To analyze the effect of carbon emission quota allocation on the locational marginal price (LMP) of day-ahead electricity markets, this paper proposes a two-stage algorithm. For the first stage of the algorithm, a multi-objective optimization model is established to simultaneously minimize the total costs and carbon emission costs of power systems. Hence, an evenly distributed Pareto optimal solution can be solved effectively by means of the normalized normal constraint method. For the second stage, a tracing model is built with the goal of minimizing the total costs of power systems and satisfying the constraints generated based on the Pareto optimal solution obtained from the first stage. Furthermore, the influence of carbon emission quota allocation on the LMP of electricity markets is analyzed, and different schemes to allocate carbon emission quotas are evaluated on a real 1560-bus and 52-unit system.

High proportions of asynchronous motors in demand-side have pressured heavily on short-term voltage security of receiving-end power systems. To enhance short-term voltage security, this paper coordinates the optimal outputs of generation and compensation in a multi-objective dynamic optimization model. With equipment dynamics, network load flows, lower and upper limitations, and security constraints considered, this model simultaneously minimizes two objectives: the expense of control decision and the voltage deviation. The Radau collocation method is employed to handle dynamics, by transforming all differential algebraic equations into algebraic ones. Most importantly, Pareto solutions are obtained through an accelerated multi-objective reinforcement learning (AMORL) method by filtering the dominated solutions. The entire feasible region is partitioned into small independent regions, to eliminate the scope for Pareto solutions. Besides, the AMORL method redefines the state functions and introduces creative state sensitivities, which accelerate the switch from learning to applying, once the agent accumulates sufficient knowledge. Furthermore, Pareto solutions are diversified via introducing some potential solutions. Lastly, the Fuzzy decision-making methodology picks up the tradeoff solution. Case studies are implemented on a practical 748-node power grid, which validate the acceleration and efficiency of the AMORL method. The AMORL method is overall superior to conventional reinforcement learning (RL) method with more optimal non-dominated objective values, much shorter CPU time, and better convergence to accurate values. Moreover, compared with another three state-of-the-art RL methods, the AMORL method takes almost the same CPU time of several seconds, but is slightly superior to the state-of-the-art methods in terms of optimal objective values. Additionally, the calculated values of the AMORL method fit the best with the accurate values during each iteration, resulting in a good convergence. INDEX TERMS Accelerated multi-objective reinforcement learning, dynamic optimization, Pareto solutions, short-term voltage security. NOMENCLATURE A. PARAMETERS

Due to the increasing uncertainty brought about by renewable energy, conventional deterministic dispatch approaches have not been very applicative. This paper investigates a nested sparse grid-based stochastic collocation method (NS-SCM) as a possible solution for stochastic economic dispatch (SED) problems. The SCM was used to simplify the scenario-based optimization model; specifically, a finiteorder expansion using the generalized polynomial chaos (gPC) theory was applied to approximate random variables as a more facile approach compared to using complicated optimization models. Furthermore, a nested sparse grid-based approach was adopted to reduce the number of collocation points while still satisfying the nested property, thereby alleviating and effectively eliminating the need for computation. The proposed approach can be directly applied to the SED optimization problem. Lastly, simulations on the modified IEEE 39-bus system and a practical 1009-bus power system were provided to verify the accuracy, effectiveness, and practicality of the proposed algorithm.

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