Modelling Developments at Power Systems Research Tom Halliburton

Modelling Developments at Power Systems Research Tom Halliburton EPOC Meeting 9 th July 2014

PSR – Power Systems Research Inc • • Offices in Rio de Janeiro Founded in late 1980 s by Mario Pereira Now has 47 staff Work split equally between consulting and software sales – And equally between local and overseas customers • Customers world wide – most countries with significant hydro generation

SDDP – mid term planning Opt. Gen – Investment planning NCP – short term scheduling

SDDP – faster solves • Parallel processing – Base SDDP licencing allows parallel processing on one PC – Base Xpress solver allows two simultaneous processes on each licence – Enhanced version of SDDP for parallel processing across multiple networked PCs – Two parallel processes reduces CPU by approx 60% • Faster solves with Cut Relaxation – Each iteration, size of LP problem increases, e. g. 18% from 1 st to 2 nd iteration. – Eliminate redundant future cost function cuts from the one stage LP problems automatically, rather than allowing user to select based on a rule

Fuel Supplies • Fuel supply contracts – Take or pay contracts, – General limits of rates and quantities of fuel supplies • Fuel storage – Coal stockpiling, gas storage • Multiple fuel contracts, supplying multiple stations • Take or pay, fuel storage add dimensions to future cost function

SDDP chronological • Chronological modelling within each week – – – – Hourly Trial version completed Flow delays down rivers Hydro plant head pond constraints Thermal plant ramp rates Random variations in wind generation Time of day effects for solar power • Requires massive parallel computing – Conceptually all the one stage optimisations can be carried out simultaneously (e. g. 50 per stage, 360 stages)

Current Issues • Modelling of risk averse management of hydro reservoirs – Apply a more risk averse approach based on a willingness to give up some expected returns to reduce probability of deficit • Approximating head effects at hydro stations without creating non-convex future cost function • Possibly take or pay contracts for hydros

Cloud Computing on Amazon Servers • All three models available on Amazon – PSR the first South American customer for Amazon, over 2 years ago – Costs US$0. 50 per processor, per hour • Covers Amazon charges and Xpress LP solver licencing fees – Processor cost has come down as most customers want storage, not CPU power – Opens up new opportunities for parallel processing • Opt. Gen 20 year case, 80 iterations, 5. 5 hours elapsed, using 16 processors • SDDP Chronological

Opt. Gen – Optimal Generation System Expansion Planning • Includes all the usual constraints for expansion planning • Find the optimal expansion plan using a MIP solver, minimising investment + operational cost • Investment costs known for each plant • System operation costs must be calculated for each node in the MIP problem • Repeated calculation of operational cost for different expansion plans result in an improving representation of the system operating cost function • Cost function has a similar form to the future cost function calculated by SDDP.

Opt. Gen Algorithm Objective: Minimise C(x) + W(x) where C(x) investment cost W(x) operating cost X(t, j) is a matrix representing new generation commissioning program

Opt. Gen with SDDP • Simple mode - Opt. Gen calculates operational cost for a number of scenarios • Alternatively, use SDDP: – Opt. Gen calculates an optimal expansion plan – SDDP calculates the system operating costs – Opt. Gen re-calculates the expansion plan using this new information • Allows plant operating capabilities and constraints to directly influence expansion planning. • End result is a least cost expansion plan and an SDDP model setup for this plan.

Opt. Gen + SDDP • Distinguishes between run of river hydros and those with storage. – Waitaki North Bank will benefit from storage management, Arnold scheme will not. • Full effects of variability of hydro inflows reflected in planning – Accounts for extra plant that might be needed to cover dry periods • Thermal unit commitment options – Base load or peaking capabilities • Coal stockpiling, gas storage • Take or pay fuel contracts associated with new plant • Variability of wind, solar can be modelled in more detail

Opt. Gen Trials • Trial study of New Zealand system – 20 year study – 80 iterations, 5. 5 hours elapsed with 16 processors – Results look reasonable

NCP • Detailed scheduling model hourly, ½ hourly or 15 minute time steps • Used for detailed day ahead planning etc. where ramp rates, start up costs, interaction of hydro plants in a river system need to be modelled • Used in centrally planned and dispatched systems – A model of this type is likely to be needed if the “NZ Power” single buyer scheme were to eventuate.

NCP Chronological • Latest extension enables SDDP model results to be studied in more detail • Solve a full year with NCP, working from an SDDP solution to give a detailed picture of one or more flow scenarios • Options to enforce SDDP’s mid-term strategies: – Use water value for end of period storage – End of period reservoir levels as a target – Total generation each period for each hydro plant