The Efficient Modelling of Steam Utility Systems

Transcription

1 The Efficient Modelling of Steam Utility Systems Jonathan Currie & David I Wilson Auckland University of Technology

2 Systems Of Interest 2 The Steam Utility System: Steam Boilers Back Pressure Turbines Steam Users Turbo Generators Deaerator & Demin Water Condensate Collection

3 Key Differences to a Chemical Process 3 On / Off? On / Off? On / Off??

4 Optimizing Utility Systems 4 Our research aim: Develop an efficient method of modelling utility systems for optimization However note for this work we are not focusing on the unit operation models (this is well researched, see our paper references) We are going to explore four avenues Simulator Model The model using by process simulators to predict system behaviour Optimizer Model A purpose built model used for optimization only Linear Model A purpose built linear model used for optimization only Global Model A purpose built nonlinear model for global optimization We are going to use two in-house developed tools together with MATLAB: JSteam A C++ library for high speed water, steam and hydrocarbon thermodynamics, with interfaces to Excel and MATLAB OPTI Toolbox A free MATLAB toolbox providing the glue between a suite of open source and academic optimization packages

5 Typical Optimization Formulations 5 Lots of sums of indices! Connect pipe j only if Formulation is overwhelming, but probably quite simple

6 Modelling Strategies Simulator Model (Sequential Modular) Free! Manual Conversion (Unroll all modules) Commercial 6 Equation Based Model (Explicit Mass & Energy Equations) Automatic Conversion (via MATLAB BARON Interface) Manual Conversion Linear Model (Explicit Equations) White-box Model (Algebraic Description) NLP Solver (IPOPT) MINLP Solver (BONMIN) MILP Solver (CBC) Global Solver (BARON) Local Solution (NLP) Local Solution (MINLP) Local Solution (MILP) Global Solution (NLP or MINLP)

7 Simulator Model 7 While the simulator model is good for simulation, as we will see it is not suited for optimization It is however the most intelligible model (which makes maintaining it much easier)

8 Equation Based Optimizer Model 8 The equation based model is currently manually generated from the simulator model This is very error-prone While it is now a text model (in MATLAB code), it is still generally readable Explicitly writing out the equations actually increases the problem size (in this work, 8x), but reduces the solving time 100x! This is based on two main reasons: A nonlinear root solver is no longer required to converge system recycles 1 st derivatives can be automatically generated

9 Global Optimizer Model 9 While this is arguably the most powerful model (it renders a global solution), it is certainly the most obtuse! The model is parsed by BARON, with derivatives, convexity identification and initial guesses all taken care of by the solver. Glad it is auto-generated? [x,fval] = baron(fun,a,rl,ru,lb,ub,nlcon,cl,cu,xtype)

10 Objective Function 10 Cost per MW of Fuel Gas [$] Cost per kwh of Electricity [$] Back Pressure Turbine On / Off Cost per tonne of Water [$] Hourly Running Cost [$] Boiler Fired Duty [MW] Turbo Generator Output [kw] Turbine Output [kw] Demineralized Water Mass Flow [tonne/hr] TG1 BPT1

11 Constraints 11 Linear: Mass Balances m 1 + m 2 m 3 = 0 (Convex, easy) Bilinear: Energy Balances h 1 m 1 + h 2 m 2 h 3 m 3 = 0 (Non-Convex, hard!) Nonlinear: Duty Based Users (among other operations) Q (h 1 h 2 ) m 1 = 0 (May be Convex or Non-Convex)

12 Tricks for Keeping Models Linear Linear Fit SSE:1.552e+04 True Cost Linear Fit Optimal Piecewise Linear Fit SSE:190.5 True Cost Piecewise Fit 12 Hourly Cost [$] Special Ordered Sets (SOS) Steam Production [Tonnes/hr] Steam Production [Tonnes/hr] An integer programming technique to approximate separable nonlinear functions using a linear piecewise formulation Can be formulated using an optimal strategy, such as nonlinear least squares Fixed Header Enthalpies Currently pressure levels are kept constant of the headers, however it is not too unrealistic to fix the temperature too Fixing the enthalpies reduces the number of bilinear energy balance equations, but it can break the overall energy balance Approximating models If we are performing operational optimization, we can fit local linear models, based on the current operating conditions. Be careful if the equipment gets switched off though during a run, the linear fit is often very unrealistic about 0 flow!

13 Summary of Results 13 Continuous Problem Results Mixed Integer Problem Results Global Optimum $2510/hr 25 ~$230/hr Mixed Integer 20 Continuous Improvement g p Local Optimum 5 $3345/hr 0 Sim Eq BARON MI Sim MI Eq MI BARON MILP 35s 0.34s M d l d S l 0.5s Solve 203s Times 3.3s 2.4s 0.04s Solve Times Same Optimization Problem Same Optimization Problem

14 Current & Future Work 14 Automatic generation of first and second derivatives As part of our OPTI Toolbox I have developed SymBuilder a simple modelling language for generating symbolic derivatives for optimization problems Speed ups of 10x realistic Investigating the solver SCIP Free (academic) global MINLP solver Currently developing a MATLAB interface Automatic generation of equation model from simulator model Bit more difficult, parsing Excel expression trees is not easy!

15 OPTI Toolbox: 15

16 JSteam Excel Add-In & JSteam Toolbox 16

17 Final Thoughts Utility systems cannot be lumped as Chemical Processes Many binary variables On/off flows Zero flows 17 Optimization Good tools (many free) Automated tools to develop necessary equations Global optimisers Take longer but give better solutions Don t forget our toolboxes & other free software

18 18 Malaysia Picture