Energy Management for Heat Intensive Production Plants using Mixed Integer Optimization

Transcription

1 20 th European Symposium on Computer Aided Process Engineering ESCAPE20 S. Pierucci and G. Buzzi Ferraris (Editors) 2010 Elsevier B.V. All rights reserved. Energy Management for Heat Intensive Production Plants using Mixed Integer Optimization Steffen Sommer, a Jens Böhm, b Achim Kienle a,c a Otto-von-Guericke-University, Uni-Platz 2, Magdeburg, Germany, steffen.sommer@ovgu.de b Rothenseer Generatorenfertigung GmbH, August-Bebel-Damm 24-30, Magdeburg, Germany, jens.boehm@enercon.de c Max-Planck-Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, Magdeburg, Germany, achim.kienle@mpi-magdeburg.mpg.de Abstract An energy management system for heat intensive production plants is presented. The aim is to minimize energy costs with respect to additional constraints concerning workshop temperature and air ventilation. The system realizes a dynamic load balance, which prevents unneeded load peaks. The problem is solved by means of mixed integer optimization. Therefore, the production plant is modeled mathematically. The energy management system provides considerable savings in energy costs. Keywords: Energy management, production plant, energy costs, scheduling, mathematical modeling, mathematical optimization, MILP 1. Introduction In this work, an energy management system for heat intensive production plants is presented. Such a system reduces electrical energy costs. High energy costs result from unneeded load peaks and high energy consumption during the production process. A process is considered, where rotor blades for wind turbines are produced in a factory work room. In general terms, plastic parts are thermally treated. Heat is released during the production of the rotor blades. The aim is to minimize the energy costs of the above mentioned process with respect to constraints concerning the sequence of all operations, workshop temperature and air ventilation. The minimization of energy costs can be achieved by means of a dynamic load balance, which prevents unneeded load peaks. The appropriate turn-on and turn-off times of every load have to be found. This problem is solved by means of mathematical optimization. To solve the optimization problem, the production plant is modeled mathematically. A time-discrete model is built. It consists of sequence constraints and elimination criteria regarding the production process, temperature and ventilation constraints and a dynamic energy balance of the complete factory work hall. All in all, a mixed integer linear program (MILP) is obtained. The optimization result represents the above mentioned dynamic load balance with optimal turn-on and turn-off times. Thus, unnecessary load peaks are prevented, and the electrical energy consumption is reduced simultaneously. Energy costs are minimized often by means of heuristic strategies. For example in [1] an energy management system for cooling, heating and power technologies using demand forecasting with historical records as ambient temperature or ambient heat radiation is presented.

2 S. Sommer et al. In contrast to this, here, a rigorous approach is proposed based on mathematical optimization leading to a scheduling problem [2] with path and dynamic constraints arising from temperature and ventilation requirements. Further publications regarding energy cost minimization in industrial processes using energy management systems are [3-5]. The optimization is also based on mathematical optimization. The main focus is on mathematical modeling of specific processes without considering additional constraints. In [3], a developed industrial load management is applied to a flour mill. The optimal operating schedule that minimizes the operating cost in an energy intensive air separation process is found in [4]. An optimal energy management of the power plant in pulp and paper mills is introduced in [5]. The goal of this study is the fulfillment of the requirements in energy and steam with the minimum possible cost. The paper is organized as follows. In the next chapter, the considered heat intensive production plant is described and modeled mathematically. After this, the optimization results are presented and compared. A summary and an outlook are given in Chapter The Production Process 2.1. Process description The production of one rotor blade consists of four (k=1,,4) operations (production steps) with different durations. They are equal to 1h, 2h, 1h and 3h. Five rotor blades (b=1,,5) have to be manufactured within 48 hours. The completion of the five parts or jobs respectively and the execution of the operations are carried out sequentially. All operations are allocated to a single machine. During the production process, an internal temperature of C and a complete air exchange per hour on average are required. For these purposes, two (l=1,2) air ventilations and one heating are available. The production steps represent the main loads. Additional loads are the heating and the air ventilations for cooling and air change. All loads consume electrical energy Mathematical process model In this section, the production process including factory hall is modeled mathematically. Due to space restrictions, the detailed mathematical model can not be presented here. A brief summary is given below. A discrete-time formulation is used because of the path constraints which have to be satisfied over the whole time horizon. The production period of 48h is divided into 48 time intervals i=1,,n i =1,,48 with the duration of t = 1h. The loads are described by the following variables: 1 Production active IPP(b, k,i)= (1) 0 else 1 Heating active IH(i) = (2) 0 else 1 Air ventilation active IL ( l, i) = (3) 0 else. The production process can be classified as a flow shop scheduling problem. Appropriate sequence constraints and elimination criteria on IPP(b,k,i) (1) concerning

