Modelling Developments at
Power Systems Research
Tom Halliburton
EPOC Meeting
9th July 2014
PSR – Power Systems Research Inc
Offices in Rio de Janeiro
Founded in late 1980s 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
SDDP – mid term planning
OptGen – Investment
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
1st to 2nd 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
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
– Apply a more risk averse approach based on a willingness
to give up some expected returns to reduce probability of
• 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
– Processor cost has come down as most customers
want storage, not CPU power
– Opens up new opportunities for parallel processing
• OptGen 20 year case, 80 iterations, 5.5 hours elapsed,
using 16 processors
• SDDP Chronological
OptGen – 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.
OptGen Algorithm
Minimise C(x) + W(x)
C(x) investment cost
W(x) operating cost
X(t,j) is a matrix representing new generation commissioning program
OptGen with SDDP
• Simple mode - OptGen calculates operational cost for a
number of scenarios
• Alternatively, use SDDP:
– OptGen calculates an optimal expansion plan
– SDDP calculates the system operating costs
– OptGen re-calculates the expansion plan using this new
• 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.
OptGen + SDDP
• Distinguishes between run of river hydros and those with
– 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
OptGen Trials
• Trial study of New Zealand system
– 20 year study
– 80 iterations, 5.5 hours elapsed with 16 processors
– Results look reasonable
• 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

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