A. V. Savkin

Y. Shi, H. D. Tuan, P. Apkarian et al.

Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These computationally intractable constraints are often expressed by linear constraints plus matrix additional rank-one constraints on the outer products of the voltage vectors. The existing convex relaxation technique, which drops the difficult rank-one constraints for tractable computation, cannot yield even a feasible point. We address these computationally difficult problems by an iterative procedure, which generates a sequence of improved points that converge to a rank-one solution. Each iteration calls a semi-definite program. Intensive simulations for the OPF problems over networks with a few thousands of buses are provided to demonstrate the efficiency of our approach. The suboptimal values of the OPF problems found by our computational procedure turn out to be the global optimal value with computational tolerance less than 0.01%.

Y. Shi, H. D. Tuan, A. V. Savkin

The problem of joint coordination of plug-in electric vehicles (PEVs) charging and grid power control is to minimize both PEVs charging cost and energy generation cost while meeting both residential and PEVs' power demands and suppressing the potential impact of PEVs integration. A bang-bang PEV charging strategy is adopted to exploit its simple online implementation, which requires computation of a mixed integer nonlinear programming problem (MINP) in binary variables of the PEV charging strategy and continuous variables of the grid voltages. A new solver for this MINP is proposed. Its efficiency is shown by numerical simulations.

Y. Shi, H. D. Tuan, T. Q. Duong et al.

The success of the transportation electricification in this century particularly requires the penentration of the internet of plug-in electric vehicles (PEVs) into the smart power grid. Beside the function of serving the traditional residential power demand, next-generation power grids also aim to support the internet of PEVs at the same time. The distinct difference between the traditional power demand and PEVs' power demand is that while the statistics of the former is rich enough for treating it as inelastic/known before hand, the latter is unknown until random PEVs' arrivals. Massive penentration of PEVs certainly causes the grid unpredictable fluctuation. The present paper considers the joint PEVs charging coordination and grid power generation to minimizing both of the negative impact of PEVs' integration and the cost of power generation while meeting the grid operating constraints and all parties' demand. The bang-bang PEVs charging strategy is adopted to exploit its simple implementation. By using a recently developed model predictive control (MPC) model for this problem, the online compuation is based on a predictive mixed integer nonlinear programming (MINP). A new solution computation for this optimization problem is developed. Its capacity of achieving the globally optimal solution is shown by numerical comparison between its performance and that by an off-line optimal solution.

Y. Shi, H. D. Tuan, A. V. Savkin et al.

Next-generation power grids will likely enable concurrent service for residences and plug-in electric vehicles (PEVs). While the residence power demand profile is known and thus can be considered inelastic, the PEVs' power demand is only known after random PEVs' arrivals. PEV charging scheduling aims at minimizing the potential impact of the massive integration of PEVs into power grids to save service costs to customers while power control aims at minimizing the cost of power generation subject to operating constraints and meeting demand. The present paper develops a model predictive control (MPC)- based approach to address the joint PEV charging scheduling and power control to minimize both PEV charging cost and energy generation cost in meeting both residence and PEV power demands. Unlike in related works, no assumptions are made about the probability distribution of PEVs' arrivals, the known PEVs' future demand, or the unlimited charging capacity of PEVs. The proposed approach is shown to achieve a globally optimal solution. Numerical results for IEEE benchmark power grids serving Tesla Model S PEVs show the merit of this approach.