1 Scheduling the TVA Hydro System Using RiverWare’s Optimization Suzanne H. Biddle, P.E. Tennessee Valley Authority

2 HL KNOXVILLE NASHVILLE CHATTANOOGA TN KY NC SC GA AL MS VA Watershed Power Service Area TVA region covers 40,000 sq miles

3 Average annual rainfall above Chattanooga is about 51 inches and runoff is about 22 inches

4 TVA operates the reservoir system to meet multipurpose objectives Navigation Flood damage reduction Power generation Recreation Water quality Water supply

5 Inputs Future value of water Hourly hydropower value Inflow forecast Initial conditions Objectives hourly generation preschedule (current day + 2 forecast days) 9 day optimization using marginal costs for water allocation daily hydro forecast (14 days) 9 day optimization using block costs for daily generation schedule 3 day optimization using block costs for hourly generation schedule River Scheduling issues two hydro forecasts each day

6 Current Day Observed Values Days Future Value of Water Days RiverWare 6-Hourly Forecast 14 Days RiverWare Hourly Preschedule 2 Days Optimization covers short term, but also considers long term tradeoff

7 Many reservoirs follow seasonal guide curves

8 These objectives are used in optimizing the hydro system Day 1 outflows are fixed Ending targets are fixed for non-storage tributaries and main river Minimum flow requirements Top and bottom of daily operating zone – non-storage tribs and main river only Minimum operations guides Flood guides Minimize spill Special operations Economic objective function

9 What does “economic objective function” mean? All operating constraints must first be satisfied Then, with any remaining flexibility: Maximize avoided operating cost + delta (value of water in storage)

10 Is water worth more this week or in future weeks?

11 After water is allocated, block cost data is used to determine which hours to run

12 The reservoir system is modeled as a whole for hydropower optimization