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Single‐phase loads and photovoltaic generation cause three‐phase imbalance in distribution systems, and prospective growth of normal chargers of electric vehicles may even increase the imbalance. The analysis of such unbalanced systems requires the three‐phase power‐flow calculation. Since existing methods require the admittance matrices of three‐phase transformers, they must be derived for all possible winding connection patterns in advance to its computer‐code implementation. This paper proposes a three‐phase power‐flow calculation method which formulates circuit equations using the modified nodal analysis, making it possible to automatically handle any winding connection. The power‐flow constraints are then embedded into the circuit equations using a fixed‐point iteration. Newton‐Raphson, backward/forward sweep and fixed‐point iteration methods are the existing three categories of solution methods. Newton‐Raphson methods may show convergence problems due to the high R/X ratios of distribution lines. Backward/forward sweep methods cannot be used, because loops are temporarily formed in a distribution system during circuit switching. These justify the use of a fixed‐point iteration. In this paper, the proposed method is validated by practical examples. [ABSTRACT FROM AUTHOR]

Three‐phase unbalanced conditions in distribution networks are conventionally caused by load imbalance, asymmetrical fault conditions of transformers and impedances of three phases. The uneven integration of single‐phase distributed generation (DG) worsens the imbalance situation. These unbalanced conditions result in financial losses, inefficient utilisation of assets and security risks to the network infrastructure. In this study, a phase‐changing soft open point (PC‐SOP) is proposed as a new way of connecting soft open points (SOPs) to balance the power flows among three phases by controlling active power and reactive power. Then an operational strategy based on PC‐SOPs is presented for three‐phase four‐wire unbalanced systems. By optimising the regulation of SOPs, optimal energy storage systems dispatch and DG curtailment, the proposed strategy can reduce power losses and three‐phase imbalance. Second‐order cone programming (SOCP) relaxation is utilised to convert the original non‐convex and non‐linear model into an SOCP model which can be solved efficiently by commercial solvers. Case studies are conducted on a modified IEEE 34‐node three‐phase four‐wire system and the IEEE 123‐node test feeder to verify the effectiveness, efficiency and scalability of the proposed PC‐SOP concept and its operational strategy. [ABSTRACT FROM AUTHOR]

Since the distribution system operator (DSO) cannot directly control prosumers with controllable resources, this study proposes an optimal dispatch method of using three‐phase distribution locational marginal prices (DLMPs) as effective economic signals to incentivise prosumers' behaviours. In the proposed three‐phase DLMP model, DLMPs for active power demand, active power output and reactive power output are calculated. To alleviate the imbalance, congestions and voltage violations in active distribution networks (ADNs), the DSO and prosumers should be coordinated. The authors develop such a coordinated control scheme for the DSO and prosumers, in which the DSO generates and broadcasts three‐phase DLMPs as price signals to induce prosumers' behaviours. They prove that given the DLMPs as settlement prices, the optimal dispatch of the ADN will also maximise the surplus of prosumers. Therefore, the power output of rational prosumers will match the optimal dispatch, resulting in better operational conditions of ADNs. Then the three‐phase imbalance, congestions and voltage violations will be well reduced. Numerical tests demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The randomness of electric vehicle (EV) charging has negative impacts on three‐phase imbalance and peak–valley difference in electric energy distribution systems. Traditional EV charging strategies have shortcomings: the performance of three‐phase imbalance mitigation may be limited if the grid‐connected EVs are extremely imbalanced on three phases; in addition, the comprehensive regulation of peak–valley difference and three‐phase imbalance is not developed, and the three‐phase imbalance of reactive power is ignored. Therefore, a real‐time multilevel energy management strategy (RMEMS) for EV charging is proposed. A tri‐level optimization model (TOM) is designed as the central system. In upper‐level optimization, the three‐phase selection (TPS) of EVs is optimized to balance active or reactive power consumption on three phases. Based on the results from upper‐level optimization, the charging active power is regulated in middle‐level optimization to reduce the peak–valley difference on each phase. In lower‐level optimization, the reactive power compensated by EV chargers is optimized based on the results from upper‐level and middle‐level optimization to balance the reactive power on three phases. Case studies show that the proposed RMEMS performs well for balancing active and reactive power consumption on three phases, and the peak–valley differences of active power consumption on each phase are all mitigated. [ABSTRACT FROM AUTHOR]