Modelling and optimization of polygeneration systems

Transcription

1 Modelling and opimizaion of polygeneraion sysems Riso Lahdelma Energy sysems for communiies Aalo Universiy Oakaari 4, ESPOO, Finland Phone:

2 Riso Lahdelma Professor a Aalo Universiy, Finland Energy for communiies Research ineress: mahemaical modelling,simulaion, opimizaion, mulicrieria decision suppor, energy sysems Career Helsinki U Tech, MSc, Sysems & Operaions Research Nokia, Sofware mehodology developmen Helsinki U Tech, PhD in Applied Mahemaics U Jyväskylä, associae professor in Mahs & SW engineering VTT (Tech Res C Finland), professor, Energy Markes U Turku, professor in Compuer Science Aalo, professor in Energy for Communiies, head of dep Dual affiliaion a Sysems Analysis Laboraory Energy Technology 2

3 Ouline of presenaion Cogeneraion Long-erm planning model Efficien reformulaion of model Efficien soluion algorihms Reformulaing non-convex models Experiences Seleced publicaions 3

4 Cogeneraion Cogeneraion means producion of wo or more energy producs ogeher in an inegraed process CHP = combined hea and power generaion Trigeneraion: disric heaing + cooling + power high pressure process hea + low pressure hea + power Technologies: backpressure urbines, combined seam&gas urbines, hea pumps Much more efficien han producing he producs separaely Energy efficiency increase 40% -> 90% Cos-efficien way o reduce CO 2 emissions Finland is one of he leading counries in cogeneraion 4

5 Generic backpressure plan for rigeneraion High pressure seam header h0 h v01 Seam urbine G p h1 h2 f1 h3 r = v01+h1-v12 Boiler Medium pressure seam f2 v12 q = v12+h2 Low pressure seam Feed waer Condenser 5

6 Cogeneraion planning Obecive is o maximize profi subec o producion consrains Hourly producion of he differen producs mus be planned ogeher Producion of hea & cooling mus mee he demand (naural monopoly) Power producion is planned o maximize he profi from sales o he spo marke (liberalized power marke) A long-erm model consiss of many hourly models in sequence E.g. an annual model consiss of 8760 hourly models Hourly forecass for demand and power price Various advanced analyses, e.g. risk analysis require solving many long-erm models based on differen scenarios Soluion mus be fas! 6

7 Long-erm planning model: Trigeneraion subec o Min uu C ( ) u xu Hx x u X u P Q R T (se of hours) uu (se of plans) where U is he se of unis (plans, conracs,...) x is he vecor of all decision variables x u is he vecor of decision variables for plan u x is he vecor of decision variables for hour C u (x u ) i he producion cos funcion for plan u X u represen plan-specific consrains H is a ransmission marix P, Q, R are he hourly demands for he hree commodiies 7

8 Decomposiion ino hourly models The long-erm model can be decomposed ino hourly models Min C ( ) uu u x u Hx P Q R u x X u uu The necessary decomposiion and co-ordinaion echniques depend on wha kind of dynamic consrains are presen Wihou dynamic consrains, decomposiion is rivial Tradiionally, he hourly model is a general LP/MILP model 8

9 Efficien model reformulaion The idea is o encode he operaing area of each plan as a convex combinaion of exreme characerisic poins ( c, p, q, r ) min subec o C u J u P u Q R u u c x J u J u J u x J u x 0 p q r x x 1 x Ju V 1 V 4 V=0.1V V V 4 V 2 V 3 9

10 Srucure of reformulaed rigeneraion model 10

11 Solving he reformulaed model The reformulaed model is an LP (or MILP) model wih a special srucure The special srucure allows he model o be solved exremely efficienly using ailored algorihms Power Simplex (PS) for CHP (wo-generaion) models Exended Power Simplex (EPS) for muli-sie CHP problems Three Commodiy Simplex (TCS) for rigeneraion problems On-line and off-line envelope consrucion algorihms (ECON, ECOFF) for CHP problems under he liberalized marke The specialized algorihms can be imes faser han generic commercial LP algorihms, such as CPLEX Speed is comparable o specialized nework algorihms 11

