Mathematical Modelling of Future Energy Systems Professor Janusz W. Bialek Durham University p1...

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



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


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


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)


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


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


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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Evaluate risk with projected fleet of wind + conventional generation

Capacity credit is conventional capacity which gives same risk in an all-conv system

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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

p11 ©J.W. Bialek, 2010Poyry: “Impact of Intermittency”, 2009

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


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


Driver 2: Rewiring Britain

Source: Robin Maclaren, ScottishPower

The aim: smoothing out the second peak

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Actual capex Capex for replace on 40yr life

Asset Management


Age and Condition: which is important?

Asset Management

Asset replacement must be undertakenin 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.


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


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


EPSRC call: Mathematics Underpinning Digital Economy and Energy

Deadline 1 July 2010, full proposal

£5 million earmarked; 7 -12 proposals will be funded


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)


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!


Mathematical Modelling of Future Energy Systems Professor Janusz W. Bialek Durham University p1...

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