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This book discusses the principles of operation and control requirements of Virtual Power Plants (VPP). VPPs are studied as dynamical systems and various sources of uncertainties and disturbances affecting their behavior are identified and mathematically modeled in the integral quadratic constraint framework. Based on the identified characteristics and requirements of the VPP, a robust hierarchical control structure is proposed to operate a VPP with multiple distributed energy resources. A set of necessary and sufficient conditions is found to design a robust, hierarchical control structure, based on the rank constrained linear matrix inequalities. To provide the virtual power plant with a smooth transition to the islanded mode, a decentralized, droop-augmented, robust voltage control structure is also developed in this book.