Dapeng Wang

This article proposes a novel N–1 interval optimal power flow (NIOPF) scheme that considers N–1 contingencies and interval uncertainties in renewable generation. Based on the scenario-equivalent decoupling method (SEDM), the NIOPF addresses the problems associated with existing methods, including constraint violations and low solution efficiency. First, the NIOPF model is formulated by integrating security constraints involving interval variables under both N–0 normal and N–1 contingency scenarios, along with scenario transition constraints. Second, a credible domain reduction method (CDRM) based on the Minkowski difference is proposed to handle interval constraints, converting them into tractable deterministic constraints that guarantee the system operates within safe limits across all uncertain scenarios. Then, the SEDM represents numerous N–1 scenarios equivalently as two positive and negative deviation scenarios, effectively reducing the dimensionality of N–1 scenarios. Next, a two-stage optimization model that integrates the N–0 normal operating scenario with the two equivalent deviation scenarios is constructed and solved iteratively to improve computational efficiency. Finally, case studies on the modified IEEE 30-bus system verify that the proposed SEDM ensures constraint satisfaction under uncertainties while improving computational efficiency. Further tests on the modified IEEE 118-bus and PEGASE 1354-bus systems confirm its engineering applicability.

This paper proposes an optimal power flow method considering interval uncertainties (OPFIU) to enhance the security and economy of power systems with high renewable energy penetration. The OPFIU incorporates bi-level interval power flow (BIPF) equations, security and operation constraints, and active power balance across two extreme renewable output scenarios. Firstly, a dynamic-balance optimization scenario method (DOSM) is proposed to solve the BIPF within the OPFIU. The BIPF involves multiple generators in dynamically balancing the system’s active power, thus reducing the conservatism prevalent in existing interval power flow methods. Next, based on the BIPF results, an adaptive security limits definition method (ASLDM) is presented to convert the OPFIU model into a deterministic optimal power flow model, making it more tractable for solution. The ASLDM not only improves the solution efficiency and convergence of existing interval optimization methods, but also provides enhanced reliability in maintaining transmission power within operational limits across a broad spectrum of uncertainty scenarios. Moreover, the ASLDM, unlike robust optimization methods that require convexification of nonlinear AC power flow equations, partially avoids potential issues such as accuracy degradation or solution infeasibility resulting from model simplifications. The Simulation results, compared with robust optimization and chance-constrained programming methods, demonstrate that the proposed ASLDM improves both solution efficiency and convergence in solving the OPFIU problem.

To account for the probability distribution information of uncertain scenarios, this letter proposes a novel interval power flow (NIPF) method based on hybrid uncertain sets. Firstly, a NIPF model is established by integrating the hybrid box-ellipsoid sets characterizing uncertainties in interval power flow (IPF), which is solved by the optimizing-scenario method (OSM). Then, a multivariate statistical analysis method (MSAM) and a chance-constrained programming-based method (CCPM) are proposed for determining the optimal radii of the ellipsoid set and side length of the box set under two scenarios, respectively, namely, the normal distributions without correlations and the arbitrary distributions with correlations. Finally, case studies validate the effectiveness and advantage of the proposed method compared with traditional IPF methods based on Monte Carlo simulation, box sets, and ellipsoid sets.

This paper expresses the output power of renewable generators and load demand as interval data and develops the interval economic dispatch (IED), as well as interval reactive power optimization (IRPO) models. The two models are generalized into a specific type of linear interval programming (LIP) and nonlinear interval programming (NLIP), respectively. A security limits method (SLM) is proposed to solve LIP and NLIP problems. As for the LIP, the maximum radii of the interval variables are first calculated by the optimizing-scenarios method (OSM) for defining security limits, and the LIP is transformed into deterministic linear programming (LP), for which its constraints are the security limits, which can be solved by the simplex method. As for the NLIP, Monte Carlo simulations were used to obtain the maximum radii of the interval variables, and the average interval ratio of the interval variables is defined to compute the security limits for transforming the NLIP to deterministic nonlinear programming (NLP), which can be solved by using the interior point method. Finally, the IED and IRPO are used to verify the effectiveness and engineering of the proposed SLM.