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Using A Dynamic Programming Method

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Table of Contents
2 OBJECTIVE 2
3 BACKGROUND 2
4 CONVEX OPTIMIZATION 2
4.1 INTRODUCTION 2
4.2 THEORY 2
4.3 ALGORITHM 2
5 NON CONVEX OPTIMIZATION 2
5.1 INTRODUCTION 2
5.2 THEORY 2
5.3 ALGORITHM 2
6 LAGRANGIAN RELAXATION FLOW CHART 2
6.1 INTRODUCTION 2
6.2 ALGORITHM FOR A UNIT COMMITMENT PROBLEM 2
7 RESULTS AND SIMULATIONS 2
7.1 TEST SYSTEM 2
7.2 RESULTS 2
8 CONCLUSIONS 2
9 FUTURE SCOPE 3
10 REFERENCES 3

OBJECTIVE
BACKGROUND
CONVEX OPTIMIZATION
INTRODUCTION
THEORY
ALGORITHM
NON CONVEX OPTIMIZATION
INTRODUCTION
THEORY
ALGORITHM
LAGRANGIAN RELAXATION FLOW CHART
INTRODUCTION
Using a Dynamic Programming method would be a tedious search of all the the possible combinations. This reduction in possible combinations would make the problem complicated and would consume a greater amount of time. This problem of reducing combinations can be eliminated by using Lagrangian relaxation method.
The Lagrangian Relaxation algorithm being implemented in basically an extension of Non - Convex Optimization to a power system. In this project, we have taken up the cost functions of each of the generators under consideration and developed the cost function to be minimized keeping the mind the generator limits as well as the load balance.
Loading constraints: Pt_load=∑_(i=1)^Ng▒〖Pit*Uit=0 〗 Generating limits: Uit*Pit_min≤Pit≤Uit*Pit_max
The objective function to be minimized i.e, the overall cost function of the generator would be the sum of cost function of each

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