Minimization of voltage deviation and power losses in power networks using Pareto optimization methods
Introduction
The operation of power networks has undergone considerable change in recent times. Several factors have influenced this change. For example, the interest in saving energy, the use of cheaper and more universal measuring devices, the growing demand from consumers for improved quality of the power supply, or even the appearance of new tools for monitoring power networks. New technologies are constantly appearing in all fields of science and engineering, including electrical engineering and power systems. Specifically, there are many elements in power distribution networks that could be automated and coordinated, such as tap changers in power transformers or tap changers in bank capacitors. The present paper deals with new computational optimization algorithms which allow a better operation of the system, achieving a better voltage profile and reduced power losses. The general problem of voltage control and optimization of power flow occurs because of the need to act on the voltage at the network nodes to ensure that it remains within acceptable limits. One of the main elements allowing this adjustment is the under load tap changer (ULTC), which can adjust the voltage ratio in discrete steps. Taking into account the combinatorial nature of this problem, different methodologies based on artificial intelligence have been applied. Some authors have proposed the use of techniques such as dynamic programming (Lu and Hsu, 1995) to control tap changers and capacitor banks in substations for 24-hour-planning. This aims to improve the efficiency of the algorithm by limiting the search space in the vicinity of an analytical solution calculated using the hourly load forecasting. This technique has even been extended to small networks with radial capacitor banks at the heads of the lines (Ruey-Hsun and Chen-Kuo, 2001). Fuzzy logic techniques have also been used (Liu et al., 2002). Other authors have used neural network techniques for voltage and power regulation in radially operated networks during one-day periods, making use of the tap changers of transformers and capacitor banks (Saric et al., 1997). Other techniques such as genetic algorithms (Haida and Akimoto, 1991) have also been implemented for voltage optimization. On the other hand, the typical problem of voltage and reactive power compensation (known as the Volt/Var problem) has been widely studied in power networks (Begovic et al., 2004).
Moreover, the variation of voltage at the system nodes due to ULTCs could involve a change in the power flow through the system lines, which must be minimized in order to avoid the power losses that occur due to the Joule effect. In this way, optimal operation of ULTCs allows voltage and power flow to be under control. Thus, this problem can be treated from a multi-objective perspective (Augugliaro et al., 2004). The traditional way of dealing with multi-objective optimization problems consists of introducing weights in a simple aggregating function (weighted sum), where weights reflect the relative significance of the different objectives. However, the main drawback of this linear combination is the difficulty to establish accurate values for the weights, especially when the objectives to be considered have different scales or represent different magnitudes. An interesting, and possibly the best way of overcoming this drawback is the use of Pareto optimization (Deb, 2001), which is a method that includes multiple criteria without using weights. This paper addresses the problem of optimizing the control of an automated power distribution network under normal operation using Pareto-optimization, where the objectives to minimize are: a voltage deviation index that gives information about the voltage profile in the network (Montoya et al., 2006), and the power loss of electrical lines due to the Joule effect.
Section snippets
Voltage regulation in electrical power networks
Currently, voltage regulation in traditional power substations for HV/MV (high/medium voltage) or MV/MV transformers is performed by under load tap changers (ULTC), whose input variables are essentially the voltage and current values measured at the outlet of the secondary circuit of the transformer, while regulation in the MV/LV (medium/low voltage) is carried out manually using vacuum tap changers. In an automated network, this process can be approached from a different, more holistic
Results and discussion
When applying heuristic methods to optimization problems it is advisable to perform a sensitivity analysis, i.e. to determine to what extent the output of the model depends upon the inputs. These sensitivity analyses require a certain number of executions of each algorithm in order to obtain robust conclusions. Thus, it is important to note that while in single-objective optimization it is straightforward to determine the median value of several runs, in Pareto-based multi-objective
Conclusions
This paper addresses the optimization problem consisting of adjusting ULTC transformers in order to regulate nodal voltages in power distribution networks and simultaneously minimize power losses. The problem is of great interest for power distribution companies because this strategy allows them to act on the main elements of the network to determine the optimal voltage profile with the aim of correcting possible deviations from nominal values and to reduce inefficiencies. At the same time
Acknowledgments
This work was partially supported by grants TIN2008-01117 (Spanish Ministry of Science and Innovation), and P2007-TIC-02988 (CICE, Junta de Andalucía).
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