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Power systemsilablri

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  • 1. Ilab METIS Optimization of Energy Policies Olivier Teytaud + Inria-Tao + Artelys TAO project-team INRIA Saclay Île-de-France O. Teytaud, Research Fellow, olivier.teytaud@inria.fr http://www.lri.fr/~teytaud/
  • 2. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● It gets more complicated in the future Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 3. Ilab METIS www.lri.fr/~teytaud/metis.html ● Metis = Tao + Artelys TAO tao.lri.fr, Machine Learning & Optimization ● Joint INRIA / CNRS / Univ. Paris-Sud team ● 12 researchers, 17 PhDs, 3 post-docs, 3 engineers ● Artelys www.artelys.com SME - France / US / Canada - 50 persons ==> collaboration through common platform ● ● Activities ● Optimization (uncertainties, sequential) ● Application to power systems O. Teytaud, Research Fellow, olivier.teytaud@inria.fr http://www.lri.fr/~teytaud/
  • 4. Academic Highlights ● ● Bandit algorithms Pascal / Nips 06 challenge on dynamic bandits MCTS for Games ● First ever win against professional players in the game of Go ● ● ● State of the art in MineSweeper Urban Rivals AI (17 M players) Planning Temporal satisficing track, IPC 2011 (International Planning Competition)
  • 5. Industrial application ● ● Building power systems is expensive power plants, HVDC links, networks... Non trivial planning questions ● ● ● Compromise: should we move solar power to the south and build networks ? Is a HVDC connection a good idea between X and Y? What we do: ● ● Simulate the operational level of a given power system (this involves optimization of operational decisions) Optimize the investments
  • 6. Specialization on Power Systems ● Planning/control ● Pluriannual planning: evaluate marginal costs of hydroelectricity ● Taking into account stochasticity and uncertainties ==> IOMCA (ANR) ● High scale investment studies (e.g. Europe+North Africa) ● Long term (2030 - 2050) ● Huge (non-stochastic) uncertainties ● Investments: interconnections, storage, smart grids, power plants... ==> POST (ADEME) ● Moderate scale (Cities, Factories) ● Master plan optimization ● Stochastic uncertainties ==> Citines project (FP7)
  • 7. Example: interconnection studies (demand levelling, stabilized supply)
  • 8. The POST project – supergrids simulation and optimization Mature technology:HVDC links (high-voltage direct current) European subregions: - Case 1 : electric corridor France / Spain / Marocco - Case 2 : south-west (France/Spain/Italiy/Tunisia/Marocco) - Case 3 : maghreb – Central West Europe ==> towards a European supergrid Related ideas in Asia
  • 9. Investment decisions through simulations ● Issues – – – ● Methods – – ● Demand varying in time, limited previsibility Transportation introduces constraints Renewable ==> variability ++ Markovian assumptions ==> wrong Simplified models ==> Model error >> optimization error Our approach ● Machine Learning on top of Mathematical Programming
  • 10. Hybridization reinforcement learning / mathematical programming ● Math programming – – – ● Nearly exact solutions for a simplified problem High-dimensional constrained action space But small state space & not anytime Reinforcement learning – – – – Unstable Small model bias Small / simple action space But high dimensional state space & anytime
  • 11. ● Students + Engineers ● ● J-J Christophe (engineer) ● A. Couëtoux (ph.D. Student) ● M-L Cauwet (ph.D. Student) ● J. Decock (ph.D. student) ● J. Liu (ph.D. Student) ● ● S. Astete Morales (ph.D. student) D. Lupien Saint-Pierre (post-doc) Old crocs: ● M. Schoenauer & M. Sebag (Research Directors) ● ● Who ? O. Teytaud (Research Fellow) Artelys www.artelys.com (most with Ph.D.) ==> many engineers and experts of power systems ● Admin. side: A.-C. Lamballe, R. Ronchaud, M. Gilliaud ● Many contacts worldwide
  • 12. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 13. The problem in one slide ● The assets: ● ● ● ● ● I have plenty of (possibly faulty) power plants (each of them located on a network) I have plenty of (stochastic) electric loads Total production = total consumption + loss (otherwise many things broken!) Many constraints on the network Decisions: ● ● ● Strategic decisions (investments) Intermediate decisions: Hydro-power = bounded resource Tactical decisions: which power plant to switch on/off
  • 14. Let us start with short term ● Thermal power plant producing p MW during 1h: productionCost =Cxp (fuel cost) + startUpCost (if it was off and p>0) + C2 x p2 - (a quadratic term for fun)
  • 15. Several time steps, several thermal power plants pi MW during 1h with power plant #i: productionCost = C x pi + startUpCosti + C2 x pi2 ==> ok, looks simple: we just optimize the sum of costs.
