LONG RANGE DISTRIBUTION SYSTEM PLANNING

Abstract

The increasing demand of electrical power combined with scarcity of energy resources and the increasing cost of energy supply have high-lighted the importance of energy conservation and elimination of losses by both producers and users of energy. At the same time the major duty of power utility is to supply the demand with good quality of service and at low cost. These requirements necessitated the proper planning of power systems. It has long been a common practice to place priorities on generation and transmission planning rather than distri bution system. As such many approaches have been developed for generation and transmission planning. Engineering judgement and experience have remained the primary tools of distribution system planning. The distribution system is a significant constituent of the power system, as is evident from the facts that it shares, about 40 ?. of investment cost, 75 -/. to 85 A of losses and about 95 °/. of consumer outages, of the total system. Further the cost of energy and power is maximum at distribution level. These facts has brought about the realization that accurate and sophis ticated planning techniques are not only essential in genera tion and transmission systems, but they are imperative in distribution system too. The average life of a distribution system is generally about thirty years. Hence, the decisions regarding

investment made today, will have long term consequences. Since, the power demand is everincreasing, there is likeli hood of changes, in loading conditions, load factor and cost of energy, during such a long time. Therefore, if a distribution system is optimally planned, on the basis of present loading conditionsf may prove to be suboptimal in long run due to increasing trend of the above factors. These facts necessitated the need for long range distribu tion system planning studies. The approaches, so far developed in various spheres of distribution system planning, in general, do not fulfil the needs of long range distribution system planning, since most of the methods, do not consider the growth factors and are suitable only for single time period planning problems. As a first step towards long range distribution system planning, mathematical models to represent cost of feeder, cost of transformer, cost of losses and voltage regulation etc. have been developed, using basic relationships. Using these models and incorporating the effect of load growth, growth in load factor and increase in cost of power and energy, models are developed to optimize system parameters viz conductor loading, transformer loading, length of feeder and voltage level. In addition to energy losses, power losses in the system are also included in the models to enable more realistic results. These models are solved by simple computational methods .Results obtained can be 'genera lized so that the same may bo used by practising engineers as general guide lines.

On the basis of the above models, the problem of sub station sizing for an interconnected system of substations is considered. A model is developed for this purpose incor porating the effect of load growth during planning period at discrete time intervals, to meet the given future demands. Each of these substations are treated as parts of an inte grated system as their expansions planning are inter dependent. Also the time intervals of the planning period are treated as interdependent, since the decision during one time interval may effect the decisions in another time inter val. Therefore, the expansions of the system are determined by minimizing the present worth of total revenue requirements, consisting expenditures of each time interval, subject to constraints based on future periodic demands and bounds on the capacities of system substations. The formulated problem is a multistage zero-one programming problem. The expansions of the substations are made in discrete step sizes. The variables associated with these step sizes may assume values either one or zero depending on whether, the step size for expansion is selected or not for that planning interval. The problem is solved by progressive dynamic programming keeping in view the dimensionality limitations of general dynamic program . A method based on implicit enumeration technique is developed to solve each stage problem. This method ex ploits the special structure of the problem. Certain skipping rules are also developed to reduce the number of vectors to be enumerated, which ultimately reduce the memory and time requirements considerably for large scale problems.

The mathematical models developed to represent feeder cost, cost of losses (power and energy loss) and feeder voltage regulation are used in formulating a generalized model for optimal grading of conductor cross section of feeder segments, along the feeder main and its branches. The problem formulated is a minimization problem where, the cost function is minimized subject to voltage drop constraint. The problem is reformulated as zero-one programming problem for a branched radial distributions feeder, which can also be used for straight radial feeders. The problem is solved by the technique developed, in earlier investigations of the present work. Some heuristic rules are developed to reduce the computational efforts. A heuristic method is also developed to solve this problem alternatively. A mathematical model is developed for the distribution network routing and substation sizing as amixed integer programming problem. The integer variables are zero-one variables representing expansion of substations and feeders and continuous variables representing their capacities. The cost function of the model consists of the fixed costs as well as variables costs associated with substation and feeder network expansions. This problem is solved by modified Bender's decomposition technique. The method presented incorporates certain heuristic rules which considerably reduce the computational requirements for solving a large scale problem.