Op%mal Scheduling of Combined Heat and Power (CHP) Plants 1 under Time- sensi%ve Electricity Prices

Transcription

1 Op%mal Scheduling of Combined Heat and Power (CHP) Plants 1 under Timesensi%ve Electricity Prices Summary In this case study, a CHP plant increases its profit by up to 20%, depending on the level of u8liza8on, when opera%onal planning accounts for variability in electricity prices. Sumit Mitra, Center for Advanced Process Decisionmaking, Carnegie Mellon University, PiKsburgh, PA Advisor: Prof. Ignacio E. Grossmann Joint work with Lige Sun, RWTH Aachen University, Germany 1. Combined heat and power genera%on plants are also called cogenera%on plants. 1

2 Underu%liza%on pressures companies to maintain global compe%%veness Capacity u8liza8on 1 of selected energyintensive industries 2 in the US (as % of nameplate capacity) 73.2% 83.7% 83.1% 78.3% 75.9% 85.3% 89.0% 68.6% 91.0% 78.8% 68.6% 51.0% Cements Paper (Mechanical Pulping) Industrial Gases Steel (Electric Arc Furnace) Alkalies and Chlorine Alumina and Aluminum U%liza%on (2006) U%liza%on (2010) While the cost of energy determines the profitability of these processes, recent developments, such as shale gas 3 and onshoring 4, give hope in revitaliza8on. 1. Federal Reserve, Industrial Produc%on and Capacity U%liza%on, March 2011; American Metal Market, 2007; CAPD analysis 2. Selected processes to: Paulus, M.; Borggrefe, F.,. The poten%al of demandside management in energyintensive industries for electricity markets in Germany, Applied Energy, 88: , Chang, J. (2010) Shale gas is the North American petrochemical industry's "Ace in the Hole", ICIS Chemical Business, March Sirkin, H.L.; Zinser, M; Hohner, D. (2011) Made in America, Again: Why Manufacturing Will Return to the U.S., BCG study. 2

3 Facing the challenge of variability, the power grid is in transi%on to the smart grid Genera8on/Supply Transmission, Distribu8on Customers/Demand Conven8onal Electricity (%medependent) Balance variability in supply & demand Electricity (%medependent) Residen8al (incl. electric cars) Commercial Renewables Load Informa%on Load Informa%on Industrial (powerintensive) improve: greenhouse gas emissions, reliability, energy security, economics Smart grid Integra8on of Renewables Microgrids 2 DemandSide Management (DSM) 1 (Distributed) Cogenera8on of electricity and heat Storage Demand Response Energy Efficiency 1. Systema%c u%lity and government ac%vi%es designed to change the amount and/or %ming of the customer s use of electricity for the collec%ve benefit of the society, the u%lity and its customers. Charles River Associates, 2005 Primer on DemandSide Management, with an emphasis on price responsive programs, CRA No. D06090, Technical report, The World Bank. 2. A microgrid refers to a local grid that can work autonomously from the central power grid. 3

4 Underu%liza%on can be a opportunity for %ghter interac%ons with the power grid 2 Use the flexibility of the CHP plant to adjust steam produc8on for variability in electricity price Fuel GT X B 1 B 3 ~ B2 HRSG ST1 Electricity prices vary on an hourly basis ST2 Power Grid Electricity Steam at different pressure levels Raw materials 1 Account for variability in electricity prices in produc8on planning 1 Products CHP plant Typically mul%ple boilers and turbines (steam, gas) Chemical plant The incen8ves given by u8li8es and grid operators to adjust power consump8on/ produc8on increase profitability, if the processes are able to cope with variability Mitra, S., I.E. Grossmann, J.M. Pinto and Nikhil Arora, "Op%mal Produc%on Planning under Timesensi%ve Electricity Prices for Con%nuous Powerintensive Processes, Computers & Chemical Engineering, 2012, 38, Samad, T.; Kiliccote, S., Smart Grid Technologies and Applica%ons for the Industrial Sector, Computers & Chemical Engineering, vol. in press,

5 A CHP plant has inherent flexibility in order to sa%sfy power and steam demand Fuel Air Fuel Water Exhaust stream (waste incinera8on plant) Water X GT B1 B3 ~ B2 Water HRSG Connec8on to power grid Exhaust Gas ST1 ST2 Power demand HP steam demand MP steam demand LP steam demand Condensate Given: Determine: Boilers (B1, B2, B3) Steam turbines (ST1, ST2) Gas turbines (GT) w/ HRSG Demand (HP, MP, LP, electricity) Hourly electricity prices e h Produc%on levels and internal flows Mode of opera%on for each equipment Sales of electricity Purchases of electricity for every hour for an en%re week How should the plant be operated in order to maximize the opera8ng profit 1, while sa8sfying power and steam demand of the chemical plant? 1. Opera%ng profit = Electricity sales (internal and external) + Steam sales Fuel costs Startup costs Electricity purchases 5

6 For each CHP plant component, the feasible region of opera%on needs to be modeled Example: Steam turbine HP steam Power M Maximum HP steam flow Exhaust steam Mr. J.S. Raworth writes 1 : Slope of Willans line : 1/n W int Maximum power output W Feasible region for turbines is expressed in terms of electricity and steam Willans line accounts for nonlineari%es in efficiency despite its linearity 2 The Willans line 3 can be applied to model the feasible region for singlestage steam turbines. How can mul8stage turbine be modeled? 1. Raworth, J.S., The genera%on of electrical energy for tramways, Engineering, vol. 63, p. 623, Mavroma%s, S.P.; Kokossis, A.C., Conceptual op%misa%on of u%lity networks and opera%onal varia%ons I. Targets and level op%misa%on, Chemical Engineering Science, vol. 53, pp , Willans, P.W., Economy Trials of a NonCondensing SteamEngine: Simple, Compound and Triple. (Including Tables and Plate at Back of Volume), Minutes of the Proceedings, vol. 93, pp ,

