Real-time prices in an entropic grid

If you talk to a control theorist today about the road to achieve an efficient, reliable, and affordable electricity supply you will most likely be told that real-time prices will be a part of its realization. Perhaps this is true. However, we argue that appropriate design using economic models that can capture the emerging physical realities is a key requirement for achieving a reliable, and "smart" electrical grid. To capture the potential pitfalls of real-time prices, we present an extension of our earlier work on dynamic markets to general network settings, allowing for more general constraints on generation and transmission. We conclude in wide generality that in the economic ideal of the competitive equilibrium, the standard results follow - the equilibrium is efficient, and average prices coincide with average marginal cost. However, these conclusions hold only on average. More importantly, we find that in the competitive equilibrium, (a) prices can be negative, (b) prices can go well above the "choke up" price - which is the maximum price consumers are willing to pay, and (c) the variance of the price decreases with increasing demand response. We illustrate these finding through numerical experiments.