Thermo-economic
optimization of a combined
heat and power plant in
Sweden
A case study at Lidköping power plant
Jarl Bergström and Conny Franzon
Supervisor
Cholada Kittipittayakorn Karlskrona, Sweden September 2020
MBA Thesis
DEPARTMENT OF INDUSTRIAL ECONOMICS www.bth.se/mba
This thesis is submitted to the Department of Industrial Economics at Blekinge Institute of Technology in partial fulfillment of the requirements for the Degree of Master of Science in Industrial Economics and Management. The thesis is awarded 15 ECTS credits.
The authors declare that they have completed the thesis work independently. All external sources are cited and listed under the References section. The thesis work has not been submitted in the same or similar form to any other institution(s) as part of another examination or degree.
Author information:
Jarl Bergström
jarl.bergstrom@nektab.se Conny Franzon
conny.franzon@gmail.com
Department of Industrial Economics Blekinge Institute of Technology SE-371 79 Karlskrona, Sweden Website: www.bth.se
Telephone: +46 455 38 50 00 Fax: +46 455 38 50 57
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Abstract
Energy production in power plants comes with both high costs and turnover whereas variations in the production strategy—that is, which boilers, coolers, or generators that should be running—have big impact on the economic result. This is especially true for a combined heat and power (CHP) plant where the production of district heating and electricity is linked, thus allowing for a higher flexibility in the production strategy and potential of increasing the revenue.
Previous research states that thermo-economic optimization can have a great impact on economic result of power plants, but every power plant is operating under a unique set of conditions depending on its location, operating market, load demand, construction, surrounding, and the like, and comparable studies on CHP plants in Sweden are very few. This study aims to fill this research gap by evaluating savings potential of a CHP plant in Lidköping, Sweden by utilizing thermo-economic optimization with the approach of combining actual historical data from the power plant with mass-flow equations and constraints to construct a mathematical MODEST model that is optimized by linear programming.
The result demonstrates a clear theoretical potential to improve earnings and the conclusion that the studied CHP would benefit by implementing optimization procedures or software to schedule production. The result was also comparable to previous research but varied over time, which highlights how unique conditions may impact the result.
Keywords: CHP, linear programming, MODEST, optimization, power plant
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Acknowledgments
The authors would like to thank Anders Ottosson, Anette Hansson, Lisa Lind, Dimitrios Angelis, and Kyriaki Anastasopoulou for valuable feedback while writing the thesis and a special thanks to Lidköping Energi, who generously has given us access to the power plant and its data, and thereby made this thesis possible.
Archangelsk, September 2020 Jarl Bergström & Conny Franzon
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Table of contents
1. Introduction ___________________________________________ 2
1.1. Problem formulation ___________________________________________________ 2 1.2. Proposed solution _____________________________________________________ 4 1.3. Delimitations _________________________________________________________ 5 1.4. Structure of the thesis __________________________________________________ 5
2. Literature review________________________________________ 6
2.1. Improvement potential of production scheduling for CHP plants ____________________ 6 2.2. Optimization methodology _______________________________________________ 8 2.3. Mathematical modeling and linear programming ________________________________ 9 2.4. Literature related to this study ___________________________________________ 10
3. Methodology __________________________________________ 11
3.1. Case study __________________________________________________________ 11 Selection of case firm/CHP ____________________________________________ 11 Ethics ___________________________________________________________ 11 3.2. Mathematical modeling and optimization ____________________________________ 12 Used design variables ________________________________________________ 13 Boundary constraints ________________________________________________ 14 Revenue function ___________________________________________________ 14 Conditions when executing the optimization _______________________________ 15 Verification _______________________________________________________ 15
4. Data collection ________________________________________ 16
Description of the Lidköping CHP _______________________________________ 16 Available production units and corresponding flow chart _______________________ 17 Limitations (boundary conditions) _______________________________________ 18 Associated production costs and revenues _________________________________ 19 Historical heat flow _________________________________________________ 21 Current guidelines for operation scheduling ________________________________ 22
5. Results and analysis _____________________________________ 23
5.1. Description of output from the optimization model ____________________________ 23 5.2. Evaluation of the period 2017-2019 ________________________________________ 26
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Why we must read the results with prudence ______________________________ 28 5.3. Performance during the seasons __________________________________________ 30 Evaluation of winter 2019 _____________________________________________ 30 Evaluation of spring/autumn 2019 _______________________________________ 36 Evaluation of summer 2019 ____________________________________________ 42 5.4. Varying spot price ____________________________________________________ 44 5.5. Verification of the result ________________________________________________ 48 Correctness of the model _____________________________________________ 48 Robustness of the model ______________________________________________ 52 5.6. Specific production guidelines ____________________________________________ 53 Which production unit should be running? _________________________________ 53 Is it profitable to resell waste heat? ______________________________________ 54 Should the DH forward temperature be raised/lowered during the day? ____________ 54 When shall turbines be run to produce electricity? ___________________________ 54 When shall cooling by DH network be active? ______________________________ 55 Should the production strategy change when a boiler is unavailable? _______________ 55 Are current “rules of thumb” appropriate? _________________________________ 57
6. Conclusions __________________________________________ 58
6.1. Summary and contribution of the study _____________________________________ 58 6.2. Discussion of the model ________________________________________________ 61 6.3. Discussion of the research method and shortcomings of the study _________________ 61 6.4. Discussion of consequences when implementing a software for real-time optimization ___ 62 6.5. Suggestions for further research __________________________________________ 62
7. References ___________________________________________ 63
8. Appendix (Process- and Instrumentation Diagrams) ______________ 68
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List of Tables
Table 1: Productions units and operational constraints _______________________________ 19 Table 2: Operational constraints for accumulator, cooling units, and turbine condensers _______ 19 Table 3: Fuel costs 2019 _____________________________________________________ 20 Table 4: Costs 2019 for starting a boiler and change load ______________________________ 20 Table 5: DH price 2019 ______________________________________________________ 21
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List of Figures
