Abstract The distributed generation as well as the com-bined production of electrical energy and heat for domes-tic use in order to increase the energy efficiency becomesmore important and both technically and financially feasi-ble. However, feasibility and efficiency can be significantlyincreased by decoupling the production of heat or poweror the referring demand in order to operate the productionunits in the most efficient way. Thermal storage systemsconnected to combined heat and power units offer the op-portunity of such a decoupling of production and demand forheat in domestic or industrial use. In this article, based on ananalysis of different thermal storage technologies, a modelis introduced for optimal operation of thermal storage con-nected to combined heat and power units in terms of the gen-eration costs or contribution margin as extension of an en-ergy generation planning and trading optimization method.Moreover, the application, coordinated operation and partic-ipation in spot markets of such plant-storage-combinationsare evaluated.
Keywords Thermal energy storage · Distributed powergeneration · Virtual power plant · Power systemsimulation · Energy management · Cogeneration
Optimierung thermischer Speicher in dezentralenErzeugungssystemen
Zusammenfassung Dezentraler Erzeugung und kombi-nierter, effizienter Produktion von elektrischer Energie und
A. Schäfer (�) · F. Grote · Univ.-Prof. Dr.-Ing. A. MoserInstitut für Elektrische Anlagen und Energiewirtschaft,RWTH Aachen, Schinkelstraße 6, 52062 Aachen, Germanye-mail: [email protected]: www.iaew.rwth-aachen.de
Wärme kommt zukünftig eine steigende Bedeutung zu,verstärkt durch politische Förderung und erreichte Kos-teneffizienz von Kleinanlagen, beispielsweise im Haus-haltsbereich. Hierzu werden so genannte Kraft-Wärme-Kopplungsanlagen verwendet. Die technische Effizienz undfinanzielle Attraktivität dieser Anlagen lassen sich aller-dings weiter steigern, indem die notwendige Erzeugungvon Wärme und elektrischer Energie bzw. die korrespon-dierende Nachfrage voneinander entkoppelt werden, so dasshierdurch der optimale Betriebspunkt eingestellt werdenkann. Eine Möglichkeit einer solchen Entkopplung stellenWärmespeicher dar, welche im Verbund mit Kraft-Wärme-Kopplungsanlagen betrieben werden. In diesem Beitragwird, basierend auf einer Analyse unterschiedlicher Tech-nologien zur Speicherung von Wärme, ein Modell zur Ab-bildung und dem optimierten Betrieb von Wärmespeichernsowie die Integration in ein Verfahren der Stromerzeugungs-und Handelsplanung vorgestellt und in exemplarischen Un-tersuchungen bewertet.
1 Background and Motivation
Climate objectives, rising fuel prices and new technical de-velopments lead to—besides an increase in power gener-ation from renewables—a need for more efficient thermalpower generation. This can be offered by combined heatand power units (CHP), which not only produce electricitybut also available heat that originates in the combustion pro-cess. The combined process leads to high overall energy ef-ficiency, which through technical developments can amountup to 90% (International Energy Agency 2007). These de-velopments also make feasible the use of small scale CHPin distributed generation both technically and economically.
Since demand for electricity and thermal energy usuallydiverge throughout the day and as it is more cost-efficient to
operate a CHP power-led than heat-led, production and useof heat and power should be decoupled as already describedin ETG-Taskforce Dezentrale Energieversorgung (2007). Byapplying a power-led operation, the achievable contributionmargin consisting of operational costs as well as of feed-in premiums and opportunity costs for electricity can be in-creased. In this context a heat-led production refers to an op-eration of the CHP following the demand for heat, not con-sidering the occurring demand for electricity. A power-ledoperation can be achieved by using a thermal energy storage,shifting the thermal energy from production to demand pe-riod. Although the power-led mode allows an increased flex-ibility in the plant operation, most of the CHP units are con-trolled heat-led nowadays, mostly due to the original scopeof covering heat demand and lacking control devices. Thispaper describes the model developed to simulate a combinedpower generation and trading system including thermal stor-age systems. The objective is the investigation of the use ofthermal storage systems in order to minimize operating costsof CHP as well as to evaluate optimal marketing of thosesystems in spot markets.