  • 16. Ilab Metis, working on power systems ● ● Principles of power system simulation ● Classical model ● Reserves constraint (for adaptivity against uncertain load, faulty power plants, renewable intermittencies) ==> rules of thumb such as “short term PP>x MW” etc ● Recourse ● Network constraints This simple model does not solve hydro ● It gets more complicated in the future ● Alternate tools: ● ● ● ● Real-time control ? Games ? Bilevel problems
  • 17. Ilab Metis, working on power systems ● ● Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse (==> when big change, reoptimize with new data ==> fast UC) ● Network constraints This simple model does not solve hydro ● It gets more complicated in the future ● Alternate tools: ● ● ● ● Real-time control ? Games ? Bilevel problems
  • 18. Ilab Metis, working on power systems ● ● Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints (“N-k” style: should be ok if k connections destroyed) This simple model does not solve hydro ● It gets more complicated in the future ● Alternate tools: ● ● ● ● Real-time control ? Games ? Bilevel problems
  • 19. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 20. Let us see why it is more complicated than that ● This optimization problem is termed “Unit Commitment” (UC). ● There is a problem with hydro-power. ● Inflows are very stochastic ● Water comes for free (nearly), but it is limited. ==> more subtle optimization here At least this uncertainty must be tackled
  • 21. How to handle hydro ? ● ● For the moment, we have seen deterministic optimization problems. Solution 1: ● ● ● ● Just optimize, assuming that inflows = average inflow value given observed information. This is so-called “Model predictive control” (many variants, e.g. using a quantile of the inflow random process). Not satisfactory if high stochasticity Solution 2: optimize a policy, not decisions.
  • 22. Bellman's solution ● ● Let's work on time steps [1,....,365x6] (6 years) Define V(x,t) = expected cost between time t and T=365*6 if ● water stock 1 = x1, ● water stock 2 = x2, ● … ● Water stock d = xd ● V(x,T) = easy to compute ● Given V(x,t), V(x,t-1) computed by UC
  • 23. V(x,t) computed Bellman-style ● V(x,t+1) is known ● V(x,t) = optimal expected cost to go = minimum of: instantaneous cost Ct(a) + future cost V(x',t+1) where x'=future state when choosing action a It is stochastic! ==> expected value.
  • 24. So far so good ● ● ● But V(x,t) is not correctly defined. It also depends on random processes (load, inflows...) ==> V(random process,x,t) It also depends on PP status (on / off) ==> we need additional variables in x, not only the stock levels.
  • 25. More complete picture ● ● Let's work on time steps {1,....,365x6} (6 years) Define V(a, x,t) = expected cost between time t and T=365*6 if ● x = all state variables ● random processes = a ● V(a,x,T) = easy to compute ● Given V(a,x,t), V(a,x,t-1) computed by UC: V(a,x,t-1) = min cost(x,decision) + V(a,x',t) with x' = nextState(a,x,t,decision)
  • 26. So, Bellman-style: ● ● ● ● We have plenty of UC problems (one for each V(a,x,t) to be computed). Usually people rewrite the optimization problems as linear problems or quadratic problems, because otherwise solving is too slow. The real problem is usually simplified a lot so that it can be solved. The problem becomes more and more complicated.
  • 27. Standard tool. This version is probably run by electricity producers in your country. We will now see phenomena which are poorly handled by this algorithm.