Figure 1: Fluctuating profitability of a CHP plant during 24 h operation (Król & Ocłoń, 2018). ____ 3 Figure 2: Results where the mathematical model is compared to historic data (Weber, Strobel, Kohne, Wolber, & Abele, 2018) _________________________________________________ 7 Figure 3: Example showing how profit of a CHP plant can differentiate when the conditions does (Chenghong, Da, Junbo, Xitian, & Qian, 2015) _______________________________________ 9 Figure 4 Modeling as a scientific method (Ivey, 1980). ________________________________ 12 Figure 5 Energy production Lidköping 2019, pareto per unit ___________________________ 17 Figure 6: Lidköping energy system ______________________________________________ 18 Figure 7: Production costs 2019 ________________________________________________ 20 Figure 8: Market divisions for electricity in Sweden __________________________________ 21 Figure 9: Nordpool spot prices [SEK/MWh] 2019 ‘Elområde 3’ _________________________ 21 Figure 10 Lidköping load demand 2019 ___________________________________________ 22 Figure 11 Example of used guideline when scheduling production at Lidköping ______________ 22 Figure 12: Common legend ___________________________________________________ 23 Figure 13: Load demand and spot price for week 1948 (week 48 in year 2019) ______________ 24 Figure 14: Optimization result during week 1948 ___________________________________ 24 Figure 15: Historic production during week 1948 ___________________________________ 25 Figure 16: Production of electricity and cooling during week 1948 _______________________ 25 Figure 17: Total profit during week 1948 _________________________________________ 26 Figure 18: Weekly revenue deviation of model vs historic production 2017–2019 ____________ 26 Figure 19: Weekly deviation in model vs actual revenue _______________________________ 27 Figure 20: Correlation between absolute and relative earnings potential ___________________ 27 Figure 21: Interval histogram of deviation in weekly revenue ___________________________ 28 Figure 22: Suggested (model) production for week 1944 ______________________________ 29 Figure 23: Actual production for week 1944 _______________________________________ 29 Figure 24: Electricity production during week 1944, model and actual production ____________ 29 Figure 25: Mis-performance of FGC; The production was first very low. Thereafter, it fluctuated and finally stopped. ____________________________________________________________ 29 Figure 26: The model varies the load from boiler 4 at a rate that an operator cannot achieve ____ 30 Figure 27: Heat demand and spot price during week 1904 _____________________________ 31 Figure 28: Production overview model during week 1904 _____________________________ 31 Figure 29: Actual production overview during week 1904 _____________________________ 31 Figure 30: Accumulated energy during week 1904 ___________________________________ 32 Figure 31: Generated electricity during week 1904 __________________________________ 32 Figure 32: Production units during week 1904 ______________________________________ 33 Figure 33: FGC during week 1904 ______________________________________________ 33 Figure 34: Economic effect during week 1904 ______________________________________ 34 Figure 35: Production units during week 1906 ______________________________________ 34 Figure 36: Accumulated energy during week 1906 ___________________________________ 35 Figure 37: Generated electricity during week 1906 __________________________________ 35 Figure 38: Usage of FGC during week 1906 _______________________________________ 35 Figure 39: Economic effect during week 1906 ______________________________________ 36 Figure 40: Revenue per production unit during week 1906 _____________________________ 36 Figure 41: Heat demand and electrical price during week 1914 __________________________ 37 Figure 42: Calculated and actual production outcome during week 1904 ___________________ 37 Figure 43: Generated electricity and dispatched energy during week 1914__________________ 38 Figure 44: Regeneration from flue gas condenser during week 1914. ______________________ 38 Figure 45: Economic results during week 1914 _____________________________________ 39 Figure 46: Heat demand and electrical price during week 1942 __________________________ 39
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Figure 47: Calculated and actual production outcome during week 1942 ___________________ 40 Figure 48: Generated electricity and dispatched energy during week 1942__________________ 40 Figure 49: Accumulator overview during week 1942 _________________________________ 41 Figure 50: Economic result during week 1942 ______________________________________ 41 Figure 51: Production units during week 1928 ______________________________________ 42 Figure 52: Generated electricity during week 1928 __________________________________ 43 Figure 53: Economic effect of week 1928 _________________________________________ 43 Figure 54 Linear demand curve to evaluate spot price ________________________________ 44 Figure 55 Legend for Figure 56 Figure 57 _________________________________________ 44 Figure 56: Result of boiler production with fixed spot price in the interval of 100-600 SEK/MWh (figure represents 600) ______________________________________________________ 45 Figure 57: Result of boiler production with fixed spot price in the interval of 700-1000 SEK/MWh (figure represents 700) ______________________________________________________ 45 Figure 58: Result of boiler production with fixed spot price in the interval of 100-1000 SEK/MW) 46 Figure 59: Result of electrical production (top row) and cooling (bottom row) with fixed spot price of 600/700 SEK/MWh _______________________________________________________ 46 Figure 60: Optimal TC1 cooling as function of heat demand for various spot prices (100-1000
SEK/MWh) _______________________________________________________________ 47 Figure 61: Cut-out from Figure 59 ______________________________________________ 47 Figure 62: Optimal production unit, week 1904, according to thesis’ model _________________ 48 Figure 63: Optimal production unit week 1904 according to Aurora’s model _______________ 49 Figure 64: Energy content in accumulator, week 1904, according to thesis’ model ____________ 50 Figure 65: Energy content in accumulator, week 1904, according to Aurora’s model __________ 50 Figure 66: Economic effect (revenue) from the thesis model for week 1904 ________________ 51 Figure 67: Economic effect (cost) from the Aurora model. The cost values from the result have been negated to simplify comparison ________________________________________________ 51 Figure 68: Load demand during week 1906, original and with white noise __________________ 52 Figure 69: Model result during week 1906, original and with white noise ___________________ 52 Figure 70: Accumulator energy content during week 1906, original and with white noise _______ 52 Figure 71: FGC production schedule as function of spot price and DH demand. Note however that the abrupt change of operating parameters in the 36–40 MWv interval that the model has calculated is not possible to follow in practice. _____________________________________________ 53 Figure 72: Production schedule for turbine condensers as function of spot price and DH demand.
Summary (left) and details (right). Yellow area indicates running at full capacity ______________ 54 Figure 73: Optimal production strategy for DH cooling. Yellow area indicates full capacity (10 MWc) _______________________________________________________________________ 55 Figure 74: Result of boiler production with fixed spot price in the interval of 100–600 SEK/MWh (figure represents 600) ______________________________________________________ 56 Figure 75: Result of boiler production with fixed spot price in the interval of 100–600 SEK/MWh (figure represents 600 SEK/MWh) when PU5 is unavailable ____________________________ 57 Figure 76: Result of boiler production with fixed spot price in the interval of 700-1000 SEK/MWh (figure represents 700 SEK/MWh) when PU5 is unavailable ____________________________ 57 Figure 77: Theoretical potential, average values 2017–2019 with weeks on horizontal axis ______ 58 Figure 78: Summary of resulting guidelines for production scheduling when all boilers are available, visualized as a decision tree ___________________________________________________ 60 Figure 79: P&I diagram ‘PC Filen’ steam system _____________________________________ 68 Figure 80: P&I diagram ‘PC Filen’ DH system _______________________________________ 69
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List of abbreviations
CHP Combined Heat and Power plant DCS Distributed Control System
A computerized control system for a process with typically many control loops, in which autonomous controllers are distributed.
DH District Heating FGC Flue gas condenser MATLAB Matrix Laboratory
Computer program developed by MathWorks Inc.
