Foundations for Understanding Volatility and Improving Operational Reliability

Abstract:

This project addresses the impact of the integration of renewable intermittent generation and the integration of sophisticated sensing, communication, and actuation capabilities into the grid on the system's reliability, volatility, and economic efficiency, and seeks to develop system architectures, along with associated optimization and control algorithms to balance such trade--offs. The high level goals of this project can be stated as follows:

1. Understand the trade--offs
2. Develop a flexible architecture that:
a. Achieves robustness and efficiency under normal operation
b. Reconfigures to mitigate fragility/risk upon approaching a state of failure

The poster summarizes three complementary projects that highlight the achievements and progress toward these goals.

1. Efficiency--Risk Tradeoffs in Electricity Markets with Dynamic Demand Response: It is shown in an abstract framework, how a tradeoff between efficiency and risk arises under different market architectures. The performance of an electricity market with dynamic demand response is examined under the non--cooperative and cooperative market architectures, both under marginal production cost pricing. The statistics of the stationary aggregate demand processes show that, although the non--cooperative load scheduling scheme leads to an efficiency loss, the stationary distribution of the corresponding aggregate demand process has a smaller tail, corresponding to less aggregate demand spikes (lower risk). It is also shown that under marginal cost pricing, neither cooperative nor non--cooperative is Pareto optimal. This suggests that marginal cost pricing rule should be revisited in order to improve the overall efficiency and robustness of power systems.

2. Robustness--Risk Tradeoffs in Energy Markets with Cooperative Storage and Renewable Generation: The value and the tradeoffs associated with ramp--constrained storage in securing robustness and mitigating risk is examined in energy systems with uncertain supply and demand, and friction in the main supply source. Robustness is defined as the expected discounted cost of energy deficits over an infinite horizon, whereas risk is defined as the probability of incurring a large energy deficit. Control for robustness is formulated as the problem of minimization of the infinite horizon expected discounted cost of energy deficits over all stationary Markovian policies. It is shown that for a linear stage cost, a myopic policy which uses storage to compensate for all shocks regardless of their size is optimal. However, for strictly convex stage costs it maybe optimal to incur a small energy imbalance in order to avoid a large energy deficits in the future. An interpretation of this result is that attempting to mitigate all small energy deficits increases the probability of large energy deficits. These results have important implications on different aspects of planning, design, and operation of energy systems. For instance, in designing market mechanisms for Virtual Power Plants (VPPs), the system operator can expect infrequent but large deviations from the scheduled output of VPP if the output deviation penalty is linear in the size of deviation, whereas, a pricing mechanism that grows nonlinearly in the size of the deviation, will result in more frequent but smaller deviations. The system operator can then choose the desired tradeoffs based on the available reserve technologies, and their cost.

3. Layered Architectures: Architecture for Congestion Control and Scheduling. The design and operation of power systems consists of solving various optimization problems at different time-- scales and by various agents at different levels of hierarchy, with different objectives and with access to different types of information. A layered approach consists in assigning the decision variables to different decision makers, embedded in a communication architecture that allows them to share a limited amount of information. The decomposition of the original problem into sub--problems assigned to different distributed decision makers with partial information yields suboptimal operation of the power system. Proper decomposition choices exploit time--scale separation, weak coupling of some phenomena, and redundancy of the devices, in order to achieve a certain level of performance with a limited exchange of information between the decision makers. An intermediate layered architecture is expected to provide a tradeoff between the performance of the exact solution and the robustness and scalability of the fully decoupled solution. The specific objective here is to design modular and scalable protocols and computational tools that enable the participation of flexible loads in the energy market to increase the grid efficiency while guaranteeing 1) satisfaction of their individual constraints 2) safe and reliable operation of the grid (global constraints). In a two--layered approach, a higher coordination layer produces a set of individual constraints on the maximum power rate of each bus in the power distribution grid. Once these auxiliary constraints are produced, the scheduling problem at the individual bus becomes a problem similar to the one considered before, and therefore becomes tractable.