Optimizing the production and distribution system of bioenergy villages

Int. J. Production Economics 147 (2014) 62–72

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Optimizing the production and distribution system of bioenergy villages Harald Uhlemair, Ingo Karschin n, Jutta Geldermann Chair of Production and Logistics, Georg-August-Universit¨ at G¨ ottingen, Platz der G¨ ottinger Sieben 3, 37073 G¨ ottingen, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 December 2011 Accepted 6 October 2012 Available online 13 October 2012

In bioenergy villages, local bioenergy plants are installed to supply electricity, which is fed into the national grid, and to heat households through a local heat distribution network. In this paper, a linear mathematical model, which economically optimizes local bioenergy production and distribution systems based on a given set of system components, is presented. The model simultaneously determines the optimal capacity of the system, the objects that should be connected to the heating network and the course of the network. Additionally, a combined heat and power (CHP) biogas plant builds the production system. The problem is modeled as a mixed integer linear program (MILP) and is applied to a village with n potential heat customers. This model offers the possibility of economically assessing various scenarios concerning different planning situations and optimizing the capacity planning for the biogas plant and the course of the district heating network. & 2012 Elsevier B.V. All rights reserved.

Keywords: Bioenergy village Biogas plant District heating Network optimization Mixed integer program (MIP)

1. Introduction The increasing shortage of resources and climate change have led to a new energy policy in Germany during the last decade. A further development of renewable energy sources and higher energy efficiency, for example, by insulating older buildings, is expected to decrease the dependency of this country on fossil fuels and reduce the emissions of greenhouse gases (Hennicke and Bodach, 2010). To reach these goals, several different laws have been passed and include the Combined Heat and Power Act (BMU, 2002) and the Renewable Energy Act (BMU, 2000). These laws set monetary incentives to use renewable energy sources and install plants with combined heat and power generators (CHP), which should realize energy efficiencies of greater than 80% (Nowak and Arthkamp, 2010). Combined heat and power generation in local heating networks can be optimized by Mixed Integer Linear Programs (MILPs) to find the optimal operating strategy (Casisi et al., 2008). By taking into account the set-up of microturbines and the lay-out of the heating network, Casisi et al. (2008) applied their model to a real, city-center situation and demonstrated the wide scope of optimizing the operation of such systems. Biogas plants can incorporate the use of renewable energy sources, producing methane from biomass, and the combination of heat and power generation, providing the fuel for a CHP facility. However, a sufficient supply of biomass must be obtained, to run

n

Corresponding author. Tel.: þ49 551 39 9044; fax: þ49 551 39 9343. E-mail addresses: [email protected] (H. Uhlemair), [email protected] (I. Karschin), [email protected] (J. Geldermann). 0925-5273/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2012.10.003

the plant effectively. Additionally, for this type of decision problem, MILPs, which model biomass locations, capacities, the logistics of transportation, and various biofuel conversion technologies, can be formulated and implemented (Kim et al., 2011). The model from this study optimizes all decisions regarding different processing plants, biomass allocation, the final products, and their transport, and considers the objective function of the overall profit. Likewise, Gronalt and Rauch (2007) proposed an evaluation method for forest fuel supply networks by comparing centralized to local approaches. This group configured wood biomass supply networks for potential heating and energy plants, and considered the overall system cost of alternative configurations. With a primary energy potential of greater than 70,000 GWh per year, which is the energy demand of approximately 3.5 million average households, biogas is a potentially important renewable energy source in Germany, especially for decentralized, local energy concepts, because it is capable of providing baseload power and heat (Vogt, 2008). Nevertheless, biogas plants have recently become the subject of substantial criticism, and issues such as the competition for land use, rising leasing rates for arable land, mono-cropping and its negative consequences on the natural scenery and biodiversity have been discussed. To mitigate and solve some of these problems, new concepts for cultivating energy crops and higher energy efficiencies of technical facilities are needed. Some first steps may involve the use of combined heat and power technologies that are supplemented by locationspecific heat concepts and the use of crop rotations in the place of mono-cropping. In Germany, the first resource-efficient energy concept of this ¨ type was realized in the bioenergy village of Juhnde in 2004. Electricity and heat are produced from biogas in a combined heat