MODEST Model for optimization of dynamic energy system with time-dependent components and boundary conditions
MWc Megawatt cooling production MWe Megawatt electricity production MWv Megawatt heat production PU Production Unit
TC Turbine condenser
White noise A random/stochastic signal with equal intensity at different frequencies
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1. Introduction
Energy can be transformed at relatively simple facilities (e.g., diesel engines that merely produces electricity) or in more complex facilities such as CHP plants in which some sort of fuel, often waste, wood chips, bio energy, or fossil fuels are combusted to simultaneously produce electricity, heat, and eventually also steam (Heberle & Brüggemann, 2014). Simultaneous production of heat and electricity is an effective way of both reducing primary energy (fuel) and emissions of carbon dioxide (Cogeneration and district energy, 2009), and is therefore a prioritized method of energy production within the EU (On energy efficiency on the promotion of cogeneration, 2012).
Simultaneous production of heat and electricity is also more efficient compared to conventional power plants that do not have this flexibility (Socaciu, 2012; Abdollahi, Wang, Rinne, & Lahdelma, 2014; Król
& Ocłoń, 2018) but this flexibility however comes with a downside: because earnings depend on which production units are in production, the variations in earnings will be higher and more complex to optimize.
During the last 40-50 years, new techniques have been developed to optimize complex energy systems based on economic parameters. These methods, called thermo-economic optimization, uses con- ventional optimization methods to minimize production costs relative to revenues for power plants (Göğüş, 2005).
The outcome from thermo-economic optimization is then used in power plants for production scheduling (i.e., the decision about which production units should be in production). In production scheduling, the cost of production is the most important factor (Amelin, 2011), but consideration also needs to be taken for other costs as well (such as that start-ups require fuel) and that constraints (such that the change rate of load cannot be unhindered) are fulfilled.
1.1. Problem formulation
Scheduling the production of energy in general (i.e., conventional power plants) requires multiple constraints to be fulfilled, whereas CHP plants have some further unique constraints:
x production of heat and electricity cannot be planned independently because it is only possible to convert around 30% of fuel energy to electric power (Cho, Smith, & Mago, 2014) and the production of heat must at least be equivalent to the current heat demand.
Utilizing an accumulator for heat storage can be beneficial but it will also make the production scheduling more complex and difficult to handle (Fang & Lahdelma, 2016).
x the selling price of DH varies seasonally whereas the price of electricity (spot price) can vary hourly.
x the local heat demand of DH customers must always be fulfilled whereas the electricity demand can be fulfilled by other, regional, suppliers.
x the need for the various energy types (heat, steam, cooling, electricity) varies heterogeneously,
x fuel costs (raw material and handling) varies by the total load whereas the efficiency varies for different loads, and
x the energy demand may fluctuate severely (several hundred percent daily), depending on the local consumer base, the types of contracts, and so on.
These factors may lead the profitability to fluctuate and even be negative throughout a day, as illustrated in Figure 1 (Król & Ocłoń, 2018).
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Figure 1: Fluctuating profitability of a CHP plant during 24 h operation (Król & Ocłoń, 2018).
Production scheduling and thermo-optimization of CHP plants is thus an intriguing task and plant managers will in practice need either dedicated software based on plant-specific models or ‘rules of thumb’ to a accomplish this task (Abdollahi, Wang, Rinne, & Lahdelma, 2014).
Multiple studies (Mohsen, Nazar, & Sepasian, 2017; Weber, Strobel, Kohne, Wolber, & Abele, 2018;
Benam, Madani, Alavi, & Ehsan, 2015; Henning, 1997; Andersson, 2012; Larsson, Velut, Runvik, Razavi, & Nilsson, 2014; Vennström, 2014; Backlund, 2016) prove that earnings can be increased when production planning is applied by utilizing thermo-economic optimization compared to ‘rules of thumb’
strategies, but local conditions must be considered when comparing or applying these studies to different CHP plants. Swedish power plants have some unique conditions whereas the energy market is characterized by:
x Low usage of oil when producing energy (30% compared to the world average of 80%) (Naturskyddsföreningen, 2020). Sweden is also among the top (#3 in year 2017) countries for upholding a sustainable energy system (World Economic Forum, 2017) by producing energy from mainly nuclear (40%) and hydro (40%) power due to high taxation, the highest in EU (European Commission, 2020).
x High (90%) usage of renewable fuel (Ahmed & Olsson, 2011)
x Relatively high utilization of district heating to fulfill the demand of heat, 50% compared to European average of 10% whereas Iceland has the highest (90%) utilization in the world (Ahmed & Olsson, 2011).
x Fairly high temperature variations during seasons due to the golf stream (Chan, et al., 2016).
x High (232 kg per capita) amount of municipal waste is recycled/collected and used for energy recovery. European average is 135, whereas Norway has the highest of 378 kg per capita (Eurostat, 2020).
x Uppermost expensive price for petrol (diesel) in the World after Norway and Hong Kong (GlobalPetrolPrices, 2020).
The economic benefit of CHP systems depend on the specific conditions under different operation strategies (Wu & RZ, 2006;32) and power plants in the same market, country, or even city can be different from each other because factors like geographic, consumer base, contracts, energy demand, connecting power lines, number of production units, generators, and available fuel can vary (Cho, Smith,
& Mago, 2014; Fang & Lahdelma, 2016).
At a general level, a research gap exists by means of experimental validation or empirical research to validate existing theoretical concepts (Cho, Smith, & Mago, 2014) and even fewer studies have been made to evaluate improvement potential of thermo-economic optimization on CHP plants in Sweden,
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especially for in-depth analysis of “why” and “how” an improvement potential exists (Gribel, 2011;
Andersson, 2012; Larsson, Velut, Runvik, Razavi, & Nilsson, 2014; Vennström, 2014; Backlund, 2016).
If this knowledge gap on “why” and “how” an improvement potential exists could be filled, CHP plants would be more competitive which in turn would benefit the development and growth of district heating.
In such a scenario, carbon dioxide emissions would be reduced (Constantinescu, 2005), supporting an European Commission environmental goal1. This motivates the main research question to be formulated as:
To what extent can thermo-economic optimization have a positive economic impact on a CHP plant in Sweden?
If thermo-economic optimization proves a positive economic impact, these sub-questions have been deemed relevant to further analyze the case:
x Does the potential vary over time (e.g., at what time of the year is thermo-economic optimization and advanced production planning most profitable, is there a seasonal difference between summer, fall, winter, and spring and does the heat demand curve affect the potential)?
x Can thermo-economic optimization be utilized for managerial decisions and answer questions such as:
o Which production unit should be running?
o Is it profitable to resell waste heat?
o Should the DH forward temperature be raised/lowered during the day?
o When should turbines produce electricity?
o When should cooling by DH network be active?
o Should the production strategy change when a boiler is unavailable?
o Are current “rules of thumb” appropriate?
1.2. Proposed solution
Optimization of system design and developing an operational strategy is one of the key elements to improve efficiency and reduce costs (Cho, Smith, & Mago, 2014). To be able to analyze how decisions of production scheduling affect the economic earnings, the system or plant behavior must first be described in a mathematical language (i.e., build a mathematical model) (Abdollahi, Wang, Rinne, &
Lahdelma, 2014). The model must have equations that fully describes the plant design, handle all mandatory constraints, and be able to calculate earnings. In this study, such a model was constructed to mimic the selected case/plant.
