INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 4, ISSUE 03, MARCH 2015 ISSN 2277-8616 129 IJSTR©2015 www.ijstr.org Sensitivity Analysis of a Mixed Integer Linear Programming Model For Optimal Hydrothermal Energy Generation For Ghana Christian John Etwire, Stephen B. Twum Abstract: This paper examines further a Mixed Integer Linear Programming model constructed for optimal hydrothermal energy generation for Ghana as in [1]. Post Optimal Analysis is carried out on the model in order to assess its stability to slight variations of some input parameters such as minimum level running costs, extra hourly running costs above minimum level and start up costs of each generator on one hand and load demands and reserve margins on the other. The results show that the firm could minimize its cost of power generation if its input parameters were comparable to those lying between the 10 percent and -10 percent range.The10 percent and -10 percent range yielded a range of investment plans for the firmand also provided a basis for the selection of the best optimal solution. Keywords: Stability, Post Optimality Analysis, Scheduling, Marginal Cost ———————————————————— 1. Introduction This study is a further development to an earlier work [1], in which mixed integer linear programming (MILP) was applied as a modeling tool to a power generation scheduling problem of a major power producer in Ghana. The aimwas to determine an optimal power production schedule that meets daily load demands at minimum cost of production and also to ascertain the marginal cost of producing electricity per day and therefore thetariff rate. The goal of this study is to perform post optimality analysis on the proposed model in [1] in order to ascertain its robustness, a range of variability under which the input parameters such as cost of running each generator at the minimum level, extra hourly cost of running each generator above its minimum level, start-up cost of each generator, load demand and reserve margin can change without affecting the optimum feasibility as well as provide a range of investment plans for the firm. Hydro-thermal power generation scheduling is a multifaceted problem consisting of Unit Commitment and Economic Dispatch problems. Unit Commitment refers to the problem of deciding on the startup and shutdown of the generators while Economic Dispatch refers the problem of deciding on the loading levels of each of the committed generators to generate enough power to satisfy load demand, budgetary and operational constraints at minimum production cost [2]. MILP has gained widespread usage in solving hydrothermal and unit commitment problems in the power sectordue to the recent improved capabilities of commercial solvers, the increased computational power of modern computers, their modeling capabilities and adaptability and ability to provide global optimal solutions. Delarue et al.,[3], Nadiaet al.,[4], Ana and Pedroso [5] and Morales-Espana et al., [6] employed MILP technique in solving varying power generation problems. The next section reviews the power generation problem and the formulated MILP model as discussed in [1] and followed by the post optimality analysis. The results and discussion section present details of the output levels of the generators resulting from the sensitivity analysis, the marginal costs of generation and some discussions. Remarks to conclude the discussions as well as point out direction for future work are made in the last section. 2. The Power Generation Problem The power generation firm operates eight power plants comprising two Hydroelectric (H i , i=1, 2) and six Thermal (T i , i=1,…, 6). These plants are committed to meeting the daily electricity load demands at some daily operational cost. The eight power plants together have twenty-four generators, ten (10) of which are for hydroelectric power generation and 14 for thermal. Each generator has to work between a minimum and a maximum level. There is an hourly cost of running each generator at its minimum level. In addition there is an extra hourly cost for each megawatt (MW) of power generated above the minimum level. Startup of a generator also involved cost. In addition to meeting the estimated daily electricity load demands, there must be sufficient generators working at any time of the day to make it possible to meet an increase in load. This increase would have to be met by the generators already operating within their permitted limits. There must be enough reserve (spinning reserve) to cater for unexpected increase in load demands or breakdown of any generator. The desire of the firm is to meet the daily load demands of consumers at minimum cost of operation of the power plants. The MILP model as in [1] is presented as follows: Minimize  =         +        +       8  =1 24  =1 Subject to   ≤   −       =     +   _______________________  Faculty of Mathematical Sciences, University for Development Studies, P. O. box 24, Navrongo, U.E.R. Ghana, West Africa. Email: jecpapa@yahoo.com