H. Uhlemair et al. / Int. J. Production Economics 147 (2014) 62–72

and power generator. Liquid manure and crops, which are cultivated from the agricultural land around the village, are the feedstock for the generation of biogas in an anaerobic digestion plant. The resulting electricity is then fed into the national electricity grid. To transport heat to villagers, a local hot water grid is installed (Ruppert, 2008).1 In this context, the following questions on production planning and logistics arise: What is the optimal course of the heating network, which potential heat customers should be connected to this network, and what capacity for the energy station should be installed? To answer these questions, an optimization model has been developed, that is composed of the CHP biogas plant as a production system and the local pipeline network as the distribution system that supplies the heat to customers. Building legislation, physical restrictions, and other political regulations are not taken into consideration. However, the costs of installation, maintenance and operation, and the expected revenues from selling heat to local customers and feeding electricity into the national grid are incorporated into the model. The model presented in this paper can be widely adjusted and allows for the representation of many different planning situations. It can be used to support decision-making during the strategic planning of an investment in local heating systems and offers the possibility to calculate an economic benchmark for any biogas plant, which is combined with a heating network, optimizing its course and the capacity of the plant. Furthermore, the model can compare various scenarios regarding, for example, the biomass availability or the willingness of households to be connected to the local heating grid. It thereby offers valuable information for potential investors and relevant stakeholders during the process of planning the installation of such a facility. The next section presents the general set-up of a district heating system based on the biomass. In Section 3, the cost for biomass allocation is estimated. In Sections 4 and 5, the energy production and distribution systems are explained and economically assessed. In Sections 6 and 7, the optimization model is shown and applied to a village with n ¼44 potential heat customers. In Section 8, various conclusions are drawn and further steps for improving the model are discussed. The last section summarizes the results.

2. District heating based on the biomass Biogas plants with combined heat and power generators offer the possibility of installing decentralized, district heating systems. Biomass is used as a renewable energy source in a highly effective manner. The chemical energy that is obtained from biomass is converted into heat and electricity, which is fed into the national grid. Furthermore, the thermal energy provides a local and independent heating source for the connected households. This section presents the general set-up of a district heating system that is based on a CHP biogas plant (see Fig. 1). Most often, local farmers initiate these heating systems, which reduces the transportation costs of the biomass. These farmers provide the feedstock for the biogas plant by growing energy crops or other types of biomass on their arable land. It was estimated that the average distance between a production site and a biogas plant was 20 km (FNR, 2007). Biomass is fed into a fermenter, which produces methane through an anaerobic 1 It should be noted that due to the regional aspect of the topic, much literature on the energy use of biomass in Germany is in German language and is issued by ministries and expert agencies such as the BMELV (Federal Ministry of Food, Agriculture and Consumer Protection) or FNR (Agency for Renewable Resources).

63

central heating plant

wood chips, straw, etc.

local farmers

digestion residues used as fertilizers biomass

households electricity

heat

biogas plant

biogas

CHP station

heat

national grid

electricity

Fig. 1. General set-up of a district heating system based on a biogas plant with a CHP generator based on Fischer (2003).

