Читать книгу Smart Grids and Micro-Grids - Umashankar Subramaniam - Страница 46

The AC voltage of the PCC is expressed as

(2.21)

Applying Kirchhoff ’s voltage equation in the phase, we get

(2.22)

(2.23)

(2.24)

To transfer the above system to synchronous reference frame, the following transformation need to be performed

(2.25)

Where T_abc2αβ, T_αβ2dq and θ are known as Clark transformation, Park transformation, and the phase angle of the grid which is obtained from PLL, respectively. The resulting system after transformation is given by

(2.26)

(2.27)

Where v_sd, u_d and i_d are PCC voltage, VSC output voltage and output current on d-axis, respectively. u_q and i_q are VSC output voltage and output current on the q-axis, respectively. One can notice from equation (2.26) and (2.27) that the system is converted to an LTI system having some coupling states. A simple control law to decouple the term is given by

(2.28)

Where v_id and v_iq are the feedback control input. for obtaining zero steady-state error, PI controller is applied to control input

(2.29)

Where e_id = (i_d(ref) – i_d), e_iq = (i_q(ref) – i_q), K_pi,d, K_ii,d, K_pi,q and K_ii,q are parameters/gains of PI controller for d-axis current and q-axis current controller. Since the system model is LTI, it can be easily analysed and the current controller can be easily designed using linear control techniques.

For the case when the microgrid in islanded mode, the converter has to regulate the voltage at PCC. By applying Kirchhoff’s law at the PCC voltage and applying the d-q transform on the resulting equations, one would obtain

(2.30)

The coupling between V_sd and V _sq is eliminated by a decoupling feed-forward compensation. One possible control law is given by

(2.31)

Where i_d(ref), i_q(ref) are reference for inner current loop and v_vd, and v_v are the feedback control input which is expressed as

(2.32)

Where e_vd = (V_{sd ( ref )} – V_sd), e_vq = (V_sq(ref) – V_sq), K_pv,d, K_iv,d, K_pv,q, and K_iv,q are parameters/gains of PI controller for d-axis current and q-axis voltage controller. The parameter of PI controller can be easily selected. For d-q transformation in islanded system, the reference angle ρ (and thus ) is decided independently.