After the model was constructed, it was then used to simulate various scheduling decisions and determine how these affect earnings. When the model was complete and verified2, optimization techniques was applied to calculate how the production should be scheduled to fulfill all constraints and maximize earnings. This resulting ‘optimized scheduling’ was then compared to actual production (by reviewing historic data) to prove an earnings potential and these ‘golden rules’ compiled into production guidelines, for the CHP plant in question.
For the mathematical modeling, a MODEST0F3 model was incorporated because this design can be used to calculate how energy demand should be covered at lowest cost and has flexibility concerning describing plant properties and constraints. Linear programming was used as optimization technique
1 https://ec.europa.eu/info/energy-climate-change-environment/overall-targets_en
2 Verification if utmost concern since results heavily depend on a correct mathematical model
3 Model for Optimization of Dynamic Energy System with Time dependent components and boundary conditions
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because it is fast and reliable and because the objective function and constraints could be expressed as linear equations. MATLAB was chosen as programming language because it allows for easy implementation of matrixes and has built-in functions for linear programming.
The study was performed in collaboration with Lidköping Energi, where empirical data was gathered and analyzed.
1.3. Delimitations
Because this study optimizes a production strategy based on available resources, margin costs are investigated. Wages and interest have, therefore, been excluded from the analysis.
Another delimitation is that load forecasting is not applied. Production scheduling in practice uses a weather-dependent model when forecasting future loads with the purpose to predict a future need and the schedule then describes how the demand can be utilized. In this study historical data has been used to at all be able to analyze the improvement potential.
A third limitation is that only one case CHP was selected because modeling and analysis is very time- consuming.
1.4. Structure of the thesis
Chapter Two includes a literature review of previous research that is related to this study (improvement potential, optimization methodology, and mathematical modeling).
In Chapter Three, we describe how the research was approached and the methodology of executing the optimization.
Chapter Four contains a description of the data that was collected and why.
In Chapter Five, we present and analyze the outcome of the optimization in both short and long-time frames and describe the identified production guidelines, improvement potential, and how the model was validated.
In Chapter Six, we describe the conclusions of this study, discuss its shortcomings, and give suggestions for further research.
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2. Literature review
Production of electricity and heat affects many areas that also are described well in the literature (Xia, Wang, Lou, Zhao, & Dai, 2016). In this study, to evaluate the saving potential of a Swedish CHP plant, the following subjects are of specific interest (Cho, Smith, & Mago, 2014):
x Improvement potential of CHP plants by utilizing optimization methods x Optimization methodology and mathematical modeling.
2.1. Improvement potential of production scheduling for CHP plants
Optimization of dynamic energy systems has been studied many times as a method to evaluate invest- ments, dimensioning or consequences regarding alternative business strategies (Henning, 1997;
Henning, 1998; Henning, Amiri, Holmgren, & Kristina, 2006). However, as stated in the introduction, only a few relevant studies are public regarding general saving potential for CHP plants in Sweden.
In a recent study from Lund’s Institute of Technology, the author used a commercial software to calculate the potential savings of a major CHP plant in Sweden (Andersson, 2012). The study was performed in two steps where first calculating the potential savings over a period in 2008 before the CHP plant was introduced to advanced production planning. Thereafter a second evaluation in 2010 was introduced to advanced production planning to evaluate the potential. The results showed that the CHP in theory would have been able to save 5.8 MSEK in 2008 and 13.76 MSEK in 2010. However, the actual outcome when the data was analyzed showed that the actual saving only reached 6.9 MSEK in 2010 which lead to the conclusion that only approximately 50% of the theoretical savings were reachable. Yet, the actual/relative saving, or cost reduction was 30%.
In another study from the Swedish research and knowledge organization Värmeforsk, the authors studied decision support for short-term production planning of district heating in Uppsala by using non- linear programming. Comparisons was made with and without optimization models and the results showed that modeling did reduce costly production peaks, delayed costly unit start-ups as well as improved the usage of accumulator (Larsson, Velut, Runvik, Razavi, & Nilsson, 2014). The expected cost reduction in this study, due to narrow constraints, were 5.4%.
In a third study from Umeå University, Lycksele CHP plant was evaluated by modeling and optimization. In this study, the author constructed a mathematical MILP (mixed-integer linear programming) model in which the CHP plant was modeled and then optimized (Vennström, 2014). The results from the optimization was then compared to the actual historical outcome to calculate and estimate the amount of cost reduction that could have been accomplished with better and more advanced planning. The results showed that the saving potential were fluctuating between 0–40% and that the load demand and electrical spot price had a strong correlation to the saving potential. With more production units running, the study showed that more error was made without the help of advanced production planning.
Similar results were found in a recent study from Luleå University of Technology in which the author evaluated the potential energy and financial saving opportunity through the implementation of advanced production planning for a CHP plant in Piteå (Backlund, 2016). In this study, historical and actual data was analyzed with the use of a commercial software and the result proved a potential saving of 10% on average. This was possible to achieve with better planning regarding temperature and heat flow adjustments, better usage of waste heat and reducing heat losses when meeting peak demands in a more efficient way. The implementation of the commercial software had a payback time of just 2 years. The author pointed out the difficulties of decision making because of the complexity of the plant as one of the main reasons to why the plant was not operating at its most optimal setting.
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Many studies on CHP plants outside of Sweden prove convincing positive results when advanced production planning is applied with the aid of optimization. However, as stated in Section 1.1 (Problem formulation), these studies are made on plants in other markets, in which different conditions are applied and can therefore experience different results from optimization and it can be difficult to make a direct comparison to studies in Sweden. However, the potential savings are still relevant to this study.
A doctoral dissertation from the University of Massachusetts–Amherst in 2014 (Gopalakrishnan, 2014) proved that through linear programming and thermo-economic practices, the operating efficiency on average could be improved by 6% and that the earning could be improved by 11% for a CHP system, which included gas and steam turbines, boilers, heat recovery steam generators, and interconnection with the centralized electric grid. The study also showed that CO2 emissions were reduced by 14% if the CHP plant was operated at its optimum.
One study showed (by using numerical optimization methods) increased earnings of 5-30% (Martelli, Capra, & Consonni, 2015), whereas another (Gebreegziabhera, o.a., 2014) suggested an improved average efficiency of nearly 10%. Two studies (Mohsen, Nazar, & Sepasian, 2017; Weber, Strobel, Kohne, Wolber, & Abele, 2018), showed that, by using mixed-integer nonlinear programming and a day-ahead schedule (by forecasting the electrical price and heat load), overall earnings could be improved by 5–10% compared to using “rules of thumb” strategies and that heat and electric generators should have been more active to correspond better to the demand or peaks in the electrical price. The model results are presented in Figure 2.
