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2014 [POWER SYSTEM OPERATION AND CONTROL]

B.Sc (Electrical Engineering)VIIIth Semester

Lagrange Relaxation

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The objectives of the power system operational planning involves the best utilization of available energy resources subjected to various constraints and to transfer electrical energy from generating stations to the consumers with maximum safety of personal/equipment, continuity, and quality at minimum cost. The operational planning involves many steps such as short term load forecasting, unit commitment, economic dispatch, hydrothermal coordination, control of active/reactive power generation, voltage, and frequency as well as interchanges among the interconnected systems in power pools etc. In the early days the power system consisted of isolated stations and their individual loads. But at present the power systems are highly interconnected in which several generating stations run in parallel and feed a high voltage network which then supplies a set of consuming centers. Such system has the advantages of running the number of stations with greater reliability and economy, but at the same time the complexity in the operational and control procedures has increased. The power industry therefore requires the services of the group of men who are specially trained to look after the operation of the system. These men are known as the system engineers and are responsible for the operation, control and operational planning of the system.Unit Commitment involves the hour-to-hour ordering of the units on/off in the system to match the anticipated load and to allow a safety margin. Having solved the unit commitment problem and having ensured through security analysis that present system is in a secure state then the efforts are made to adjust the loading on the individual generators to achieve minimum production cost on minute-to-minute basis. This loading of generators subjected to minimum operation cost is in essence the economic dispatch. Load forecasting gives an accurate picture of the expected demand over the following few hours. In an anticipation of the variations in demand and for reasons of economic operation of the system the unit commitment activity is carried out.

Lagrange Relaxation Method

In 1983, A. Merlin, proposed a new implementation in solving UCP by Lagrangian relaxation method. Numerous developments were envisaged, to make the algorithm flexible such as simultaneous management of pumping units, probabilistic determination of the spinning reserve. This decomposition method used is flexible and Lagrange multiplier provides a new solution to the conventional problem. In 1987, R. Nieva, proposed an approach to solve very large and complex UCP. The proposed approach gives an estimate of suboptimality that indicates the closeness of the solution near to the optimum. In contrast with the technique of Lagrangian Relaxation, this approach makes no attempt of maximizing the dual function. In 1988, F. Zhuang, presented an LR method for large scale problem. The algorithm in divided into three phases. First the Lagrangian dual of the unit commitment is maximized with standard subgradient techniques, second a reserve-feasible dual solution is find, and finally ED is performed. On 100 units to be scheduled over 168 hours, gives a reliable performance and low execution times. Both spinning and time-limited reserve constraints are treated. In 1989, S. Virmani et al. presented a paper in which they provide an understanding of the practical aspects of the Lagrangian Relaxation methodology for solving the thermal UCP. In 1995, R. Baldick formulated UCP in generalized form and solved using LR method. The algorithm, presented, approximately solves the dual optimization problem. The algorithm was slower in solving the special

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cases of the generalized UCP than algorithms demonstrated by other authors. The approach has been tested for ten units for a time period of 24 hours. In 1995, W.L. Peterson, proposed a Lagrange Relaxation to incorporate unit minimum capacity and unit ramp rate constrains. The proposed method is used in finding a feasible UC schedule considering a new approach for ramping constraints. The algorithm incorporates other practical features such as boiler fire-up characteristics and non-linear ramp up sequences.In 2000, A. G. Bakirtzis, demonstrated the difference between the lambda values of the economic dispatch and the UCP based on economic interpretation of the Lagrangian Relaxation solution framework. During the LR solution of the UCP two sets of lambdas are used. Although both set of lambdas represent marginal cost of electricity. The first one, is assigned as a Lagrange multiplier (Lambda) to the UC power balance equations and second one, is the Lagrange multiplier of the power balance equation in the economic dispatch problem. In 2004, W. P. Ongsakul, proposed an enhanced adaptive Lagrangian relaxation (ELR). Enhanced LR approach consists of heuristic search and adaptive LR. ALR is enhanced by introducing new 0-1 decisions. After the ALR the best feasible schedule is obtained. The heuristic search is used to fine tune the schedule. The total system production costs are less for the large scale system. The computational time is much less compared with others approaches. In 2005, D. Murtaza, et al.presented an algorithm for the unit commitment schedule using the Lagrange relaxation method by taking into account the transmission losses. For better convergence and faster calculation, a two stage Lagrange relaxation was provided. First, conventional Lagrange relaxation was applied in order to determine the unit commitment schedule neglecting transmission loss. The results are then input to the proposed method, and the unit commitment schedule including transmission losses was produced.

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