System and method for impedance measurement using series and shunt injection
A method for impedance measurement in a three-phase AC system is provided. The method includes injecting a shunt perturbation signal into the three-phase AC system and collecting a response to the shunt perturbation signal, and injecting a series perturbation signal into the three-phase AC system and collecting a response to the series perturbation signal. The response to the shunt perturbation signal and the response to the series perturbation signal are then transferred from abc coordinate to dq coordinates. At least one impedance of the three-phase AC system is calculated based on the response to the shunt perturbation signal and the response to the series perturbation signal.
1. A method of impedance measurement in a three-phase alternating current (AC) system, the method comprising:
connecting a perturbation injector to the three-phase AC system, the perturbation injector comprising a voltage source inverter having a shunt injection circuit and a series injection circuit that are operable without active DC power addition;
connecting by the perturbation injector the shunt injection circuit to the three-phase AC system;
injecting by the shunt injection circuit a shunt perturbation signal into the three-phase AC system;
collecting by a collection circuit of an impedance measurement unit a response to the shunt perturbation signal;
switching by the perturbation injector from the shunt injection circuit to the series injection circuit;
injecting by the series injection circuit a series perturbation signal into the three-phase AC system;
collecting by the collection circuit of the impedance measurement unit a response to the series perturbation signal;
transferring by an instrumentation platform computer the response to the shunt perturbation signal and the response to the series perturbation signal from three-phase (abc) coordinates to direct and quadrature (dq); and
calculating by a control circuit at least one impedance of the three-phase AC system based on the response to the shunt perturbation signal and the response to the series perturbation signal.
2. The method of claim 1 , wherein the shunt perturbation signal is configured according to the following:
[
I
sd
(
s
)
I
sq
(
s
)
]
=
Z
Ldq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
I
pd
(
s
)
I
pq
(
s
)
]
[
I
Ld
(
s
)
I
Lq
(
s
)
]
=
Z
Sdq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
I
pd
(
s
)
I
pq
(
s
)
]
where Z Sdq (s) is a source impedance matrix, Z Ldq (s) is a load impedance matrix, I sd (s) is a d-axis source current, I sq (s) is a q-axis source current, I pd (s) is a d-axis perturbation current, I pq (s) is a q-axis perturbation current, I Ld (s) is a d-axis load current, and I Lq (s) is a q-axis load current.
3. The method of claim 1 , wherein the series perturbation signal is configured according to the following:
[
V
sd
(
s
)
V
sq
(
s
)
]
=
Z
Sdq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
V
pd
(
s
)
V
pq
(
s
)
]
[
V
Ld
(
s
)
V
Lq
(
s
)
]
=
Z
Ldq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
V
pd
(
s
)
V
pq
(
s
)
]
where Z Sdq (s) is a source impedance matrix, Z Ldq (s) is a load impedance matrix, V sd (s) is a d-axis source voltage, V sq (s) is a q-axis source voltage, V pd (s) is a d-axis perturbation voltage, V pq (s) is a q-axis perturbation voltage, V Ld (s) is a d-axis load voltage, and V Lq (s) is a q-axis load voltage.
4. The method of claim 1 , wherein the series perturbation signal is of the form:
x
(
t
)
=
sin
(
2
π
(
f
0
+
f
1
-
f
0
2
T
t
)
t
)
,
where f 0 is a start frequency, f 1 is an end frequency, T is a duration of at least one of the first perturbation signal and the second perturbation signal; and t is a time.
5. The method of claim 1 , wherein the action of transferring the response to the shunt perturbation signal and the response to the series perturbation signal from abc coordinate to dq coordinates comprises:
transforming an AC voltage to direct current (DC) voltage components; and
transforming an AC current to DC current components.
6. The method of claim 1 , wherein the action of calculating at least one impedance of the three-phase AC system comprises:
identifying frequency points of interest; and
calculating impedance at each identified frequency point.
7. A system for performing impedance measurement in a three-phase alternating current (AC) system, comprising:
a perturbation injector connectable to the three-phase AC system, the perturbation injector comprising a voltage source inverter having a shunt injection circuit configured to inject a shunt perturbation signal into the three-phase AC system and a series injection circuit configured to inject a series perturbation signal into the three-phase AC system, the voltage source inverter being selectively switchable from the shunt injection circuit to the series injection circuit, both of which are operable without active DC power addition;
a collection circuit configured to collect a response to the shunt perturbation signal and a response to the series perturbation signal; and
a control unit configured to transfer the response to the shunt perturbation signal and the response to the series perturbation signal from three-phase (abc) coordinates to direct and quadrature (dq) and to calculate at least one impedance of the three-phase AC system based on the response to the first perturbation signal and the response to the second perturbation signal.
8. The system of claim 7 , wherein the shunt injection circuit is configured to inject the shunt perturbation signal according to the following:
[
I
sd
(
s
)
I
sq
(
s
)
]
=
Z
Ldq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
I
pd
(
s
)
I
pq
(
s
)
]
[
I
Ld
(
s
)
I
Lq
(
s
)
]
=
Z
Sdq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
I
pd
(
s
)
I
pq
(
s
)
]
where Z Sdq (s) is a source impedance matrix, Z Ldq (s) is a load impedance matrix, I sd (s) is a d-axis source current, I sq (s) is a q-axis source current, I pd (s) is a d-axis perturbation current, I pq (s) is a q-axis perturbation current, I Ld (s) is a d-axis load current, and I Lq (s) is a q-axis load current.
9. The system of claim 7 , wherein the series injection circuit is configured to inject the series perturbation signal according to the following:
[
V
sd
(
s
)
V
sq
(
s
)
]
=
Z
Sdq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
V
pd
(
s
)
V
pq
(
s
)
]
[
V
Ld
(
s
)
V
Lq
(
s
)
]
=
Z
Ldq
(
s
)
(
Z
Sdq
(
s
)
+
Z
Ldq
(
s
)
)
-
1
[
V
pd
(
s
)
V
pq
(
s
)
]
where Z Sdq (s) is a source impedance matrix, Z Ldq (s) is a load impedance matrix, V sd (s) is a d-axis source voltage, V sq (s) is a q-axis source voltage, V pd (s) is a d-axis perturbation voltage, V pq (s) is a q-axis perturbation voltage, V Ld (s) is a d-axis load voltage, and V Lq (s) is a q-axis load voltage.
10. The system of claim 7 , wherein the series perturbation signal is of the form:
x
(
t
)
=
sin
(
2
π
(
f
0
+
f
1
-
f
0
2
T
t
)
t
)
,
where f 0 is a start frequency, f 1 is an end frequency, T is a duration of at least one of the first perturbation signal and the second perturbation signal; and t is a time.
11. The system of claim 7 , wherein the control unit is configured to transform an AC voltage to direct current (DC) voltage components, and transform an AC current to DC current components.
12. The system of claim 7 , wherein the control unit is configured to calculate the impedances of the three-phase AC system at each frequency point.