As per the objective of the paper, the results are segregated into two parts for the analysis, viz., (i) quantitative analysis on the applicability of conventional methods for RESMs, and (ii) comparative analysis of proposed and conventional methods subjected to various test conditions.
Analysis on the applicability of conventional tuning methods for microgrids
As discussed in Sect. 4.1, conventional methods, viz., OLTR (ZN-1, WJC, CHR, CC) and EPI (ISE, ISTE, ISTSE, IATE) are tested for their applicability to RESM. The efficacy of these methods is assessed in two test modes, viz., one is when using for parameter tuning in the single-loop system, i.e., only the current controller (or inner-loop) based RESM and another is when using for parameter tuning in dual-loop system, i.e., for V/I controller-based RESM. In both the test modes, time-domain and frequency-domain responses are plotted during the normal condition (no disturbance) as shown in Fig. 11 and Fig. 12 to understand the applicability of OLTR and EPI methods to RESMs. Various time-domain index (viz., delay time (Tdt), rise time (Trt), settling time (Tst), peak-overshoot (Pov)) and frequency-domain index (viz., phase margin (PM), gain margin (GM)) are computed to identify the superior method among these conventional methods. From these results, the following remarks could be noted.
For the single-control loop-based system From Fig. 11, it is observed that all the conventional OLTR and EPI tuning methods worked satisfactorily as per the computed frequency/time-domain performance index.
For the dual-control loop-based system From Fig. 12a, c, it is observed that the OLTR methods worked satisfactorily. But, From Fig. 12b, d, it is clear that the EPI methods which worked well for single-control loop-based system are failed for dual-control loop system and leads to instability.
The corresponding performance index is also undetermined from Fig. 12b, d. Hence, a pole-zero plot is drawn, as shown in Fig. 12e to observe the location of poles. Form this, it is seen that, EPI methods lead to the existence of open-loop pole (or closed-loop zero) located on the very far right-half of s-plane, which represents an unstable system.
As it is advised by IEEE-1547, IEEE-519 standards to use both V/I control loops for robust RESM operation during transients, and based on the observations described above, it is concluded that the EPI methods are not suitable for RESMs application. Further, from Table 9, it is understood that the CC method shows better response in most of the index compared to other methods. Hence, the CC method is considered to assess the usefulness of the proposed MPZC method when subjected to different test conditions.
Comparative analysis of the proposed method and conventional method
To justify the efficacy of the proposed method, different test cases referred in Table 10 are applied, and the corresponding results of proposed MPZC method and conventional best (CC) method are compared. These test cases are considered in a way to resemble practical smoothly varying reactive load as well as largely varying nonlinear load (e.g., arc furnace, welding machines, etc.). The resultant simulation results are shown through Fig. 13, 14, 15 and 16 and the collective quantitative comparisons with respect to the standard tolerances are provided in Table 11.
Test case-T1 (of Table 10) is used to examine the stabilization capacity of the RESM system subjected to conventional and proposed methods. For analysis, time-domain and frequency-domain responses are plotted as given in Fig. 13. From Fig. 13a, it is seen that, even with more rise time, the proposed method leads to smooth response with faster settling time compared to the conventional method. Another major benefit is that it exhibits zero overshoot at startup, while it is dominant (18.5%) when using the conventional method. Similarly, from the frequency-domain response shown in Fig. 13b, it is witnessed that the phase margin is increased from 90° to 97.2° when using the proposed method. This increase in the stability margin boosts the RESM system’s stabilization capacity during transients.
Test cases-T2 and T3 (of Table 10) are used to analyze the system response during disturbances. For the analysis, various voltage characteristic index [viz., waveshape, rate of change of voltage (dv/dt), over-voltage, under-voltage, total harmonic distortion (THD)] and frequency characteristic index [viz., under-frequency, over-frequency, rate of change of frequency (df/dt)] are obtained. In Test case-T2, a disturbance of very low frequency (10 Hz) compared to nominal frequency (50 Hz) is injected as shown in Fig. 14a and in Test case-T3, a nonlinear disturbance of ± 1 pu varying magnitude is injected as shown in Fig. 16a for the comparative study of conventional and proposed methods. From the frequency characteristics given in Figs. 14b and 16b, it is witnessed that the proposed method noticeably decreased the frequency deviation from its rated value compared to the conventional method. Also, from Fig. 14b, it is noticed that the use of conventional method causes a huge df/dt of 1.82 Hz/sec, which exceeds the standard limit of ± 1 Hz/sec as given in Table 11. This is a severe issue that can result in unwanted load shedding or loss of utility-grid connection, concerns with phase balancing, real-power balancing, power hums/electromagnetic interferences for domestic appliances, etc. On the other side, the proposed method reduced the df/dt from 1.82 to 0.61 Hz/sec, which adheres the standard limit of ± 1 Hz/sec. This helps in improving the transient frequency response and can address the majority of the concerns mentioned above. Also, from Fig. 14c, it is noticed that the dv/dt is significantly reduced when using the proposed method.
As noted in Table 11, the dv/dt obtained with the conventional method violated the standard limit of ± 3 V/sec, which can damage the sensitive electric/electronic devices connected to the system. Similarly, in the 3-phase voltage profile given in Fig. 15a, b, a reactive load disturbance resulted in 4.92% of over-voltage and 9.05% of under-voltage with the conventional method, which got noticeably reduced to 1.19% and 1.75%, respectively, with the proposed method. Control of over/under voltages is very vital as these can transform to high impact swell/sags. Also, from Fig. 16c, d, it is noticed that the conventional method leads to a huge variation in voltage profile for a nonlinear load variation, while, the proposed method improved the voltage profile and exhibits smooth response. The voltage deviations further lead to harmonic distortion, which is measured as THD . From Figs. 15c and 16e, it is noticed that the proposed method exhibits low THD value of 0.77% and 1.21%, and the conventional method exhibits high THD of 3.30% and 5.37%, respectively, for the reactive and nonlinear load variations. Thus, the conventional method violated the standard limit of 5% as notified in Table 11. Having lower THD, the proposed method helps in preserving the voltage waveform shape during disturbances, which is a critical requisite for the integration of RESM and utility-grid.