Method for suppressing circulating current in modular multilevel converter for high voltage direct-current transmission

1. A method for suppressing circulating currents of a, b, c phases in a modular multi-level converter for a high voltage direction-current (HVDC) transmission system converting an alternating current (AC) into a direct current (DC) and vice versa, transmitting energy using a DC cable, and having the modular multilevel converter generating a high voltage source by stacking a plurality of sub-modules in series, the method comprising:

receiving circulating currents in each of a phase, b phase, and c phase in an 3 phase stationary reference frame, a DC current i dc flowing in a DC cable, a current reference value i* dc of a DC component that needs to flow in the DC cable;

controlling AC components of the circulating currents in each of a phase, b phase, and c phase to become zero; and

outputting a compensation value V* diffj for suppressing a harmonic component of the circulating current,

wherein the controlling of AC components of the circulating currents comprises:

calculating the current reference value i* dc of the DC component that needs to flow in the DC cable by equation of i* dc =P acpower /V dc (with P acpower :known);

extracting a current i* dc -i dc of an AC harmonic component flowing in a DC link terminal by eliminating the DC current i dc flowing in the DC link terminal from the current reference value i* dc of the DC component; and

controlling the current i * dc -i dc of an AC harmonic component flowing in a DC link terminal to become zero,

wherein the controlling of AC components of the circulating currents further comprises:

calculating AC components i t of the circulating currents i diffj by eliminating an ⅓ of the DC current i dc from the circulating currents i diffj ; and

removing the AC components i zj of the circulating currents i diffj ,

wherein the removing of the AC components i zj is performed in the 3-phase stationary reference frame by Equation V j _ diffcrtripple _ rej _ ref =PIR[i* zj −i zj ] (with i* zj =0, j=a, b, c) by applying a Proportional-Integral and Resonant (PIR) controller having an infinite gain at a frequency of ±2ω 0 when an angular frequency ω 0 equals to 2πf 0 at a power system frequency of f 0 ,

here,

PIR

⁡

[

error

]

=

{

K

P

+

K

i

s

+

2

⁢

K

r

⁢

s

s

2

+

(

2

⁢

⁢

ω

0

)

2

}

×

error

a, b, c: division factors for dividing 3-phase system voltage into a-phase, b-phase, c-phase

P acpower : converted AC power by modular multi-level converter

V dc : DC cable voltage (DC_link voltage) of HVDC,

i* zj : AC component reference value among components of circulating current

V j _ diffcrtripple _ rej _ ref : output value after controller for suppressing AC component of circulating current

K p , K i , K r : proportional gain, integral gain, proportional gain of resonant controller error: signal input including error information

s: d( )/dt in Laplace transform.

2. The method of claim 1

wherein the current i * dc -i dc of the AC harmonic component becomes zero by allowing the extracted current i* dc -i dc of the AC harmonic components to be an input value of the Proportional-Integral and Resonant controller and controlling the Proportional-Integral and Resonant controller having a resonant point at a frequency of +2ω 0 .

3. The method of claim 1 , wherein the outputting of the compensation value V* diffj for suppressing the harmonic component of the circulating current comprises generating voltage reference values V* diffa , V* diffb , V* diffc of the circulating current suppression component by adding up an output value V j _ diffcrtripple _ rej _ ref of the circulating current of an AC component suppression controller and an output value V dccrtripple _ rej _ ref of the DC cable current of the AC component suppression controller.

4. The method of claim 3 , wherein the outputting of the compensation value V* diffj for suppressing the harmonic component of the circulating currents comprises calculating voltage reference values V pj , V nj of an upper arm and a lower arm of the modular multilevel converter by Equations

V

pj

=

V

dc

2

-

V

j

⁢

-

⁢

ref

-

V

diffj

*

⁢

⁢

(

with

⁢

⁢

j

=

a

,

b

,

c

)

⁢

⁢

and

V

nj

=

V

dc

2

+

V

j

⁢

-

⁢

ref

-

V

diffj

*

⁢

⁢

(

with

⁢

⁢

j

=

a

,

b

,

c

)

so as to be linked with a control algorithm of the modular multilevel converter,

here,

V j-ref : controller output for controlling reactive power and active power (or DC_link voltage control) of multilevel converter

V dc : DC cable voltage (DC_link voltage) of HVDC.

