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Price-Based Unit Commitment

Price-Based Unit Commitment. PBUC FORMULATION maximize the profit

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Page 1: Price-Based Unit Commitment. PBUC FORMULATION  maximize the profit

Price-Based Unit Commitment

Page 2: Price-Based Unit Commitment. PBUC FORMULATION  maximize the profit

PBUC FORMULATION

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PBUC FORMULATION

maximize the profit

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PBUC FORMULATION System Constraints

These constraints represent a GENCO’s special requirements. For example, a GENCO may have minimum and maximum generation requirements in order to play the game in the energy market. Because of reliability requirements, a GENCO may pose lower and upper limits on its spinning and no-spinning reserves. These constraints can be relaxed otherwise.

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PBUC

System Fuel Constraints (For a “FT” type of fuel)

System Emission Constraint

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PBUC

Unit Constraints

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PBUCUnit Minimum ON/OFF Durations

Unit Ramping Constraints

Unit Fuel Constraints

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PBUC SOLUTION

Lagrangian relaxation is used to solve PBUC. The basic idea is to relax coupling constraints

(i.e., coupling either units, time periods, or both) into the objective function by using Lagrangian multipliers.

The relaxed problem is then decomposed into subproblems for each unit.

The dynamic programming process is used to search the optimal commitment for each unit.

Lagrangian multipliers are then updated based on violations of coupling constraints

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Solution without Emission or Fuel Constraints

Using Lagrangian multipliers to relax system constraints (i.e., energy and reserve), we write the Lagrangian function as

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Single-Unit DP The Lagrangian term for one unit at a single period is given as

follows

The separable single-unit problem is formulated as

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Optimality Condition

When the unit is ON, the derivatives of the Lagrangian function with respect to P, R, and N are

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optimality condition

when the unit is ON, the optimality condition is

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Optimality Condition when the Unit is OFF

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Multipliers Update

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Economic Dispatch

Once the unit commitment status is determined, an economic dispatch problem is formulated and solved to ensure the feasibility of the original unit commitment solution.

subject to energy, reserve, and unit generation limits

quadratic or linear programming can be applied to solve this problem

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Economic Dispatch for Non-spinning Reserve

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Economic Dispatch for Spinning Reserve

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Economic Dispatch for Spinning Reserve

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Economic Dispatch for Energy

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Economic Dispatch for Energy

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Convergence Criterion Suppose that the solution from unit commitment is SU

and the solution from economic dispatch is SE Substituting SU into the Lagrangian function, we would

get the Lagrangian value, LU. Substituting SE into the Lagrangian function we would get

the Lagrangian value, denoted as LE The relative duality gap (RDG)

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Solution with Emission and Fuel Constraints

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Optimality Condition

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Multipliers Update for Emission and Fuel Constraints

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Multipliers Update for Emission and Fuel Constraints

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Economic Dispatch

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Energy Purchase

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Derivation of Steps in Update of Multipliers

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Derivation of Steps in Update of Multipliers

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Optimality Condition

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Bidding Strategy Based on PBUC

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Bidding Strategy

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Case Study of 5-Unit System

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Case 1: Impact of the Energy Market Price

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Case 1: Impact of the Energy Market Price

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Case 2: Impact of Ramp Rates

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Case 2: Impact of Ramp Rates

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Case 3: Impact of Fuel Price Variations

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Case 3: Impact of Fuel Price Variations

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Case 5: Impact of Different LMPs

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Case 5: Impact of Different LMPs

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Case 5: Impact of Different LMPs

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