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captured by NREL in the Oahu Island, Hawaii [4]. For simplicity, constant inverter efficiency (89.5%) is used in the simulations. To select the ramp-rate threshold limit to apply the inverse characteristic in (7.13), RRlim is selected by observing the ramp-rate during slow variation of PDC from 7:00 hours to 9:00 hours. During this time frame, more than 99% of the ramp-rates were less than 3 W/sec, as shown in Fig. 7.10(a).

Therefore, to allow for this variation, RRlim is set to a higher value of 5 W/sec.

MARRmax in (7.14) is also set to 5 W/sec for the same purpose.


Fig. 7.9. Network integration model of the PV-storage dynamic system. (a) The test LV feeder. (b) Schematic of the system inside a household.

Fig. 7.10. PVRR during slow variation with the progress of the day. (a) Energy used to control the worst case fluctuation and MARR characteristic.

Simulation trials have been run using a range of 0.1≤≤ 50. For  ≤ 1, fluctuation mitigation performance does not improve much, whereas with  > 1, deterioration of the fluctuation mitigation performance appears with ≥ 20. The value of  has been selected as 5 (with Watt to kW conversion: 0.005). The storage devices are allowed to operate between a typical range of 40% to 100% SoC. To allow for charging and

Time [Hour]

7:00 7:30 8:00 8:30 9:00

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PDC [kW] PVRR[W/sec]

Slow increase of PDC

with day progress

99% of PVRR is below 3 W/sec


PDC [kW]

1 2 3 4 5

SoC [%]



(2.5%) SoCUB


MARR 67% of the total energy


Worst case fluctuation of PDC

discharging for ramp-rate control, SoCref is set to 70%, which is at the mid-point of the allowable range of SoC. The SoC bands, SoCLB and SoCUB, are selected considering the worst case fluctuation of PDC from the rated value (4 kW for the PV systems in the network under study) to zero at the worst-case ramp-rate of PDC-rated/sec and after the fall, PDC does not recover due to a continuous cloudy period. The PDC profile with the storage support is shown in Fig. 7.10(b), where the ramp-rate control is performed according to (7.14), as shown using the MARR profile. SoCLB is set to 2.5% which corresponds to the amount of energy that can control the ramp-rate at the value of MARRmin for about 5 minutes which is sufficient for bringing emergency power online or disconnecting sensitive loads safely. SoCUB is set to 5% which accounts for about 67% of the total energy used for bringing PDC to zero at a controlled ramp-rate. The parameters used for the simulation of the proposed ramp-rate control strategy are given in Table 7-I in the Appendix. Initially, the results of the quasi-steady state simulations using 1-sec resolution data are presented to investigate the validity of the strategy over a daylong variation. Later, dynamic simulation results in milliseconds time-frame are presented.

PV panel DC power, PDC (multiplied by the inverter efficiency), the storage compensation power PCOMP, and the inverter output PINV are shown in Fig. 7.11(a) and 11(b) for the moving average control and the proposed strategy, respectively. For moving average control, a 20-min moving average [9] of PDC is used.


Fig. 7.11. Mitigation of PV output fluctuation. (a) Using moving average. (b) Using the proposed ramp-rate control stramp-rategy.

In general, both of the methods (moving average and the proposed approach) can

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mitigate the fluctuations in PV output, as observed from Fig. 7.11. However, detailed investigations reveal the specific advantages of the proposed approach. Fig. 7.12(a) shows PDC and PINV profiles in a shorter window, from 10:00 hour to 13:00 hour.


Fig. 7.12. Mitigation of PV output fluctuation. (a) PDC and PINV profiles. (b) PCOMP with moving average control. (c) PCOMP with the proposed strategy.

According to the proposed strategy, PINV tracks PDC when the ramp-rate of PDC does not exceed the desired ramp-rate at that time. Therefore, the proposed strategy does not need to operate the storage at all the times. In contrast, (7.10) suggests that the moving average method needs to continue the storage operation due to the past history of PDC, even if it is not necessary as the ramp-rate is within desired limit. This is observed from PCOMP profiles in Fig. 7.12(b) for the moving average methods and 12(c) for the proposed approach. In Fig. 7.12(c), zero values of PCOMP arehighlighted using dotted

circular shapes. Examining the PCOMP profiles it is found that according to the proposed strategy, the storage device operates for about 50% less time in the 10 hours period (from 8:00 to 18:00 hrs) in comparison to the moving average method. This can contribute to increase the lifetime of a battery storage device.

The percentage ratio of PINV to PDC, based on the profiles in Fig. 7.12(a), is compared between the proposed approach and moving average method in Fig. 7.13. Due to the dependency of previous PDC values, PINV obtained from the moving average method is different (lower) than PDC, even during the periods when PDC exhibits very low fluctuation. In contrast, the proposed approach tracks PDC in those periods and therefore, the PINV to PDC ratio is higher using the proposed approach, as compared to the moving average method.