fermentation process. Farmers can then use the residues from this process as fertilizers after fulfilling certain requirements of the German fertilizer directive (BMELV, 2008). A combustion engine is fueled by biogas that consists of approximately 50% methane and produces electricity and heat (FNR, 2010). This electricity is not used locally but is fed into the national grid. A portion of the thermal energy (between 20% and 30%) is often used to regulate the temperature of the fermentation process if the CHP station is installed on the site of the biogas plant (FNR, 2010). However, most of the heat can be sold to local households, which are connected through a heating network. To have a backup system and for extremely cold days during the winter, a central heating plant can be installed. The concept of using thermal energy from the combustion process for heating purposes should ensure independence from large, energy-producing companies and the volatile prices of fossil fuels. However, deciding which households to connect to the heating network and what plant capacity to install is complex. The costs of biomass allocation, investments into the production system and heating network, operating costs of the plants, and the revenues and allowances for selling electricity and heat must be considered. Network flow models, which minimize the operating costs of existing micro-CHP systems, have been proposed by Cho et al. (2009); however, this group focused on operational planning. Gustafsson and Karlsson (1991) used a linear programming method to optimize the combination of electricity production, purchase and heat production in a district heating system while considering the lowest possible operating cost per year. Lahdelma and Hakonen (2003) presented an optimized linear programming algorithm that was based on an hourly load forecast to determine the cost-efficient operation of a CHP-system. They also focused on the day-to-day planning and operation of the facility and the mathematical details of the algorithm for solving the model. However, none of these models have been used for location planning or with the planning of a biogas production system.

3. Costs of biomass allocation To estimate the economic consequences of installing a biogas plant and a heating network, the net present value method is widely used in investment decisions. The net present value (NPV) of an investment is the present value of all present and future cash flows that are generated within a certain planning horizon t¼ 1,y,T. A NPV Z 0 indicates that the investment is at least as profitable as an investment that returns the discount rate i. Therefore, the investment can be prioritized and recommended. For a NPV o0, the investment should be rejected, at least from an economic point of view. To calculate the NPV of various plants with different capacities, the costs of operating the plant must be considered. This analysis includes an estimation of the biomass costs as a function of the installed capacity. The functions and variables that were utilized are shown in Table 1. To minimize the costs of biomass delivery, storage, and transportation, a linear programming method can be used

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The average weighted cost has been calculated by assuming that the distance from field to farm is 3 km. Thus, the overall production costs BCkm per ton of substrate for the selected bioenergy village can be written as a function of the field-plant distance xkm, in kilometer, as the following equation:

Table 1 Declaration of the used functions and variables. Functions and variables

Description

AC kW ½h Ala ½h BC km ½h=t

Annual biomass costs depending on the plant capacity Annual allowances depending on the plant capacity Biomass costs per ton depending on the field-plant distance Biomass costs per ton depending on the plant capacity Initial investment for a biogas plant with given capacity k Annual operating costs depending on the plant capacity Variable representing the distance between field and plant Variable representing the installed capacity of the plant

BC kW ½h=t I0k ½h OC a ½h xkm xkW

Table 2 ¨ Substrate costs for different energy crops [h=t] fresh mass (Dohler, 2006). Energy crop

Harvest yield (t/ha)

Substrate costs ðh=tÞ

Maize Winter wheat Winter triticale Winter rye

52.8 44 44 44

37.94 36.01 35.72 37.71

Weighted average cost

36.89

(Cundiff et al., 1997). Peart and Brook (1992) presented a simulation model to evaluate the harvesting and handling of energy crops and residues that were transported from farms and forests to a conversion plant on a year-round basis. However, these approaches only consider the biomass supply chain for the biofuel production system and do not include the local heat network in the model. 3.1. Overall costs of energy crops Generally, the costs of energy crops depend substantially on site-related factors of the arable land in which the plants are grown. These factors include the size of the field, its distance from the farm, and the harvest yield [t/ha] of the fresh mass. Furthermore, several other adjustable parameters are integrated into the calculations such as the wage rate (here: wage ¼ 15 h=h) and the lease (here: lease ¼ 163 h=ha). According to a previous study, when using these parameter settings and different site-related factors, the costs for production and logistics of the energy crops vary from 33 h=t to 51 h=t (KTBL, 2008). When a field size of 5 ha is assumed, the average distance to a farm is approximately 3 km ¨ ¨ (Dohler, 2006). Based on the previous works (Dohler, 2006; Becker, 2009; KTBL, 2008) and with the harvest yields that are given in Table 2, the costs for the different energy crops (i.e., whole crop silage) are calculated. Thus, the weighted average costs for energy crops with the above-mentioned assumptions are 36:89 h =t, and the variable costs that are included in this ¨ calculation amount to 0:24 h=km according to Dohler (2006). The substrate costs [h=t] of the energy crops must be weighted with the harvest yield [t/ha] because of crop rotation, which implies, that the four different crops are all cultivated on equally large shares of land around the plant. Thus the ensilaged maize accounts for a higher percentage of the used biomass than the other energy crops because of its higher harvest yield per hectare. Using the average production and delivery costs of 36:89 h=t as a starting point, the substrate costs per ton can be determined as a function BCkm of the distance between the field and the plant.

