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The rapid growth of the behind-the-meter (BTM) distributed generation has led to initiatives to reform the net energy metering (NEM) policies to address pressing concerns of rising electricity bills, fairness of cost allocation, and the long-term growth of distributed energy resources. This article presents an analytical framework for the optimal prosumer consumption decision using an inclusive NEM X tariff model that covers existing and proposed NEM tariff designs. The structure of the optimal consumption policy lends itself to near closed-form optimal solutions suitable for practical energy management systems that are responsive to stochastic BTM generation and dynamic pricing. The short and long-run performance of NEM and feed-in tariffs (FiT) are considered under a sequential rate-setting decision process. Also presented are numerical results that characterize social welfare distributions, cross-subsidies, and long-run solar adoption performance for selected NEM and FiT policy designs. 

Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two- part paper. Part I investigates dispatch-following incentives of profit-maximizing generators and shows that, under mild conditions, no uniform-pricing scheme for the rolling-window economic dispatch provides dispatch-following incentives that avoid discriminative out-of-the-market uplifts. A nonuniform pricing mechanism, referred to as the temporal locational marginal pricing (TLMP), is proposed. As an extension of the standard locational marginal pricing (LMP), TLMP takes into account both generation and ramping-induced opportunity costs. It eliminates the need for the out-of-the-market uplifts and guarantees full dispatch-following incentives regardless of the accuracy of the demand forecasts used in the dispatch. It is also shown that, under TLMP, a price-taking market participant has incentives to bid truthfully with its marginal cost of generation. Part II of the paper extends the theoretical results developed in Part I to more general network settings. It investigates a broader set of performance measures, including the incentives of the truthful revelation of ramping limits, revenue adequacy of the operator, consumer payments, generator profits, and price volatility under the rolling-window dispatch model with demand forecast errors. 

We study the deadline scheduling problem for multiple deferrable jobs that arrive in a random manner and are to be processed before individual deadlines. The processing of the jobs is subject to a time-varying limit on the total processing rate at each stage. We formulate the scheduling problem as a restless multi-armed bandit (RMAB) problem. Relaxing the scheduling problem into multiple independent single-arm scheduling problems, we define the Lagrangian priority value as the greatest tax under which it is optimal to activate the arm, and establish the asymptotic optimality of the proposed Lagrangian priority policy for large systems. Numerical results show that the proposed Lagrangian priority policy achieves 22%-49% higher average reward than the classical Whittle index policy (that does not take into account the processing rate limits). 

Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two-part paper. Part I investigates dispatch-following incentives for generators under the locational marginal pricing (LMP) and temporal locational marginal pricing (TLMP) policies. Extending the theoretical results developed in Part I, Part II evaluates a broader set of performance measures under a general network model. For networks with power flow constraints, TLMP is shown to have an energy-congestion-ramping price decomposition. Under the one-shot dispatch and pricing model, this decomposition leads to a nonnegative merchandising surplus equal to the sum of congestion and ramping surpluses. It is also shown that, comparing with LMP, TLMP imposes a penalty on generators with limited ramping capabilities, thus giving incentives for generators to reveal their ramping limits truthfully and improve their ramping capacities. Several benchmark pricing mechanisms are evaluated under the rolling-window dispatch and pricing models. The performance measures considered are the level of out-of-the-market uplifts, the revenue adequacy of the system operator, consumer payment, generator profit, level of discriminative payment, and price volatility. 

The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors and the presence of bad and missing data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation via deep learning neural network outperforms existing benchmarks.