Control method for single-phase grid-connected LCL inverter

1. A method of controlling the grid-side current of a single-phase grid-connected converter having an LCL filter connected between an output of the converter and the grid, the method comprising the steps of:

measuring, by a processor of a computing device, a grid voltage (v S ) and at least one signal in a group of signals consisting of a grid-side current (i 0 ), a converter-side current (i 1 ) and a capacitor voltage (v C0 );

estimating a fundamental component (v S,1 ) of the grid voltage (v S );

forming a grid-side current reference (i 0 *), a converter-side current reference (i 1 *) and a capacitor voltage reference (v C0 *) for the grid-side current of the LCL filter using the estimated fundamental component of the grid voltage (v S,1 );

forming estimates for any of the non-measured signals in said group of signals;

forming a grid-side current difference term (ĩ 0 ), a converter-side current difference term (ĩ 1 ) and a capacitor voltage difference term ({tilde over (v)} C0 ) from the differences between references and the measured and/or estimated values of said signals;

forming an injection term for damping the resonance of the LCL filter by using an active damping injection mechanism (ADI), in which the grid-side current difference term (ĩ 0 ), the converter-side current difference term (ĩ 1 ) and the capacitor voltage difference term ({tilde over (v)} C0 ) are used;

forming an estimate of a harmonic distortion term ({circumflex over (φ)}) using the grid-side current difference term (ĩ 0 ); and

controlling the output voltage (e) of the converter on the basis of the grid voltage, formed injection term and formed estimate of the harmonic distortion term ({circumflex over (φ)}) to produce a grid side (i 0 ) current corresponding to the current reference.

2. A method as claimed in claim 1 , wherein the fundamental frequency (ω 0 ) of the grid voltage is known, and the estimating of the fundamental component (v S,1 ) of the grid voltage comprises:

determining a value for a quadrature companion signal (φ S,1 ) by integrating the product of the opposite value of fundamental component of the grid voltage (v S,1 ) and the fundamental frequency of the grid voltage (ω 0 );

determining the difference ({tilde over (v)} S ) between the grid voltage and the fundamental component of the grid voltage (v S,1 );

adding the product of the quadrature companion signal (φ S,1 ) and the fundamental frequency of the grid voltage (at) to the product of the difference ({tilde over (v)} S ) and the estimation gain (λ 1 ); and

determining the value of the fundamental component of the grid voltage (v S,1 ) by integrating the sum of the addition.

3. A method as claimed in claim 1 , wherein the magnitude of the current reference (i 0 *) for the grid-side current is proportional to an approximate of the delivered power (P).

4. A method as claimed in claim 1 , wherein:

the fundamental frequency (ω 0 ) of the grid voltage and the quadrature companion signal (φ S,1 ) are known;

the capacitor voltage reference (v C0 *) is approximated by the fundamental component of the grid voltage (v S,1 ); and

the converter-side current reference (i 1 *) is approximated by the product of the capacitor capacitance (C 0 ), fundamental frequency (ω 0 ) and the quadrature companion signal (φ S,1 ) added to the grid-side current reference (i 0 *).

5. A method as claimed in claim 1 , wherein the converter-side current (i 1 ) is measured and the grid-side current (i 0 ) and the capacitor voltage (v C0 ) are estimated using an observer, where

the observer dynamics are given as:

C

0

⁢

ξ

.

1

=

-

α

1

⁡

(

ξ

1

-

e

)

-

ξ

2

+

(

L

1

C

0

⁢

α

1

2

-

L

1

L

0

⁢

α

2

+

1

)

⁢

i

1

L

0

⁢

ξ

.

2

=

(

1

+

α

2

)

⁢

(

ξ

1

-

L

1

C

0

⁢

α

1

⁢

i

1

)

-

v

S

-

α

2

⁢

e

,

where ξ and ξ 2 are observer states, L 1 is the converter-side inductor inductance, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency and

a grid-side current estimate (î 0 ) and a capacitor voltage estimate ({circumflex over (v)} C0 ) are reconstructed according to:

v

^

C

⁢

⁢

0

=

ξ

1

-

L

1

C

0

⁢

α

1

⁢

i

1

i

^

0

=

ξ

2

+

L

1

L

0

⁢

α

2

⁢

i

1

where α 1 and α 2 are two design parameters which fulfill α 1 >0 and 1+α 2 >0.

6. A method as claimed in claim 5 , wherein the tuning of two design parameters α 1 and α 2 is based on a desired bandwidth (ω BW ) and said parameters are tuned according to:

α 1 =√{square root over (2)}ω BW C 0

α 2 =ω BW 2 L 0 C 0 −1.

7. A method as claimed in claim 1 , wherein the converter-side current (i 1 ) and the capacitor voltage (v C0 ) are measured and the grid-side current (i 0 ) is estimated using an observer, where

the observer dynamics are given as:

L

0

⁢

ξ

.