Figure 2: Results where the mathematical model is compared to historic data (Weber, Strobel, Kohne, Wolber, & Abele, 2018)
A study of a CHP plant near a large residential complex with 1,000 units in Tehran showed that the total cost and fuel consumption could be reduced by 4.5–30% depending on the circumstances (Benam, Madani, Alavi, & Ehsan, 2015).
Two recent studies conducted in Finland showed that the total efficiency increased and the total net costs were reduced when advanced production planning was applied (Fang & Lahdelma, 2016;
Abdollahi, Wang, Rinne, & Lahdelma, 2014).
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2.2. Optimization methodology
Optimization (also called mathematical programming) deals with maximization or minimization of a function, defined on a permissible amount. In thermo-economic optimization, the problem narrows into mainly two sub-problems: the Unit Commitment Problem and the Dispatch Problem (Amelin, 2011).
The optimization is performed in two steps: first, the available production units are defined, and the result are then used to allocate production between the operational units. Both problems are clearly described in the literature, with slightly more emphasis on the latter.
For CHP plants, the combination of energy production must be optimized which, for example, was analyzed by Gustafsson and B. G. (1991), whose model also took purchase of electricity with a year- long horizon into account, and Majic et al. (2013), who compared two linear programming models; one consists of a production unit and included the consumption of electricity and heat and the other model also included an accumulator. The benefits of including not only production units but also the distri- bution network and accumulator was further clarified by Larsson (2014). By modeling with an accumulator, it is possible to delay the start of additional production units and this also provides an opportunity to manage load variations and a possibility of production beforehand when the cost may be lower. This is partly true for the unit commitment problem, but especially in the dispatch problem.
Methodology for also considering the subsequent distribution has been developed by Rossing et al.
(2005), who used two contributing models for production and distribution.
Sheblé et al. (1994) provided an overview of the unit commitment problem, although without further analysis. The problem was analyzed more closely by Subir et al. (1998), which drew the conclusion that the problem could be appropriately handled by dynamic programming using limited selection. The latter authors also recommended that economic factors alone should not be the only target variable in the optimization; environmental considerations should also be taken.
For example, the dispatch problem was dealt with by Cho et al. (2009), who developed a general flow model for a thermal power plant that also included efficiency parameters.
There is a specific issue of how forecast uncertainties in, for example, the initial demand analysis (load forecast) can be handled. For this, Moradi et al. (2013) used particle swarm optimization, which iteratively evaluates candidate solutions and so on using quality parameters to evaluate the cost modeling of a thermal power plant. The method is effective at evaluating large datasets but does not guarantee an optimal solution. Another method is stochastic optimization with scenario trees, which was described by Dotzauer (2002).
Daily/weekly variations in fuel prices due to the market setting the prices can also significantly vary profits. An example of this is represented in Figure 3 (Chenghong, Da, Junbo, Xitian, & Qian, 2015), which indicates that pin point accuracy is needed to maximize earnings of a CHP plant, which is very difficult without mathematical optimization.
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Figure 3: Example showing how profit of a CHP plant can differentiate when the conditions does (Chenghong, Da, Junbo, Xitian, & Qian, 2015)
2.3. Mathematical modeling and linear programming
Literature is abundant for general optimization and partly also for applications when modeling existing technologies for CHP plants. For mathematical models, both deterministic and heuristic methods have been studied, with an emphasis on the former such as linear programming and Mixed-Integer Programming (where both continuous and integer variables were used in modeling). For example, non- linearity was treated by Ashok et al. (2003), who used a Newton-based algorithm for the evaluation of production scheduling.
Linear programming is an optimization technique for a system of linear (i.e., a straight line when it is graphed) constraints and a linear objective function. An objective function defines the quantity to be optimized, and the goal is to find variable values that maximize/minimize the objective function. The simplex algorithm is a commonly used method for linear programming. In this method described by Anderson et al. (2012), constraints (expressed as inequalities) defines a polygonal region where the solution typically resides at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions and variants of this procedure has been used. For example, Lahdelma et al. (Lahdelma & Hakonen, 2002) used a special structure in modeling and developed a specialized
“Power Simplex” algorithm for the evaluation. Their algorithm is now also used in commercial software.
Another described procedure is the MODEST modeling language, which is a method to apply con- ventional optimization methods on linear energy systems (Henning, 1997). MODEST is an acronym for model for optimization of dynamic energy system and utilizes linear programming to minimize capital and operational costs. MODEST was originally established as a method to evaluate investments and dimensioning but is also used for thermo-economic optimization and production scheduling.
There are additional linear methods that further improve the performance and/or stability of algorithms.
Thorin et al. (Thorin, Brand, & Weber, 2005) described Mixed-Integer Programming (MIP) together with Lagrange relaxation and pieced up an optimization interval in shorter periods for separate evaluation. Alternative ways to solve MIP are, for example, the Branch-and-Bound method described by Dotzauer (2002), and this method has the advantage that calculations can be interrupted when a sufficiently precise solution is considered to have been found or by implementing a rolling horizon that Bishi et al. (2017) suggested reducing the calculation requirement over a longer period of time.
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Existing literature has few shortcomings in general mathematical optimization applications (one example is ANN1F4 models that do not seem to be particularly well-researched for optimization) but have a few more for practical applications. Examples include optimization of energy consumption (which in the future is expected to be of even greater importance), optimization when energy is allowed to be stored in an accumulator (which increases the complexity rate), or management of situations with abnormally low/high market prices, which implies the possibility of performance improvement by avoiding optimization steps. Another example where the literature has shortcomings is sensitivity analyzes on how variances in input variables affects the result and practical implications unless accounting for that the production of power plants in practice is continuous. If such consideration is not taken, then the computations will result in that energy storage (water in reservoirs or heat in an accumulator) is exhausted at the end of the scheduling period, which is not desirable from an operational perspective.
2.4. Literature related to this study
Existing literature shows, for defined cases/CHPs, that thermo-economic optimization has a potential to improve earnings compared to using “rules of thumb” when scheduling the production of energy. The cases are, however, plant-specific and uses different methods when both implementing a mathematical model and executing the optimization. A research gap exists in that CHPs are unique and multiple implementation methods exists and that studies related to saving potential on CHP plants when implementing thermo-economic optimization on the Swedish market are very few. The studies that exist showed a positive potential to reduce production costs in the range of 0–40% but the saving potential fluctuate significantly and are related to many factors.
As for the modeling and optimization, literature is abundant with a variety of well-described implementation methodologies (linear programming is one), whereas which are applicable depends on the specific case (i.e., in this study, we deemed the MODEST method to be the most suitable method to use in this case). One general conclusion is, however, that two steps should be followed when executing the model: (1) unit commitment followed by dispatching and (2) that an accumulator is a very, if not the most, valuable tool for optimization.
The literature also reveals and that the results may fluctuate greatly when the conditions does, thus indicating that model robustness is of concern and should be included in the study.
4 Artificial Neural Networks
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3. Methodology
In this chapter we first describe and motivate the concept of case study and thereafter the mathematical modeling and optimization. For a discussion on shortcomings of the method, see Chapter 6.3 on page 61.
