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An optimal static voltage stability margin (SVSM) control model considering the uncertain wind farm output is proposed, in which the probability distribution of SVSM is required to satisfy the chance and variance constraints. A probabilistic distribution control method is proposed to solve the model. First, a linear weighted sum of B-spline basic functions is introduced to approximate the analytical function between the probability density function (PDF) of SVSM and control variables. Next, the analytical expression of the PDF of SVSM corresponding to a control variables’ sample is derived, and the sample of corresponding B-spline function weights is obtained, thus forming a series of ‘control variables-weights’ samples. Then, the analytic functions between weights and control variables are obtained using the generated samples to train a radial basis function neural-network, and the analytical function between the PDF of SVSM and control variables is obtained. After that, the chance and variance constraints are transformed into general nonlinear constraints with respect to control variables. Moreover, a method of selecting key control variables by calculating sensitivities is proposed to increase computational efficiency. Test results on the IEEE-39 bus system and an actual provincial power grid demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates a comprehensive optimization method of determining the size and location of dynamic voltage restorers (DVRs) in distribution network considering customers’ demand for sag mitigation. The objective is to minimize the investment of DVRs subject to customers’ satisfaction. In the objective function, the unit price per kVA of DVR was described by a continuous function of the capacity to calculate the investment. In the constraints, a mitigation expectation index (MEI) was proposed to assess the customers’ demand for mitigation. The MEI indicates the proportion among all sag events affecting customers, which were expected to be mitigated by the customers. It is represented by the cumulative probability of residual voltage of sag events. To improve the computational efficiency, the binary encoding for the locations and real encoding for the output voltage of DVRs are combined as chromosomes in multiple population Genetic Algorithm (MPGA). The proposed method was testified with the IEEE 33 bus distribution system with different sensitive loads. Optimal results were obtained to satisfy different customers’ demand for sag mitigation efficiently. [ABSTRACT FROM AUTHOR]

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, 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 such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails. [ABSTRACT FROM AUTHOR]

This letter presents a novel optimization framework of formulating the three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework that is less complex than the existing optimization frameworks involving uncertainty, and 2) convex such that it admits polynomial-time algorithms and mature distributed optimization methods. To construct this UaO framework, a methodology of learning-aided uncertainty-aware modeling, with prediction errors of stochastic variables as the measurement of uncertainty, and a theory of data-driven convexification are proposed. Theoretically, the UaO framework is applicable for modeling general optimization problems under uncertainty. [ABSTRACT FROM AUTHOR]

Deferrable power-driven demands such as water and thermal ones possess a capability of energy storage which can be exploited to further optimize electric systems. This paper proposes a new optimized scheduling framework for electric grids by simultaneously exploiting the high-inertia thermal dynamics and lossless water storage. Unlike previous ideas in the literature, both water and thermal demands are managed to realize the long-term and short-term load-shifting strategies, respectively. First, distributed water/thermal loads are aggregated where the virtual storage can be represented by battery models. Then, a further optimized scheduling framework is proposed with a mixed-integer nonlinear programing problem. Comparative studies show that the water storage offers outstanding flexibility for electric system via pumps scheduling, especially for the electric load-shifting strategy in a long time-horizon thanks to the lossless water-storage process. Meanwhile, the thermal storage can directly support short-term electric load-shifting to avoid price spikes of electricity. Numerical results show that the proposed method can reduce the total cost of micro-grids by maximizing the usage of renewable energy sources, avoiding price spikes, and reducing dependence on high-cost centralized energy-storage facilities provided that the critical water-energy demands are preserved. [ABSTRACT FROM AUTHOR]

A branch flow model (BFM) is used to formulate the AC power flow in general networks. For each branch/line, the BFM contains a nonconvex quadratic equality. A mathematical formulation of its convex hull is proposed, which is the tightest convex relaxation of this quadratic equation. The convex hull formulation consists of a second-order cone inequality and a linear inequality within the physical bounds of power flows. The convex hull formulation is analytically proved and geometrically validated. An optimal scheduling problem of distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is investigated in this paper. To capture the performance of both the battery and converter, a second-order DES model is proposed. Following the convex hull of the quadratic branch flow equation, the convex hull formulation of the nonconvex constraint in the DES model is also derived. The proposed convex hull models are used to generate a tight convex relaxation of the DES optimal scheduling problem. The proposed approach is tested on several radial systems. A discussion on the extension to meshed networks is provided. [ABSTRACT FROM PUBLISHER]

A temperature insensitive vector curvature sensor of photonic crystal fiber (PCF) is presented based on core-offset splicing and waist-enlarged fiber taper. Obvious red and blue shifts in transmission spectrum appear at two symmetrical bending directions with sensor length of 10, 13, 16, and 19 mm and vector curvature of 0.12–1.06 m–1. The longer the sensor length is, the larger the curvature sensitivity is. The corresponding sensitivity with concave bending and convex bending are increased on average by 0.44 and 0.43 nm/m–1, respectively, while the sensor length increases per 1 mm. Moreover, when sensor length is 16 mm, the temperature sensitivity is only 1.73 pm/°C in 20–90 °C; therefore, it has the temperature insensitive property. Obviously, the reported sensor could avert cross-sensitivity of temperature and curvature when measured together. It is prospective being used in industrial production, building monitoring, aerospace, and other fields in view of its easy fabrication, simple structure, and high sensitivity. [ABSTRACT FROM PUBLISHER]

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second-order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter semidefinite programming (SDP) relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder. [ABSTRACT FROM AUTHOR]

In this paper, distributed energy storage (DES) devices, like batteries and ultra-capacitors, are used to alleviate detrimental impacts of high penetration photovoltaic (PV) resources on distribution systems. The impacts are studied at mainly two time resolutions—one minute and one hour. To determine accurately the size of the required DES for the purpose of mitigating the impacts of large-scale distributed PV, sizing procedures based on OpenDSS are proposed. After determining the total size of the required DES, optimization techniques can be used to choose the optimal locations for the DES along the feeder, which is a continuous optimization problem taking into account equality constraints of the AC power flow. The continuity of the problem and the radial network structure make it possible to apply a convex optimization technique called second order cone programming (SOCP) relaxation to obtain the globally optimal solution and avoid the problem of NP-hardness. The exactness of the introduced SOCP relaxation is sensitive to the chosen objective function and additional quadratic equalities. The necessary and sufficient condition of exactness for the SOCP relaxation of the DES optimal allocation and operation in radial distribution systems is studied. The proposed methods are applied to an actual feeder in the southwestern US with high penetration of PV using actual measured data. The simulation results demonstrate the efficacy of the proposed approaches. [ABSTRACT FROM PUBLISHER]

Information framework of optimal reactive power dispatch (ORPD) and the essential characteristics of coordinated reactive power optimization (RPO) in multi-area large-scale power systems are introduced in this paper. We consider that the change of optimal solutions (control settings) cannot be captured by simply using an equality constraint of the boundary values as which the voltages at boundary buses and power flows in tie lines are referred to. While many previous methods were proposed by using change of the boundary values to evaluate the change of optimal solutions, which might lead to failure in convergence, this paper puts forward a coordination strategy according to the correspondence between optimal solutions and boundary values based on a probing mechanism. This method is applied to a 472-bus power system; the simulation results show that the RPO scheme based on this strategy has strong convergence capability and high efficiency. Moreover, the proposed coordination strategy allows the transmission system operators (TSOs) to choose objective function and optimization algorithm independently. [ABSTRACT FROM PUBLISHER]