BC km ðxkm Þ ¼ 36:89hþ 0:24 h=km  ðxkm 3Þkm ¼ 36:17h þ0:24xkm h:

ð1Þ

The variable xkm represents the transport distances in kilometer, and these figures will differ for other regions, depending on various economic and site-related factors. In the following section, the substrate costs will be defined as a function of the size of the biogas plant. 3.2. Substrate costs and plant size The modeled biogas plant runs with a substrate mixture of 70% energy crops and 30% liquid manure, which is supplied by the local farmers at no charge. It is assumed that the energy crops are grown on equally large shares of land to allow for an effective crop rotation. The energy content of the different substrates is calculated and displayed in Table 3 and is based on the previous studies (FNR, 2004, 2008; Karpenstein-Machan, 2005). For these calculations, an operating time for the biogas plant of 8000 h a year, an electrical efficiency of 35%, and a loss of inventory in the store room of 12% due to natural decay are assumed (FNR, 2008). The average energy content kWel =t of fresh mass must be weighted again with the harvest yields of the different energy crops because the weight percentages are not equally distributed. Thus, approximately 0:0327 kWel can be installed with 1 t of this substrate mixture per year (i.e., 30% liquid manure, 70% energy crops). Given the size of a biogas plant, it is possible to determine the amount of energy crops and arable land that are needed to run the plant under the above-mentioned assumptions. When considering the varying distance between the farm and field and the average harvest yield per hectare of 46.2 t, the average substrate cost per ton as a function of the installed power xkW, in kilowatt, can be calculated for a selected biogas plant using the pffiffiffiffiffiffiffiffi following equation: BC kW ðxkW Þ ¼ 36:17 þ0:0333  xkW ½h=t. Because the needed amount of energy crops also depends on the size of the plant, the yearly costs ACkW for the substrates can be expressed as a function of the installed power xkW in the plant as follows: pffiffiffiffiffiffiffiffi ð2Þ AC kW ðxkW Þ ¼ 21:41xkW  ð36:17 þ 0:0333  xkW Þ½h: When incorporating this function to estimate the total substrate costs that depend on the installed power, the NPV for different plant capacities can be calculated using exemplary data from the literature. If the actual costs for operating a biogas plant are known for a given location, the NPV can be calculated for this particular planning situation. The production system of the biogas plant will be further described in the following section. Table 3 Energy content of the biomass [kWel =ðt FMÞ] calculations based on FNR (2004, 2008), and Karpenstein-Machan (2005). Substrate

DS/(t FM)

oDS/t DS

m3 CH4 =ðt oDSÞ

kWel =ðt FMÞ

Maize Triticale Wheat Rye Liquid manure

0.35 0.35 0.35 0.35 0.10

0.96 0.932 0.936 0.935 0.80

360 342 342 342 187.5

0.0464 0.0428 0.0430 0.0428 0.0065

Weighted average

0.0327

FM, fresh mass; DS, dry substance; oDS, organic dry substance energy content methane: 9:97 kWh=m3 .