In Sect. 2, the system considered is presented (2.1).Moreover, the different options and technologies for ther-mal storage systems are analyzed and a model for simulat-ing sensible heat storage systems is introduced (Sects. 2.2and 2.3). In the following Sect. 3, the optimization methodfor energy generation and trading planning is introduced aswell as the necessary extensions in order to allow the inclu-sion of the developed model of thermal storage in the opti-mization method. In Sect. 4 results of exemplary investiga-tions, applying the extended optimization model, are shown.Key aspects of the paper are summarized in Sect. 5.
2 System Model and Analysis
2.1 System Overview and Components
The system under consideration, depicted in Fig. 1, consistsof thermal and electrical loads as well as of spot and reservemarkets. The electrical load, spot and reserve markets haveto be met by the CHP and other power plants. Other powerplants include all types of thermal and hydro power plantsas well as renewables. The thermal demand is modeled asan arbitrary number of thermal nodes, each having a singlethermal load. To each thermal node any number of thermalstorage units and CHP can be connected, whilst each com-ponent can only be connected to one single node.
Therefore, the system not only allows modeling of elec-trical load coverage but also modeling of any number of dif-ferent heat consumers. Within the bounds of their operatingdiagram the CHP produce the thermal energy, which can bestored in and out of the thermal storage in each period tomatch thermal energy supply and demand.
2.2 Thermal Energy Storage
Heat, in thermodynamics, is thermal energy that transcendsa system border. Thermodynamically it is a flow quantity,meaning that by definition it cannot be stored. Only therelated energy in form of heat transmitted energy can bestored (Jany et al. 2008). Thermal energy storage systemsare differentiated by the physical storage principle as wellas by the time horizon of the storage (Fisch et al. 1992).
Temporal storage systems are sub-classified in short termstorage, also called buffer storage, and long term thermal
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Fig. 2 Thermal storageclassified by physical storageprinciple (Fisch et al. 1992)
storage, also called seasonal storage. Short term storage isused for time periods from an hour up to one week whilelong term storage is used for a time horizon from one weekup to one year (Von Helden 2008).
Referring to physical storage, four different principles areused. These are sensible, latent, sorptive and chemical stor-age as shown in Fig. 2. In the figure from left to right theapplication currently observed in reality decreases while thetheoretical specific heat capacity—the thermal energy thatcan be stored in relation to its mass—increases (Von Helden2008).
Chemical thermal storage uses the input resp. output en-ergy of chemical reactions. With the input of thermal en-ergy two reactants are separated while by combing themthermal energy is being released again. The required energyis highly dependent on the reactants applied (Von Helden2008). Sorptive thermal storage uses highly porous materi-als with a strong affinity to water molecules, e.g. silica gels.Due to its structure it possesses a high surface area, allowingit to absorb high quantities of water in relation to its mass.By adsorbing water heat is released, which has to be inducedinto the process again to separate the water from the surface(Adam et al. 2003; Moore and Hummel 1986).
Latent heat storage is based on the phase change of thestorage material. It uses the principle that in the transforma-tion from one state of matter to another—e.g. from solid toliquid—a large amount of energy is needed while the sensi-ble heat of the material only slightly changes. Reversing theprocess, the energy is released again (Oertel 2008). Typicalmaterials applied are hydrates and paraffins (Mehlig 2002).
Sensible heat storage systems store thermal energy by achange in the material’s temperature. Determinants for thechoice of a storage medium are the specific costs, its massand its specific heat storage capacity, which is a measure forthe amount of energy that can be stored per change of tem-perature and per mass (Bosnjakovic and Knoche 1998). Typ-ical liquid mediums are water and oil, solid ones are gravel,sand and concrete. In addition, mixed-forms exist as well,
Table 1 Volumetric heat capacity of different storage mediums at20°C (Fisch et al. 1992)
Medium Volumetric heat capacity [kJ/m3K]
Water 4,175
Gravel, sand 1,278–1,420
Concrete 1,672–2,074
Oil 1,360–1,620
e.g. gravel/water storage (Dincer and Rosen 2011). The spe-cific heat capacities for several of the typical storage mediaare shown in Table 1.