3 Energy Management for Heat Intensive Production Plants using the considered time-discrete case have to be implemented. Four sequence constraints are needed to mathematically describe the production flow. The first constraint determines the time interval where the first operation of the first job (k=1, b=1) starts. The second and the third constraint are necessary to guarantee that an operation k and a job b start only if the previous operation k-1 and the last operation of the previous job b-1 have been finished. The fourth constraint determines the time interval where the last operation of the last job starts. This time interval depends on the duration of the last operation. Elimination criteria are additional constraints which can reduce the solution set to improve the computational performance. For other scheduling problems like job shop problems for example, these conditions have to be adapted appropriately. Furthermore, the model consists of the temperature constraint K T(i) K (4) and the air exchange constraint. The number of internal air exchanges is n Ex 1 per hour on average. A dynamic energy balance, from which the internal temperature T(i) can be computed in every time interval, is implemented in discrete form: T ( i 1) T ( i) ρ V C + Air Hall P, Air = Q& P(i + 1)+Q& H(i + 1) Q& Air(i + 1) Q& T(i + 1)+Q & R(i + 1).(6) t It contains the elements heat power regarding the heating QH & (i) and the thermal operations of the production process QP & (i), cooling power concerning the ventilators QAir(i) &, heat transfer of the building QT & (i) and ambient heat radiation QR & (i). ρ Air, V Hall and C P,Air are the density of air, the volume of the factory building and the specific heat capacity of air. The objective function is equal to the energy costs J=E Tot ER+P max DC, (7) which depends on the total consumption of energy E Tot and the maximum power value P max during a specific time period. ER is the Energy rate or the price per kwh in /kwh, and DC is the demand charge in /kw. The following equations are needed: ETot = PTot(i) t, (8) P P Tot max i (i)= IPP(b,k,i)P el, P(k)+ IL(l,i)P el, Air(l)+ IH(i)P el, H, (9) b = max( PTot(i) ). i k l P Tot (i) is the total power of one time interval. It is equal to the sum of all load powers (9). Pel, P(k) is the electric power of operation k, Pel, Air(l) is the electric power of air ventilation l, and Pel, H is the electric power of the heating. The mathematical model of the heat intensive production process including optimality criterion (7) represents a mixed integer linear program (MILP). (5) (10)

4 S. Sommer et al. 3. Optimization Results The optimization problem from Chapter 2 is solved using GAMS/CPLEX [6,7]. To demonstrate the energy management system, a winter scenario is considered. In this context, a typical ambient temperature curve with -3 C Text(i) 2 C (11) is assumed. Some important process parameters are summarized in Table 1. The optimal production process is presented by the Gannt-Chart in Fig. 1. The time intervals are marked, where the loads are active. This solution ensures minimal energy costs subject to the mentioned constraints. The temperature curves are shown in Fig. 2. The computational characteristics are: Intel Core 2 Quad CPU, Q8400, 2.66GHz, # of binary/continuous variables: 2784/292, # of equations/constraints: 7167, CPU time: 4000s. The active production intervals are evenly distributed over the available production period of 48h. Thus, the heat release is used efficiently in the case of low ambient temperatures to hold the desired minimum internal temperature. The use of the heating is necessary. It is active in 33 of 48 time intervals. It can be inactive during the outstanding heat intensive production steps two and four. The air ventilations are only activated to provide the minimum air exchange of n Ex =1 (5). Therefore, 24 active intervals concerning air ventilation l=1 or 12 active intervals concerning air ventilation l=2 are necessary. The air ventilation is primarily in operation, if no production is activated. The reason is that the heat effect of the production process must not be compensated by cooling air ventilators. A concurrent activity of production and air ventilation takes only place in intervals where the outstanding heat intensive production steps two and four are active. Thus, the cooling influence on the internal temperature is minimized. The average internal temperature of T =294K is approximately equal to the desired minimum temperature of T min =291.15K. During the 48h winter scenario the electrical energy of E Tot =1027.3kWh (8) with a maximum power of P max =30.1kW (10) is consumed. The overall energy costs (7) are equal to The optimal solution is compared with a conventional solution (Fig. 3, CPU time 62s), where only the total energy consumption is minimized. That means the optimality criterion is J=E Tot. (12) During 48h, the total energy of E Tot =1019.1kWh (8) with a maximum power of P max =74.6kW (10) is consumed. From (7), energy costs of are computed. The energy management system provides savings in energy costs of Parameter Value Parameter Value ρ Air 1.184kg/m 3 V Hall 25000m 3 C P,Air 1.005KJ/kg/K Pel, P(k) ( )kW P el, H 4.1kW P Air(l) el, (18 36)kW ER 0.05 /kwh DC 10 /kw Table 1. Process parameters

5 Energy Management for Heat Intensive Production Plants using IH IL2 IL1 Loads IPP4 IPP3 IPP2 IPP Time interval Figure 1. Gannt-chart, winter scenario, optimal solution Finally, the power curves of the optimal production process and the conventional production process are compared (Fig. 4). In contrast to the conventional production process, no unneeded load peaks occur during the optimal process. 4. Conclusions The resume of this contribution is as follows. An energy management system for heat intensive production plants, which can be regarded as a new scheduling problem with energy costs as optimality criterion and additional constraints concerning the climatic conditions in the factory work hall, has been introduced. The energy management system provides considerable savings in electrical energy costs. In future work, we plan to derive simplified procedures from the rigorous optimization results because the optimization process may be quite time-consuming. Figure 2. Temperature curves, winter scenario, optimal solution

6 S. Sommer et al. IH IL2 IL1 Loads s IPP4 IPP3 IPP2 IPP Time interval Figure 3. Gannt-chart, winter scenario, conventional solution Figure 4. Power curves, winter scenario References [1] K. Mařik, Z. Schindler and P. Stluka, 2008, Decision support tools for advanced energy management, Energy, Vol. 33, [2] R. L. Graham et al., 1979, Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics 5, [3] S. Ashok and R. Banerjee, 2001, An Optimization Mode for Industrial Load Management, IEEE Transactions on Power Systems, Vol. 16, No. 4, [4] M. G. Ierapetritou et al., 2002, Cost Minimization in an Energy Intensive Plant Using Mathematical Programming Approaches, Ind. Chem. Res., Vol. 41, No. 21, [5] H.K. Sarimveis et al., 2003, Optimal energy management in pulp and paper mills, Energy Conversion and Management, Vol. 44, [6] R. Rosenthal, 2008, GAMS A User s Guide, GAMS Development Corporation Washington [7] GAMS Development Corporation Washington, 2008, GAMS The Solver Manuals