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In this paper, a two-stage optimal charging scheme based on transactive control is proposed for the aggregator to manage day-ahead electricity procurement and real-time EV charging management in order to minimize its total operating cost. The day-ahead electricity procurement considers both the day-ahead energy cost and expected real-time operation cost. In the real-time charging management, the cost of employing the charging flexibility from the EV owners is explicitly modelled. The aggregator uses a transactive market to manage the real-time charging demand to provide the regulating power. A model predictive control (MPC) based method is proposed for the aggregator to clear the transactive market. The realtime charging decisions of the EVs are determined by the clearing of the proposed transactive market according to the realtime requests and preferences of the EV owners. As such, the aggregators decisions in the real-time EV charging management and regulating power markets can be optimized. At the same time, the charging requirements and response preferences of the EV owners are respected. Case studies using real world driving data from the Danish National Travel Surveys were conducted to verify the proposed framework. Index Terms-Electric vehicles (EVs), regulating power, transactive control, transactive energy, two-stage optimization.

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Phase imbalance in the UK and European low voltage (415V, LV) distribution networks causes additional energy losses.A key barrier against understanding the imbalanceinduced energy losses is the absence of high-resolution time-series data for LV networks. It remains a challenge to estimate imbalance-induced energy losses in LV networks that only have the yearly average currents of the three phases. To address this insufficient data challenge, this paper proposes a new customized statistical approach, named as the CCRE (Clustering, Classification, and Range Estimation) approach. It finds a match between the network with only the yearly average phase currents (the data-scarce network) and a cluster of networks with time series of phase current data (data-rich networks). Then CCRE performs a range estimation of the imbalance-induced energy loss for the cluster of data-rich networks that resemble the data-scarce network. The Chebyshev's inequality is applied to narrow down this range, which represents the confidence interval of the imbalance-induced energy loss for the data-scarce network. Case studies reveal that, given such few data from the data-scarce networks, more than 80% of these networks are classified to the correct clusters and the confidence of the imbalance-induced energy loss estimation is 89%.

Fast decoupled state estimation (FDSE) is proposed for distribution networks, with fast convergence and high efficiency. Conventionally, branch current magnitude measurements cannot be incorporated into FDSE models; however, in this paper, branch ampere measurements are reformulated as active and reactive branch loss measurements and directly formulated in the proposed FDSE model. Using the complex per unit normalization technique and special chosen state variables, the performance of this FDSE can be guaranteed when it is applied to distribution networks. Numerical tests on seven different distribution networks show that this method outperforms Newton type solutions and is a promising method for practical application.

Widespread three-phase imbalance causes inefficient uses of low voltage (LV) network assets, leading to additional reinforcement costs (ARCs). Previous work that assumed balanced three phases underestimated the reinforcement cost throughout the whole utility by more than 50%. Previous work that quantified the ARCs was limited to individual network components, relying on full sensory data. This paper proposes a novel methodology that will scale the ARC estimation at a utility level, when the data concerning the imbalance of circuits or transformers are scarce. A novel statistical method is developed to estimate the volume of assets that need to be invested by identifying the relationship between the triangular distribution of circuit imbalance and that of circuit utilization. When there are more data available in future, accurate probability distributions can be constructed to reflect the network condition across the whole system. In light of this, two novel generalized ARC estimation formulas are developed that account for generic probability distributions. The developed methodology is applied to a real utility system in the UK, showing that: 1) three-phase imbalance leads to ARCs that are even greater than the reinforcement costs in the balanced case; 2) a 1% increase in the demand growth rate, the maximum degree of imbalance (DIB) and the maximum nominal utilization rate leads to over 10%, approximately 1% and 2% increases in the ARCs, respectively; and 3) the ARC is not sensitive to the minimum DIB values and the minimum nominal utilization rates.