For seasonal heat storage large aboveground storage sys-tems, either filled with water or gravel/water-mix, are typi-cally used. They require a minimum size to reduce the spe-cific cost. Underground storage systems are also researchedto minimize building costs. These can either be natural orartificial water filled pits, rock formations or natural un-derground water storage with a high horizontal, but almostno vertical transmissivity, called aquifer (Fisch et al. 1992;Becker 2006).
The different types of thermal storage systems can be dis-tinguished considerably from each other by means of theusable temperature and temporal range as well as costs andmarket maturity (Oertel 2008).
Sensible thermal storage is the most developed and ap-plied way of thermal storage today. Especially in the shortterm as buffer storage, warm water storage systems are stan-dard for heating homes and facilities. The reasons mostly arethe high specific heat storage capacity and low costs as wellas wide availability of water. Also in short term, solid matterstorage is practicable for temperatures above 100°C. Theseare not yet ready-to-market, but in final testing phases (Oer-tel 2008). None of the different possibilities of undergroundseasonal thermal storage has so far been proven to be tech-nically or economically superior. Several pilot projects haveproven the feasibility of such storage techniques, but noarea-wide use has been established yet (Oertel 2008).
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Latent heat storage systems, also called phase changematerials (PCM), have the advantage of greater energy den-sities over sensible heat storage, leading to a significantlyreduced space required. A disadvantage in the technical im-plementation is the comparably little heat transfer betweenPCM and the transfer medium which leads to the needfor big contact areas. Some PCM have reached marketabil-ity, especially in building service engineering as low tem-perature buffer storage in walls. For a broader applicationthough, new materials with higher energy densities and abetter heat transfer are being researched (Oertel 2008).
Chemical and sorptive storage systems are seen to havegreat potential due to their high possible energy densities.Advantage of both technologies is nearly lossless storage ofenergy over time which is why current research focuses onusing it for seasonal thermal storage. High losses in the en-ergy transfer process are disadvantageous as well as too highreaction temperatures for common thermal storage. Currentresearch is focusing on finding new materials to decreasestorage costs and reaction temperatures (Oertel 2008).
2.3 Modeling of Thermal Energy Storage
By the analysis in Sect. 2.2 the different technologies forstoring thermal energy have been described. It could beshown that, although latent, sorptive and chemical storageoffer higher energy densities than sensible storage systemsdo, the former are still in research for the most part and notyet widely applied. Therefore, the derived model for thermalenergy storage aims at describing sensible thermal storagesystems, but can also easily be adapted to other technolo-gies if those become more relevant in the future.
The thermal energy that can be stored in a sensible ther-mal storage can be described according to (1) as the productof the volume V of the storage, density ρ and specific heatcapacity c of the material applied and the difference betweenthe temperature τ of the storage medium and the minimumreflux temperature τmin (Fisch et al. 1992).
Q = V · ρ · c · (τ − τmin) (1)
Sensible thermal storage systems are charged and dis-charged either by a heat transfer medium, which can be iden-tical to the storage medium, or through a heat exchanger.The resulting heat exchange processes within the storage arecomplex, depending on the temperature of the medium in acertain area of the storage, on the temperature of the enteringmedium as well as on time. Mathematically exact modelingis only possible by means of a complex, CPU-intensive finiteelements model which is, due to its time-consuming calcu-lations and the temporal discretization in the optimization,neither necessary nor practicable for the purposes of energygeneration and trading planning (Becker 2006). Therefore,a simplified model is derived that is still able to describe theenergy flows in the relevant time frame.
Fig. 3 Modeling of a 3-layer thermal storage
For modeling the thermal storage instead of a finite ele-ments model a model with an eligible number of layers ischosen. Leveling of the water occurs due to the decreas-ing specific density of water with increasing temperature.A similar approach has already been investigated and pro-posed in Becker (2006). This allows modeling of the energyflows in and out of the storage and the losses over time aswell as the flows within the storage. This becomes relevantfor modeling seasonal thermal storage systems due to theirlong charging and discharging time based on their geome-try (Dincer and Rosen 2011).
