Line Losses Minimization in Electrical Power Network Using Particle Swarm Optimization
Chapter One
Objectives of the Study
The specific objectives of the study are;
– To highlight the impact of line losses on electric power networks
– To examine the essence of Particle swarm optimization
– To assess how particle swarm optimization can be utilized in minimizing line losses in electric power networks.
CHAPTER TWO
LITERATURE REVIEW
Line Losses
These are losses that occur naturally and consist mainly of power dissipation in electricity system components such as transmission and distribution lines, transformers and measurement systems.[5]. The distance of transmission line are usually very long from the generating stations and also a very good distance to the distributing stations, there by generating losses as: the joule effect, where energy is lost as heat in the conductor (a copper wire for example); magnetic losses, where energy dissipates into the dielectric effect, where energy is absorbed in the insulating material. The Joule effect in transmission cables accounts for losses approximately 2.5% while losses in transformers ranges between 1% and 2%.
Resistive (Skin) Loss
Although the conductors in a transmission line have extremely low resistivity, they are not perfect. This section seeks to quantify that loss through computation of the skin depth and power attenuation factors [7]. The amount of resistive loss in a system can be found estimated by using corona-free transmission line equations to find the amount of power delivered to any point along the wire and subtracting the initial amount of power. The equations are as indicated in [8]
P(z) = P(0)e-2αz = P(0)e-zRt/(Lc) ………………………. ……………. 2.1
PRloss (0: z) = P(0) – P(z) …………………………………………2.2
%PRloss = = 1 – e-zRt/ (Lc) ……………………………………..2.3
Where, c is the speed of light and L, the inductance per unit length of the transmission line is given as:
L = (μ/Π)ln (d/a) …………………………………………….2.4
Fig. 1: Resistive Loss on a Al transmission line as a function of radius as a percentage loss over 1000km. The equations for calculating Rl, the resistance per unit length, can be shown below.
δ = ) ………………………..2.5
IB in this equation is correction factor found by using the first two Bessel I function
Using the above equations, the total amount of power lost due to resistance is equal to the power at a given distance minus the initial power. The parameters listed below summaries the results of these equations can be found in Table 1. In it, there are estimated losses of a typical US power line made of aluminum (case 1), a Nigeria power line at 50Hz (case 2), and a line made out of silver (case 3). A comparison of cases 1 and 3 show that building a long transmission cable can save in resistance loss (about $19M/year), but would cost significantly more to build ($18.5B) at 2010 market prices [8]
Copper losses
One type of copper loss is i2r loss. INRF lines the resistance of the conductors is never equal to zero. Whenever current flows through one of these conductors, some energy is dissipated in form of heat. This heat loss is a power loss. With copper braid, which has a resistance higher than solid tubing, this power loss is higher. Another type of copper loss is due to skin effect. When dc flows through a conductor, the movement of electrons through the conductor’s cross section is uniform. The situation is somewhat different when ac is applied. The expanding and collapsing fields about each electron encircle other electrons. This phenomenon, called self-induction, retards the movement of the encircled electrons.
The flux density at the center is so great that electron movement at this point is reduced. As frequency is increased, the opposition to the flow of current in the center of the wire increases. Current in the center of the wire becomes smaller and most of the electron flow is on the wire surface. When the frequency applied is 100 megahertz or higher, the electron movement in the center is so small that the center of the wire could be removed without any noticeable effect on current. You should be able to see that the effective cross-sectional area decreases as the frequency increases. Since resistance is inversely proportional to the cross-sectional area, the resistance will increase as the frequency is increased. Also, since power loss increases as resistance increases, power losses increase with an increase in frequency because of skin effect. Copper losses can be minimized and conductivity increased in an RF line by plating the line with silver. Since silver is a better conductor than copper, most of the current will flow through the silver layer. The tubing then serves primarily as a mechanical support.
Dielectric losses
Dielectric losses result from the heating effect on the dielectric material between the conductors. Power from the source is used in heating the dielectric. The heat produced is dissipated into the surrounding medium. When there is no potential difference between two conductors, the atoms in the dielectric material between them are normal and the orbits of the electrons are circular. When there is a potential difference between two conductors, the orbits of the electrons change. The excessive negative charge on one conductor repels electrons on the dielectric toward the positive conductor and thus distorts the orbits of the electrons. A change in the path of electrons requires more energy, introducing a power loss. The atomic structure of rubber is more difficult to distort than the structure of some other dielectric materials. The atoms of materials, such as polyethylene, distort easily. Therefore, polyethylene is often used as a dielectric because less power is consumed when its electron orbits are distorted.
Radiation and induction losses
Radiation and induction losses are similar in that both are caused by the fields surrounding the conductors. Induction losses occur when the electromagnetic field about a conductor cuts through any nearby metallic object and current is induced in that object. As a result, power is dissipated in the object and is lost. Radiation losses occur because some magnetic lines of force about a conductor do not return to the conductor when the cycle alternates. These lines of force are projected into space as radiation and this result in power losses. That implies power supplied from the source is not fully getting to the load.
Corona Losses
Corona loss occurs if the line to line voltage exceeds the corona threshold [8]. Corona can occur within voids of an insulator, at the conductor or at the insulator interface. Rough surfaces are more liable to corona because the unevenness of the surface decreases the value of the breakdown voltage. It can be detected due to its visible light in form of purple glow consisting of micro arcs and its sound can be heard through its hissing and cracking sound. The smelling of the presence of ozone production is noticed during corona activity.
