LOSS MINIMIZATION IN TRANSMISSION AND DISTRIBUTION SYSTEM

Abstract

The demand for electrical energy is increasing exponentially with the time and it has become necessary for the electrical industry to transport a large amount of power over large and complex transmission and distribution system. Rirther, the increasing cost of new generation, transmission and distribution facilities, and continuous power shortages have made the industry conscious of emrgy lost in transpor-tation to the customer. The first step in conservation of energy is elimination of all waste. Electric power system must be made as efficient as possible so that the power that is generated from scarce energy sources reaches the consumer to the maximum possible extent. This study is directed to-wards the development of efficient mathematical models and methods to minimize the losses in large transmission and distribution networks in the design and operation phases. The first model presented in this study minimizes the real power losses, the deviation from the optimal active power despatch, and the difference between percentage sharing of reactive power among generators. The objective function is optimized such that the power flow equations and cons-traints imposed upon the variables by the system operating conditions and design considerations are satisfied. All problem variables are decomposed in two se ts i.e. independent and dependent variables to reduce the complexity of the problem. Gerrator terminal voltage magnitude, transformer tap positions, and setting of reactive power sources avail-able in the system are taken as independent variables. Load node voltage magnitudes and reactive power generation from various generating sources are taken as dependent variables. The reduced gradient is then calculated using sensitivity relationship between dependent and independent variables. Two types of formulation of loss minimization probleth, are in use at present. The first is linear programming appro ach and the second is he ssi an approach. Bo th o f these . methods are time consuming and require more computer storage. These methods, are not suitable to solve large power system problems. Based on approximation of hessian or its inverse with first order derivatives and exploiting sparsity and symme try, three new appro aches are suggested to so lve the problem of losses minimization in. transmission system. The new appro aches are sui table to so lve large powe r systems as these methods require less computer storage and computation . time. • First method is based on the Quasi Newton method of updating the inverse Hessian. The Breyden-Fletcher-Gold Farb-Shanno (BFGS) update is used in this study which is the best current update. formula for use in un-copstrained mization. It overcomes the conditioning problem resulting into computational efficiency. The method has global convergence and is robust and stable. The step length is • calculated by using unidimensional search 'technique. In the second method much of the: computation which takes place in unidimensional search for step length is avoided. It is based on Fletcher! s method and uses an approximate step size, which helps further in reducing the computer storage and computa-tional burden. Third method is based on the Tointts sparse hessian updating procedure which exploits sparsity and symmetry of the hessian matrix. Thereby the computer time and sttrtigtr,requtri*etitiit further reduced. This method has a global convergence and Q-super linear rate of convergence. These new appro aches are suitable to so lve large power sys terns as these methods require less computer storage and computation time. Correction in the groups of decision variables are carried out simultaneously as well as hierarchically. Provision Qfyegtive compensation at the load nudes is another important way to reduce transmission losses. A model is presented in this study to reduce transmission losses via optimum reactive .compensation planning in the system. In this model the cost function is the summation of the cost of real power losses, installation and 0 M cost of reactive compen-sation, and the difference between percentage sharing of reactive power by generators. The power flow equations and the limit on variables are taken as constraints. Because of large number of variables and constraints involved, and both the cost function and cons traints being non-linear, the problem is quite a challenging one from computational consi-derations. The complexity and size of problem has motivated -iv- the decomposition of the problem variables into two groups comprising of state and decision variables. Sensitivity relationship between dependent and independent variables is used to find out the reduced gradient. Three new approaches based on Quasi Newton method, Fle tchert s method, and sparse hessian method of non-linear programming are presented to solve this problem. These methods have significant advantages over the linear programming technique and other second order derivative methods, as described in previous paragraph. Large power systems have to handle large quantum of power to' be transported over long distances. As the power system size increases it becomes extremely difficult to handle the problem of loss minimization due to large number of variables. Besides, computational effort and storage require-ment increase s exponentially with the increase in number of variables. To overcome these difficulties, a decomposition method is developed. In this method a large power system is decomposed into a number of sub-systems and each sub-system is solved independently. This method is very efficient for large power systems. The distribution system constitutes a significant part of a to tal power system. Since the distribution voltage le vel is low and the low distribution system is extensive, this system is prone tr., have more losses compared to the other parts of the system. Moreover the energy cost at the distri-bution level will be maximum and it will lead t: more severe -v- financial implications. Minimization of losses in distribu, tion system therefore, yields maximum benefits. One way to achieve it is by optimal conductor gradation in the distri-bution system. In all the methods in use for distribution system planning economic benefits arising out of voltage boost along the feeder are neglected to simplify the procedure, which is incorrect. These benefits are significant and by neglecting them only suboptimal solutions are arrived at. In the present formulation of optimal conductor gradation for multi-ended radial feeder and interconnected system, these economic bene-fits are accurately accounted for. The cost function includes the summation of cost of power (KW) and energy (KWH) losses, installation, operation and maintenance cost of distribution lines. Group variational method is used to solve the problem. The proposed model takes into account the non-uniform distri-bution of loads in the distribution system,,load growth, growth in load factor with the time, and growth in cost of electrical energy and distribution system equipments. Application of shunt capacitor in distribution system to improve power factor is another way to reduce losses signi-ficantly in the distribution system. The application of shunt capacitor results in a heavy reduction of system losses, appreciable release in system capacity, and produces a uniform voltage boost along the distribution system. In the methods in use for optimal shunt capacitor installation,. benefits arising from the voltage boost due to application -vi- of shunt capacitor in the system is neglected to simplify the problem. These economic benefits are significant and their neglect results in the sub-optimal solution. The solution procedure presented in this study takes into account, the benefits arising from the voltage boost due to application of shunt capacitor in the system. The method is 'capable of solving multi-ended and interconnected radial feeders. The method takes into account the non-uniform distribution of loads, growth in cost of energy, growth in labour and power.system eqUipment cost, load growth, growth in load factor with time, and graded conductor in the distribution system. The cost function in-cludes the cost of installation, operation and maintenance of shunt capacitors and cost of power (KW) and energy (KWH) :losses. Group variational method is used to solve this problem.