3.1. Case study
This thesis has been arranged as a case study because the research question imposes both a quantitative research and need of context-specific knowledge on real-life performance whereas a case study allows for in-depth analysis (Saunders, Lewis, & Thornhill, 2016). According to Yin (2009) and Starman (2013), a case study may also be the preferred method when:
x “how” or “why” questions are being posted, x the investigator has little control over events and
x the focus is on a current phenomenon within a real-life context.
A case study is thus deemed as a potent and suitable research method to answer the research question.
Selection of case firm/CHP
When selecting the case, multiple criterions were required (and desirable) to perform this study. Most important, the CHP plant should have (Henning, 1997):
x Multiple2F5 production units available because otherwise, the optimization potential would be low (Socaciu, 2012).
x Available and logged actual (historic) data for comparison with model output to be able to conduct an analysis comparable to previous and relative research (Gribel, 2011; Andersson, 2012; Larsson, Velut, Runvik, Razavi, & Nilsson, 2014; Vennström, 2014; Backlund, 2016).
x No current use of optimization software.
x A willingness of the firm to be evaluated.
x A reachable distance so that it is possible to visit.
The power plant in Lidköping, Sweden fulfills the mentioned criterions and was selected as case company.
Ethics
Case studies, especially single cases as this, may encounter ethical issues if the publication exposes a person to some risk of harm (McCurdy, 2011). For this thesis, a controversy may occur for the firm and its managers if the results later turn out to be suboptimal (somewhat dampened because the information has been officially published) and a further ethical consideration would be lack of informed consent.
To avoid eventual harm or lack of consent to participants, the paper has been submitted to the operations manager for approval prior to publication which can also reduce the risk of presenting wrong or misinterpreted results (Ghauri & Grönhaug, 2010).
5 Besides the criteria of having multiple production units, to further have a complex mix of fuel (oil, wood) and energy (heating, cooling) types would be the preferred choice.
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3.2. Mathematical modeling and optimization
To analyze the economic impact of production scheduling decisions, the plant must be described using mathematical language so optimization techniques can be applied. The activity to describe plant behavior is referred to as building a mathematical model, which can thereafter be used to predict or calculate impact. Modeling is a common scientific method to abstractly describe system behavior in a
“conceptual world” that can be used to resolve problems in the “real world” (Ivey, 1980). See Figure 4.
Figure 4 Modeling as a scientific method (Ivey, 1980).
An important concept in mathematical modeling is linearity. Models are linear when their basic algebraic, differential, or integral equations are such that the magnitude of their behavior is proportional to the input. The linear MODEST methodology was used to model and analyze data because its purpose is to calculate how energy demand should be met at the lowest possible cost and have the flexibility to describe plant properties. This model, developed by the Dag Henning at the Division of Energy Systems at Linköping’s Institute of Technology, uses linear programming in which the constraints and boundaries are set up to mimic an energy system (Henning, 1997). The objective function is normally set to satisfy energy demand at minimum cost but may also be aimed toward reducing CO2 emissions, storage, or working hours.
The collected data (see Chapter 0 on page 16) was thus assembled into a MODEST model whereas the research question was formulated as a cost function (i.e., written as follows):
[ ( )], . . € (1) where ( ) is the object function, is the requested result vector, and is the permissible solution.
Details about the setup and verification processes are described in the forthcoming sections.
For optimization, a multitude of general techniques exists such as continuous, (bound) constrained, derivative-free, discrete or linear programming (Neos guide, 2019). The latter has been extensively studied. For example, Yokoyama et al. demonstrated that MILP can be an effective technique when applied in a gas turbine CHP plant (Yokoyama, Matsumoto, & Ito, 1994) and a study on a cogeneration plant in Shanghai proved effectiveness when using mixed-integer nonlinear programming (Ren &
Weijun, 2008;28). Sakawa et al. formulated scheduling problems and demonstrated the effectiveness of mixed binary linear programming when applied to district heating plants problems (Sakawa, Kato, &
Ushiro, 2000) and Lozano et al. used a linear programing model to determine an optimal production strategy corresponding to the minimum variable cost (Lozano, Carvalho, & Serra, 2009).
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Due to proven effectiveness, and because model equations are linear, linear programming has been used for optimization. MATLAB was selected as programming language because it is a potent programming environment that allows for easy matrix manipulation and has built-in functions to utilize linear programming.
Used design variables
For each component in the system, individual constraints , ( ) ≤ ( ) ≤ , ( ) were set according to Table 1 and Table 2, for any time period, = 1,2,3, … ,8760.
Thereafter, a design vector containing all design variables for the forthcoming optimization was introduced as:
= [ ( ), ( ), ( ), … ( )]
The vector must fulfill the constraints
, ( )
, ( )≤ ( ) ≤ 1 3.2.1.1. Production units
Production unit constraints can be in the form of (Henning, 1997):
x gap constraints (whether a unit can either run at a defined load (e.g., 40–100%) or be turned off),
x startup and shutdown constraints/costs,
x load change constraints (i.e., rate of change), and x up and down time-dependent constraints.
Control variables were introduced for units with time-dependent constraints. For a unit , with design variable , these variables were introduced as follows:
x On/off variables
( ) = {0,1}
x Heat flow variables
0 ≤ ( ) ≤ 1 x Startup/shutdown variables
( ) = {0,1}
These variables were then set to satisfy the following constraints:
x Gap constraints
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− ( ) + , ( ) + 1 − , ( ) = 0 (2)
−( ( ) − ( )) ≤ 0 (3)
x Startup and shutdown constraints/costs
( ) − ( − 1) − ( ) = 0 (4)
x Load change constraints/costs
− ( ) + ( − 1) ≤ any load change limitations (5)
x Up and down time constraints
( ) ( − 1) − ∑ ( ) ≤ 0 (6)
= no. of periods that a unit must be on/off 3.2.1.2. Accumulator
For every period , the following constraints were defined:
∑ ( ( ) − ( )) ≤ − (7)
∑ (− ( ) + ( )) ≤ −( − ) (8)
Boundary constraints
Energy balances ∑ ( ) = ∑ ( ) were applied for each unit, formulated as:
= (9)
where the matrix sums all equality constraints that needs to be equal to . These equality constraints form the system and connects the nodes within the model. Because the CHP can generate more heat than the demand, the energy system has some additional inequality constraints, formulated as:
≤ (10)
where the matrix sums all inequality constraints that should be less than or equal to . These constraints can minimize the cost function in (1 but are not necessary to satisfy the equality constraints, which gives the model freedom to generate more heat or steam than is necessary to run the generators or load the accumulator, for example).