5. The method of claim 1 , wherein when the circulating currents i diffa , i diffb , i diffc at the 3-phase stationary reference frame are expressed in a 2-phase stationary reference frame (α-β frame), a compensation value V α _ diffcrtripple _ rej _ ref for suppressing an α-axis AC harmonic component of the circulating current is calculated by an equation V α _ diffcrtripple _ rej _ ref =PIR[i* diffα −i diffα ], and a compensation value V β _ diffcrtripple _ rej _ ref for suppressing a β-axis AC harmonic component of the circulating current is calculated by an equation V β _ diffcrtripple _ rej _ ref =PIR[i* diff β −i diff β ],

here,

i diffα : α-axis component

i diffβ : β-axis component

i* diffα : reference value with respect to α-axis circulating current

i* diffβ : reference value with respect to β-axis circulating current.

6. The method of claim 1 , wherein when the circulating currents i diffa , i diffb , i diffc at the 3-phase stationary reference frame are expressed in a d-q rotating coordinate system and components of the circulating currents of a, b, c phases are divided into positive sequence components i p diffd , i p diffq , negative sequence components i n diffd , i n diffq , and a zero sequence component i 0 diff , wherein the components i p diffd , i p diffq , i n diffd , i n diffq , i 0 diff of the circulating currents are simultaneously removed.

7. The method of claim 6 , wherein:

a reference voltage V p diffd for suppressing a d-axis positive sequence component circulating current i p diffd is calculated by an equation

V diffd p =PI[− i diffd p ];

a reference voltage V p diffq for suppressing a q-axis positive sequence component circulating current i p diffq is calculated by an equation

V diffd p =PI[− i diffd p ];

a reference voltage V n diffq for suppressing a d-axis negative sequence component circulating current i n diffd is calculated by an equation

V diffd n =PI[− i diffd n ];

a reference voltage V n diffq for suppressing a q-axis negative sequence component circulating current i n diffq is calculated by an equation

V diffq n =PI[− i diffq n ];

and a reference voltage V 0 diff for suppressing a zero sequence component circulating current i 0 diff is calculated by an equation

V diff 0 =PI[− i diff 0 ]

here,

PI

⁡

[

error

]

=

{

K

p

+

K

i

s

}

×

error

.

8. A method for suppressing circulating currents in a modular multi-level converter for a high voltage direction-current (HVDC) transmission system converting an alternating current (AC) into a direct current (DC) and vice versa, transmitting energy using a DC cable, and having a modular multilevel converter generating a high voltage source by stacking a plurality of sub-modules in series, the method comprising:

receiving circulating currents in each of a phase, b phase, and c phase in an abc 3-phase stationary reference frame, a DC current i dc flowing in a DC cable, a current reference value i* dc of a DC component that needs to flow in the DC cable;

controlling AC components of the circulating currents in each of a phase, b phase, and c phase to become zero; and

outputting a compensation value V* diffj for suppressing a harmonic component of the circulating current,

wherein the controlling of AC components of the circulating currents comprises:

calculating the current reference value i* dc of the DC component that needs to flow in the DC cable by equation of i* dc =P acpower /V dc (with P acpower :known),

wherein the controlling of AC components of the circulating currents further comprises:

calculating AC components i zj of the circulating currents i diffj by eliminating an ⅓ of the current reference value i* dc of the DC component from the circulating currents i diffj ; and

removing the AC components i d of the circulating currents i diffj ,

wherein the removing of the AC components i zj is performed in the 3-phase stationary reference frame by Equation V j _ diffctripple _ rej _ ref =PIR[i* zj −i zj ] (with i* zj =0, j=a, b, c) by applying a Proportional-Integral and Resonant (PIR) having an infinite gain at a frequency of ±2ω 0 when an angular frequency ω 0 equals to 2πf 0 at a power system frequency of f 0 ,

here,

PIR

⁡

[

error

]

=

{

K

p

+

K

i

s

+

2

⁢

⁢

K

r

⁢

s

s

2

+

(

2

⁢

⁢

ω

0

)

2

}

×

error

a, b, c: division factors for dividing 3-phase system voltage into a-phase, b-phase, c-phase

P acpower : converted AC power by modular multi-level converter

V dc : DC cable voltage (DC_link voltage) of HVDC,

i* zj : AC component reference value among components of circulating current

V j _ diffcrtripple _ rej _ ref : output value after controller for suppressing AC component of circulating current

K p , K i , K r : proportional gain, integral gain, proportional gain of resonant controller

error: signal input including error information

s: d( )/dt in Laplace transform.