Control system configured for, and a method for, emulating a virtual synchronous machine of a grid-forming voltage source converter
A method for grid forming control using a voltage source converter (VSC), connected to a grid at a point-of-common-coupling (PCC), is provided. The method comprises calculating a converter voltage reference for the VSC based at least on a reference current, calculating a phase-angle of an electromotive force (EMF) voltage vector of the VSC based on at least an active power reference, calculating a voltage amplitude of the EMF voltage vector based on at least a grid voltage at the PCC and a grid voltage reference, calculating the reference current by feeding the EMF voltage vector through a virtual admittance, and limiting the active power reference and the voltage amplitude based at least on a maximum allowed current threshold associated with operation of the VSC such that the reference current does not exceed said maximum allowed current threshold.
1 . A control system configured for grid forming control using a voltage source converter (VSC) connected to a grid at a point-of-common-coupling (PCC), the control system comprising:
an alternate current (AC) controller configured to calculate a converter voltage reference (V c,ref ) for the VSC based at least on a reference current (I g,ref );
an active-power controller configured to calculate a phase-angle (θ EMF ) of an electromotive force (EMF) voltage vector (V EMF ) of the VSC based on at least an active power reference (P g,ref ); and
a voltage controller configured to calculate a voltage amplitude (V EMF ) of the EMF voltage vector (V EMF ) based on at least a grid voltage (V g ) at the PCC and a grid voltage reference (V g,ref );
wherein the EMF voltage vector (V EMF ), comprising the phase-angle (θ EMF ) and the voltage amplitude (V EMF ), minus the grid voltage (V g ) are multiplied by a virtual admittance to calculate the reference current (I g,ref ),
said control system further comprising:
a current limiter configured to prevent operation of the VSC above a maximum allowed current threshold (l lim );
an active power reference limiter configured to limit the active power reference (P g,ref ) input to the active-power controller based at least on the maximum allowed current threshold (l lim ); and
a voltage limiter configured to limit the voltage amplitude (V EMF ) output from the voltage controller based at least on the maximum allowed current threshold (l lim );
wherein the limitation of the active power reference (P g,ref ) and the limitation of the voltage amplitude (V EMF ) prevent the reference current (I g,ref ) from exceeding the maximum allowed current threshold (I lim );
wherein the active power reference (P g,ref ) is a sum of an active power setpoint (P set,ref ) and an inertial active power reference (P H ); and
wherein the control system further comprises an inertial phase-locked loop (IPLL) unit configured to calculate the inertial active power reference (P H ) based on the grid voltage (V g ) at the PCC and the converter voltage reference (V c,ref ).
2 . The control system according to claim 1 , wherein the IPLL is configured to calculate the inertial active power reference (P H ) as a function of a calculated grid frequency derivative and a desired inertia time constant.
3 . The control system according to claim 1 , wherein the IPLL further comprises an anti-windup function.
4 . The control system according to claim 1 , wherein the AC controller is configured to calculate the converter voltage reference (V c,ref ) for the VSC based on the reference current (I g,ref ), a grid voltage (V g ) at the PCC, and a grid current (I g ) at the PCC.
5 . The control system according to claim 1 , wherein the active power reference limiter is configured to limit the active power reference (P g,ref ) input to the active-power controller based on the maximum allowed current threshold (l lim ), the grid voltage (V g ) at the PCC, and/or reactive power (Q g ) at the PCC.
6 . The control system according to claim 5 , wherein the active power reference limiter is configured to limit the active power reference (P g,ref ) input to the active-power controller below an active power threshold (P lim ) which is calculated according to:
P
lim
=
(
❘
"\[LeftBracketingBar]"
v
g
❘
"\[RightBracketingBar]"
I
lim
)
2
-
Q
g
2
.
7 . The control system according to claim 1 , wherein the active power reference limiter is further configured to limit the active power reference (P g,ref ) input to the active-power controller based on grid codes received from a system operator and/or active power and/or reactive power (Q g ) at the PCC.
8 . The control system according to claim 1 , wherein the grid voltage reference (V g,ref ) and/or an active power setpoint (P set,ref ) are received from a system operator.