The temporal change in temperature in a layer m dependson the geometry of the storage and the temporal heat transferthrough convection and conduction. The main heat transportwithin the storage occurs by way of convection, while thetemporal energy losses result from conduction through thestorage shell as shown for a 3-layer-model in Fig. 3. In thismodel, n represents the number of layers considered with τ1
to τn as temperature corresponding to the layer. Temporalmass flow of the medium into and out of the storage is indi-cated by min and mout , τin and τout represent the medium’stemperature, whereas τenv is the temperature of the environ-ment. The losses through conduction in each layer m arerepresented by Qcond,loss,m and the heat transport from layerm to m + 1 by heat conduction and convection is indicatedby Qcond,m and Qconv,m respectively.
In order to optimize the storage as part of the entire sys-tem it has to be described mathematically. The storage isdescribed as a network-flow model as depicted in Fig. 4 be-low for a 3-layer storage model. A network-flow model isa special case of linear programming. It is a directed graph,consisting of arcs and nodes, in which each arc points fromone node to another (Iri 1969). Each node presents a supplyvalue, being either positive or negative. Each arc is restricted
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by a lower and an upper capacity bound, the minimum ca-pacity for each arc being zero (Ahuija et al. 1988).
The network-flow model of the thermal storage consistsof a source for each time period and a drain node as well as anode for each layer. Arcs connect source, drain and storagenodes within each time period as well as between the peri-ods. Losses reduce the transferable heat between the time in-tervals. The resulting network-flow model is shown in Fig. 4.The exchange capacities between source, drain and the lay-ers as well as losses which are modeled as a constant rate ofthe storage capacity for each time period are given as inputparameters into the model.
Therefore, for each node of the storage an equation ofcontinuity, consisting of all incoming and outgoing nodes,can be applied. Equation (2) shows the continuity equationexemplarily for the first layer in the first time interval. Itis obvious that no energy can be stored within a node, but
Fig. 4 3-Layer thermal storage as a network-flow model
either has to be transferred to the next layer or to the drainor to be shifted into the next time interval instead.
−xt,in + xt.layer+1 + xt1,layer = −xlosses (2)
3 Optimization Method
Based on the anteceding analysis, an existing optimizationmethod for energy generation and trading planning has beenextended in order to allow consideration and optimization ofthermal storage units.
Since planning of energy dispatch is a highly complexoptimization problem including not only nonlinear and in-teger decisions, such as minimum power output of powerplants, but also inter-temporal time dependencies, e.g. byconsidering storage systems or primary energy constraints, aclosed-loop formulation of the optimization problem is onlypossible by applying Mixed Integer Quadratic Programming(MIQP) or decomposition approaches (Bazaraa et al. 2006).
Application of MIQP to larger problems of energy gener-ation and trading planning usually leads to very long, hardlymanageable computing times and high demands regardingmain memory. In contrast, decomposition methods are prac-tically approved and offer acceptable computing times aswell as sufficient accuracy by dividing the actual main prob-lem into smaller sub-problems, which can be solved itera-tively by coordinating the individual solutions (Zhu 2009).In addition, all nonlinear characteristics and integer de-cisions of each of the different components and marketscan be considered in this approach. Hence, a decomposi-tion approach, the so called Lagrange relaxation, is appliedin the optimization method. Figure 5 gives an overviewof the extended method (Zhu 2009; Bazaraa et al. 2006;Verein Deutscher Ingenieure 2007; Lew Verteilnetz GmbH2010).
Fig. 5 Scheme of the extendedenergy generation and tradingoptimization method
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The objective of the method is the minimization of costsor maximization of the contribution margin of a given gen-eration portfolio under consideration of both electrical andthermal load constraints. In the existing method, the opti-mization of the dispatch of hydraulic generation units, suchas (pumped) storage plants, is possible as well as of ther-mal single process units and cogeneration units. Addition-ally participation in the spot market for electrical energyand the disposition of systems reserve at the respective mar-kets are possible to increase the units’ profit. This method isextended by the developed model for representing thermalstorage systems in this paper. Therefore now, in the extendedmodel, thermal storages can be added to each thermal nodeto cover thermal demand if heat production by CHP is notsufficient or to store superfluous thermal energy to cover alater demand, which has not been possible yet.
