Clemson University Electric Power Research Association

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 GenerationScheduling • 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 + λΦ • 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 • 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 njdF + 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 No jmax Σ njqj – qT ≤ ε2 j = 1 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. First 12 hours Second 12 hours First Thermal 204.92 MW 190.66 MW Second Thermal 186.10 MW 244.42 MW First Hydro 156.76 MW 117.66 MW Second Hydro 269.97 MW 367.71 MW First 12 hours Second 12 hours First Thermal 194.79 MW 183.30 MW Second Thermal 292.15 MW 350.16 MW Third Thermal 79.38 MW 48.58 MW Hydro 249.54 MW 336.72 MW 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:

13. CONCLUSIONS • The proposed algorithm has beensuccessfullytested 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