CHAPTER THREE
RESEARCH METHODOLOGY
Research Design
The cost of transmission lines tower and conductors and power losses during the operation often limit the available transmission capacity [1]. There are many cases where economic energy delivery is constrained by the transmission capacity. In a deregulated environment, an effective electric grid is vital to provide reliable electric energy supplies to customers at all voltage levels [2].
Recently, increased demands on electric energy transmission and the need to provide access to generating companies and customers have created tendencies toward lower security and reduced quality of supply. The FACTS technology is promising to reduce some of these difficulties by enabling utilities to get more performance from their transmission facilities and to enhance grid reliability [3]. An optimal power flow (OPF) approach was proposed to minimize network energy losses by means of reactive power control using FACTS devices while satisfying the nework operating voltage and thermal limits.
The idea of optimal power flow was introduced in the early 1960s as an extension of conventional economic dispatch to determine the optimal settings for control variables with respect to various constraints. The term OPF is used as a general name for a large series of network optimization problems. Many different approaches have been proposed to solve OPF problems.
The general OPF problem is formulated to minimize the general objective function F(x, u) while satisfying constraints g(x, u) = 0 and/or h(x, u) ≤ 0 where g(x, u) represents nonlinear equality constraints (power flow equations) and h(x, u) is nonlinear inequality constraints on the vectors x and u. The vector x contains the dependent variables including bus voltage magnitudes and phase angles and the reactive power output of generators designed for bus voltage control. The vector x also includes fixed parameters, such as reference bus angles, uncontrolled active and reactive powers for generators and loads, fixed impedances, line parameters, etc. The active power losses minimization is usually required when cost minimization is the main goal.
The following assumptions are usually made to formulate the losses objective:
- Losses minimization is made following the cost minimization. Hence the active power generations excluding the slack bus generation are held at their optimal values.
- Generator bus voltages and transformer tap ratios are used as control state variables. Shunt reactances and phase-shifting transformers angles are held at their rated values.
- Transformer tap ratios are treated as continuous variables during the optimization. Afterwards they are adjusted to the nearest tap position and reiterated.
- Current flows are controlled approximately, using restrictions on the real and imaginary components of the complex voltage drop across the lines.
CHAPTER FOUR
Research DATA PRESENTATION AND ANALYSIS
Data Development Procedures
We consider 14 nodes in a power system with two voltage levels: 400 kV and 220 kV. The first five nodes are on 400 kV and the others are on 220 kV. Node 1 is a slack bus. The different voltage levels are connected by three phase control transformers 400/231 kV with tap changer on the secondary side ±11×1.13 % (Fig. 2).
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
Conclusion
This study describes theoretical and practical issuesconcerning line losses minimization in electric power networks using Particle Swarm Optimization. Thestudy utilized FACTS devices such as STATCOM for voltage control and active power losses optimization. The idea and development with applying STATCOM for the optimization is presented.
STATCOM provides an improvement in power quality and active power consumption stabilisation. This effect could be used in applications where a variable load voltage should be compensated. It would result in a power stability improvement and decrease a risk of line losses caused by those sources. Using STATCOM, we are able to control the voltage at the node to which this device is connected and at the same time it is possible to reduce active line losses.
The shown simulation provides information for STATCOM design and placement in power grids. Applying Particle Swarm Optimization showed the potentials to use this method in power grids to improve their operation and selected criteria.
Recommendations
- Simplification of particle swarm optimization. The general observation is that the behaviour of a PSO swarm is not well understood in terms of how it affects actual optimization performance, especially for higher-dimensional search spaces and optimization problems that maybe discontinuous, noisy and time-varying. To counter these, there is need to adopt the use of the accelerated particle swarm optimization (APSO) which is standardized and easy to understand by even lay persons
- Convergence Issues: One of the major problems in the use of PSO is convergence issues. To overcome it, there is the need to develop an orthogonal learning strategy for an improved use of the information already existing in the relationship between p & g, so as to form a leading converging exemplar and to be effective with any PSO topology.
- Variant standardization: PSO is a vast field and this has led to the development of numerous variants for basic PSO algorithm.
Therefore there is a need for the use of a well-known, strictly-defined standard algorithm that provides a valuable point of comparison which can be used throughout the field of research to test new advances. The latest standard PSO 2011 (SPSO 2011) is highly recommended.
REFERENCES
- EPSO-best-of-two-worlds meta-heuristic applied to power system problems,” in Proc. Congr. Evol. Comput., 2002, vol. 2, pp. 1080–1085.
- A. A. Esmin, G. Lambert-Torres, and A. C. Zambroni de Souza, “A hybrid particle swarm optimization applied to loss power minimization,” IEEE Trans. Power Syst., vol. 20, no. 2, pp. 859–866, May 2005.
- A. Abido, “Particle swarm optimization for multimachine power system stabilizer design,” in Proc. IEEE Power Eng. Soc. Summer Meeting, 2001, vol. 3, pp. 1346–1351.
- El-Gallad, M. El-Hawary, A. Sallam, and A. Kalas, “Particle swarm optimizer for constrained economic dispatch with prohibited operating zones,” in Proc. Canadian Conf. Elect. Comput. Eng., 2002, vol. 1, pp. 78–81.
- . Mantawy and M. S. Al-Ghamdi, “A new reactive power optimization algorithm,” in Proc. IEEE Power Tech. Conf., 2003, vol. 4, pp. 6–11.
- I. El-Gallad, M. E. El-Hawary, and A. A. Sallam, “Swarming of intelligent particles for solving the nonlinear constrained optimization problem,” Eng. Intell. Syst., vol. 9, no. 3, pp. 155–163, 2001.
