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This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the standard SDP relaxation (the best one is within 99.96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than the standard SDP relaxation. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

The flexible distribution network presents a promising architecture to accommodate highly integrated distributed generators and increasing loads in an efficient and cost-effective way. The distribution network is characterised by flexible interconnections and expansions based on soft open points, which enables it to dispatch power flow over the entire system with enhanced controllability and compatibility. Herein, we propose a multi-resource dynamic coordinated planning method of flexible distribution network that allows allocation strategies to be determined over a long-term planning period. Additionally, we establish a probabilistic framework to address source-load uncertainties, which mitigates the security risks of voltage violations and line overloads. A practical distribution network is adopted for flexible upgrading based on soft open points, and its cost benefits are evaluated and compared with that of traditional planning approaches. By adjusting the acceptable violation probability in chance constraints, a trade-off between investment efficiency and operational security can be realised. Flexible distribution networks with soft open points present a promising way to accommodate distributed generators and increasing loads. Here, authors present a multi-resource dynamic coordinated planning method, allowing allocation strategies to be determined over long-term planning periods.

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

To calculate the harmonic power flow of the distribution network with large-scale distributed grid-connected inverter, this paper first establishes the harmonic source model based on the grid-connected control strategy and modulation mode of inverters, then establishes the harmonic network according to the parameters and harmonic frequency of the distribution network so as to calculate the high-order harmonic power flow in the distribution network. The accuracy and practicability of the proposed method are verified by the simulation results of Matlab/Simulink platform for a distribution network model with multiple distributed grid-connected inverters.

Flexible distributed energy resources, such as energy storage systems (ESSs), are increasingly considered as means for mitigating challenges introduced by the integration of stochastic, variable distributed generation (DG). The optimal operation of a distribution system with ESS can be formulated as a multi-period optimal power flow (MPOPF) problem which involves scheduling of the charging/discharging of the ESS over an extended planning horizon, e.g., for day-ahead operational planning. Although such problems have been the subject of many works in recent years, these works very rarely consider uncertainties in DG, and almost never explicitly consider uncertainties beyond the current operational planning horizon. This article presents a framework of methods and models for accounting for uncertainties due to distributed wind and solar photovoltaic power generation beyond the planning horizon in an AC MPOPF model for distribution systems with ESS. The expected future value of energy stored at the end of the planning horizon is determined as a function of the stochastic DG resource variables and is explicitly included in the objective function. Results for a case study based on a real distribution system in Norway demonstrate the effectiveness of an operational strategy for ESS scheduling accounting for DG uncertainties. The case study compares the application of the framework to wind and solar power generation. Thus, this work also gives insight into how different approaches are appropriate for modeling DG uncertainty for these two forms of variable DG, due to their inherent differences in terms of variability and stochasticity.

This work presents a methodology for segregation of transmission losses of active and reactive power flows based on load flow study with unity vs actual power factor of load buses. The proposed methodology applied on existing 12 bus Indian power system having five transmission lines, 12 power transformers, five load buses, 13 shunt capacitor banks. Hourly actual system parameters of test system, viz. active and reactive power demand, tap position of transformers, ON/OFF status of shunt capacitor banks and swing bus voltage gathered from the grid substations and simulation studies performed on MiPower software for separation of losses. In second part, bus reactive demand is mitigated through automatic switched shunt capacitor banks and its effect on system voltage profile, loading of transmission system elements, number of operations of on load tap changer and losses are presented.

Power flow control has become increasingly important in recent years in the area of smart power systems that have to integrate increased shares of variable renewable energy sources. The unified power flow controller (UPFC) provides in real‐time, simultaneously or selectively, active and reactive power flow control as well as voltage control in smart power systems. Several models and methods have been suggested for the control, analysis, operation, and planning of UPFCs in smart power systems. This study introduces a review of the state‐of‐the‐art models and methods of UPFCs in smart power systems, analysing and classifying current and future research trends in this field.

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC’20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon’s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.

With the rapid development of distributed generators (DGs) and increasing power penetration level of renewable energy sources (RESs), it is a critical issue for any power system to operate safely and continuously in the presence of uncertainty and variability (i.e., power fluctuations) of generated power and demanded power. The introduction of controllable power generators and power storage devices is dispensable for mitigating this problem. To satisfy the power supply–demand balancing requirement, the power flow assignment is essential under power balance constraint. However, due to the physical power limitation constraints of power generators and loads, capacity limitation of power storage devices, and connection arrangement, it is hard to achieve power balance. In this paper, a system characterization is proposed that describes the relationship between power generators, loads, storage devices and connections among them. The proposed characterization system should be satisfied to guarantee safe operation of a given power flow system by preserving the SOC bounds of storage devices. That is, to have a feasible power flow assignment, there are many issues such as how the power limitations (i.e., maximum and minimum power levels) of power generators and loads must be decided, how large be the capacity of a storage device, and the physical arrangement of connections that must be considered. This paper also shows an optimization problem that consists of optimizing storage capacity, the use of power generators both renewable and non-renewable, and matching with the power demand. Several demonstration scenarios are discussed in this paper for the application and validation of our proposed system characterization.

This paper presents application of a new effective metaheuristic optimization method namely, the Jaya algorithm to deal with different optimum power flow (OPF) problems. Unlike other population-based optimization methods, no algorithm-particular controlling parameters are required for this algorithm. In this work, three goal functions are considered for the OPF solution: generation cost minimization, real power loss reduction, and voltage stability improvement. In addition, the effect of distributed generation (DG) is incorporated into the OPF problem using a modified formulation. For best allocation of DG unit(s), a sensitivity-based procedure is introduced. Simulations are carried out on the modified IEEE 30-bus and IEEE 118-bus networks to determine the effectiveness of the Jaya algorithm. The single objective optimization cases are performed both with and without DG. For all considered cases, results demonstrate that Jaya algorithm can produce an optimum solution with rapid convergence. Statistical analysis is also carried out to check the reliability of the Jaya algorithm. The optimal solution obtained by the Jaya algorithm is compared with different stochastic algorithms, and demonstrably outperforms them in terms of solution optimality and solution feasibility, proving its effectiveness and potential. Notably, optimal placement of DGs results in even better solutions.