  • 28. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 29. New decision variables ● Day-ahead adaptivity: some big companies (loads) accept “adaptivity” contracts: ● ● ● At 5pm, the producer says “tomorrow, I multiply prices by 10” (he can do so 22 days per year) The other days, prices are reduced With renewable energy, uncertainty increases; the principle above can be generalized: ● ● Small time scales, smaller consumers Other loads: heat networks, fridges, electric vehicles
  • 30. Summary: models ● ● ● ● Simple UC problem = optimizing deterministically. Advanced version = (spinning) reserves (this is also simplified). Hydro-power (& other stocks!): in Bellman's solution we must solve plenty of UC problems and take into accounts stocks; this involves computing V(a,x,t) backwards (traditionally Bellman, but you might use your favorite game algorithm). Investment problem on top of all this.
  • 31. Still too simple ● ● ● Ok, we solve plenty of UC for computing the hydro power or other stocks. Theoretically, solves the problem of uncertainty in inflows (but very expensive) Many other uncertainties are not negligible: ● ● ● PP directly connected to distribution networks: voltage issues introduce many constraints. Wind power uncertainty: day-ahead planning often wrong ==> real-time Long term: how to get the probability that PV units become cheaper than XXX in 2050 ?
  • 32. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 33. Real-time control, #1 Some power plants have a real-time control: Not enough power ==> implies more power output ● Too much power ==> implies less power output ==> “P” (proportional) control ● This is necessary. Power plants to not accept frequency change. So we must regulate frequencies in real-time.
  • 34. Real-time control #2 Some PPs have a real-time control #1: Not enough power ==> implies more power output ● Too much power ==> implies less power output ==> “P” (proportional) control ● Additional control for market constraints: If flow “Spain → France” too high, then increase power output in Spain (PI control).
  • 35. Real-time control Some PPs have a real-time control #1: Not enough power ==> implies more power output ● Too much power ==> implies less power output ==> “P” (proportional) control ● Additional control for market constraints: If flow “Spain → France” too high, then increase power output in Spain (PI control). Not very satisfactory. When day-ahead market based on wrong wind forecasts, the resources management is very bad: - by law, grid owners (sometimes) must buy wind power - day ahead market orders already decided - the grid owner must find people for buying excess electricity (or destruction!) ==> negative prices
  • 36. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 37. Games ? ● Looks like a game ● Uncertainties = weather, load, wind... ● Actions = switching on/off, which power output ● Many players; for us, one-player game ==> maximum social welfare policy (politicians and economist will have to find rules for the political/economical/ecological solution to be implemented...) ● Winning = low cost + low pollution
  • 38. ● ● ● ● Games ? Consequence Of Uncertainties = weather, load, wind... deregulation Looks like a game Actions = switching on/off, which power output Many players; for us, one-player game ==> maximum social welfare policy (politicians and economist will have to find rules for the political/economical/ecological solution to be implemented...) ● Winning = low cost + low pollution
  • 39. So the game model for us Just one player Who controls all the Pps, all the networks. He optimizes the social welfare. At each time step: - observes the state (inflows history, stock levels, PP status...) - makes decisions (switch on/off, produce power) - gets reward (economy / ecology)
  • 40. Outline ● ● Ilab Metis, working on power systems Principles of power system simulation ● Classical model ● Reserves constraint ● Recourse ● Network constraints ● This simple model does not solve hydro ● Future is (even) more complicated Alternate tools: ● Real-time control ? ● Games ? ● Bilevel problems ●
  • 41. Bilevel problems Simple version: I have K possible systems: ● Today's European grid ● The same + a big new HVDC connection ● The same + X MW of wind power ● ... Which one is best ? I spend T hours, each simulation of one of them needs (e.g.) one hour, how do I choose which system to simulate. LOOKS LIKE A NICE BANDIT PROBLEM
  • 42. Non-stationary bilevel problems I have K possible systems: ● Today's European grid ● The same + a big new HVDC connection ● The same + X MW of wind power ● ... In fact, I have to optimize the management of each system. If I optimize during simulations, options become better ==> non-stationary bandit problem.