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

Hybrid Energy Resources The combined use of the energy resources Example Hydro-Thermal Hydro-Thermal -Nuclear

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.

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.

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 )

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

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 ]

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

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

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.

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: 367.71 MW 269.97 MW Second Hydro 117.66 MW 156.76 MW First Hydro 244.42 MW 186.10 MW Second Thermal 190.66 MW 204.92 MW First Thermal Second 12 hours First 12 hours 336.72 MW 249.54 MW Hydro 48.58 MW 79.38 MW Third Thermal 350.16 MW 292.15 MW Second Thermal 183.30 MW 194.79 MW First Thermal Second 12 hours First 12 hours

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.

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

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