1. Mathematical Modelling of Future Energy Systems Professor Janusz W. Bialek Durham University p1 ©J.W. Bialek, 2010

2. Outline l Drivers for power system research l Current and future power system l Examples of mathematical and statistical challenges based on my work l Funding opportunities p2 ©J.W. Bialek, 2010

3. p3 ©J.W. Bialek, 2010 Main research drivers for power system research in the UK l “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) l Driver1 : Grid integration of renewables and Smart Grids l 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

4. Modelling of power networks l A network is a planar graph with nodes (buses, vertices) and branches (lines, edges) l GB high-voltage transmission network consists of 810 nodes and 1194 branches l UCTE and US interconnected networks consist of several thousands nodes l For most analyses, the network is described by algebraic equation (Current and Voltage Kirchhoff’s Laws) l Electromechanical stability of rotating generators is described by differential equations

5. p5 ©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

6. p6 ©J.W. Bialek, 2010 Future power system (2020/30) l Very high number (1000s) of uncontrollable renewable plants connected at both transmission and distribution level l Stochastic and highly distributed generation l Need to model distribution networks (much denser, tens/hundreds of thousands of nodes)

7. p7 ©J.W. Bialek, 2010 l Smart metering enabling demand response (Smart Grids) o Demand not deterministic any more l Possible electric cars + storage o storage and time-shifting demand create much stronger linkages between time periods in power system models l Interactions with gas and transport networks l In short: the future power system will be complex and stochastic

8. What’s needed p8 ©J.W. Bialek, 2010 l 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 l Probabilistic planning and operation tools: l Move from traditional direct control to stochastic and hierarchical control

9. 3 examples based on work in Durham p9 ©J.W. Bialek, 2010

10. Example 1: Risk calculations and capacity credits (CD) l 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 p10 ©J.W. Bialek, 2010 l Evaluate risk with projected fleet of wind + conventional generation l Capacity credit is conventional capacity which gives same risk in an all-conv system

11. Example 2: How to model the resource in system studies l Current approach: hindsight, i.e. use historic wind time series l Can give robust modelling results but provides limited insight l Needed: stochastic spatial/temporal characterisation of resource l Use it for stochastic system studies: would give a better scentific understanding into what drives results p11 ©J.W. Bialek, 2010 Poyry: “Impact of Intermittency”, 2009

12. Example 3: Keeping reserve vs just-in-time delivery p12 ©J.W. Bialek, 2010 l Doubling of operating generation reserve by 2020 due to intermittency of wind if current approach is used National Grid, 2009

13. p13 ©J.W. Bialek, 2010 l Significant cost as reserve needed 24/7 l Just-in-time approach: use flexible demand/storage, rather than just thermal generation, to provide a back-up for wind l Must not increase risk l Statistics + Stochastic Control + Operational Research

14. p14 ©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 1950/511960/611970/711980/811990/912000/012010/112020/212030/312040/41 £m (97/98 Prices) Actual capexCapex for replace on 40yr life

15. Asset Management p15 ©J.W. Bialek, 2010 Age and Condition: which is important?

16. Asset Management l Asset replacement must be undertaken in a timely way –Condition monitoring, diagnostics –Prognostics –Often limited historical information: equipment is replaced before it fails l New challenge: reliability of offshore wind farms –£75 billion industry –Reliability might be a bottleneck due to a limited and costly access l Involvement of statisticians and mathematicians needed: e.g. Bayesian statistics. p16 ©J.W. Bialek, 2010

17. Funding opportunities for energy research l RCUK Energy Programme is the largest £220M, bigger than the others taken together (Digital Economy 103M, Nanoscience 39M, Healthcare £36M) l Preference of UKRC for interdisciplinary research l SuperGen (Sustainable Power Generation and Supply) is the flagship initiative in Energy Programme p17 ©J.W. Bialek, 2010

18. EPSRC: Grand Challenges in Energy Networks l Look 20-40 years ahead l Scoping workshop held in March 2010 l A number of themes identified including –Flexible Grids –Uncertainty and Complexity –Energy and Power Balancing l £8M (?) Call expected to be announced in summer p18 ©J.W. Bialek, 2010

19. EPSRC call: Mathematics Underpinning Digital Economy and Energy l Deadline 1 July 2010, full proposal l £5 million earmarked; 7 -12 proposals will be funded p19 ©J.W. Bialek, 2010

20. What is reactive power? l Motors are electromagnetic devices and need coils to produce magnetic fields l Because current is ac (alternating), energy to supply the magnetic field oscillates between the source and the inductor (at 100 Hz) l That oscillating power is called reactive (imaginary) power – symbol Q (real power P) l On average the energy transfer is zero (you cannot use it for any purpose) but there is always an instantaneous flow of energy l There is no reactive power in dc circuits

21. Nasty effects of reactive power l Causes real power losses (because of oscillating power transfers) l Takes up capacity of wires l Causes voltage drops (proportional to the distance it travels): ΔV= (PR + QX)/V l You cannot transfer reactive power over long distances l Compensation by capacitance (voltage support) p21 ©J.W. Bialek, 2010

22. Conclusions l Grid integration of renewables, Smart Grids and the need to rewire Britain create a huge pull for new research l Collaboration with mathematicians and statisticians is crucial l Significant funding opportunities l Reactive power is not small beer! p22 ©J.W. Bialek, 2010