7 Complex plant components (e.g. mul%stage turbines) are modeled with a convex region M Maximum HP steam flow Slope of Willans line : 1/n 1st D C HP steam 1 st stage Extrac8on steam 2 nd stage Power Exhaust steam E A constant extrac%on flow zero extrac%on line B Slope of Willans line : 1/(n 1st +n 2nd ) W 1st, int W 2nd, int + W 1st, int Maximum power output W Highpressure steam is expanded in mul8ple stages to predefined pressure levels according to the requirements of the chemical plant. Flowrates for individual steam flows are degrees of freedom. The idea of the Willans line is extended for mul%stage steam turbines. The resul%ng diagram is known in industry as extrac8on diagram 1. Convex combina8on of extreme points represents the whole opera%ng region. 1. Jacobs, J.A.; Schneider, M., Cogenera%on Applica%on Considera %ons, GE Energy report. 7

8 A set of states is used to capture the transient behavior of CHP plant components Addi8onal model requirements State graph for CHP plant components The equipment cannot violate thermal stress limits during start- ups (size and unit specific). Startup procedure and the associated %me required depend on the cri8cal down8me crt (cold vs warm startup) During startups, precomputed trajectories might be available. Once the equipment is running/ shutdown, there is a minimum up8me/down8me Rateofchange constraints apply. State graph represents modes (nodes) for each hour and allowed transi8ons (arcs). Each logic restric%on is translated into a mathema%cal constraint using proposi8onal logic 1. Emphasis on efficient formula8on (w.r.t. problem size and solu%on %me) The presented modeling techniques are applied to all other plant components (mul8fuel boilers, gas turbines with HRSG incl. supplemental firing) analogously. 1. Raman, R.; Grossmann, I.E., Modeling and Computa%onal Tech niques for Logic Based Integer Programming, Computers & Chemical Engineering, vol. 18, p. 563,

9 The model has 70,009 constraints, 49,535 variables (8,722 binaries) and can be solved within 2 minutes 1 Objec8ve func8on: Maximize opera8ng profit over an en8re week (7*24 hours = 168 8me periods) Disjunc8on over opera8ng modes to describe feasible region of opera8on Logic constraints to model restric8ons of the state graph for each CHP plant component Ramping constraints Mass balances and demand constraints Addi8onal constraints (e.g. energy exchange with the grid, restric8ons on shutdowns) 1. Despite the large size, all cases can be solved in less than 2 minutes (except case A with no restric%ons, which takes about 9 minutes). The commercial solver CPLEX was employed with default setngs in GAMS on a Intel i72600 (3.40 GHz) machine with 8 GB RAM, using a termina%on criterion of 0% op%mality gap. 9

10 Our case study 1 shows significant profit improvements depending on u%liza%on Depending on case, 100% is equivalent to $500700k/week. Decreasing u8liza8on Capacity u8liza8on as percentage of maximum steam produc8on Constant produc8on: Steadystate opera8on at one opera8ng point for the en8re week. Less restric8ons (in terms of weekly component shutdowns) Variable produc8on: Produc8on profile is op8mized according to 8me- sensi8ve electricity prices Different restric8ons on allowed shutdowns per plant component Compare marginal value of shutdown with projected cost of wear and tear 1. Mitra, S.; Sun, L.; I.E. Grossmann, Op%mal Scheduling of Industrial Combined Heat and Power Plants under Timesensi%ve Electricity Prices, submiked to Energy,

11 Weekly profiles for a case with 61% u%liza%on 1 and 2 shutdowns allowed per component Electricity price profile Steam profiles for boilers and gas turbine Electricity profiles for steam and gas turbines HP steam input profiles for steam turbines MP, LP and cond. output profiles for steam turbines 1. Capacity u%liza%on as percentage of maximum steam produc%on. 11 1

12 At the interface of the chemical industry and the power grid, challenging mul%scale problems arise Overview of my PhD work 1 Data Stochas8c Uncertainty in electricity prices Demand uncertainty Stochas%c programming Determinis8c Focus of today s talk: Shortterm scheduling Combined heat and power genera%on Air separa%on, cement Integra8on of opera%onal and strategic (design, retrofit) decisionmaking Bilevel decomposi%on algorithm Mul%ple plants, supply chain Single plant Opera8onal Strategic (design) modeling Decisions solu8on method 1. In collabora%on with Praxair, collaborators: Jose M. Pinto, Nikhil Arora, Larry Megan. 12 1

13 Update: Strategic Problem We incorporated improvements in logic constraints that originate from the new opera%onal paper on combined heat and power (CHP) plants. postchp modifica%ons: 1. m M m M z h p,m,m = y h p,m p P, h H, m M z h p,m,m = y h 1 p,m p P, h H, m M replaced The reformulation by difference (12) (13) of them requir (removes zvariables for selftransi%ons) 2. minimum up and down%me replaced by %ghter version (see IBM paper by Rajan and Takri%, 2005) postchp2 modifica%ons: minimum stay for transi%onal modes also replaced by %ghter version 13 1

14 New Results for Strategic Problem Problem size Constraints Variables Binaries ESCAPE 191, ,293 18,826 postchp 93, ,261 14,794 postchp2 87, ,261 14,794 MIP OBJ CPUs gap allowed ESCAPE % postchp % postchp % postchp % postchp % (deviacons within tolerance; postchp has beger bound, therefore OBJ is higher for 2% case) RMIP OBJ CPUs ESCAPE e postchp e postchp e ESCAPE is the version of the code that we used to produce the results in the ESCAPE paper. 14 1