Optimal Operation of Power Systems with Energy Storage under Uncertainty: A Scenario-based Method with Strategic Sampling

The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is formulated using the chance-constrained optimization (CCO) modeling paradigm, where the constraints include the nonlinear energy storage and AC power flow models. Based on the emerging scenario optimization method which does not rely on pre-known probability distribution functions, this paper develops a novel solution method for this challenging CCO problem. The proposed meth-od is computationally effective for mainly two reasons. First, the original AC power flow constraints are approximated by a set of learning-assisted quadratic convex inequalities based on a generalized least absolute shrinkage and selection operator. Second, considering the physical patterns of data and motived by learning-based sampling, the strategic sampling method is developed to significantly reduce the required number of scenarios through different sampling strategies. The simulation results on IEEE standard systems indicate that 1) the proposed strategic sampling significantly improves the computational efficiency of the scenario-based approach for solving the chance-constrained optimal PSO problem, 2) the data-driven convex approximation of power flow can be promising alternatives of nonlinear and nonconvex AC power flow.

Ensemble learning based linear power flow

This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as a basic learner to capture the linear relationships between the bus voltage as the independent variable and the active or reactive power as the dependent variable in rectangular coordinates. Then, gradient boosting (GB) and bagging as ensemble learning methods are introduced to combine all basic learners to boost the model performance. The fitted linear power flow model is also relaxed to compute the optimal power flow (OPF). The simulating results of standard IEEE cases indicate that (1) ensemble learning methods outperform PR and GB works better than bagging; (2) as for solving OPF, the data-driven model excels the DC model and the SDP relaxation in the computational accuracy, and works faster than ACOPF and SDPOPF.

Ensemble Learning based Convexification of Power Flow with Application in OPF

This paper proposes an ensemble learning based approach for convexifying AC power flow equations, which differs from the existing relaxation-based convexification techniques. The proposed approach is based on the quadratic power flow equations in rectangular coordinates. To develop this data-driven convex model of power flow, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms, i.e. gradient boosting (GB) and bagging, are introduced to combine learners to boost model performance. Based on the learned convex models of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases illustrate that, 1) GB outperforms PR and bagging on the prediction accuracy, 2) in context of solving OPF, the proposed data-driven convex model outperforms the conventional SDP relaxation in both accuracy and computational efficiency.