H. Uhlemair et al. / Int. J. Production Economics 147 (2014) 62–72

4. Modeling of the biogas plant as a production system In biogas plants, biomass is fed into a digester, where an anaerobic fermentation process produces biogas. Subsequently, the biogas is treated (e.g., desulphurization and drying), stored, and usually utilized in a combined heat and power station (CHP). The CHP can be installed on-site or spatially separated from the biogas plant. In the latter case, a pipeline transports biogas from the digester to the CHP (FNR, 2010). An additional option for utilization would be to process biogas to have natural gas qualities and to then feed it into the regular gas network (Becker, 2009). 4.1. Calculation of the net present value The NPV of different plant capacities is needed to incorporate an estimation of the economic value for various capacities into the model. To calculate these NPVs, the revenues from feeding electricity into the national grid, investment costs, biomass costs and operating costs must be considered. According to the German Renewable Energy Act (BMU, 2004), the annual electricity allowances ALa are fixed and guaranteed for 20 years, and these allowances are dependent on the year that the biogas plant is installed and initially operates. The investment costs per kilowatt of installed power will decrease with higher capacities because of possible economies of scale. When using Eq. (3), the initial investment I0k ½h for different plant capacities k can be estimated, and a power of 0.6887 effectuates a decreasing investment per kilowatt of installed power due to economies of scale. The value of the scale coefficient, which is regularly used in chemical engineering for plant constructions, ranges between 0.6 and 0.7 (Williams, 1947; Remer and Chai, 1990), and this value has been calculated based on data from a biogas monitoring program (FNR, 2009). Last, the variable xkW represents the installed electrical power. : I0k ¼ 20,577:65  x0:6887 kW

ð3Þ

The annual biomass costs ACkW (as calculated in Section 3) depend on the plant capacity xkW, and the annual operating costs OCa can be estimated to be a function of the installed power xkW and must include maintenance, labor, insurance and laboratory costs (Becker, 2009; FNR, 2007). The NPV can be consequently calculated for a planning horizon of T years with a discount rate i as a function of the installed power xkW using the following equation: NPVðxkW Þ ¼ I0k þ

T X ALa ðxkW ÞAC kW ðxkW ÞOC a ðxkW Þ : ð1þ iÞn n¼1

ð4Þ

4.2. Net present value according to EEG 2009 The EEG 2009 awards several different bonuses, such as the basic allowance, a bonus for using renewable raw materials in the plant, and a bonus for using at least 30% liquid manure as a substrate, for operating a biogas plant with a CHP station (BMU, 2004). The allowances for a plant that initially operated in 2009 are given in Table 4. These values decrease with a degression rate of 1% each year for all plants, that began running in subsequent years. The allowances are then calculated for equivalent plant sizes, which are assumed to run all year long for a total of 8760 h. A biogas plant with an installed power of 350 kW that runs only 8000 h a year has, therefore, an equivalent plant capacity of 350 kW ð8000 h=a=8760 h=a ¼ 320 kWÞ. The annual allowances Ala that are paid for this plant, when assuming that the liquid manure and the renewable raw material bonuses were given and that the plant began operating in 2010, would then add up to Ala ¼ 548,191:08h. This paper calculates the NPV for plants that

65

Table 4 Amount of allowances ½h ct=kWh granted by the renewable energy act 2009 for plants, which started to operate in 2009 and 2010 (BMU, 2004). Equivalent plant size

o 150 kW

Basic allowance þ Renewable material þ Liquid manure

11.67 7 4

9.18 7 1

8.25 4 0

Sum (2009) Sum (2010) CHP bonus

22.67 22.44 3

17.18 17.01 3

12.25 12.13 3

150–500 kW

500–5000 kW

began operation in the year 2010; therefore, the single allowances that are given in Table 4 must be reduced by 1%. Given these data, the annual allowances Ala from feeding electricity into the grid can be calculated for all of the different plant sizes. Because the bonus for operating a CHP station depends on the amount of heat that is externally used, this bonus is set aside, but it is included in the optimization model (see Section 6). To calculate the annual operating costs OCa as a function of the installed power, the following various matters of expense must be taken into account (Becker, 2009; FNR, 2007):

 maintenance of the CHP station: 0:015h=kWhel  maintenance of other technical components: 2% of the       

investment fixed labor costs: 6810:75h variable labor costs: 53:19h=kWel insurance costs: 1% of the investment operating supplies: 0.3% of the investment internal electricity consumption (7%): 0:0975h=kWhel overhead: 10h=kWel laboratory costs (6 analyses/year): 120h=analysis

