System and method for impedance measurement using chirp signal injection
A method for impedance measurement using chirp signal injection is provided. The method includes injecting at least one chirp signal into the three-phase AC system, and collecting at least one response to the at least one chirp signal. The method further includes transferring the at least one response from abc coordinates to dq coordinates. At least one impedance is calculated based on the at least one response to the at least one chirp signal.
1. A method of impedance measurement for a three-phase alternating current (AC) system, comprising:
connecting an injection circuit of an impedance measurement unit to the three-phase AC system, the injection circuit comprising a voltage source inverter configured for drawing power from the three-phase AC system to charge a capacitor and for using discharged power from the capacitor to inject chirp signals into the three-phase AC system;
injecting by the injection circuit at least one chirp signal into the three-phase AC system;
collecting by a collection circuit of the impedance measurement unit at least one response to the at least one chirp signal;
transferring by an instrumentation platform computer the at least one response from three-phase (abc) coordinates to direct and quadrature (dq) coordinates; and
calculating by a control circuit at least one impedance of the three-phase AC system based on the at least one response to the at least one chirp signal.
2. The method of claim 1 , wherein the at least one chirp signal includes one of the set consisting of a d-axis chirp signal and a q-axis chirp signal.
3. The method of claim 1 , wherein the at least one chirp signal includes a d-axis chirp signal and a q-axis chirp signal.
4. The method of claim 3 , wherein at least one of the d-axis chirp signal and the q-axis chirp 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 d-axis chirp signal and the q-axis chirp signal, and t is a time.
5. The method of claim 1 , wherein the action of transferring the at least one response from abc coordinates to dq coordinates comprises:
transforming an AC voltage response to direct current (DC) voltage components; and
transforming an AC current response to DC current components.
6. The method of claim 1 , wherein the action of calculating the impedances of the three-phase AC system comprises:
identifying frequency points of interest; and
calculating impedance at each frequency point of interest.
7. The method of claim 1 , further comprising:
generating a virtual perturbation signal through an injection transfer function matrix; and
collecting a response to the virtual perturbation signal,
wherein the action of calculating at least one impedance includes calculating an impedance based on the response to the virtual perturbation signal and the at least one response to the at least one chirp signal.
8. The method of claim 7 , wherein the action of generating a virtual perturbation signal through an injection transfer function matrix comprises:
generating the virtual perturbation signal using the equation
G
inj
(
s
)
=
[
G
injd
(
s
)
G
injq
(
s
)
]
,
where G inj (s) is the injection transfer function matrix, G injd (s) is a d-axis injection transfer function, and G injq (s) is a q-axis injection transfer function.
9. The method of claim 8 , wherein the action of generating a virtual perturbation signal through an injection transfer function matrix comprises:
generating two independent perturbation signals using the equations
G inj1 ( s )=[ A 1 B 1 ] T , G inj2 ( s )=[ A 2 B 2 ] T ,
where G inj1 (s) is a first injection transfer function matrix, G inj2 (s) is a second injection transfer function matrix, G inj1 is a first transfer function, G inj2 is a second transfer function, A 1 is a first element in the transfer function G inj1 , A 2 is a first element in the transfer function G inj2 , B 1 is a second element in the transfer function G inj1 , B 2 is a second element in the transfer function G inj2 , and T is a transpose symbol.
10. The method of claim 9 , wherein matrices [A 1 B 1 ] T and [A 2 B 2 ] T are vectors.
11. The method of claim 10 , wherein the matrices [A 1 B 1 ] T and [A 2 B 2 ] T are independent and constant vectors.
12. A system for performing impedance measurement for a three-phase alternating current (AC) system, comprising:
an injection circuit comprising a voltage source inverter (VSI) connectable to the three-phase AC system and a capacitor, the VSI being configured for drawing power from the three-phase AC system to charge the capacitor and for using discharged power from the capacitor to inject at least one chirp signal into the three-phase AC system;
a collection circuit configured to collect at least one response to the at least one chirp signal;
a control unit configured to transfer the at least one response from three-phase (abc) coordinates to direct and quadrature (dq) coordinates and to calculate at least one impedance of the three-phase AC system based on the at least one response to the at least one chirp signal.
13. The system of claim 12 , wherein the injection circuit is configured to inject at least one of the set consisting of a d-axis chirp signal and a q-axis chirp signal into the three-phase AC system.
14. The system of claim 13 , wherein when the injection circuit is configured to inject a d-axis chirp signal and a q-axis chirp signal into the three-phase AC system.
15. The system of claim 14 , wherein at least one of the d-axis chirp signal and the q-axis chirp 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 d-axis chirp signal and the q-axis chirp signal, and t is a time.
16. The system of claim 12 , wherein the control unit is configured to transform an AC voltage response to direct current (DC) voltage components and transform an AC current response to DC current components.
17. The system of claim 12 , wherein the control unit is configured to identify frequency points of interest and calculate impedance at each frequency point of interest.
18. The system of claim 12 , wherein:
the injection circuit is further configured to generate a virtual perturbation signal through an injection transfer function matrix;
the collection circuit is further configured to collect a response to the virtual perturbation signal; and
the control unit is further configured to calculate an impedance based on the response to the virtual perturbation signal and the at least one response to the at least one chirp signal.
19. The system of claim 18 , wherein the injection circuit is configured to generate the virtual perturbation signal using the equation
G
inj
(
s
)
=
[
G
injd
(
s
)
G
injq
(
s
)
]
,
where G inj (s) is the injection transfer function matrix, G injd (S) is a d-axis injection transfer function, and G injq (s) is a q-axis injection transfer function.
20. The system of claim 19 , wherein the injection circuit is configured to generate two independent perturbation signals using the equations
G inj1 ( s )=[ A 1 B 1 ] T , G inj2 ( s )=[ A 2 B 2 ] T ,
where G inj1 (s) is a first injection transfer function matrix, G inj2 (s) is a second injection transfer function matrix, G inj1 is a first transfer function, G inj2 is a second transfer function, A 1 is a first element in the transfer function G inj1 , A 2 is a first element in the transfer function G inj2 , B 1 is a second element in the transfer function G inj1 , B 2 is a second element in the transfer function G inj2 , and T is a transpose symbol.
21. The system of claim 20 , wherein matrices [A 1 B 1 ] T and [A 2 B 2 ] T are independent and constant vectors.
22. The system of claim 12 wherein the injection circuit further comprises, for each phase of the three-phase AC system, an L-C filter and a transformer connected in series between the VSI and the three-phase AC system.