Considering the economics and securities for the operation of a power system, a semi-definite programming (SDP) model for the security-constrained unit commitment (SCUC) problem is described here, which is directly solved by the interior-point method for SDP within the polynomial times. The proposed method is promising for the SCUC problems because of its excellent convergence and the ability of handling the non-covex integer variables. No model decomposition and initial relaxation are needed when applying the SDP-based method. When the solution contains minor mismatches in the integer variables, a simple rounding strategy is used to correct the non-integer into integer efficiently. Different test cases from 6 to 118 buses over a 24 h horizon are presented. Extensive numerical simulations have shown that the proposed method is capable of obtaining the optimal UC schedules without any network and bus voltage violations, and minimising the operation cost as well.

This letter presents a robust optimization-based AC optimal power flow (RACOPF) model for power networks with uncertain wind power generation. Numerical results on three test systems with uncertain wind power show that the RACOPF outperforms the robust DC-OPF model in the literature.

Small-Signal Stability Constrained Optimal Power Flow (SSSC-OPF) can provide additional stability measures and control strategies to guarantee the system to be small-signal stable. However, due to the nonsmooth property of the spectral abscissa function, existing algorithms solving SSSC-OPF cannot guarantee convergence. To tackle this computational challenge of SSSC-OPF, we propose a Sequential Quadratic Programming (SQP) method combined with gradient sampling for SSSC-OPF. At each iteration of the proposed SQP, the gradient of the spectral abscissa function is randomly sampled at the current iterate and additional nearby points to make the search direction computation effective in nonsmooth regions. The method can guarantee SSSC-OPF is globally and efficiently convergent to stationary points with probability one. The effectiveness of the proposed method is tested and validated on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system.

Frequency dynamics during primary frequency control is closely related to pre-disturbance operating conditions, the disturbance, and equipment characteristics. How to rigorously express such a relation in a frequency stability constrained optimal dispatch problem is still an open question. This paper presents an optimal power flow (OPF) model for generation redispatch that considers dynamic frequency response constraints to ensure frequency stability during primary frequency regulation. The distinct feature of the model is that the dynamic frequency response is formulated as a set of differential algebraic equations (DAEs), which allows considering the transient behavior of frequency and mechanical/electromagnetic power for each generator during primary frequency control period. Based on the solution of the optimization problem, a definition of the primary reserve for each unit is proposed according to the maximum of incremental mechanical power. This definition helps meet the adequacy requirement of primary frequency response and achieve partial frequency restoration. Simulation results on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system and the modified IEEE 54-machine 118-bus system validate the effectiveness of the proposed model and reveal the strong coupling between frequency dynamics and the predisturbance generation.