Optimal Power Flow in Direct Current Networks

The optimal power flow (OPF) problem determines power generations/demands that minimize a certain objective such as generation cost or power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints

Optimal Power Flow in Direct Current Networks Using the Antlion Optimizer

This document presents a solution method for optimal power flow (OPF) problem in direct current (DC) networks by implementing a master-slave optimization methodology that combines an antlion optimizer (ALO) and a power flow approach based on successive approximation (SA ). In the master stage, the ALO determines the optimal amount of power to be delivered by all the distributed generators (DGs) in order to minimize the total power losses in the distribution lines of the DC network. In slave stage, the power flow problem is solved considering constant power loads and power outputs of DGs as constants. To validate the effectiveness and robustness of the proposed model, two additional comparative methods were implemented: particle swarm optimization (PSO) and black hole optimization (BHO). Two distribution test feeders (21 and 69 nodes) were simulated under different scenarios of distributed power generation. The simulations, conducted in MATLAB 2018$b$, show that the proposed method (ALO) presents a better balance between power loss minimization and computational time required to find the optimal solution regardless of the size of the DC network

Metaheuristic Optimization Methods for Optimal Power Flow Analysis in DC Distribution Networks

In this paper is addressed the optimal power flow problem in direct current grids, by using solution methods based on metaheuristics techniques and numerical methods. For which was proposed a mixed integer nonlinear programming problem, that describes the optimal power flow problem in direct current grids. As solution methodology was proposed a master–slave strategy, which used in master stage three continuous solution methods for solving the optimal power flow problem: a particle swarm optimization algorithm, a continuous version of the genetic algorithm and the black hole optimization method. In the slave stages was used a methods based on successive approximations for solving the power flow problem, entrusted for calculates the objective function associated to each solution proposed by the master stage. As objective function was used the reduction of power loss on the electrical grid, associated to the energy transport. To validate the solution methodologies proposed were used the test systems of 21 and 69 buses, by implementing three levels of maximum distributed power penetration: 20%, 40% and 60% of the power supplied by the slack bus, without considering distributed generators installed on the electrical grid. The simulations were carried out in the software Matlab, by demonstrating that the methods with the best performance was the BH/SA, due to that show the best trade-off between the reduction of the power loss and processing time, for solving the optimal power flow problem in direct current networks

Multi-objective optimal power flow considering the multi-terminal direct current

Introduction. In recent years, transmission systems comprise more direct current structures; their effects on alternating current power system may become significant and important. Also, multi-terminal direct current is favorable to the integration of large wind and solar power plants with a very beneficial ecological effect. The novelty of the proposed work consists in the effects of the aforementioned modern devices on transient stability, thus turn out to be an interesting research issue. In our view, they constitute a new challenge and an additional complexity for studying the dynamic behavior of modern electrical systems. Purpose. We sought a resolution to the problem of the transient stability constrained optimal power flow in the alternating current / direct current meshed networks. Convergence to security optimal power flow has been globally achieved. Methods. The solution of the problem was carried out in MATLAB environment, by an iterative combinatorial approach between optimized power flow computation and dynamic simulation. Results. A new transient stability constrained optimal power flow approach considering multi-terminal direct current systems can improve the transient stability after a contingency occurrence and operate the system economically within the system physical bounds. Practical value. The effectiveness and robustness of the proposed method is tested on the modified IEEE 14-bus test system with multi-objective optimization problem that reflect active power generation cost minimization and stability of the networks. It should be mentioned that active power losses are small in meshed networks relative to the standard network. The meshed networks led to a gain up to 46,214 % from the base case.Вступ. В останні роки системи передачі електроенергії включають в себе більше структур постійного струму; їх вплив на енергосистему змінного струму може стати значним і важливим. Крім того, багатотермінальний постійний струм є сприятливим для інтеграції великих вітрових та сонячних електростанцій з дуже позитивним екологічним ефектом. Новизна запропонованої роботи полягає у впливі вищезазначених сучасних пристроїв на перехідну стабільність, що виявляється цікавим питанням для дослідження. На наш погляд, вони становлять нову проблему та додаткову складність для вивчення динамічної поведінки сучасних електричних систем. Мета. Ми шукали розв’язання задачі перехідної стабільності, обмеженої оптимальним потоком потужності в мережах змінного/постійного струму. Збіжність для забезпечення оптимального потоку енергії була глобально досягнута. Методи. Розв’язання задачі було здійснено в середовищі MATLAB за допомогою ітеративного комбінаторного підходу між оптимізованим обчисленням потоку потужності та динамічним моделюванням. Результати. Новий підхід, що обмежує перехідну стабільність, з урахуванням багатотермінальних систем постійного струму може покращити перехідну стабільність після виникнення непередбачених ситуацій та економічно експлуатувати систему у фізичних межах системи. Практичне значення. Ефективність та надійність запропонованого методу перевіряється на модифікованій тестовій 14-шинній системі IEEE з використанням багатоцільової задачі оптимізації, яка відображає мінімізацію витрат на активну генерацію електроенергії та стабільність мереж