Abstract-Microgrid-containing parallel-connected inverters, where each inverter is controlled by decentralized active power/voltage frequency and reactive power/voltage magnitude droop control laws results in flexible and expandable systems. These systems have been known to have stability problems for large values of active power/voltage frequency droop control gain. However, so far the stability analysis of multi-inverter systems has always been performed in a computationally intensive manner by considering the entire microgrid. In a practical microgrid, where the number of inverters may be large or the capacity of the units may differ, it becomes essential to develop a method by which stability can be examined without much computational burden. The system of differential algebraic equations has been simplified using justifiable assumptions to result in a final expression that allows the stability of the microgrid to be examined separately with respect to the droop control laws of each inverter transformed into an equivalent network. Moreover, the procedure allows taking into consideration the R/X ratio of the interconnecting cables. Analysis of final expressions validate the stability results reported in literature. Experimental results on hardware show the stable operation of the microgrid.
The decentralized control of a line interactive UPS through p p p-ω ω ω and q q q-V V V droop control requires measurement only of variables local to the UPS and does not require a communication link. The droop control strategy has been known to result in unstable systems for large gain constants. This paper begins with a behavioral approach to system representation and presents the transfer function of the controlled system. By determining the location of the poles and zeros of the open loop transfer function, comments are made about the stability of the controlled system for various gains. The value of control gain that causes instability can be determined analytically. Simulations in Scilab are used to show the change in the poles of the controlled system with changes in control gain. Experimental results have been presented to show the operation of the line interactive UPS in transient state. Index Terms-Decentralized control, behavioral theory of systems, Uninterruptible Power Supply (UPS), Digital Signal Processor (DSP). I. INTRODUCTION A line interactive Uninterrupted Power Supply (UPS) isan excellent solution to improve the reliability of electric power to a critical load [1], [2]. A line interactive UPS is connected to the distribution system (which will be called as ac grid) and the load through a single interface without an additional rectifier. When the ac grid is healthy, the UPS shares the power demanded by the load with the grid, while during grid outages, the load is supplied by the UPS. In this paper, the decentralized control of a line interactive UPS will be examined where the UPS is controlled by measurement of variables local to the UPS. For this purpose, the droop control strategy is analyzed and implemented.In the droop control strategy [3]-[9] , the frequency ω and the magnitude V of the UPS output voltages are not constants but are made to vary with respect to the power supplied by the UPS. The frequency ω is varied with respect to the active power p supplied by the UPS while the magnitude V is varied with respect to the reactive power q supplied. Previous studies have presented stability analysis of the UPS with droop control strategy [4], [5], [7]-[9]. The study has been focused on the dominant poles of the controlled system that are closest to the imaginary axis of the complex s plane. Several studies have shown through simulations how the poles of the closed loop system become unstable for large droops [4], [7], [9]. However, a conclusive theoretical proof of stability of the controlled system has not been presented.In this paper, a behavioral approach has been used to model the UPS connected to the ac grid. The system is shown
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