EE533 Power Operations Automatic Generation Control Optimization Review and Economic Dispatch

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EE533 Power OperationsAutomatic Generation
ControlOptimization Review and Economic Dispatch

• Satish J Ranade
• Fall 05

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From LFC to Economic Allocation
Economic dispatch
MW
LFC distributes based on response
Units pick up load a capacity
??
LFC minutes
Governor seconds
Time
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From LFC to Economic Allocation
Economic dispatch
MW
Pref changes
Coal
Gas
Time
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The Economic dispatch problem

• Given
• N units on-line
• System Load Loss
• Equals Area Net Generation- Net Interchange when
  ACE0
• Determine
• MW allocation(Schedule) for each Unit
• Minimize Fuel and Variable OM cost
• Constraints A constrained
• Unit capacity, Reserves optimization problem

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The Economic dispatch problem

• Minimize
• Pi

CT C1(P1)C2(P2)CN(PN)
P1P2PN PT
Pimin Pi Pimax i1,2,,N
Ci(Pi) Fuel Variable OM cost (/H) unit i Pi
Net MW output Unit I Pimin, Pimax Min and
Maximum Capacity Unit i
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The Economic dispatch problem Common sense
solution
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The Economic dispatch problem Common sense
solution
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The Economic dispatch problem Common sense
solution
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The Economic dispatch problem Common sense
solution
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The Economic dispatch problem Common sense
solution
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Optimization
Unconstrained
Constrained
Continuous Discrete
Non-smooth
Smooth
Search Based
Gradient Based Method
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Optimization
Search
Gradient Based Tree-Based Stochastic
Heuristic
Based on Decomposition
Subproblems
Search
Gradient Based Tree-Based Stochastic
Heuristic
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Optimization
Min f(x) f() continuous and differentiable
scalar function X real variable Stationarity
condition df/dx0 For min d2f/dx2gt0
max
df/dx0
Local Min
df/dx0
Global Min
Convex function has a unique global minimum
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Optimization
Min f(x) f() continuous and differentiable
scalar function x real variable
vector Stationarity condition df/dx0 For min
d2f/dx2gt0
max
df/dx0
Local Min
df/dx0
Global Min
Convex function has a unique global minimum