9 . The control system according to claim 1 , wherein the grid voltage reference (V g,ref ), before being input to the voltage controller, is subtracted by an output of a droop function having the reactive power (Q g ) at the PCC as an input.
10 . The control system according to claim 1 , wherein the voltage controller is further configured to calculate the voltage amplitude (V EMF ) of the EMF voltage vector by subtracting the grid voltage reference (V g,ref ) by the grid voltage (V g ), by integrating the subtracted grid voltage reference (V g,ref ), and by adding a rated system voltage (V rated ) to the integrated and subtracted grid voltage reference (V g,ref ).
11 . The control system according to claim 1 , wherein a difference between the voltage amplitude (V EMF ) of the voltage controller and the voltage amplitude (V EMF ) output from a voltage limiter is multiplied by a feedback gain (k back ) and subtracted from the grid voltage reference (V g,ref ) input to the voltage controller.
12 . The control system according to claim 1 , wherein a voltage limit (V lim ) calculated by the voltage limiter to limit the voltage amplitude (V EMF ) output from the voltage controller is calculated by summing the grid voltage (V g ) at the PCC and a voltage drop across a virtual impedance, wherein the virtual impedance is equal to the inverse of the virtual admittance, and wherein the voltage drop across the virtual impedance is calculated by the EMF voltage vector (V EMF ), comprising the phase-angle (θ EMF ) and the voltage amplitude (V EMF ), minus the grid voltage vector (V g ) being multiplied by the virtual admittance.
13 . The control system according to claim 11 , wherein a voltage limit (V lim ) calculated by the voltage limiter to limit the voltage amplitude (V EMF ) output from the voltage controller is calculated according to:
V
lim
=
V
g
+
P
g
,
ref
-
Q
max
conj
(
V
g
)
(
R
V
+
j
X
V
)
wherein Q max is a maximum amount of available reactive power and (R V +jX V ) is a virtual impedance which is equal to the inverse of the virtual admittance.
14 . The control system according to claim 13 , wherein the maximum amount of available reactive power (Q max ) is determined based on an allowed apparent power and the active power reference (P g,ref ).
15 . The control system according to claim 13 , wherein the maximum amount of available reactive power (Q max ) is calculated according to:
Q
max
=
(
V
g
*
I
lim
)
2
-
P
g
,
ref
*
P
g
,
ref
.
16 . The control system according to claim 1 , wherein the current limiter is configured for current limitation so as to at least partly preserve an angle of the reference current (I g,ref ) in accordance with a geometrical shape.
17 . The control system according to claim 1 , wherein the maximum allowed current threshold (l lim ) is based on at least one of: an ambient temperature at the VSC, a safe operating area (SOA) of the VSC, or a temperature of semiconductors of the VSC.
18 . A method for grid forming control using a voltage source converter (VSC) connected to a grid at a point-of-common-coupling (PCC), the method comprising:
calculating a converter voltage reference (V c,ref ) for the VSC based at least on a reference current (I g,ref );
calculating a phase-angle (θ EMF ) of an electromotive force (EMF) voltage vector of the VSC based on at least an active power reference (P g,ref );
calculating a voltage amplitude (V EMF ) of the EMF voltage vector based on at least a grid voltage (V g ) at the PCC and a grid voltage reference (V g,ref );
calculating the reference current (I g,ref ) by feeding the phase angle (θ EMF ) and the voltage (V EMF ) of the EMF voltage vector through a virtual admittance; and
limiting the active power reference (P g,ref ) and the voltage amplitude (V EMF ) based at least on a maximum allowed current threshold (l lim ) associated with operation of the VSC such that the reference current (I g,ref ) does not exceed said maximum allowed current threshold (I lim );
wherein the active power reference (P g,ref ) is a sum of an active power setpoint (P set,ref ) and an inertial active power reference (P H ); and
wherein the method further comprises calculating the inertial active power reference (P H ) based on the grid voltage (Ve) at the PCC and the converter voltage reference (V c,ref ).
19 . The method of claim 18 , further comprising preventing operation of the VSC above said maximum allowed current threshold if the reference current (I g,ref ) is above said maximum allowed current threshold.