Revenue function
Thereafter, the revenues and costs were summarized as a cost vector , which depends on the fuel composition and includes efficiencies for the respective boilers. Finally, the objective function was set to minimize f(x):
15 ( ) = ∑ ∑ , , . . =
≤
≤
, ( )
, ( )≤ ( ) ≤ 1
(11)
This function was solved by the MATLAB MILP solver ‘intlinprog.’ However, because the boilers can also be individually shut off (e.g., be in service), these modes,6 denoted as m, must be individually considered (Amelin, 2011).
The model algorithm can, thus, be summarized as follows: For each mode m, apply a mixed-integer solver. If the constraints are fulfilled, then save the value of knxn into vector F. After all modes have been analyzed, the result (lowest cost) is defined as the minimum value in F.
Conditions when executing the optimization
When executing the model against actual load demand, the following terms were applied to mimic actual historic conditions:
1. If a production unit were not available (e.g., shut off, maintenance or failure) at the time of execution, the unit was set unavailable in the model as well.
2. At the start of every period, the accumulator was set to contain 400 MWh of stored energy. The total amount of energy in the accumulator was never allowed to exceed min/max constraints (see Section 4.1.3).
3. The sum of transferred energy during the actual time of execution was set as an equality constraint. As an example, if the energy in the accumulator was raised from 400 MWh to 600 MWh during a period, the same condition was applied to the model.
4. Received waste heat, load demand, and spot price were set to be identical in the model.
The optimization was executed in two steps:
A. The model was first run against actual heat demand and electrical spot price to calculate the most economic operation mode during the studied period.
The result was compared to actual (historical) scheduling to identify differences, which were then highlighted and further analyzed. The comparison provided information if the thermo- economic earnings could have been improved
B. The model was thereafter run against a set of increasing constraints to define thresholds (e.g., at what point it would be beneficial to start generators and the like).
The result was used to create a recommendation of production guidelines, also summarized as a decision tree
Verification
When developing a mathematical model that aims to mimic an actual process, validity and reliability are of utmost concern. The validity was verified by comparing the results with another model that was built by another team in commercial software and fed with the same historic data. The robustness of the model was verified by applying alternate load forecasts (i.e., historic data with white noise applied).
6 10 boilers have 210 = 1024 possible combinations
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4. Data collection
During the study, the following data was necessary (Henning, 1997) to construct the MODEST model and was collected:
x Information about all available production units and how these are connected, x limitations and boundary conditions (e.g., power, and allowable rate of change), x associated costs and revenues to form the objective function,
x historical heat flow data, and
x current guidelines for operational scheduling.
Details, such as reasons for gathering which data and how, are described in sections below.
Description of the Lidköping CHP
The energy system consists of two power plants that produce 180 MWv, 10 MWe, and 25 MWc in total, primarily by incinerating household waste, wood chips, and fat, as well as by utilizing excessive heat from a local industry. The heat can be stored in an accumulator, alternatively be cooled off to retain production of electricity. The CHP plant distributes electricity to the grid and DH in a proprietary system toward buildings and two industrial customers ‘Lantmännen Reppe’ and ‘Odal.’
Essentially, household and industrial waste and waste-classified wood chips (‘RT-flis’) are incinerated in the boilers. The power plant also has the possibility to burn fat and oil to handle peak demand during winter. The main plant ‘PC Filen’ consists of four solid fuel boilers and three fat and oil boilers. The backup power plant ‘PC Släggan’ has three oil boilers, totaling 75 MW.
The CHP has two turbines for electricity production, totaling 9.5 MW and two cooling stations totaling 25 MWc. Cooling heat off can be necessary to maintain electricity production when the heat demand is low.
The CHP utilizes several boilers (hereafter referred to as Pun, where n = 1–6, 8, 21–23) (see Figure 6 on page 18) and a steam and a hot water system. The hot water system can further be divided into an external and an internal circuit. PU1 and PU2 are connected to the internal hot water circuit. PU3 and PU4 are connected to the steam system and have a drain to the inner hot water circuit corresponding to about 15% of the total power. PU5, PU6, and PU8 are connected to the steam system. Boilers PU3–PU8 can be individually run and use different fuels. Two dump condensers (DC1 and DC2), two turbine condensers (TC1 and TC2) and ‘Reppe’ are connected to the steam system. DC1 is connected to the internal hot water circuit, which feeds ‘Odal’ and the outer hot water circuit. DC2, waste heat, flue gas condensation (RGK) and the condensate from TC1 and TC2 are all connected to the external hot water circuit. TC1 also has the possibility to cool off a maximum of 15 MW of heat surplus. Finally, the external hot water circuit feeds the DH network.
The CHP primarily run the boilers with the lowest cost (PU6, followed by PU5), according to Figure 5.
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Figure 5 Energy production Lidköping 2019, pareto per unit
Available production units and corresponding flow chart
Information about production units was collected by reviewing P&I3F7-Diagrams (see Figure 79 and Figure 80 on page 68) that illustrates piping and objects (e.g., valves, pumps and instruments) and was used to form mass balance equations and combined into a mass-flow diagram for the mathematical model.
7 Process and Instrumentation
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Figure 6: Lidköping energy system
Figure 6 illustrates the identified heat flows, and the vectors used in the mathematical model are also presented. Legend of the energy system:
Pun Production units
DCn Direct condensers
TCn Turbine condensers
Flue gas condenser Flue gas condenser connected to PU3-PU6 Internal hot water circuit Power plant internal district heating circuit External hot water circuit External district heating system
District heating Heat exchangers at private customer’s premises Odal Heat exchanger at industrial customer’s premises
Reppe Industrial steam customer
Heat flow variables used for the model PC Släggan Backup production facility with tree boilers
Model inputs are the boilers (PU1–PU8, PU21–PU23) and outputs the bottom line6F8 on Figure 6 with data according to Table 1. The demand is characterized as load on DH, Reppe and Odal, and any cooling or production of electricity is categorized as overproduction.
Limitations (boundary conditions)
This information was used to accurately mimic the CHP and to find production constraints (e.g., power and allowable rate of change) when modeling the CHP. For this, existing plant documentation (data sheets) was investigated, and informal conversations were held with the operators. The constraints have been summarized in Table 1 and Table 2.
8 ‘District heating’, ‘Cooling unit DH’, ‘Odal’, ‘Cooling unit TC1’, ‘Electric power grid’ and ‘Reppe’
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Table 1: Productions units and operational constraints
PU1 PU2 PU3 PU4 PU5 PU6 FGC PU8 PU21 PU22 PU23 Efficiency [%] 0,9 0,9 0,88 0,88 0,88 0,88 0,9 0,9 0,9 0,9
Max. power [MW] 15 15 14 14 20 21 B) 8 25 25 25
Min. power [MW] 6 6 12 12 15 15 3 10 10 10
Max. load change [MW/h] 0 0 2 2 2 2 0 0 0 0
Minimum run time [h] 1 1 5 5 5 5 8 1 1 1 1
Cooling time [h] 1 1 24 24 24 24 8 1 1 1 1
Further constraints C) C) A), C) A), C) C) C) C) C)
The following notes applies for Table 1:
A) PU3 and PU4 have a constant hot water drain equivalent to 20% of the boilers’ power, the rest is transferred to the steam system.
