Price-Based Unit Commitment. PBUC FORMULATION maximize the profit

Price-Based Unit Commitment

PBUC FORMULATION

PBUC FORMULATION

maximize the profit

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.

PBUC

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

System Emission Constraint

PBUC

Unit Constraints

PBUCUnit Minimum ON/OFF Durations

Unit Ramping Constraints

Unit Fuel Constraints

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

Solution without Emission or Fuel Constraints

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

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

Optimality Condition

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

optimality condition

when the unit is ON, the optimality condition is

Optimality Condition when the Unit is OFF

Multipliers Update

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

Economic Dispatch for Non-spinning Reserve

Economic Dispatch for Spinning Reserve

Economic Dispatch for Spinning Reserve

Economic Dispatch for Energy

Economic Dispatch for Energy

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)

Solution with Emission and Fuel Constraints

Optimality Condition

Multipliers Update for Emission and Fuel Constraints

Multipliers Update for Emission and Fuel Constraints

Economic Dispatch

Energy Purchase

Derivation of Steps in Update of Multipliers

Derivation of Steps in Update of Multipliers

Optimality Condition

Bidding Strategy Based on PBUC

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Bidding Strategy

Case Study of 5-Unit System

Case 1: Impact of the Energy Market Price

Case 1: Impact of the Energy Market Price

Case 2: Impact of Ramp Rates

Case 2: Impact of Ramp Rates

Case 3: Impact of Fuel Price Variations

Case 3: Impact of Fuel Price Variations

Case 5: Impact of Different LMPs

Case 5: Impact of Different LMPs

Case 5: Impact of Different LMPs