Optimal Frequency Control of a Microgrid

Author Name(s): G. Mallesham, Krishna Degavath
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The paper provides an introduction to the complex problem of controlling a Microgrid. After defining the various terms used throughout the paper, a specific problem involving the control of a linear system with a constant load is stated. Both classical methods like PI control and optimal control method of quadratic performance index were attempted for designing the controller. The former was used to determine the improvement in performance achieved by using state feedback. The latter was found to be significantly better, and satisfied all the requirements, even when the load varied randomly with time


This is the first of a series of the papers that the authors intend to write on the control of a smart grid. It represents the cooperative effort on the part of two researchers, who have considerable experience in two different areas i.e. power systems and control theory. It is motivated by the strong belief on the part of both authors that such cooperation between workers in the two fields will be needed to address many of the problems that will arise in the future in energy management. This paper, as well as future contributions, will be organized to help such a mixed audience. The papers will deal with multiple energy sources which cooperate to meet the energy demands of a Microgrid (defined later), while optimizing a chosen performance index [1]. The problem is open ended since, at every stage, a variety of choices are open to the designer. These include the primary and secondary sources in the system, the criteria by which they are introduced into the system, the qualitative characteristics desired of the overall system, and the realization of these responses using appropriate qualitative performance criteria with fixed or adaptive parameters, At every stage, the requirements of power system engineers and those of control theorists are taken into account. The latter includes stability, robustness and satisfactory performance under a variety of perturbations on the system.

It is a truism in control system design that the simplest controller that can achieve all the objectives is the one that is generally chosen. This is because the simplest controller is also quite often the most robust. In view of this, in the present and future papers the controller structures will successively be made more complex only when some criterion or criteria are not met. Further, rational explanations will be provided for any increase in complexity. The Since the authors expect these papers to be of interest to a mixed audience drawn from multiple disciplines, every effort will be made to explain the problems addressed in both qualitative and quantitative terms, so that they can appreciate the choices made. Also, since this paper is the first of the series, a proper terminology is included for the benefit of the reader.


Using both classical and modern methods based on optimal control, controllers were designed for a Microgrid. In each case the best parameters were obtained, and the corresponding responses of the overall system were simulated. The study of classical controllers is important to realize the best response that can be achieved using simple controllers. These responses are compared with that obtained using quadratic control, which requires significantly more information.

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