Optimizing power flow of AC–DC power systems using artificial bee colony algorithm
Introduction
Many studies were performed for the stability and power flow solutions of HVDC systems so far [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. All of them use the numerical methods. There are two basic approaches for solving the power flow equations of AC–DC power systems in literature. The first is the sequential approach [15], [16], [17]. In this method, the alternating current (AC) and direct current (DC) equations are solved separately by successive iterations. Although the implementation of the sequential method is easy, it has convergence problems associated with certain situations and are the state vector does not contain explicitly the dc variables. The second approach is known as the unified approach [18].
The scientists have used many different methods for solving OPF problem of purely AC power systems so far [19], [20], [21], [22], [23], [24], [25]. These methods are numerical and heuristic methods. According to the results reported in literature, it can be seen that heuristic methods are superior from the numerical methods [21], [22], [23], [24], [25]. The important one of the advantages of heuristic methods is that they convergence to the optimum solution in more short time than others and convergence fewer local minimum.
ABC algorithm is a new population based heuristic optimization method proposed by Karaboga [26]. Recently, successful applications of ABC algorithm to the power systems attract attention [27], [28], [29], because ABC algorithm is an efficient and effective algorithm in order to determine the global minimum points of nonlinear and non-convex problems.
In this study, the real model for the transformers is used. In the real model of transformer, also the impedance values of the transformers vary as the tap ratios of the transformers vary, and thus the bus admittance matrix of the power system also varies. The power system calculations are accomplished without inclusion the impact of the transformers to the Jacobian matrix. Thus, the transformers in the power system can be selected as the control variables. In heuristic method, each individual select a different tap ratio change of for each transformer and the bus admittance matrix of the power system is calculated uniquely for each individual. This process increases computational time of the software.
After this introduction, the modeling of DC transmission link is represented in Section 2. The ABC methodology is explained in Section 3. ABC algorithm based optimal power flow solution of AC–DC power system is explained in Section 4. In Section 5, to demonstrate validity, the efficiency and the effectiveness of the proposed method, simulation results of the modified 5-node test system and the New England 39 bus test system with an HVDC link is given and the obtained results are extensively evaluated and compared to those obtained by other methods. Finally, the conclusions and discussions are represented in Section 6.
Section snippets
The modeling of DC transmission link
Before analyzing DC transmission system, it is necessary to model the converters for two sides of DC links. The modeling is made based on widely accepted assumptions in the literature. The assumptions are as follows [18]:
- •
The main harmonic values of current and voltage in AC power system is balanced.
- •
The other harmonics except the main harmonic are ignored.
- •
The ripples in the current and voltage wave form of DC link are ignored.
- •
The thyristors used in the converters are accepted as ideal switch and
Illustration of ABC algorithm
The ABC algorithm was proposed by Karaboga in 2005 [26]. The algorithm has been successfully applied in distinct fields of science such as electrical engineering, mathematics, mechanical engineering and civil engineering since 2005 [33], [34], [35], [36].
The ABC algorithm is a population based algorithm created by the inspiration from the food pursuit of honey bees. In the algorithm the bees are divided into two groups: the worker bees and non-worker bees. The non-worker bees consist of
ABC algorithm based optimal power flow solution of AC–DC power system
It is significant the determination of the state and the control variables to solve OPF problem of AC–DC power systems. Furthermore, these control variables should be the same as those of the problem to be optimized. The control variables of this optimization problem are selected as follows:where pgi except the slack bus pgslack, is the generator active power outputs, vgi is the generator voltage magnitudes, Ng is the number of
Simulation results
To show the validity, efficiency, and effectiveness of ABC algorithm for optimal power flow solution of AC–DC power system, the proposed method is tested on two test systems which are the modified 5-node test system [38], [39] and the modified New England 39 bus test system [40], [41] in this study. The system data for two test systems is given in Refs. [38], [39], [40], [41].
In the study, the simulation interval for ABC algorithm is taken into account as 100. This value is the same as that in
Conclusion and discussion
ABC algorithm was applied to OPF problem of purely AC power systems and its validity and efficiency in this area was shown. In this study, a power flow optimization of two AC–DC test systems is realized by using ABC algorithm for the first time and the real transformer representation is also used for the transformers in the power systems. For this purpose, the modified 5-node test system and the modified New England 39-bus test system are selected and OPF problem of these are solved to show the
References (41)
The power flow algorithm for balanced and unbalanced bipolar multiterminal AC/DC systems
Electr Power Syst Res
(2003)- et al.
Simultaneous allocation of capacitors and voltage regulators at distribution networks using genetic algorithms and optimal power flow
Int J Electr Power Energy Syst
(2012) - et al.
A solution to the optimal power flow using genetic algorithm
Appl Math Comput
(2004) - et al.
Optimal power flow solution using fuzzy evolutionary and swarm optimization
Int J Electr Power Energy Syst
(2013) - et al.
