Post on 17-Dec-2015
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TECHNICAL SEMINAR-2004
Dipanwita Dash [1]
UNIT COMMITMENT
Under the guidance of
Mr. Debasisha Jena
Presented by
Dipanwita Dash
Roll # EE200157176
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TECHNICAL SEMINAR-2004
Dipanwita Dash [2]
INTRODUCTION
Committing a generating unit
Unequal distribution of industrial load
Problem of unit commitment in electrical power systems
The problem and methods for its solution – described in following sections
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TECHNICAL SEMINAR-2004
Dipanwita Dash [3]
UNIT COMMITMENT PROBLEM
It is not economical to run all the units available all the time Optimum allocation (commitment) of generators (units) at each generating station at various load levels To determine the units of a plant that should operate for a particular load– problem of UCThere should be least operating costThis problem is important for thermal plants
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CONSTRAINTSSpinning reserve: It makes up the loss of the most heavily loaded unit in a given period of time.
Thermal Unit Constraint:
Minimum Up Time
Minimum down time
Crew constraint
start-up cost
Must-run: Some units are given this status
Fuel constraint
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Dipanwita Dash [5]
Lets postulate the following situation:A loading pattern must be established for M periods There are N units to commitAny one unit or a combination of units can supply the loads.
The total number of combinations to try each hour is C (N, 1) + C (N, 2) + …+ C (N, N-1) + C (N, N) = 2N–1
C (N, j) is the combination of N items taken j at a time.Maximum number of possible combinations is (2N-1) M
SOLUTION METHODS
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TECHNICAL SEMINAR-2004
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The techniques for the solution of the unit commitment problem are as follows:
Priority-list scheme: the most efficient unit is loaded first
Dynamic Programming (DP):
Forward DP approach
Backward DP approach Mixed Integer Linear Programming (MILP)
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Backward DP Approach:The solution starts at the last interval and proceeds back the initial point
Fcost(K, I) = Min [Pcost (K, I) + Scost(I, K: J,K+1) + Fcost(K+1,J)]
where
Fcost (K, I) = minimum total fuel cost
Pcost (K, I) = minimum generation cost
Scost (I, K: J, K+1) = incremental start-up cost. {J} = set of feasible states in interval K+1.
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TECHNICAL SEMINAR-2004
Dipanwita Dash [8]
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Forward DP Approach The initial conditions are easily specified Previous history of the unit can be computed at each stage Fcost (K, I) = Min [Pcost (K, I) + Scost (K-1, L: K, I) +
Fcost (K-1, L)] where Fcost (K, I) =least total cost to arrive at state (K, I) Pcost (K, I) = production cost for state (K, I). Scost (K-1, L: K, I) = transition cost for state (K-1, L)
to state (K, I) where state (K, I) is the Ith combination in hour K.
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TECHNICAL SEMINAR-2004
Dipanwita Dash [10]
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TECHNICAL SEMINAR-2004
Dipanwita Dash [11]
EXAMPLE OF DPThe problem is to find out the minimum cost from A to N At the terminal of each stage there is a set of choices of nodes {Xi} to be chosen
The symbol Va (Xi, Xi+1) represents the cost of traversing stage a (=1…V)
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fI(X1) : Minimum cost for the 1st stage is obvious :
fI(B) : VI(A, B) = 5.
fI(C) : VI(A, C) = 2.
fI(D) : VI(A, D) = 3.
fII(E)= min [fI(X1) + VII(X1, E)]
{X1}
= min [5+11, 2+8, 3+ ] =10
X1 =B =C =D
fII(F) = min [, 6, 9] = 6, X1 = C
fII(G) = min [, 11, 9] = 9,X1 = D
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TECHNICAL SEMINAR-2004
Dipanwita Dash [13]
(X2) E F GfII (X2) 10 6 9Path X0X1 AC AC ADTracing back, the path of minimum cost is found as
follows: Stage {Xi} fi
1 B, C, D 5, 2, 3 2 E, F, G 10, 6, 9 3 H, I, J, K 13, 12, 11, 13 4 L, M 15, 18 5 N 19
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CONCLUSION
By optimal scheduling of generating units, we can save time, power and cost
Important for industrial application
Dynamic programming method gives a reliable solution
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Dipanwita Dash [15]