After reading the input data, the iterative Lagrange relax-ation is applied in the second stage of the method. The mainoptimization problem is divided into the mentioned sub-systems. Thermal and CHP units are optimized by dynamicprogramming, whereas linear programming is applied onhydraulic units. The participation in spot markets is solvedanalytically and the disposition in the reserve markets byquadratic programming (Verein Deutscher Ingenieure 2007;Deutscher Bundestag 2009). Thermal storage sub-problemis added as a separate component in this stage of the opti-mization, solved individually by network flow programmingas described in Sect. 2.
Compliance with the cross-system constraints of electri-cal and thermal load and system reserve are coordinated bythe Lagrange coordinators. Electric load on the one side andsystem reserve on the other side are coordinated by the La-grange variables λt and μt in each time interval. For thecoordination of thermal loads, the variables ϑj,t for eachtime interval t and each thermal node j are introduced. Af-ter each iteration the resulting thermal energy flows in eachperiod and thermal node are balanced against the thermalproduction from CHP, followed by an appropriate adjust-ment of the Lagrange-coordinator. Hence, ϑj,t is increasedif the output of thermal storage and CHP do not meet thethermal load in the referring node. ϑj,t is decreased, if theload and the demand of the storage do not exceed the pro-duction from CHP in node j and time interval t accordingly.For updating the different Lagrange coordinators, a sub gra-dient method is applied in order to gain convergence towardsthe optimum (Bazaraa et al. 2006).
After the first stage of the optimization method, it can-not be ensured in any case that all cross-system constraintsare met in each time interval, especially, if computationtime is not unlimited. Therefore, after reaching a feasiblesolution or the maximum number of predetermined itera-tion cycles, the optimization process continues by includ-ing the startup decisions from the separate optimization
into a closed-loop optimization, thus eliminating all inte-ger decisions and transforming the problem into a continu-ous quadratic problem. In the final optimization stage, theso called “hydrothermal energy dispatch”, the entire sys-tem with all markets and components is solved by quadraticprogramming. Thermal storage systems have been imple-mented in this stage as a network-flow problem as well,modeled according to Sect. 2.
Results of the optimization method are the hourly dis-patch of each unit as well as the total generation costs orcontribution margin, information regarding the level of thestorage and participation of the units in the different mar-kets. Moreover, information on consumed primary energyas well as emitted greenhouse gases can be obtained.
4 Exemplary Investigations
Exemplary investigations prove the functionality and showbasic results of the extended optimization model. First thefunctionality of the model is proved by applying it to a syn-thetic thermal load, covered by CHP with and without ther-mal storage connected (Plausibility Investigations). Then theadditional monetary value of a thermal storage is shown in arealistic application in a twin house (Investigation I). After-wards, an investigation of a small local heat system is pre-sented (Investigation II).
4.1 Plausibility Investigations
The first optimization problem is set up to demonstrate thefunctionality of the model. In order to show the influenceof a thermal storage, the operation of a small scale CHPwith a linear operating diagram between minimal and max-imal power output according to Table 2 was optimized withand without a thermal storage against a thermal load of11 kWh/h and an electric load of 6 kWh/h for the first 16hours of each day as well as 2 kWh/h thermal and 0 kWh/helectrical load for the last 8 hours of each day for the opti-mization period of one week. This fictive CHP is more flexi-ble than most real plants, especially household CHP usuallyhave a more restrictive operating diagram. The thermal stor-age considered represents a sensible storage with a volumeof 1,000 l and losses of approximately 12% per day. A totalamount of 58 kWh can be stored in the storage. Thus, thestorage is a typical one for an apartment flat.
