Reactive Power Sharing Under Mismatch Feeder Impedance and Complex Loads Conditions

The power sharing curves of islanded MG when supplying nonlinear loads, star connected and delta connected three phase unbalanced loads are illustrated in Fig (). As depicted from figures, at the beginning the three-phase six-pulse diode-bridge rectifier of RL load is connected up to t=2.5 s at that time the star connected unbalanced load is coupled up to 4.5 s and a delta connected unbalanced load coupled again until 6 s where all three different loads are connected at the same time. As it can be seen, the from Fig (voltage) the DGs unit closer to the PCC i.e with less power line impedance experienced low voltage drop and provide high reactive power to the common load as show in Fig (Q). This is because the DG of less feeder impedance has a smaller inertia therefor its response time to support the load step is smaller compared to the other DG units of larger feeder impedance.

As all DGs units are operating under identical droop gains on the other hand with different feeder impedance hence the active power output of the inverters based standard PI controller in voltage-current loops are tracking each to ensure a balanced real power sharing in both transient and steady state keeping the operational frequency in acceptable operating limit as shown in Fig (P) and (f). Even though all DGs units have equal droop gains, there is unbalance in reactive power sharing in steady state mode caused by the mismatch feeder impedances as shown in Fig (Q). Hence there is steady state error in reactive power sharing and unbalance in voltage output caused by unbalanced voltage drop in the power line impedance as shown in Fig (V).

With the proposed compensation method based on the Virtual impedance, the output voltage of all DGs units are balanced with a safe transient as depicted in Fig (V). With the suggested harmonic and voltage unbalance compensation scheme, the results shown in Fig (V) shows the tracking performance of voltage-current loop can. The figure shows an effective tracking of the reference signals throughout a steady state for that reason, the output voltage is kept in operating limit of standalone MG in transient and steady state mode.

Fig (Q) shows the reactive power sharing of three DG units. There is an adaptive configuration of operating set points as system load changes. Thus the balanced reactive power sharing is achieved due to the designed compensation algorithm based on the adaptive virtual impedance as well as the PIR. The compensation of voltage losses across the feeder impedance ensure a balanced system voltage that results in an efficient reactive power sharing since the reactive power sharing is proportional to the voltage.

From Fig.x and Fig Y due to the effects of droop control the frequency and voltage deviation are HZ and V respectively. By applying the secondary control level, the voltage magnitude and frequency were restored to the nominal operating range as shown in Fig X1 and X2. Hence the power output of each inverter is increased after the restoration process as shown in Fig.Y

The secondary control loops cause the real power output by each inverter to increase while the power sharing between the inverters was not affected.

The frequency and voltage deviations inherent to the droop algorithm are equal to Hz and V as shown in Figs. 13 and 14 respectively. The frequency of the microgrid was restored to the nominal value after a settling time of 3 s as shown in Fig. 13. Similarly the microgrid voltage was restored to the nominal value after a settling time of 8 s as shown in Fig. 14. Hence, the proposed algorithms achieve the requirements of equal reactive power sharing, voltage and frequency restoration according to the design constraints considered, thereby indicating the effectiveness of the algorithms.