1

=

-

α

1

⁢

ξ

1

+

(

1

+

C

0

L

0

⁢

α

1

2

)

⁢

v

C

⁢

⁢

0

+

α

1

⁢

i

1

-

v

S

,

where ξ 1 is an observer coefficient, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency, and

a grid-side current estimate (I) is reconstructed according to:

i

^

0

=

ξ

1

-

C

0

L

0

⁢

α

1

⁢

v

C

⁢

⁢

0

where α 1 is a design parameter.

8. A method as claimed in claim 7 , wherein the tuning of the design parameter α 1 is based on a desired bandwidth (ω BW ), and said parameter is tuned according to:

λ

1

=

-

α

1

L

0

where λ 1 is the pole of the observer dynamics.

9. A method as claimed in claim 1 , wherein the grid-side current (i 0 ) and the capacitor voltage (v C0 ) are measured and the converter-side current (i 1 ) is estimated using an observer, where

the observer dynamics are given as:

L

1

⁢

ξ

.

1

=

-

α

1

⁢

ξ

1

-

(

1

+

C

0

L

1

⁢

α

1

2

)

⁢

i

1

+

α

1

⁢

v

C

⁢

⁢

0

+

e

,

where ξ 1 is an observer coefficient, C 0 is the capacitor capacitance and L 1 is the converter-side inductor inductance of the LCL filter and ω res the natural resonance frequency, and

a grid-side current estimate (î 0 ) is reconstructed according to:

i

^

1

=

ξ

1

+

C

0

L

1

⁢

α

i

⁢

i

1

where α 1 is a design parameter.

10. A method as claimed in claim 9 , wherein the tuning of the design parameter α 1 is based on a desired bandwidth (ω BW ), and said parameter is tuned according to:

λ

1

=

-

α

1

L

1

where λ 1 is the pole of the observer dynamics.

11. A method as claimed in claim 1 , wherein the forming of the injection term comprises:

multiplying the grid-side current difference term (ĩ 0 ) by a constant R 0 ;

multiplying the converter-side current difference term (ĩ 1 ) by a constant R 1 ;

multiplying the capacitor voltage difference term ({tilde over (v)} C0 ) by a constant R 2 ; and

forming the injection term by adding the products together.

12. A method as claimed in claim 11 , wherein the constants are defined as

R 1 =0.45ω res L 1

R 2 =0.05ω res 2 L 1 C 0

R 0 =0.25ω res 3 L 0 C 0 L 1 −R 1

where L 1 is the converter-side inductor inductance, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency.

13. A method as claimed in claim 1 , wherein the forming of the estimate of the harmonic distortion term ({circumflex over (φ)}) comprises summation of k harmonic components ({circumflex over (φ)} 1 −{circumflex over (φ)} k ).

14. A method as claimed in claim 1 , wherein the fundamental frequency (ω 0 ) of the grid voltage is known, and forming of a harmonic component with an index number k ({circumflex over (φ)} k ) comprises:

determining a value for a quadrature companion signal ({circumflex over (ψ)} k ) by integrating the product of the opposite value of the harmonic component ({circumflex over (φ)} k ) and the fundamental frequency (ω 0 ) of the grid voltage multiplied by the value of index number k;

adding the product of quadrature companion signal ({circumflex over (ψ)} k ) and the fundamental frequency of the grid voltage (ω 0 ) multiplied by the fundamental frequency (ω 0 ) to the product of the grid-side current difference (ĩ 0 ) and the design parameter (γ k ); and

determining the value of the harmonic component ({circumflex over (φ)} k ) by integrating the sum of the addition.

15. A method as claimed in claim 14 , wherein

the design parameter (γ k ) is set as γ k =2.2/T kr , where T kr is the desired response time for each kth harmonic component, evaluated between 10% and 90% of a step response of the amplitude of the corresponding sinusoidal perturbation.

16. A method as claimed in claim 1 , wherein the injection voltage (e) is formed by subtracting the estimate of harmonic distortion term ({circumflex over (φ)}) and the injection term from the grid voltage (v S ).

17. A method as claimed in claim 2 , wherein:

the fundamental frequency (ω 0 ) of the grid voltage and the quadrature companion signal (φ S,1 ) are known;

the capacitor voltage reference (v C0 *) is approximated by the fundamental component of the grid voltage (v S,1 ); and

the converter-side current reference (i 1 *) is approximated by the product of the capacitor capacitance (C 0 ), fundamental frequency (ω 0 ) and the quadrature companion signal (φ S,1 ) added to the grid-side current reference (i 0 *).

18. A method as claimed in claim 17 , wherein the converter-side current (i 1 ) is measured and the grid-side current (i 0 ) and the capacitor voltage (v C0 ) are estimated using an observer, where

the observer dynamics are given as:

C

0

⁢

ξ

.

1

=

-

α

1

⁡

(

ξ

1

-

e

)

-

ξ

2

+

(

L

1

C

0

⁢

α

1

2

-

L

1

L

0

⁢

α

2

+

1

)

⁢

i

1

L

0

⁢

ξ

.

