Mathematical Modelling of Future Energy
Systems
Professor Janusz W. Bialek
Durham University
p1 ©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
p2 ©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
p3 ©J.W. Bialek, 2010
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
Today’s power system
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)
p5 ©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)
p6 ©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
p7 ©J.W. Bialek, 2010
What’s needed

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
p8 ©J.W. Bialek, 2010
3 examples based on work in Durham
p9 ©J.W. Bialek, 2010
Example 1: Risk calculations and capacity
credits (CD)
ECC (MW)
ECC (%)
1000
4000
10%
Year
Year
0%
2019
2018
2017
2016
2018
2017
2019
20162015
0
5%
20152014
500
3000
Wind ECC (%)
15%
20142013
Capacity credit is
conventional capacity
which gives same risk
in an all-conv system
1500
5000
2011
2011
2012
2012
2013

– What is the ‘capacity credit’ of the wind generation
9000
Evaluate risk with
With wind
3000
30%
8000
projected fleet of wind
Without wind
2500
25%
7000
+ conventional
2000
20%
6000
generation
2010
2010

Question: what is the risk of installed generating
capacity being inadequate to support peak demand in
a system with high wind penetration
Wind ECC (MW)
Effective Margin (MW)

p10 ©J.W. Bialek, 2010
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
Poyry: “Impact of Intermittency”, 2009
p11 ©J.W. Bialek, 2010
Example 3: Keeping reserve vs just-in-time delivery

Doubling of operating generation reserve by 2020
due to intermittency of wind if current approach is
used
National Grid, 2009
p12 ©J.W. Bialek, 2010

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
p13 ©J.W. Bialek, 2010
Driver 2: Rewiring Britain
UK Distribution
Gross Capital Expenditure
£m (97/98 Prices)
2500
2000
1500
1000
500
0
Capex
forthe
replace
on 40yr
life
TheActual
aim:capex
smoothing
out
second
peak
Source: Robin Maclaren, ScottishPower
p14 ©J.W. Bialek, 2010
Asset Management
Age and Condition: which is important?
p15 ©J.W. Bialek, 2010
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.
p16 ©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
p17 ©J.W. Bialek, 2010
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
p18 ©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
p19 ©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): ΔV= (PR + QX)/V

You cannot transfer reactive power over long
distances

Compensation by capacitance (voltage support)
p21 ©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!
p22 ©J.W. Bialek, 2010