Improved Decoupling Control Strategy of MMC-HVDC System Connected to the Weak AC Power Grid

Abstract

In order to make full use of the regulation capabilities and avoid energy loss caused by coupling effect, a mathematical model of MMC-HVDC system was deduced. Subsequently, the coupling mechanism between the AC current and stations of the MMC system were analyzed via nonlinear equation. On the basis of mechanism analysis, the effects of inter-coupling in MMC-HVDC system connected to weak AC power grid were weakened by adding the dynamic feedforward compensation into the control system. In addition, to ensure the system stability and improve dynamic performance of the proposed controller, the control parameters design method was proposed based on the Hurwitz criterion and the time-domain mathematical calculations. By combining the two parts of the control system, an improved decoupling control strategy applicable to MMC system was proposed. Taking MMC-HVDC system as an example, the simulation based on PSCAD/ EMTDC verified the effectiveness of the proposed method.

Appendix

The differential equations for the dynamics of SM capacitors is expressed as follow:

$$du_{C\_dc} /dt = \frac{1}{{6C_{m} }} \cdot I_{dc} + \frac{{u_{sq} i_{sq} }}{{4C_{m} U_{dc} }} + \frac{{u_{sd} i_{sd} }}{{4C_{m} U_{dc} }} + \frac{{u_{cirq} i_{cirq} }}{{2C_{m} U_{dc} }} + \frac{{u_{cird} i_{cird} }}{{2C_{m} U_{dc} }}$$

(32)

The fundamental frequency components of the AC fluctuation are expressed as

$$\left\{ \begin{aligned} du_{C\_ac1d} /dt & = - \omega u_{C\_ac1q} - \frac{1}{{4C_{m} }}i_{sd} - \frac{{I_{dc} u_{sd} }}{{3C_{m} U_{dc} }} - \frac{{u_{sq} i_{cirq} }}{{2C_{m} U_{dc} }} - \frac{{u_{sd} i_{cird} }}{{2C_{m} U_{dc} }} \\ & \quad - \frac{{u_{cirq} i_{sq} }}{{4C_{m} U_{dc} }} - \frac{{u_{cird} i_{sd} }}{{4C_{m} U_{dc} }} \\ du_{C\_ac1q} /dt & = \omega u_{C\_ac1d} - \frac{1}{{4C_{m} }}i_{sq} - \frac{{I_{dc} u_{sq} }}{{3C_{m} U_{dc} }} - \frac{{u_{sd} i_{cirq} }}{{2C_{m} U_{dc} }} - \frac{{u_{sq} i_{cird} }}{{2C_{m} U_{dc} }} \\ & \quad - \frac{{u_{cirq} i_{sd} }}{{4C_{m} U_{dc} }} - \frac{{u_{cird} i_{sq} }}{{4C_{m} U_{dc} }} \\ \end{aligned} \right.$$

(33)

The double frequency components of the AC fluctuation are expressed as

$$\left\{ \begin{gathered} du_{C\_ac2d} /dt = - \omega u_{C\_ac2q} + \frac{1}{{2C_{m} }}i_{cird} + \frac{{I_{dc} u_{cird} }}{{3C_{m} U_{dc} }} - \frac{{u_{sq} i_{sq} }}{{4C_{m} U_{dc} }} + \frac{{u_{sd} i_{sd} }}{{4C_{m} U_{dc} }} \hfill \\ du_{C\_ac2q} /dt = \omega u_{C\_ac2d} + \frac{1}{{2C_{m} }}i_{cirq} + \frac{{I_{dc} u_{cirq} }}{{3C_{m} U_{dc} }} + \frac{{u_{sd} i_{sq} }}{{4C_{m} U_{dc} }} + \frac{{u_{sq} i_{sd} }}{{4C_{m} U_{dc} }} \hfill \\ \end{gathered} \right.$$

(34)

The triple frequency components of the AC fluctuation are expressed as

$$\left\{ \begin{gathered} du_{C\_ac3x} /dt = 3\omega u_{C\_ac3y} - \frac{{i_{cirq} u_{sd} }}{{2C_{m} U_{dc} }} - \frac{{u_{sq} i_{cird} }}{{2C_{m} U_{dc} }} - \frac{{u_{cird} i_{sq} }}{{4C_{m} U_{dc} }} - \frac{{u_{cirq} i_{sd} }}{{4C_{m} U_{dc} }} \hfill \\ du_{C\_ac3y} /dt = - 3\omega u_{C\_ac3x} - \frac{{i_{cirq} u_{sq} }}{{2C_{m} U_{dc} }} - \frac{{u_{sd} i_{cird} }}{{2C_{m} U_{dc} }} - \frac{{u_{cirq} i_{sq} }}{{4C_{m} U_{dc} }} - \frac{{u_{cird} i_{sd} }}{{4C_{m} U_{dc} }} \hfill \\ \end{gathered} \right.$$

(35)

