This brief proposes a pricing-based energy control strategy to remove the peak load for smart grid. According to the price, energy consumers control their energy consumption to make a tradeoff between the electricity cost and the load curtailment cost. The consumers are interactive with each other because of pricing based on the total load. We formulate the interactions among the consumers into a noncooperative game and give a sufficient condition to ensure a unique equilibrium in the game. We develop a distributed energy control algorithm and provide a sufficient convergence condition of the algorithm. The energy control algorithm starts at the beginning of each time slot, e.g., 15 min. Finally, the energy control strategy is applied to control the energy consumption of the consumers with heating ventilation air conditioning systems. The numerical results show that the energy control strategy is effective in removing the peak load and matching supply with demand, and the energy control algorithm can converge to the equilibrium.
Optimizing the performance of a multi-core microprocessor within a power budget has recently received a lot of attention. However, most existing solutions are centralized and cannot scale well with the rapidly increasing level of core integration. While a few recent studies propose power control algorithms for many-core architectures, those solutions assume that the workload of every core is independent and therefore cannot effectively allocate power based on thread criticality to accelerate multi-threaded parallel applications, which are expected to be the primary workloads of many-core architectures. This paper presents a scalable power control solution for many-core microprocessors that is specifically designed to handle realistic workloads, i.e., a mixed group of single-threaded and multi-threaded applications. Our solution features a three-layer design. First, we adopt control theory to precisely control the power of the entire chip to its chip-level budget by adjusting the aggregated frequency of all the cores on the chip. Second, we dynamically group cores running the same applications and then partition the chip-level aggregated frequency quota among different groups for optimized overall microprocessor performance. Finally, we partition the group-level frequency quota among the cores in each group based on the measured thread criticality for shorter application completion time. As a result, our solution can optimize the microprocessor performance while precisely limiting the chip-level power consumption below the desired budget. Empirical results on a 12-core hardware testbed show that our control solution can provide precise power control, as well as 17% and 11% better application performance than two state-of-the-art solutions, on average, for mixed PARSEC and SPEC benchmarks. Furthermore, our extensive simulation results for 32, 64, and 128 cores, as well as overhead analysis for up to 4,096 cores, demonstrate that our solution is highly scalable to many-core architectures.
This paper proposes a cooperative demand response scheme for load management in smart grid. The cooperative demand response scheme is formulated as a constrained optimization problem that generates a Pareto-optimal response strategy profile for consumers. Comparing with the noncooperative response strategy (i.e., Nash equilibrium) obtained from the oneshot demand management game, the Pareto-optimal response strategy reduces the electricity costs to the consumers. We further develop an incentive-compatible trigger-and-punishment mechanism to avoid the noncooperative behaviors of the selfish consumers. Furthermore, the cooperative demand response scheme is applied to achieve load management of industrial refrigerated warehouses. To implement the cooperative demand response scheme in large-scale systems, we group the refrigerated warehouses into clusters and utilize the cooperative demand response scheme within each cluster. Numerical results demonstrate that the cooperative demand response scheme can reduce the electricity costs, drop the electricity prices, and curtail the total energy consumption in comparison with the noncooperative demand response scheme.
Under the assumption that two asset prices follow an uncertain volatility model, the maximal and minimal solution values of an option contract are given by a two dimensional Hamilton-Jacobi-Bellman (HJB) PDE. A fully implicit, unconditionally monotone finite difference numerical scheme is developed in this paper. Consequently, there are no time step restrictions due to stability considerations. The discretized algebraic equations are solved using policy iteration. Our discretization method results in a local objective function which is a discontinuous function of the control. Hence some care must be taken when applying policy iteration. The main difficulty in designing a discretization scheme is development of a monotonicity preserving approximation of the cross derivative term in the PDE. We derive a hybrid numerical scheme which combines use of a fixed point stencil and a wide stencil based on a local coordinate rotation. The algorithm uses the fixed point stencil as much as possible to take advantage of its accuracy and computational efficiency. The analysis shows that our numerical scheme is l∞ stable, consistent in the viscosity sense, and monotone. Thus, our numerical scheme guarantees convergence to the viscosity solution.
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