1Clemson University Electric Power Research Association

GENERATION SCHEDULING WITH HYBRID ENERGY

RESOURCES IN A DEREGULATED POWER SYSTEM

Manas Trivedi

2Clemson University Electric Power Research Association

Presentation Outline• Hybrid Energy Resources and the increasing interest in their generation Scheduling

• Hydro-thermal generation coordination, working , operation

• Method used to solve generation scheduling of hydro-thermal coordination

• Economic Dispatch Problem

• Transmission Loss Equation Derivation

• Hydrothermal Scheduling Problem

• Algorithm used to solve the hydro thermal generation scheduling problem

• Schedule the generation for the two different cases with taking network losses of the IEEE 14-bus system into account

• Conclusions

3

Hybrid Energy Resources

• The combined use of the energy resources

Example• Hydro-Thermal• Hydro-Thermal -Nuclear

4

Objective of Hydro-thermal Generation Scheduling

• Use the hydro energy for profit maximization that leads to thermal cost minimization of a hydro-thermal system.

• Formulate Long Term Hydro-Thermal coordination as a cost minimization problem.

5

Method Used to Solve the Hydro-thermal Scheduling

• Lagrangian Relaxation method is used to solve the hydro-thermal scheduling.

• Lagrangian Multipliers are updated in all the iterations to meet the constraints.

6

Economic Dispatch Problem

• Objective Function

FT = F1 +F2 +F3 +F4 +………+Fn = Σ Fi(Pi)

• Constraint Function N Φ = 0 = Pload + Ploss – Σ Pi i = 1 • Lagrange Function

L= FT + λ Φ

• Finding the minimum cost operating condition

dL / dPi = (dFi (Pi) /dPi) + λ ((dPloss /dPi)-1) = 0

λ = (dFi (Pi) /dPi ) / (1- (dPloss /dPi))

• (incremental cost rate of unit) λ = Lni (dFi (Pi) /dPi )

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Network Loss Equation Calculation

Steps:

• Zbus formation of Network• To express the system loss in terms of only generator

currents• Transform the generator currents into the power outputs

Loss Equation

Ploss = Σi Σj Pi Bij Pj + Σi Bio Pi + Boo

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HydroThermal Scheduling Problem

• Problem

Min FT = Σ nj Fj

nj = length of jth interval

• Subject to Σ nj qj = Qtot (total water discharge)

• Pload j – PHj – PSj = 0 (load balance)

• Σ nj = Tmax

• Adding the network losses to the problem Ploadj + Plossj – PHj – PSj = 0

• Lagrange Function becomes L = Σ [nj F (PSj ) + λj (Ploadj + Plossj – PHj – PSj )]+ γ [Σ nj qj (PHj ) – Qtot ]

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Hydro Constraints

• Reservoir Water at the Start of Schedule

• Reservoir Water at the end of Schedule

• Limitation of the Reservoir Volume

• Inflow to the Reservoir

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A λ – γ ITERATION SCHEME FOR HYDRO-THERMAL SCHEDULING WITH LOSSES

SELECT INITIAL VAUES FOR

λK , γ, Psk

SET j = 1

Solve the coordination equations

nj dF + λj ∂PLOSS = λj

dPsj ∂PSj

γ nj dF + λj ∂PLOSS = λj

dPsj ∂PSj

PLOADj + PLOSSj – PHj – PSj ≤ ε 1

FIND qj (PHi )

j = jmax

jmax

Σ njqj – qT ≤ ε2 j = 1

OUTPUT SCHEDULES

ProjectNew λj

No

No

No Project new γ value

yes

yes

yes

j=j+1

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STEPS FOLLOWED IN PROGRAM

• Reading and Storing Line data and Bus data.

• Formation of Zbus of the given system using Zbus building algorithm.

• Calculation of Transmission Loss B Coefficients.

• Hydro-Thermal generation scheduling with network loss.

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ResultsRunning the program for the following two cases:

• Case 1: Two thermal and two hydro units.

• Case 2: Three thermal and one hydro unit

The load pattern for a day is assumed to be as follows:

• Load for first 12 hours of the day = 800 MW

• Load for next 12 hours of the day = 900 MW

We get

Case1:

Case2:

367.71 MW269.97 MWSecond Hydro

117.66 MW156.76 MWFirst Hydro

244.42 MW186.10 MWSecond Thermal

190.66 MW204.92 MWFirst Thermal

Second 12 hoursFirst 12 hours

336.72 MW249.54 MWHydro

48.58 MW79.38 MWThird Thermal

350.16 MW292.15 MWSecond Thermal

183.30 MW194.79 MWFirst Thermal

Second 12 hoursFirst 12 hours

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CONCLUSIONS

• The proposed algorithm has been successfully tested for generation scheduling of two different cases using the IEEE 14-bus system.

• The method maximizes the production profits of the hydrothermal power system by efficient use of the hydro energy.

• The derived loss equation used in algorithm by the Zbus method provides accurate generation schedules.

14

FUTURE WORK

• To develop a general algorithm for generation scheduling in power systems with hybrid energy resources

• The proposed method will determine the optimal allocation of energy resulting from random availability of source during different sub-periods of a year so that the expected benefits are maximized

15Clemson University Electric Power Research Association

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