And the differential equations of circulating currents are

$$\left\{ \begin{aligned} di_{cird} /dt & = - 2\omega i_{cirq} - \frac{{Nu_{C\_ac2d} }}{{2L_{arm} }} - \frac{{Nu_{C\_dc} i_{cird} }}{{U_{dc} L_{arm} }} - \frac{{R_{arm} }}{{L_{arm} }}i_{cird} \\ & \quad + N\frac{{u_{C\_ac1d} u_{sd} - u_{sq} u_{C\_ac1q} }}{{2U_{dc} L_{arm} }} + N\frac{{u_{C\_ac3x} u_{sq} - u_{sd} u_{C\_ac3y} }}{{2U_{dc} L_{arm} }} \\ di_{cirq} /dt & = 2\omega i_{cird} - \frac{{Nu_{C\_ac2q} }}{{2L_{arm} }} - \frac{{Nu_{C\_dc} i_{cirq} }}{{U_{dc} L_{arm} }} - \frac{{R_{arm} }}{{L_{arm} }}i_{cirq} \\ & \quad + N\frac{{u_{C\_ac1q} u_{sd} - u_{sq} u_{C\_ac1d} }}{{2U_{dc} L_{arm} }} + N\frac{{u_{C\_ac3x} u_{sq} - u_{sd} u_{C\_ac3y} }}{{2U_{dc} L_{arm} }} \\ \end{aligned} \right.$$

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where L_eq = L_T + L_arm/2 is the AC system equivalent impedance; R_eq = R_T + R_arm/2 is the AC system equivalent resistance.

If the MMC station adopts the active power/reactive power control mode with the conventional strategy, the mathematical association model can be derived as

$$\left\{ \begin{gathered} x_{1} = \int {(P_{ref} - \frac{3}{2}u_{sd} i_{sd} - \frac{3}{2}u_{sq} i_{sq} )dt} \hfill \\ x_{2} = \int {(Q_{ref} - \frac{3}{2}u_{sd} i_{sq} + \frac{3}{2}u_{sq} i_{sd} )dt} \hfill \\ i_{sdref} = k_{p1} (P_{ref} - \frac{3}{2}u_{sd} i_{sd} - \frac{3}{2}u_{sq} i_{sq} ) + k_{i1} x_{1} \hfill \\ i_{sqref} = k_{p2} (Q_{ref} - \frac{3}{2}u_{sd} i_{sq} + \frac{3}{2}u_{sq} i_{sd} ) + k_{i1} x_{2} \hfill \\ x_{3} = \int {(i_{sdref} - i_{sd} )dt} \hfill \\ x_{4} = \int {(i_{sqref} - i_{sq} )dt} \hfill \\ u_{cdref} = u_{sdm} - \omega L_{eq} i_{sq} - k_{i3} x_{3} - k_{p3} (i_{sdref} - i_{sdm} ) \hfill \\ u_{cqref} = u_{sqm} + \omega L_{eq} i_{sd} - k_{i4} x_{4} - k_{p4} (i_{sqref} - i_{sqm} ) \hfill \\ \end{gathered} \right.$$

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When the MMC station adopts the proposed control strategy, the mathematical association model can be derived as

$$\left\{ \begin{gathered} x_{1} = \int {(P_{ref} - \frac{3}{2}u_{sd} i_{sd} - \frac{3}{2}u_{sq} i_{sq} )dt} \hfill \\ x_{2} = \int {(Q_{ref} - \frac{3}{2}u_{sd} i_{sq} + \frac{3}{2}u_{sq} i_{sd} )dt} \hfill \\ i_{sdref} = k_{p1} [P_{ref} - \frac{3}{2}u_{sd} i_{sd} - \frac{3}{2}u_{sq} i_{sq} - G_{fc2} \cdot \Delta Q] + k_{i1} x_{1} \hfill \\ i_{sqref} = k_{p2} [Q_{ref} - \frac{3}{2}u_{sd} i_{sq} + \frac{3}{2}u_{sq} i_{sd} - G_{fc1} \cdot \Delta P] + k_{i1} x_{2} \hfill \\ x_{3} = \int {(i_{sdref} - i_{sd} )dt} \hfill \\ x_{4} = \int {(i_{sqref} - i_{sq} )dt} \hfill \\ u_{cdref} = u_{sdm} - \omega L_{eq} i_{sq} - k_{i3} x_{3} - k_{p3} (i_{sdref} - i_{sdm} ) + G_{fc3} \cdot \Delta U_{dc} \hfill \\ u_{cqref} = u_{sqm} + \omega L_{eq} i_{sd} - k_{i4} x_{4} - k_{p4} (i_{sqref} - i_{sqm} ) + G_{fc4} \cdot \Delta U_{dc} \hfill \\ \end{gathered} \right.$$

(38)

From Fig. 7, the circulation suppression controller, is expressed in d-q coordinates as

$$\left\{ \begin{gathered} x_{5} = \int {(i_{cirdref} - i_{cird} )dt} \hfill \\ x_{6} = \int {(i_{cirqref} - i_{cirq} )dt} \hfill \\ u_{cird} = - 2\omega L_{arm} i_{cird} - k_{icir} x_{5} - k_{pcir} (i_{cirdref} - i_{cird} ) \hfill \\ u_{cirq} = 2\omega L_{arm} i_{cirq} - k_{icir} x_{6} - k_{pcir} (i_{cirqref} - i_{cirq} ) \hfill \\ \end{gathered} \right.$$

(39)

The DC line is an equivalent circuit of π type, as shown in Fig. 

Fig. 13

π-type equivalent of DC line

13.

The current on a DC line can be represented as

$$L_{d} \frac{{dI_{dc} }}{dt} = U_{dc1} - U_{dc2} - R_{d} I_{dc}$$

(40)

where C_eq = 6*C_m/N; R_d and L_d are the equivalent resistance and inductance of the DC line between node station 1 and station 2; I_dc represents the DC current.