Mathematical Modelling of Future Energy
Systems
Professor Janusz W. Bialek
Durham University
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©J.W. Bialek, 2010
Outline
Drivers for power system research
Current and future power system
Examples of mathematical and statistical challenges
based on my work
Funding opportunities
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©J.W. Bialek, 2010
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©J.W. Bialek, 2010
Main research drivers for power system research
in the UK
“Any feasible path to a 80% reduction of CO2 emissions
by 2050 will require the almost total decarbonisation of
electricity generation by 2030”
(Climate Change Committee
Building a Low Carbon Economy
2008)
Driver1 : Grid integration of renewables and Smart Grids
Driver 2: Rewiring Britain
–
The UK electricity infrastructure is about 40 years old
= lifetime of equipment
–
On

shore and off

shore wind requires a significant
extension of the existing grid
Modelling of power
networks
A network is a planar graph with
nodes (buses, vertices) and
branches (lines, edges)
GB high

voltage transmission
network consists of 810 nodes
and 1194 branches
UCTE and US interconnected
networks consist of several
thousands nodes
For most analyses, the network
is described by algebraic
equation (Current and Voltage
Kirchhoff’s Laws)
Electromechanical stability of
rotating generators is described
by differential equations
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©J.W. Bialek, 2010
o
Limited number of controllable
power stations
o
Demand highly predictable
o
Operation demand

driven
o
Only transmission network fully
modelled (~1000 nodes) as
distribution network is passive
o
Deterministic planning and
operation
•
Generation and
transmission reserve to
account for contingencies:
(N

1)
Today’s power system
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©J.W. Bialek, 2010
Future power system (2020/30)
Very high number (1000s) of uncontrollable renewable plants
connected at both transmission and distribution level
Stochastic and highly distributed generation
Need to model distribution networks (much denser,
tens/hundreds of thousands of nodes)
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©J.W. Bialek, 2010
Smart metering enabling demand response (Smart Grids)
o
Demand not deterministic
any more
Possible electric cars + storage
o
storage and time

shifting demand create much stronger
linkages between time periods in power system models
Interactions with gas and transport networks
In short: the future power system will be complex and stochastic
What’s needed
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©J.W. Bialek, 2010
Modelling of highly distributed and stochastic generation and
demand
o
Stochastic characterisation of resource and demand
o
Aggregation of distributed generation and demand
o
Modelling of interactions
o
Human behaviour
Probabilistic planning and operation tools:
Move from traditional direct control to stochastic and
hierarchical control
3 examples based on work in Durham
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©J.W. Bialek, 2010
Example 1: Risk calculations and capacity
credits (CD)
Question: what is the risk of installed generating
capacity being inadequate to support peak demand in
a system with high wind penetration
–
What is the ‘capacity credit’ of the wind generation
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©J.W. Bialek, 2010
3000
4000
5000
6000
7000
8000
9000
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Year
Effective Margin (MW)
With wind
Without wind
Evaluate risk with
projected fleet of wind
+ conventional
generation
Capacity credit is
conventional capacity
which gives same risk
in an all

conv
system
0
500
1000
1500
2000
2500
3000
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Year
Wind ECC (MW)
0%
5%
10%
15%
20%
25%
30%
Wind ECC (%)
ECC (MW)
ECC (%)
Example 2: How to model the resource in system
studies
Current approach:
hindsight, i.e. use
historic wind time series
Can give robust
modelling results but
provides limited insight
Needed: stochastic
spatial/temporal
characterisation of
resource
Use it for stochastic
system studies: would
give a better scentific
understanding into what
drives results
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©J.W. Bialek, 2010
Poyry: “Impact of Intermittency”, 2009
Example 3: Keeping reserve vs just

in

time delivery
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©J.W. Bialek, 2010
Doubling of operating generation reserve by 2020
due to intermittency of wind if current approach is
used
National Grid, 2009
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Significant cost as reserve needed 24/7
Just

in

time approach: use flexible demand/storage,
rather than just thermal generation, to provide a
back

up for wind
Must not increase risk
Statistics + Stochastic Control + Operational
Research
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©J.W. Bialek, 2010
Driver 2: Rewiring Britain
Source: Robin Maclaren, ScottishPower
The aim: smoothing out the second peak
UK Distribution
Gross Capital Expenditure
0
500
1000
1500
2000
2500
£m (97/98 Prices)
Actual capex
Capex for replace on 40yr life
Asset Management
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Age and Condition: which is important?
Asset Management
Asset replacement must be undertaken
in a timely way
–
Condition monitoring, diagnostics
–
Prognostics
–
Often limited historical information: equipment is replaced before
it fails
New challenge: reliability of
offshore wind farms
–
£75 billion industry
–
Reliability might be a bottleneck
due to a limited and costly access
Involvement of statisticians and mathematicians needed: e.g.
Bayesian statistics.
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©J.W. Bialek, 2010
Funding opportunities for energy research
RCUK Energy Programme is the largest £220M, bigger
than the others taken together (Digital Economy 103M,
Nanoscience 39M, Healthcare £36M)
Preference of UKRC for interdisciplinary research
SuperGen (Sustainable Power Generation and Supply) is
the flagship initiative in Energy Programme
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EPSRC: Grand Challenges in Energy Networks
Look 20

40 years ahead
Scoping workshop held in March 2010
A number of themes identified including
–
Flexible Grids
–
Uncertainty and Complexity
–
Energy and Power Balancing
£8M (?) Call expected to be announced in summer
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©J.W. Bialek, 2010
EPSRC call: Mathematics Underpinning Digital
Economy and Energy
Deadline 1 July 2010, full proposal
£5 million earmarked; 7

12 proposals will be funded
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©J.W. Bialek, 2010
What is reactive power?
Motors are electromagnetic devices and need coils to
produce magnetic fields
Because current is ac (alternating), energy to supply the
magnetic field oscillates between the source and the
inductor (at 100 Hz)
That oscillating power is called reactive (imaginary)
power
–
symbol Q (real power P)
On average the energy transfer is zero (you cannot use
it for any purpose) but there is always an instantaneous
flow of energy
There is no reactive power in dc circuits
Nasty effects of reactive power
Causes real power losses (because of oscillating
power transfers)
Takes up capacity of wires
Causes voltage drops (proportional to the distance it
travels):
Δ
V= (PR + QX)/V
You cannot transfer reactive power over long
distances
Compensation by capacitance (voltage support)
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©J.W. Bialek, 2010
Conclusions
Grid integration of renewables, Smart Grids and the
need to rewire Britain create a huge pull for new
research
Collaboration with mathematicians and statisticians is
crucial
Significant funding opportunities
Reactive power is not small beer!
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©J.W. Bialek, 2010
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