Monday, 19 December 2016

Cost Minimisation Of Power Generation In Kaduna State University: The Lagrange Method


Managers of large scale industries or organizations, especially ones that are characterized by large electricity consumptionare challenged at many fronts to find means tooptimize costs of power consumption. There are many methodologies to optimizing the cost involved in power systems optimization. In this regard, this study presents an effort developed to solve optimal power flow (economic dispatch) problem by minimizing the cost of generation using the lagrangian multiplier method. The approach is validated by lagrangian method found in technical literatures. The systemcan also assist operators in thermal power plants and every other organizations that have need to minimize their cost of power generation so as to plan for generation in the most economic way. A result obtained from the application explains the importance and needfulness of optimization in high power consumption organizations.



According to Huijuan (2008), an optimization problem, which minimizes or maximizes a real function, is of great use to today’s world. It is divided into constrained and unconstrained optimization. It uses and application spans through science, engineering, economics, etc. More so, everyday life can be formulated as constrained optimization problems, such as the minimization of the energy of a particle in physics; how to maximize the profit of the investments in economics.
Power system optimization has evolved with developments in computing and optimization theory. In the first half of the 20th century, the optimal power flow problem was “solved” by experienced engineers and operators using judgment, rules of thumb, and primitive tools, including analog network analysers and specialized slide rules. Gradually, computational aids were introduced to assist the intuition of operator experience.

The optimal power flow problem was first formulated in the 1960’s, but has proven to be a very difficult problem to solve. Linear solvers are widely available for linearized versions of the optimal power flow problem, but nonlinear solvers cannot guarantee a global optimum, are not robust, and do not solve fast enough. In each electricity control room, the optimal power flow problem or an approximation must be solved many times a day, as often as every 5 minutes (Anya et al (2013))
The high demand and use of power in various industries and organizations is one amongst many reasons that necessitated the issue of power generation optimization. Organizations spend tons of money on a daily basis to generate power to meet their daily demand in running operations. These organizations as much as are in need of power would need to device mean to reduce the cost of running their generating systems so as not to run at loss.

 Best methods of economic dispatch or optimal power flow are what are usually employed to resolve power optimization problems. The objective is to systematically seek the lowest cost of electricity production that will be consistent with the power demand. In minimizing cost, optimal power flow (OPF) will increase use of more efficient generating unit and at the same time addresses two essential issue- better fuel usage and reduced greenhouse gas emission that will result from less efficient generation. Optimal power flow (OPF) hence, seeks to minimize the total cost of power production or generation while satisfying the loads involved. (Anireh et al (2013).

In the resolution of economic dispatch problems several techniques have been proposed and also available to solving optimal power flow problem with varied degree of successes. These techniques can be divided into two main categories, the algorithmic mathematical solution and artificial intelligent solution as reported in several literatures. Among the algorithmic solutions are Interior point (IP) algorithm, Simplex algorithm (SA), Quadratic programming (QP), and Dynamic programming (DP). Lagrange relaxation method (LRM), linear programming (LP), Non-linear programming (NLP) and Newton-based methods have also been reported. (Anireh et al (2013)


Large industries and organizations today are characterized by large amount of work operations. These industries require huge amounts of power on daily basis to run operations. As a result of this large power consumption, big sums of money are expended to meet this consumption level through continuous fuel purchase to run the systems. Hence, there is a need to device all possible means to minimize the amount of money spent on the fuel that run these systems. 


The aim of this project is to minimize the cost of power generation in Kaduna State University and the objectives are as follows:
1.      Formulate an economic dispatch optimal power flow theory.
2.      Collect the data associated with the running of the generators such as cost of fuel consumption and generators capacity
3.      Formulate the cost function alongside the restriction or constraint.
4.      Solve the function and restriction using the Lagrange method to obtain values of unknown as well as the incremental rate.


The significance of this study is to help reduce the cost at which generating systems produce power for use in industries and organization. But more particularly, this project takes Kaduna State University as a case study.


This study is restricted to Kaduna State University which is our case study, and only considers five power generating systems, two of which are used in the day to day administrative operation of the university and three others in powering the three female hostels that are sited within the main campus.


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