Fig. 7.13. PDC to PINV ratio.

The ramp-rate profiles of PDC and PINV from 10:00 hour to 13:00 hour are shown in Fig. 7.14(a); the ramp-rates of PINV can be controlled within a specified limit by operating the storage device according to the proposed strategy. The ramp-rates of PINV

with 20-min moving average control of storage device are compared with those obtained using the proposed strategy in Fig. 7.14(b) for the time period when the maximum negative and positive ramp-rates in PDC appeared. For reference, the ramp-rate of PDC is also included in Fig. 7.14(b). During the negative fluctuation of PDC with a ramp-rate of -1.767 kW/sec, the proposed strategy controls the PINV ramprate at -0.0028 W/sec which comes from the inverse characteristic in (7.13). With the 20-min moving average, the ramp-rate of PINV is -1.485 W/sec, which is not controlled at this value; rather it is produced as a result of the previous PDC samples over the last 20 min period. During the positive ramping event at 1.725 kW/sec, the ramp-rate with the proposed strategy is 0.0029 W/sec which is controlled using (7.13), whereas, with the

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PINVto PDC Ratio [%]

moving average it is 0.0183 W/sec, which is not actually controlled to this value.

Although the moving average method provides significant fluctuation mitigation at the expense of operating the storage device all the time, the proposed strategy provides better mitigation during the time of fluctuation with a high ramp-rate (such as the one shown in Fig. 7.14).

Fig. 7.14. Ramp-rate control. (a) The ramp-rate profiles of PDC and PINV. (b) Comparison of the PINV

ramp-rates obtained using the moving average control and the proposed strategy.

Fig. 7.15. The usefulness of the proposed inverse characteristic in the improvement of fluctuation mitigation.

The usefulness of the proposed MARR characteristics in (7.13) and (7.14) can also be observed in Fig. 7.15 where the PV output fluctuation mitigation using the proposed

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inverse MARR characteristic from 12:00 hours to 13:00 hours is compared with a constant MARR value of 5 W/sec. The proposed inverse MARR and SoC droop based characteristics can mitigate the fluctuation better than a constant MARR value. For reference, the fluctuation mitigation using the 20-min moving average is also included in Fig. 7.15.

The PCC voltage profile at household no. 28 (HH 28) of the test feeder from 10:00 hours to 13:00 hours is shown in Fig. 7.16(a). For reference, PCOMP profile is also shown in Fig. 7.16(b). When sharp decrease in PCC voltage appears as a result of sudden decrease in PV output, energy storage device is discharged to control the high negative ramp-rates. This action mitigates the associated voltage dips. Again, when sharp rise in PCC voltage appears due to sudden increase in PV output, energy storage device is charged to control the positive ramp-rates and this action mitigates the sharp voltage rise as well. Without the proposed ramp-rate control strategy, the voltage ramp-rate at 10 hr : 16 min : 54 sec (when the largest negative ramp-rate in the PV output appeared) is -9.3 V/sec and at 10 hr : 16 min : 58 sec (when the largest positive ramp-rate in PV output appeared) is 9.1 V/sec. Controlling the ramp-rate of PV output using the proposed strategy, the PCC voltage ramp-rate is reduced to less than 0.1 mV/sec.


Fig. 7.16. Mitigation of PCC voltage fluctuation using the proposed strategy. (a) PCC voltage profile. (b) PCOMP profile.

The validation of the proposed strategy in a dynamic environment is tested using the proposed PV-storage integrated system model using 1 millisecond time step and the

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results are presented in Fig. 7.17. The largest ramp-rate observed in the PV output data used for the daylong simulation is used for this purpose. The dynamic simulation is performed with the data shown in Table 7-II in the Appendix.

The PV output decreases at a ramp-rate of -1.767 kW/sec at 10 hr : 16 min : 54 sec.

Fig. 7.17(a) shows that following the negative ramp-rate of PDC, PCOMP increases within a few milliseconds time to increase the PINV at the level that maintains the desired ramp-rate MARR specified at the time. After 4 seconds time, the PDC again increases with a ramp-rate of 1.725 kW/sec at 10 hr : 16 min : 58 sec. Fig. 7.17(b) shows that following the positive ramp-rate of PDC, PCOMP decreases to the level necessary to maintain the desired ramp-rate of PINV at that time. The impact of the storage time constant Tsto is also shown in Fig. 7.17; PINV with Tsto of 5 milliseconds settles down faster and with less swing as compared to the PINV with Tsto of 20 milliseconds. Therefore, a storage device with a fast response time is necessary for a satisfactory mitigation of the fluctuation.


Fig. 7.17. Performance analysis using the proposed dynamic model. (a) Negative ramp-rate control; (b) Positive ramp-rate control.