A hybrid artificial bee colony assisted differential evolution algorithm for optimal reactive power flow
Int J Electr Power Energy Syst
(2013) - et al.
Optimal power flow using gravitational search algorithm
Energy Convers Manage
(2012) Artificial bee colony optimization for multi-area economic dispatch
Int J Electr Power Energy Syst
(2013)- et al.
Comparative performance analysis of artificial bee colony algorithm in automatic generation control for interconnected reheat thermal power system
Int J Electr Power Energy Syst
(2012) - et al.
Artificial bee colony algorithm solution for optimal reactive power flow
Appl Soft Comput
(2012) - et al.
A comparative study of artificial bee colony algorithm
Appl Math Comput
(2009)
Artificial bee colony algorithm for optimization of truss structures
Appl Soft Comput
High voltage direct current modeling in optimal power flows
Int J Electr Power Energy Syst Eng
A new approach based on genetic algorithm for optimal reactive power flow solution in multi-terminal AC–DC systems
Przeglad Elektrotechniczny
Load flow based on newton’s method using norton equivalent circuit for an AC–DC multiterminal system
Eur Trans Electr Power
Improved load-flow techniques for integrated AC–DC systems
Proc IEE
A way to improve AC power transfer limits, HVDC links used to stabilize electric power systems
ABB Rev, Power Syst Stab
Cited by (31)
Bi-objective dependent location quadratic assignment problem: Formulation and solution using a modified artificial bee colony algorithm
2018, Computers and Industrial EngineeringCitation Excerpt :The ABC algorithm is a swarm-based meta-heuristic and it mimics the foraging behavior of honeybees to search for better solutions within the solution space (Karaboga, 2005). Because of its powerful convergence ability, it has been widely applied in several optimization problems, such as leaf-constrained minimum spanning tree problem (Singh, 2009), power flow optimization and optimal sizing of photovoltaic systems (Kiliç & Ayan, 2013; Mohamed, Elarini, & Othman, 2014), image processing (Cuevas, Zaldívar, Pérez-Cisneros, Sossa, & Osuna, 2013), optimal design of shell and tube heat exchangers (Sahin, Kılıc, & Kilic, 2011), parametric optimization of non-traditional machining processes (Samanta & Chakraborty, 2011), and job shop scheduling (Banharnsakun et al., 2012). Some examples of multi-objective optimization using ABC algorithm include solving standard non-linear problems (Zou, Zhu, Chen, & Zhang, 2011; Xiang, Zhou, & Liu, 2015), frequency assignment problem (Maximiano, Vega-Rodríguez, Gómez-Pulido, & Sánchez-Pérez, 2013), reliable DNA sequence design (Chaves-González, Vega-Rodríguez, & Granado-Criado, 2013), multi-objective single model assembly line balancing problem with uncertain task times (Saif, Guan, Liu, Zhang, & Wang, 2014), multi-objective flexible job shop scheduling problem with maintenance activities (Li, Pan, & Tasgetiren, 2014), multi-objective optimal power flow design considering cost, loss and emission (Chen, Bo, & Zhu, 2014), simultaneous sequencing and balancing problem for mixed model assembly line (Saif, Guan, Liu, Wang, & Zhang, 2014), uncertain multi-objective traveling salesman problem (Wang, Guo, Zheng, & Wang, 2015), time-cost-quality trade-off problem for a construction project (Tran, Cheng, & Cao, 2015), etc.
Computational intelligence techniques for maximum power point tracking in PV systems: A review
2018, Renewable and Sustainable Energy ReviewsOptimal power flow of two-terminal HVDC systems using backtracking search algorithm
2016, International Journal of Electrical Power and Energy SystemsCitation Excerpt :The comparative results obtained by the BSA and ABC algorithms [11] for this test system are given in Table 4. As shown in the table, the minimum costs by BSA and ABC algorithm [11] were 1145.7612 $/h and 1145.9525 $/h, respectively. It is evident that the cost generated by BSA for this test system was also lower than that generated by the ABC algorithm, and the results generated by BSA were kept within their limits.
Impact of DC link control strategies on the power-flow convergence of integrated AC-DC systems
2016, Ain Shams Engineering JournalArtificial bee colony based algorithm for maximum power point tracking (MPPT) for PV systems operating under partial shaded conditions
2015, Applied Soft Computing JournalStochastic optimal power flow incorporating offshore wind farm and electric vehicles
2015, International Journal of Electrical Power and Energy SystemsCitation Excerpt :Results obtained for this case are then compared with other methods proposed in state of the art literature. Since there is no much literature available which deals with AC–DC optimal power flow, the results obtained by GABC are compared with the results obtained by Genetic algorithm (GA) [38], basic artificial bee colony algorithm (ABC) [38] and Lagrange multiplier method (LM) [42]. The modified 5-bus test system with two-terminal HVDC link is shown in Fig. 5.