Stability, voltage performance and power sharing issues of inverter-based microgrids via LMI optimization

Numerous small distributed energy resources (DERs) form a new generation of power systems the microgrid. In general, a microgrid stands for a cluster of DERs, which can collectively operate as an individual low-voltage power system during islanded mode. A microgrid can also be operated in connected mode with a large power system. DERs are often interfaced to a microgrid through power electronic inverters, forming an inverter-based microgrid. As inverters obtain very different characteristics to conventional generation units (e.g. synchronous generators), characteristics of microgrids significantly differ from those of conventional power systems. As a result, popular stabilizing and power sharing approaches, which are applied to conventional power systems, are no longer effective for the control of islanded microgrids. For the case of islanded parallel-connected inverter-based microgrids, a novel power control approach together with a thorough stability analysis are developed in this thesis. Dynamics of lower control levels of inverters are relatively fast and can be neglected. For the stability analysis of microgrids at the power control level, inverters are considered to be ideal voltage sources with controllable voltage magnitudes and phase angles. In order to avoid fast communication and control interconnection between inverters, a decentralized power control approach is proposed. The control approach requires clock synchronization between inverters, which can be realized by the global positioning system. The main goal at the power control level is the control of power flows within a microgrid, where the closed-loop stability is an essential requirement. For a normal operation of loads, the performance of voltages and frequencies in the sense of magnitude deviations and higher-frequency harmonics is also important. From a power system perspective the stability of microgrids is investigated in the sense of small-signal stability. In the thesis the stability of microgrids is analyzed by using control system techniques. For the nominal stability analysis, a linearized model of microgrids is derived. There are different uncertainties and disturbance sources to the stability of microgrids such as load dynamics, load and line uncertainties and changes of power references. Accordingly, stability of microgrids against the aforementioned uncertainties and disturbances is investigated. Load dynamics are considered by including load models in the stability analysis. With respect to load and line uncertainties, robust stability of a microgrid and robust performance of inverter output voltages are studied in the H∞ control. With a proposed decentralized power control loop, inverter controllers are synthesized by using the linear matrix inequality (LMI) technique. Different LMI problems are proposed to design decentralized inverter controllers to guarantee the asymptotic stability of an overall microgrid. Furthermore, a droop-based power sharing control is proposed. Although a desired power sharing performance is not analytically proved, it will be shown via simulation that power sharing between inverters is achieved without causing stability and voltage performance problems. The effectiveness of proposed microgrid models and related controller design methods are validated via computer simulations.