Modelling Developments at
Power Systems Research
Tom Halliburton
EPOC Meeting
9th July 2014
PSR – Power Systems Research Inc
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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
generation
SDDP – mid term planning
OptGen – 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
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
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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
• 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
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
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
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.
OptGen + 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
OptGen 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