Table 2 Specifications of CHP used in Investigation I
min output [kW] max output [kW]
Thermal 2 12
Electric 1 6
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Fig. 6 Resulting operatingschedule from Investigation I
Fig. 7 Energy level in the threelayers of a storage during thefirst 48 hours of loading
The resulting operating schedules for the two systems areshown in Fig. 6. Part A of the figure pictures the electricaland thermal production of the CHP without an additionalthermal storage. Part B includes the thermal storage. Due tothe CHP’s operating diagram, in case A 16 kWh of superflu-ous thermal energy is produced in the first 16 hours as wellas 8 kWh of superfluous electrical energy in the last 8 hoursof each day. With the use of a thermal storage in case B, thesurplus thermal energy from the first 16 hours is stored andshifted to the last 8. Having the thermal demand covered, theCHP is switched off, not producing surplus electrical energy
in these hours. Thus, the example proves the functionalityof the implemented model for thermal storage. It is obviousthat in the case without a thermal storage system a surplusof thermal energy is produced which might not be dissipatedin the case of larger CHP without additional cooling.
Figure 7 pictures the energy content of the same storagewith three layers in a synthetic loading process during thefirst 48 hours. It shows the time lag between the loadingof the first (1), middle (2) and last layer (3). This exam-ple shows how the layer model can be used to limit the en-ergy inflow to the storage and the amount of energy being
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Table 3 Specification of CHP used in Investigation II
min output [kW] max output [kW]
Thermal 4 8
Electric 1.3 3
available for extraction from the storage. The form of thesecurves is dependent on the chosen parameters limiting theflows between the layers.
This proves that the loading of a thermal storage can besimulated using the presented model, but is not consideredin the following investigations, because in reality small stor-ages can be loaded within the time frame of one hour. Hence,modeling of one layer in the case of decentralized thermalenergy storages is sufficient.
4.2 Investigation II
Secondly, a CHP is operated and optimized in order to coverthe demand of a large twin house. The CHP has a linearoperating diagram within the minimal and maximal valuesfor electric and thermal energy as specified in Table 3. At themost efficient operating point, the plant has a total efficiencyup to 90%, consisting of a thermal efficiency of 65% and anelectric efficiency of 25%.
The thermal demand of the twin house for one yearamounts to 31,227 kWh and the electric demand to12,232 kWh. For simulating a realistic demand behavior,the yearly demand is fitted according to standardized de-mand profiles (Verein Deutscher Ingenieure 2007). Besidesthe CHP, the house also has an additional heating unit witha maximal thermal power output of 20 kW to cover thermalpeak demand. Surplus electrical energy can be sold at thespot market with a CHP bonus of 0.0511€/kWh and one forobviated grid fees of 0.0018 €/kWh. The electrical energythat is produced and used for self-consumption is only com-pensated with the CHP bonus (Lew Verteilnetz GmbH 2010;Deutscher Bundestag 2009). Additional electrical energycan be obtained from the grid using a regular utility sup-ply contract with a price of 0.18 €/kWh. In order to ex-amine the influence of a thermal storage on operation andcosts, the CHP is simulated without and in combination witha hot water storage of 1,000 l and an hourly loss rate of0.5%/h of its capacity respectively. The year considered is2010. The simulation has been conducted in an hourly timescale.
The results of the simulation with and without hot waterstorage, focusing on occurring costs, are shown in Fig. 8. Itcan be observed that the use of the storage reduces the totalcosts by 7.2%, which equals 162 €/year in total value. Theinfluence of the storage is also visible in the different coststructure resulting from the optimization. While the produc-tion costs are higher considering the thermal storage also
Table 4 Full-load hours of CHP and additional heating unit in Inves-tigation II
No thermal storage Thermal storage included
CHP 4,531 4,832
Additional heating unit 101 0
having to cover its losses of 2540 kWh for the entire year,less electrical energy has to be obtained from the supply con-tract, while more energy can be fed into the grid, resultingin higher revenues from the spot market. By far the majorshare (approx. 95%) of the cost reduction results from theincreased use of the produced energy.
The influence of the storage on the operation cycles isalso visible in the amount of full-load hours of the CHP andthe heating unit as shown in Table 4. Applying the storage,the CHP shows a higher rate of utilization and efficientlyshifts surplus energy towards hours when demand cannot becovered independently and use is not efficient.
