There has been a global push for many years to increase our use of clean, renewable electric energy. State and local governments of many countries adopted renewable portfolio standards, which require a certain percentage of electric energy production to come from renewable resources. Reliable power system operation requires the continuous balance of supply and demand at every moment in time. However, large-scale integration of variable generations such as solar and wind can significantly alter the dynamics in a grid because wind and solar resources are intermittent. The power output can have fast fluctuation due to various reasons such as weather change and system reliability of a large number of turbines. Generators that use renewable energy to produce electricity often must be sited in locations where wind and solar resources are abundant and sufficient space exists for harnessing them. However, these locations are likely far away from population centers that ultimately consume the energy. The required transmission grids present additional challenges in various aspects including operational control, economic concerns, and policy-making.
Mathematical models that adequately represent the dynamic behavior of the entire wind or solar plant at the point of interconnection are a critical component for daily analysis and for computer model simulations. The analysis and simulations are used by system planners and operators to assess the potential impact of power fluctuations, to perform proper assessment of reliability, and to develop operating strategies that retain system stability and minimize operational cost and capital investment. Traditional models used by power industry cannot meet this goal for power grids with a large-scale integration of intermittent generators, but active research on better models is being carried out by several organizations and institutions. IEEE Power and Energy Magazine had two issues (Vol. 11(6) and Vol. 9(9)) that focus on several aspects of wind power integration.
Technically, storage is an ideal flexible resource that is quick to respond to the fluctuation of generation and demand. Its functions include provision of energy arbitrage, peak shifting, and storing of otherwise-curtailed wind. In the case of battery storage it can be deployed close to the load in a modular fashion. However, efficiency issues coupled with the high capital costs make the justification of new storage difficult. A report from the American Institute of Mathematics in 2012 arising from a workshop there dealt with some technical problems related to storage, such as the linear programming model that optimizes the required battery storage size and a nonlinear optimal control problem for batteries of predetermined size. The 17 page report is available here. Review articles can also be found in the IEEE magazine issues mentioned above.
Power systems are reliability-constrained; i.e., they must perform their intended functions under system and environmental conditions. Intuitive or rule-of-thumb approaches currently used in the industry will be inadequate for future power systems. More sophisticated quantitative techniques and indices have been developed for many years and they are still an active focus of research. The work involves many areas of mathematics, including the mathematical concepts and models of reliability, nonlinear optimization, and large-scale simulations. References can easily be found in many journals such as IEEE Transactions on Power Systems.
Naval Postgraduate School