B) Maximum power is 17% of the combined power from PU3–PU6 and limited to 8 MW.
C) The total DH distribution from ‘PC Filen’ is limited to maximum 85 MWv, henceforward ‘PC Släggan’ must be started.
Table 2: Operational constraints for accumulator, cooling units, and turbine condensers
Storage Cooling Turbine
Acc. DH TC1 TC1 TC2
Max. power [MW] 10 15 4 3
Min. power [MW] 0 0 1 1
Max. load change [MW/h] 50 Max. energy [MWh] 700 Min. energy [MWh] 100
Minimum down time [h] 48 48
Alpha [%] 15 19
Associated production costs and revenues
The costs for the CHP plant were calculated by retrieving data from the company’s accounting system and consists of the following:
x fuel costs,
x the costs of boiler starting and load changes, and
x production costs for operations, maintenance, and consumables.
The power plant may incinerate 130 kilotons of waste and wood chips per year according to the environmental permission. Incineration of waste is preferred because both the cost is negative and because it also incurs reduced production costs. The available amount of waste is however confined.
4.1.4.1. Production costs
The fuel costs are summarized in Table 3.
20 Table 3: Fuel costs 2019 Fat Waste Wood Oil
Fuel cost [SEK/MWh] 590 -158 100 1,044
Note that the cost of waste is negative because the CHP is compensated for incinerating waste.
The costs for starting a boiler and/or change the load has been summarized in Table 4.
Table 4: Costs 2019 for starting a boiler and change load
PU1 PU2 PU3 PU4 PU5 PU6 PU8 PU21 PU22 PU23
Load change [SEK/MW] 10 10 50 50
Start [kSEK] 1 1 20 20 40 180 1 1 1 1
The production costs consist of maintenance costs for consumables (i.e., chemicals, sand, lime, and coal), wear and tear parts, flushing and blasting, waste handling costs, and explicit maintenance costs for each boiler. Solid fuel boilers are, due to waste management, more expensive in operation than fat and oil boilers. PU6 is also cheaper than the other solid fuel boilers as the waste does not need to be crushed before incineration. The result is visualized in Figure 7.
Figure 7: Production costs 2019
4.1.4.2. Revenues
The company revenues come from selling district heating, steam, and electricity whereas the pricing strategy is to differentiate DH price in three periods (winter,9 spring/autumn or summer5F10) depending on demand. Table 5 describes the price for 2019.
9 December to March
10 June to August 0,0 100,0 200,0 300,0 400,0 500,0
PU1 PU2 PU3 PU4 PU5 PU6 PU8 PU21 PU22 PU23
SEK/MWh
Production costs 2019
Consumables and wear and tear Flushing and blasting
Operation and maintenance waste management Operation and maintenance boiler
21 Table 5: DH price 2019 Winter Spring/Autumn Summer
Price [SEK/MWh] 431 326 106
During 2019, industrial customers (Reppe, Odal) paid 410 and 423 SEK/MWh, respectively.
The revenue from sales of electricity follows the spot price of electricity. In Sweden, the electricity market is divided in four location-based areas, illustrated in Figure 8. For Lidköping, area ‘SE3’ or ‘Elområde 3’ applies.
The spot price is officially available and was gathered from Nordpool, the result has been visualized in
Figure 9.
Figure 9: Nordpool spot prices [SEK/MWh] 2019 ‘Elområde 3’
Historical heat flow
By exporting historical data from the plant DCS, the following heat flows were given:
x Heat demand from steam and district heating consumers, x production unit 1–8 and 21–23,
x generator unit 1–2, x cooling unit 1–2,
x excessive heat from nearby industry, and x storage tank inlet and outlet.
Figure 8: Market divisions for electricity in Sweden
22 The results have been condensed into Figure 5 and Figure 10.
Figure 10 Lidköping load demand 2019
Current guidelines for operation scheduling
The company is currently using an Excel sheet for production plans one week ahead, whereas some real- time values are imported from an emission monitoring system. An example is presented in Figure 11.
Figure 11 Example of used guideline when scheduling production at Lidköping
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5. Results and analysis
In this chapter we present the produced result when executing the optimization. First, a longer timer period (2017–2019) was evaluated, and thereafter details of 2019 were studied, starting by evaluating performance during the seasons. Finally focus was put on how the result was affected when conditions (i.e., the spot price) varied.
5.1. Description of output from the optimization model
This introductory section describes how model output should be interpreted throughout the chapter. The legend in Figure 12 applies to all figures in this report that do not have individual legends.
Figure 12: Common legend
The optimization started with loading input data about load demand and spot price for a defined8F11 timeframe, exemplified in Figure 13.
11 Week 48 of 2019 have been used in the example.
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Figure 13: Load demand and spot price for week 1948 (week 48 in year 2019)
The model thereafter calculated an optimized production strategy (e.g., which boilers or condensers should have been in production to fulfill the load demand at the lowest cost). See Figure 14.
Figure 14: Optimization result during week 1948
The result was then compared to how the CHP had been operated in practice (actual production) during the same period. See Figure 15. In this example, the production values are fairly identical. One difference is that PU3 (circled area) was stopped a half day later compared to the proposed or optimized solution.
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Figure 15: Historic production during week 1948
The model calculated and compared the production of electricity and cooling. See Figure 16.
Figure 16: Production of electricity and cooling during week 1948
Finally, MATLAB visualized the profit for both the model and the actual historic production, whereas the difference indicates the sought-after earnings potential. In Figure 17, the actual profit (red dashed line) from the CHP plant was 2,816 kSEK whereas profit would have been 3,370 kSEK if the CHP had
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been run, as the model suggests (blue solid line) (i.e., an earnings potential of 554 kSEK for this week, despite only minor differences in production strategy).
Figure 17: Total profit during week 1948
5.2. Evaluation of the period 2017-2019
Figure 18 illustrates the combined result when the model was executed for the years 2017–2019 and how the model compared to actual production. The figure illustrates a clear absolute earnings potential for the firm, averaging about 357 kSEK per week, especially during winter when the load demand was peaking.
Figure 18: Weekly revenue deviation of model vs historic production 2017–2019
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The relative earnings potential, compared to actual (historic) values, as illustrated in Figure 19, varied 5-20 % during fall-winter-spring and was as high as 100 % during summer. That is, the absolute potential was higher when the load is high, but the relative potential was higher when the load was low.
Figure 19: Weekly deviation in model vs actual revenue
Even if the relative potential is higher during summer, it is still the period of the year where the absolute potential is at minimum due to the low thermo-economic turnover (as illustrated in Figure 10 on page 22). The relationship between relative and absolute improvement potential is presented in Figure 20.
Figure 20: Correlation between absolute and relative earnings potential
It can also be noted that the revenue during the individual weeks varied considerably with a standard deviation of 169 kSEK. See Figure 21.