2

=

(

1

+

α

2

)

⁢

(

ξ

1

-

L

1

C

0

⁢

α

1

⁢

i

1

)

-

v

S

-

α

2

⁢

e

,

where ξ 1 and ξ 2 are observer states, L 1 is the converter-side inductor inductance, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency and

a grid-side current estimate (î 0 ) and a capacitor voltage estimate ({circumflex over (v)} C0 ) are reconstructed according to:

v

^

C

⁢

⁢

0

=

ξ

1

-

L

1

C

0

⁢

α

1

⁢

i

1

i

^

0

=

ξ

2

+

L

1

L

0

⁢

α

2

⁢

i

1

where α 1 and α 2 are two design parameters which fulfill α 1 >0 and 1+α 2 >0.

19. A method as claimed in claim 17 , wherein the converter-side current (i 1 ) and the capacitor voltage (v C0 ) are measured and the grid-side current (i 0 ) is estimated using an observer, where

the observer dynamics are given as:

L

0

⁢

ξ

.

1

=

-

α

1

⁢

ξ

1

+

(

1

+

C

0

L

0

⁢

α

1

2

)

⁢

v

C

⁢

⁢

0

+

α

1

⁢

i

1

-

v

S

,

where ξ 1 is an observer coefficient, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency and

a grid-side current estimate (î 0 ) is reconstructed according to:

i

^

0

=

ξ

1

-

C

0

L

0

⁢

α

1

⁢

v

C

⁢

⁢

0

where α 1 is a design parameter.

20. A method as claimed in claim 17 , wherein the grid-side current (i 0 ) and the capacitor voltage (v C0 ) are measured and the converter-side current (i 1 ) is estimated using an observer, where

the observer dynamics are given as:

L

1

⁢

ξ

.

1

=

-

α

1

⁢

ξ

1

-

(

1

+

C

0

L

1

⁢

α

1

2

)

⁢

i

1

+

α

1

⁢

v

C

⁢

⁢

0

+

e

,

where ξ 1 is an observer coefficient, C 0 is the capacitor capacitance and L 1 is the converter-side inductor inductance of the LCL filter and ω res is the natural resonance frequency, and

a grid-side current estimate (î 0 ) is reconstructed according to:

i

^

1

=

ξ

1

+

C

0

L

1

⁢

α

i

⁢

i

1

where α 1 is a design parameter.

21. A method as claimed in claim 17 , wherein the forming of the injection term comprises:

multiplying the grid-side current difference term (ĩ 0 ) by a constant R 0 ;

multiplying the converter-side current difference term (ĩ 1 ) by a constant R 1 ;

multiplying the capacitor voltage difference term ({tilde over (v)} C0 ) by a constant R 2 ; and

forming the injection term by adding the products together, and

wherein the constants are defined as

R 1 =0.45ω res L 1

R 2 =0.05ω res 2 L 1 C 0

R 0 =0.25ω res 3 L 0 C 0 L 1 −R 1

where L 1 is the converter-side inductor inductance, C 0 is the capacitor capacitance and L 0 is the grid-side inductor inductance of the LCL filter and ω res is the natural resonance frequency.

22. A method as claimed in claim 17 , wherein the forming of the estimate of the harmonic distortion term ({circumflex over (φ)}) comprises summation of k harmonic components ({circumflex over (φ)}−{circumflex over (φ)} k ).

23. A method as claimed in claim 15 , wherein the injection voltage (e) is formed by subtracting the estimate of harmonic distortion term ({circumflex over (φ)}) and the injection term from the grid voltage (v S ).

24. A converter in association with a LCL filter, the converter comprising:

means for measuring a grid voltage (v S ) and at least one signal in a group of signals consisting of a grid-side current (i 0 ), a converter-side current (i 1 ) and a capacitor voltage (v C0 ), the means for measuring including at least one processor of a computing device;

means for estimating a fundamental component (v S,1 ) of the grid voltage (v S );

means for forming a grid-side current reference (i 0 *), a converter-side current reference (i 1 *) and a capacitor voltage reference (v C0 *) for the grid-side current of the LCL filter using the estimated fundamental component of the grid voltage (v S,1 );

means for forming estimates for any of the non-measured signals in said group of signals;

means for forming a grid-side current difference term (ĩ 0 ), a converter-side current difference term (ĩ 1 ) and a capacitor voltage difference term ({tilde over (V)} C0 ) from the differences between the references and measured/estimated values of said signals;

means for forming an injection term for damping the resonance of the LCL filter by using an active damping injection mechanism (ADI), in which the grid-side current difference term (ĩ 0 ), the converter-side current difference term (ĩ 1 ) and the capacitor voltage difference term ({tilde over (v)} C0 ) are used;

means for forming an estimate of a harmonic distortion term ({circumflex over (φ)}) using the grid-side current difference term (ĩ 0 ); and

means for controlling the output voltage (e) of the converter on the basis of the grid voltage, formed injection term and formed estimate of the harmonic distortion term ({circumflex over (φ)}) for producing a grid side (i 0 ) current corresponding to the current reference.