Fig. 3 (a) Single line diagram of DSTATCOM (b) Phasor Diagram
Fig. 3(a) shows the single line diagram of single phase DSTATCOM connected to a single phase system. Consider fig 3(b) which shows phasor diagram of compensated single phase system.
Here, id is direct axis compensating current, iq is the reactive component of compensating current, Vt is the load voltage which is needed to be kept at 1 p.u. Current ‘i ’ is the necessary compensating current which is to be injected to the system and it is the vector sum of id and iq
The compensated current i is given as:
i = I*sin( \(\omega t+(\phi_{1}\mathbf{+\ }\delta\mathbf{\ }\)))    (2)
which is resolved to,
i = I*cos \(\mathbf{\ }\delta\)*sin( \(\omega t+\phi_{1}\)) + I*sin \(\mathbf{\ }\delta\)*cos( \(\omega t+\phi_{1}\))     (3)
i = id*sin( \(\omega t+\phi_{1}\)) +iq *cos( \(\omega t+\phi_{1}\))       (4)
where id = I*cos δ and iq = I*sin δ        (5)
Here, id = 0 since constant DC source is connected across VSC terminals and iq is the q-axis current component which is required to maintain PCC voltage at 1 p.u.
Here one should note that for extraction of reference signals for the other two phases the reference signal generated for the respective phases should be displaced by an angle of 120 degrees each.
Fig. 4 shows the control block diagram for reference signal generation for DSTATCOM using concept of single phase d-q theory for VCM operation. From the fig. it is seen that load voltages Vta, Vtb, Vtc are individually compared with 1 p.u value and the error in these values are sent to three separate PI controllers. These errors in each of the three phases generate iqa, iqb, iqc from the PI controllers. iqa, iqb,iqc are q-axis reactive current component as observed in eq.(5). Now as seen from equation (4), iq current obtained from PI controllers are then multiplied with cosωt to obtain i*a. For obtaining i*b and i*c the function cosωt is shifted by 120 and 240 degrees respectively. Here, a constant voltage source is used for the VSC and thus the d-axis current component or active current component id is zero.