Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices

TLDR: In this article, a generalized mode model for combined heat and power (CHP) plants is presented, which can account for different operating modes, e.g. fuel switching for boilers and supplementary firing for gas turbines, and transitional behavior.

About: This article is published in Energy.The article was published on 2013-06-01 and is currently open access. It has received 236 citations till now. The article focuses on the topics: Peaking power plant & Distributed generation.

Figures

Figure 3: A: Conceptual representation of a single-stage steam turbine. B: Willans line relationship for a single-stage steam turbine in mode “on”.

Figure 8: Flowsheet of the CHP plant

Table 1: Output data for each individual plant component, from which the feasible region is created. HP steam: 111 bar, 520◦C; MP steam: 21 bar, 320◦C; LP: 4.5 bar, 180◦C. Units: ton/hr for steam, MW for electricity.

Figure 5: State graph for a gas turbine with heat recovery steam generator (HRSG).

Table 6: Electricity price for the given week in $/MWh.

Table 5: Hourly constant steam (ton/hr) and electricity demand (MWh) for the different cases. The percentages represent the level of utilization depending on the maximum steam/electricity output of the CHP plant. In case A-45%-B1ST1off, boiler B1 and steam turbine ST1 are switched off permanently due to low capacity utilization.

Frequently asked questions

Q1. What have the authors contributed in "Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices" ?

In this paper, the authors describe a generalized mode model on a component basis that addresses the operational optimization of industrial CHP plants. The authors provide an industrial case study and study the impact of different scenarios for under-utilization. Furthermore, the authors emphasize the use of mathematically efficient logic constraints that allow solving the large-scale models fast. 

Q2. What future works have the authors mentioned in the paper "Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices" ?

In this paper, the authors have presented a generalized mode model on a component basis for the optimal scheduling of combined heat and power plants under time-sensitive electricity prices. The authors applied the model successfully to a real-world industrial CHP plant. The efficient deterministic formulation the authors reported can serve as a basis for the development of models based on the frameworks of stochastic programming ( Birge and Louveaux, 2011 [ 74 ] ) or robust optimization ( Ben-Tal et al., 2009 [ 75 ] ), which address uncertainty in electricity price data originating e. g. from intermittent renewable energy sources. 

Q3. Why is it possible to describe the feasible region only in the utility space?

Due to the implied mass balance, it is possible to describe the feasible region only in the utility space of extraction flow, exhaust flow and power. 

Q4. What is the effect of temporary shutdowns on the economic performance of the CHP plant?

Temporary shutdowns increase the operational profit since production is stopped when market conditions are not in favor to the production of surplus electricity. 

Q5. What is the logic constraint used to link the transitional variables for each plant component?

The logic constraint (15) is used to link the mode variables yhc,m for each plant component with the corresponding transitional variables zh c,m,m . Constraint (17) enforces that forbidden transitions cannot be active. 

Q6. Why is MILP the preferred method for practitioners?

As noted by Hedman et al. (2009) [50], nowadays, MILP is the method of choice for practitioners due to advances in solution algorithms and computing power. 

Q7. How much improvement can be observed from allowing shutdowns?

For cases with lower utilization (A, B, E), the impact of allowing shutdowns is higher (up to 20 % improvements compared to the base case) compared to the cases with higher utilization (C, D, F, G, H), where mostly 5% improvements can be observed. 

Q8. What is the common mode model used for CHP plants?

Mitra et al. (2012) [60] use a mode model to optimize the operation for continuous power-intensive processes under time-sensitive electricity prices in the following two ways: an aggregated mode model is used for air separation plants and individual plant components are modeled for cement plants (grinder). 

Q9. How long does it take to solve a case?

Despite the large size, all cases can be solved in less than 2 minutes (except case A with no restrictions, which takes about 9 minutes). 

Q10. What is the way to describe the feasible region of a steam turbine?

They describe the feasible region of steam turbines in the power output-heat output space (for a single pressure level) with linear inequalities based on operating data. 

Q11. What is the feasible region of operation for fuel fl?

the feasible region of operation for fuel fl can be subdivided into load ranges that the authors call sub-modes sm ∈ SMc,m (for mode m of component c).