controllable and preferred behaviour during fault events. It is possible to inject reactive current during the LVRT event or impress any other predefined current reference.

[0108] The grid support may also be run with reduced nominal power, e.g. 10-20%, in applications that have only low energy storage capability, such as in UPS systems or in PV with low or no energy storage. A certain percentage of the nominal power could be reserved for grid support whereas the remaining power requirement of the application is handled with conventional current control.

[0109] FIGS. 11a and 11b show another preferred embodiment of the present disclosure as a schematic block diagram. In particular, FIG. 11a relates to an alternative implementation with a virtual mechanical governor instead of a current source governor. This is inter alia achieved by connecting the output signal of the droop control block to the PLL block. Thereby, a virtual mechanical speed governor is emulated. Analogously to the control scheme as shown in FIG. 3a, the factor k.sub.VSM may also be fed into the PLL block and/or the speed control block and/or the virtual admittance block. The description of features that correspond to the first embodiment will be omitted.

[0110] FIG. 12 shows the alternative configuration with respect to the scheme proposed in FIG. 4. Instead of using the current source as a governor, a virtual mechanical governor can be implemented that changes the power flow by advancing or delaying the rotor angle of the VSM. This is achieved by removing the direct connection of the droop block to the current controller. Instead, an additional input is required for the PLL block that turns the governor power reference P.sub.ref into a virtual rotor angle shift.

[0111] In other words, FIG. 12 shows a system according to an embodiment having a droop control unit 1, a current control unit 2, a virtual admittance unit 3 and a phase locked loop (PLL) unit 4. The virtual admittance unit 3 and the PLL unit 4 are configured to emulate an inertia of the VSM and a virtual current source 5 is connected in parallel to the VSM. In this embodiment, an output signal of the droop control unit 1 is connected to the PLL unit 4 in order to emulate a virtual mechanical speed governor.

[0112] The following applies to both embodiments and control methods, respectively. A current source may be connected in parallel to the VSM by using the input i.sub.d,ref2 to the current controller which can be manipulated independently of the VSM. It is still possible to adjust the nominal power of the VSM with the factor k.sub.VSM. However, with reduced nominal power P.sub.N,VSM of the VSM, P.sub.set can only be varied inside the range of +−P.sub.N,VSM, otherwise the VSM could be overloaded due to the increased virtual reactance. To utilize the full power capability of the converter, it is required to work with the current source input i.sub.d,ref2, which is independent of the nominal power of the VSM.

[0113] Optionally, an active damping branch (e.g. a virtual damping resistor) may be connected in parallel to the current source. Thus,

i.sub.ad,dq=Ga.sub.d,dq(s).Math.V.sub.pcc,dq  (33)

[0114] Such an active damping branch usually employs a band-pass filter such that it is effective only in a certain frequency range. The difference to the virtual stator impedance introduced before is that the active damping branch is multiplied with the PCC voltage directly, without calculating the voltage difference between PCC voltage and virtual back-emf voltage V.sub.v. It therefore creates a current in another direction than the virtual stator impedance, i.e. for a virtual resistor, the damping current is in phase with the PCC voltage. The active damping branch is not affected by the scaling of the nominal power of the VSM with the factor k.sub.VSM introduced elsewhere herein, it is therefore also active if the VSM effect is set to zero. The active damper branch could potentially be used in both embodiments, i.e. the variant using a current source governor and the variant using the virtual mechanical governor.

[0115] FIG. 13 depicts an equivalent circuit of the control concept using an active damper in parallel to the current source. FIG. 14 is a detailed view of the implementation of an active damper branch.

[0116] Optionally, two PLL blocks could be implemented. The current controller could run in a reference frame created with a fast PLL for improved performance whereas the response of the VSM is emulated with a slow PLL. Instead of a dq-frame based approach with PI current control blocks, the concept can also be implemented using any other current control method, such as current control based on proportional-resonant (PR) control, state-feedback control, LQR or MPC.

[0117] The implementation of the control method is not restricted to the synchronous dq-reference frame, but it can be implemented in any other reference frame, such as the stationary alpha-beta reference frame, or the phase oriented abc reference frame, or any other suitable reference frame. The proposed control method according to the embodiments described above is not restricted to three-phase systems. It can be implemented also for single-phase systems.

[0118] In case of an operation on the asymmetric conditions, the following measures may be taken to adapt the system thereto.

[0119] A positive/negative/zero sequence separator block can be used to extract and separate positive/negative/zero sequence components of the PCC voltage and of the converter current and use specific control schemes for the individual sequences. An improved negative sequence current control can be achieved with proportional resonant (PR) blocks tuned at the second harmonic frequency in the dq-reference frame.

[0120] Zero back-emf may be emulated for the negative-sequence component current response of a VSM, having different parameters for the positive and negative sequence virtual admittance. The harmonic current control with proportional resonant (PR) blocks can be tuned to specific harmonic frequencies or their counterpart in the dq-reference frame.

[0121] According to present disclosure, the control method proposed greatly reduces complexity of a grid forming vector current control while improving the response to faults or irregularities in the system.

[0122] FIG. 15 is a schematic diagram of a grid forming vector current control system according to the present disclosure. The system is configured to emulate a virtual synchronous machine (VSM) by a droop control unit 1, a current control unit 2, a phase lock loop (PLL) unit 4 and a virtual current source 5.

[0123] Other aspects, features, and advantages will be apparent from the summary above, as well as from the description that follows, including the figures and the claims.

[0124] While embodiments have been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. It will be understood that changes and modifications may be made by those of ordinary skill within the scope of the following claims. In particular, the present disclosure covers further embodiments with any combination of features from different embodiments described above and below.

[0125] Furthermore, in the claims the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single unit may fulfil the functions of several features recited in the claims. The terms “essentially”, “about”, “approximately” and the like in connection with an attribute or a value particularly also define exactly the attribute or exactly the value, respectively. Any reference signs in the claims should not be construed as limiting the scope.

LIST OF CITATIONS

[0126] [1] J. Rocabert, A. Luna, F. Blaabjerg and P. Rodriguez, “Control of Power Converters in AC Microgrids,” in IEEE Transactions on Power Electronics, vol. 27, no. 11, pp. 4734-4749, November 2012 [0127] [2] S. D′Arco and J. A. Suul, “Virtual synchronous machines—Classification of implementations and analysis of equivalence to droop controllers for microgrids,” 2013 IEEE Grenoble Conference, Grenoble, 2013, pp. 1-7 [0128] [3] Y. Sun, X. Hou, J. Yang, H. Han, M. Su and J. M. Guerrero, “New Perspectives on Droop Control in AC Microgrid,” in IEEE Transactions on Industrial Electronics, vol. 64, no. 7, pp. 5741-5745, July 2017