1. GENERATION SCHEDULING WITH HYBRID ENERGY RESOURCES IN A DEREGULATED POWER SYSTEM
Manas Trivedi
Clemson University Electric Power Research Association

2. 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
Clemson University Electric Power Research Association

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 )

7. 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

8. HydroThermal Scheduling 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 ]

9. 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

10. 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
Project
New λj No
PLOADj + PLOSSj – PHj – PSj ≤ ε 1
yes
FIND qj (PHi ) No
j = jmax
j=j+1
yes
jmax
Σ njqj – qT ≤ ε2
j = 1 No
Project new
γ value
yes
OUTPUT SCHEDULES

11. 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.

12. Results Running 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: MW MW
Second Hydro MW MW
First Hydro MW MW
Second Thermal MW MW
First Thermal
Second 12 hours
First 12 hours MW MW
Hydro
48.58 MW
79.38 MW
Third Thermal MW MW
Second Thermal MW MW
First Thermal
Second 12 hours
First 12 hours

13. 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

15. QUESTIONS ?
THANK YOU
Clemson University Electric Power Research Association