Hence, the heating unit is no longer necessary and morecosts can be saved as well. Therefore not only savings of7.2% of the yearly variable costs for covering thermal andelectrical load can be saved, but also installation costs of anadditional heating unit are omitted. These savings are likelyto exceed the annual investment costs of a thermal storage,making sensible heat storage feasible. It is to be noted thatthose are endogenous results of the model due to perfectforesight that might not be fully applicable to reality.
An exemplary schedule of the CHP and the storage is pic-tured in Fig. 9. It shows the thermal production of the CHPwith and the CHP without thermal storage for an exemplaryweek in December. While the CHP without storage closelyfollows the thermal demand, the CHP with storage is ableto operate more often at its maximum capacity, filling thestorage, and at its minimum capacity with the storage cov-ering the gap. This more binary operation mode leads to theconclusion that in case of the assumed nearly constant effi-ciency in the operating diagram the advantages of operatingthe CHP exceed the losses from a highly frequent switchingduring the operation. Moreover, the continuous operation ofthe CHP unit is additionally caused due to the comparablyhigh demand for heat in the winter.
4.3 Investigation III
A further investigation is carried out to examine the advan-tages of a local heat system represented by a large storageover single storage systems.
In order to do so, two model runs are set up. In both runsten CHP with a power output according to Table 3 and ef-ficiency rates ranging from 72 to 90% are used. For ther-mal and electrical demands for each CHP values from theprevious investigation are taken. In the first run each plant
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Fig. 8 Resulting costs with andwithout storage
Fig. 9 Thermal production ofCHP with and without storagein an exemplary week inDecember
has a sensible thermal storage of 1,000 l, in the second runall CHP share the total thermal load and the large storageof 10,000 l. The results from this simulation are shown inFig. 10. The application of one big storage as opposed tosingle storage results in savings of 4.9%. This is equal to1,107 €/year in total value. In this investigation, it is as-sumed that the thermal nodes are in a close geographicalarea so that losses due to heat transportation are negligible.These losses are likely to lead to a decrease of achievableearnings in case of long distance transportation between theheat consumers. However, the model proposed can also beapplied in order to model longer distances of heat transporta-tion by increasing the number of layers.
In conclusion, this investigation shows the savings result-ing from more efficient use of the power plants by substitut-ing less efficient ones. This example hints that local heat
systems, e.g. in residential areas, can help improving the ef-ficiency of distributed energy production.
5 Conclusion and Outlook
In this article, an integrated energy generation and tradingoptimization method has been presented which allows mod-eling of distributed generation systems including CHP andthermal energy storage.
An analysis of current developments of thermal en-ergy storage shows that whilst many new technological ap-proaches are currently researched, today’s standard ther-mal storage is still a hot water sensible storage. Based onthis analysis, a model for the optimization of thermal stor-age systems has been developed and presented, allowing
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Fig. 10 Resulting costs withsingle storage and local heat net
modeling of the flows from and towards the thermal stor-age.
For modeling a network-flow formulation of the thermalstorage over time has been chosen, contributing both thelosses occurring by heat exchange with the storage’s envi-ronment over time and the number of different layers ofthe storage that can occur especially in larger heat storagesystems. The model of the thermal energy storage has beenincluded in an existing power generation and trading pro-gram in order to evaluate the added value of thermal storagein systems with CHP and different demand nodes for ther-mal energy and participation in markets for electrical en-ergy.
First results of the extended model prove the function-ality of the method and show the positive influence on theoperation of a CHP as well as resulting monetary savings.An exemplary simulation provides annual savings of 7.2%by using the storage compared to the situation without thestorage and the possibility to forego an extra conventionalheating unit for covering the peak thermal demand. An-other investigation shows the savings resulting from theconnection of the thermal loads to a local heat net as op-posed to the single load covering. This results in lower costsof 4.9%.
Future investigations should include additional simula-tions with thermal and electric load data obtained from realhouseholds, not reverting to load profiles as well as the con-sideration of a more decreasing efficiency in partial load ofthe power plants which could lead to a higher frequency ofswitching during the operation of the CHP. Moreover, theextended simulation could be used to evaluate the businesscase for optimizing decentralized CHP with thermal storageagainst both spot and system reserve markets.
The thermal storage model itself could be furthermoredeveloped to simulate different storage technologies in casethey become more relevant in the future.
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