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.

Considering single-phase to ground (SPG) faults accounting for more than 80% of all faults, neutral ineffectively grounded mode (NIGM) is the most promising choice for medium voltage (MV) islanded microgrids (MGs) to enhance operation reliability. But due to the weak fault current and flexible network topology of islanded MGs, it is difficult to detect SPG fault lines. To solve this issue, this paper firstly analyzes the SPG fault characteristics of the MV islanded MGs with different NIGMs and network topologies. It is found that the looped MGs have a virtual terminal, i.e., the point where zero-sequence current (ZSC) is zero. And the feature differences between fault and non-fault lines are revealed. Based on that, an SPG fault line identification method is proposed. The main criterion is constructed based on the skewness signs of high frequency zero-sequence voltage (ZSV) and ZSC. Additionally, the fundamental amplitude of the difference between the actual ZSC received from another terminal and the ZSC calculated from local ZSV and ZSC is used to formulate an auxiliary criterion. Finally, the effectiveness of the proposed method is validated in a 10kV islanded MG model considering different NIGMs, different fault conditions, arc grounding faults, and the influences of the line parameter, operating point and measurement noises.

Existing fault location approaches necessitate the deployment of micro-phasor measurement units ( $\boldsymbol {\mu }$ PMUs) at all terminal buses to achieve precise fault location on any line, leading to high costs and limited applicability in large, unbalanced active distribution networks (ADNs) with numerous branches. To address this issue, this paper proposes a cost-effective fault location method based on a sparse hybrid measurement scheme (SHMS), which replaces $\boldsymbol {\mu }$ PMUs on branches with conventional measuring devices (CMDs). First, a sparse fault current extraction method is proposed, and the conditions for the uniqueness of the sparse fault current solution are provided. Building on these results, a low-cost SHMS is proposed. Finally, a two-stage fault location method is presented to precisely locate faults on any line within ADNs. For the unbalanced IEEE 123-bus test system with numerous branches, the proposed method requires only $13~\boldsymbol {\mu }$ PMUs and 32 CMDs—compared to the conventional requirement of $45~\boldsymbol {\mu }$ PMUs—to locate faults on any line, thereby significantly reducing measurement costs. Simulation results indicate that, under diverse fault conditions, the fault location success rate reaches 98.30% for three-phase main lines and 96.16% for branches.

The fault ride through (FRT) control of inverter-based distributed generators (IBDGs) is quickly activated after a fault to limit the output current within 2 per unit. There is a phase jump phenomenon at the commencement of FRT control. However, the low fault current level and time-varying phase could make it difficult to guarantee the rapidity and the selectivity of islanded microgrid protection. In this paper, the transient characteristics of islanded microgrids are analyzed considering the influence of IBDG fault response and flexible network topology. The solution reveals the phase jump direction and magnitude difference between internal and external fault currents. Then, the energy value, the skewness value of directional morphological gradient, and peak polarity of incipient fault current are applied to formulate the protection criteria. The proposed protection scheme offers the following features: faulted phase selection capability, insensitivity to fault inception angle, adaptation to changes in the network topology, noise immunity with signal to noise ratio (SNR) down to 1dB, and low communication bandwidth requirements. The simulation results verify the effectiveness of proposed scheme for various fault conditions.

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.