12 Speed of differen algorihms CHP planning agains power marke Tes models (A1-A6) 3 o 8 convex plans Yearly (8760 h) planning models wihou dynamic consrains Consrains: o , variables: o Soluion ime on a 2.2 GHz Penium 4 PC Speedup agains CPLEX: 400 o 2300 imes CPU (ms) From scrach Reusing previous resuls Model CPLEX PS ECON ECOFF CPLEX PS ECON ECOFF A A A A A A Average

13 Non-convex CHP model Can be formulaed as a Mixed Ineger Linear Programming (MILP) model Necessary when eiher (or boh) The cos funcion is non-convex P-Q he characerisic is non-convex Idea Pariion he obecive funcion ino convex pars Pariion he characerisic ino convex pars Use binary variables o choose in which area o operae A binary variable can only have value 0 or 1 R. Lahdelma

14 Sample non-convex cogeneraion model R. Lahdelma

15 Non-convex cogeneraion model Characerisic is pariioned ino 3 convex pars A is se of areas o which x belongs Define zero-one variables y1, y2, y3, and allow exacly one of hem o have value 1. y-variables selec which corner poins are allowed in convex combinaion U* is se of non-convex plans R. Lahdelma

16 Experiences Experimens wih oher plan models have showed ha he number of exreme poins ypically varies from 10 o 70 for rigeneraion plans from 5 o 20 for CHP plans This number of exreme poins is very reasonable The mehod works well in he case of 1, 2 or 3 commodiies In more complex models he combinaorial explosion may become a problem Similary, he mehod can handle efficienly only a fairly small number of 0/1 variables CHP/Polygeneraion modelling 16 and opimizaion

17 Seleced publicaions Lahdelma R., Hakonen H., An efficien linear programming algorihm for combined hea and power producion. European Journal of Operaional Research 148(1), Makkonen S., Lahdelma R., Non-convex power plan modelling in energy opimizaion. European Journal of Operaional Research 171(3), Makkonen S., Lahdelma R., Asell A.-M., Jokinen A., Muli-crieria decision suppor in he liberalized energy marke. Journal of Muli-Crieria Decision Analysis 12(1), Rong A., Figueira J., Lahdelma R., An efficien algorihm for bi-obecive combined hea and power producion planning under he emission rading scheme. Energy Conversion and Managemen 88, Rong A., Figueira J., Lahdelma R., A wo phase approach for he bi-obecive non-convex combined hea and power producion planning problem. European Journal of Operaional Research 245, Rong A., Hakonen H., Lahdelma R., An efficien linear model and opimizaion algorihm for muli-sie combined hea and power producion. European Journal of Operaional Research 168(2), Rong A., Hakonen H., Lahdelma R., A varian of he dynamic programming algorihm for uni commimen of combined hea and power sysems. European Journal of Operaional Research 190(3), Rong A., Hakonen H., Lahdelma R., A dynamic regrouping based sequenial dynamic programming algorihm for uni commimen of combined hea and power sysems. Energy Conversion and Managemen 50(4), Rong A., Lahdelma R., Grunow M., An improved uni decommimen algorihm for combined hea and power sysems. European Journal of Operaional Research 195(2), CHP/Polygeneraion modelling 17 and opimizaion

18 Seleced publicaions Rong A., Lahdelma R., Luh P., Lagrangian relaxaion based algorihm for rigeneraion planning wih sorages. European Journal of Operaional Research 188(1), Rong A., Lahdelma R., An efficien linear programming model and opimizaion algorihm for rigeneraion. Applied Energy 82(1), Rong A., Lahdelma R., An effecive heurisic for combined hea and power producion planning wih power ramp consrains. Applied Energy 84(3), Rong A., Lahdelma R., CO2 emissions rading planning in combined hea and power producion via muli-period sochasic opimizaion. European Journal of Operaional Research 176(3), Rong A., Lahdelma R., Efficien algorihms for combined hea and power producion planning under he deregulaed elecriciy marke. European Journal of Operaional Research 176(2), Rong A., Lahdelma R., An efficien envelope-based Branch and Bound algorihm for nonconvex combined hea and power producion planning. European Journal of Operaional Research 183(1), Wang H., Lahdelma R., Abdollahi E., Jiao W., Zhou Z., Modelling and opimizaion of he smar hybrid renewable energy for communiies (SHREC). Renewable Energy CHP/Polygeneraion modelling 18 and opimizaion