This paper presents a cold-start linear branch flow model named modified DistFlow. In modified DistFlow, the active and reactive power are replaced by their ratios to voltage magnitude as state variables, so that errors introduced by conventional branch flow linearization approaches due to their complete ignoring of network loss terms are reduced. Based on the path-branch incidence matrix, branch power flows and nodal voltage magnitudes can be written in succinct matrix forms. Subsequently, the proposed modified DistFlow model is applied to the problem of reactive power optimization and network reconfiguration, transforming it into a mixed-integer quadratic programming (MIQP). Simulations show that the proposed modified DistFlow has a better accuracy than existing cold-start linear branch flow models, and the resulting MIQP model for reactive power optimization and network reconfiguration is much more computationally efficient than existing benchmarks.

The problem of optimal planning of plug-in electric vehicle (PEV) charging stations is studied. Different from many other works, we assume the station investor to be a new private entrant into the market who intends to maximize its own profit in a competitive environment. A modified Huff gravity-based model is adopted to describe the probabilistic patronizing behaviors of PEV drivers. Accordingly, a bi-level optimization model is formulated to decide not only the optimal site and size of the new charging station, but also the retail charging prices in the future operation stage. Based on the specific characteristics of the problem, the operation level sub-problem is reformulated to a convex programming and an efficient solution algorithm is designed for the overall bi-level optimization. Numerical examples of different scales demonstrate the effectiveness of the proposed modeling and computation methods, as well as the importance of considering the competitive effects when planning the charging station.

The development of active distribution grids brings with it a demand for a higher accuracy of state estimation. Micro-phasor measurement units (μPMUs) deployed in distribution grids provide necessary but insufficient support for the state estimation of enhanced performance. This paper deals with a decentralized PMU-based robust state estimation of active distribution grids incorporating microgrids. The PMU-based robust state estimation is formulated as a quadratic programming problem and solved in a decentralized manner to accommodate the autonomous operation mode among microgrids, as well as to preserve information privacy between different operators. During each iteration of the decentralized method, each microgrid evaluates its bad measurements and sends its local optimization objective with respect to boundary states to the utility grid for a unified optimization. The proposed iteration scheme between the utility grid and microgrids has significant advantages over regular iteration methods, in terms of its convergence rates and minimal data exchange between operators. Case studies of different systems are presented that demonstrate the exactness and efficiency of the proposed method.

This paper proposes an augmented Lagrangian-based safe off-policy deep reinforcement learning (DRL) algorithm for the carbon-oriented optimal scheduling of electric vehicle (EV) aggregators in a distribution network. First, practical charging data are employed to formulate an EV aggregation model, and its flexibility in both emission mitigation and energy/power dispatching is demonstrated. Second, a bilevel optimization model is formulated for EV aggregators to participate in day-ahead optimal scheduling, which aims to minimize the total cost without exceeding the given carbon cap. Third, to tackle the nonlinear coupling between the carbon flow and power flow, a bilevel model with a carbon cap constraint is formed as a constrained Markov decision process (CMDP). Finally, the CMDP is efficiently solved by the proposed augmented Lagrangian-based DRL algorithm featuring the soft actor-critic (SAC) method. Comprehensive numerical studies with IEEE distribution test feeders demonstrate that the proposed approach can achieve a fine tradeoff between cost and emission mitigation with a higher computation efficiency compared with the existing DRL methods.

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.