# Mathematical Modelling of Future Energy

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21 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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Mathematical Modelling of Future Energy
Systems

Professor Janusz W. Bialek

Durham University

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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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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

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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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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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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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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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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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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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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Poyry: “Impact of Intermittency”, 2009

Example 3: Keeping reserve vs just
-
in
-
time delivery

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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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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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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
-

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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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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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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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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