Mathematical Modelling of Future Energy Systems

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

2. Outline • Drivers for power system research • Current and future power system • Examples of mathematical and statistical challenges based on my work • Funding opportunities

3. 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

4. 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

5. Today’s power system • Limited number of controllable power stations • Demand highly predictable • Operation demand-driven • Only transmission network fully modelled (~1000 nodes) as distribution network is passive • Deterministic planning and operation • Generation and transmission reserve to account for contingencies: (N-1)

6. 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)

7. Smart metering enabling demand response (Smart Grids) • Demand not deterministic any more • Possible electric cars + storage • 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

8. What’s needed • Modelling of highly distributed and stochastic generation and demand • Stochastic characterisation of resource and demand • Aggregation of distributed generation and demand • Modelling of interactions • Human behaviour • Probabilistic planning and operation tools: • Move from traditional direct control to stochastic and hierarchical control

9. 3 examples based on work in Durham

10. 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 • Evaluate risk with projected fleet of wind + conventional generation • 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 • 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

12. 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

13. 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

14. Driver 2: Rewiring Britain UK Distribution Gross Capital Expenditure 2500 2000 1500 £m (97/98 Prices) 1000 500 0 1950/51 1960/61 1970/71 1980/81 1990/91 2000/01 2010/11 2020/21 2030/31 2040/41 The aim: smoothing out the second peak Actual capex Capex for replace on 40yr life Source: Robin Maclaren, ScottishPower

15. Asset Management Age and Condition: which is important?

16. 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.

17. 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

18. 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

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

20. 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

21. 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)

22. 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!