Consequently, the annual operating costs OCa can be calculated as a function of the installed power of the plant. When considering all of the above-mentioned characteristics and assumptions, which include the annual substrate costs ACkW and the allowances Ala, the NPV for every capacity can be calculated as a function of the installed power xkW according to Eq. (4). This NPV is used to economically value biogas plants for a planning horizon of 20 years, and the discount rate i is assumed to be 5%. The function pc : fck g-R is derived, which assigns the NPV to each capacity ck. In Fig. 2, the results are shown for a selected number of combined heat and power biogas plant capacities, and this selection shows and summarizes the course of the net present values that are subject to different capacities. For capacities higher than 900 kWel , the net present values decrease more. In the following section, local heating networks are described in more detail.

5. Modeling of the heating network as the distribution system In most local heating networks, hot water is transported via a pipeline from the energy station to all heat customers, where it is directly inducted into the heating system. A transmission station is necessary to adjust the pressure and volume conditions from the primary pipeline network to the individual heating system, and this network should be optimized regarding its size and course. To economically assess district heating as part of the concept of bioenergy villages, the investment of the network components must be taken into account and will be included in the model.

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H. Uhlemair et al. / Int. J. Production Economics 147 (2014) 62–72

1,000,000 842,185 800,000

723,810 625,003 556,932

600,000

374,037

400,000 200,000

198,469

0 100 kW

200 kW

300 kW

400 kW

500 kW

700 kW

900 kW

-200,000 -294,439

-400,000 Net Present Value € Fig. 2. Net present values for biogas stations.

5.1. Net present value of the network components The examined network consists of all houses that can be connected to the local heating system, and all potential pipeline segments between those houses. The NPV of the houses and the pipeline segments allow for an economic evaluation of the network. Thus, the annual revenues Ria and costs Cia and the initial investments Ii0 for each house and each network segment i are required. The initial investments include payments for the transmission station and pipelines and incomes from governmental grants and connection fees, which are charged to the customers’ accounts. Annual cash flows include maintenance and revenues from yearly fees and revenue from selling heat to the recipients. The NPV for a house or network segment i is then calculated as NPV i ¼ Ii0 þ

T X Ria C ia , ð1þ iÞn n¼1

ð5Þ

where T is the planning horizon, given in years, and i is the discount rate. In the following paragraph, exemplary data from ¨ Juhnde are given for the houses and the network segments (Ruppert, 2008). The operator of the biogas plant sells heat to customers who are connected to the heating network for 0:029 h=kWh, and each heat customer must pay a one-time connection fee of 2000h and a yearly fee of 500h. The operating company pays the transmission station for every heat customer (1700h), the pipeline (200h=meter), and the maintenance costs (2% of the pipeline costs each year). Furthermore, governmental grants of 80 h=m for the pipeline and 1800h for each heat customer are assumed. When considering a planning horizon of T¼20 years and a discount rate of i ¼ 5%, the NPV of every heat recipient and pipeline segment can be calculated based on the above-mentioned data.

NPV pv ðvi Þ to node vi A V, node v0 A V represents the production plant, and nodes V\fv0 g are the potential heat customers. The edges eij of the graph G are the segments of the heat network, and the edge-weight pe ðeij Þ is the NPV for segment eij. The nodeweight pv ðvi Þ represents the NPV of customer vi. B DV is a subset of V and includes the production plant v0 A V and the profitable heat customers V 0 D V\fv0 g. E0 D E are the segments of the optimal course of the grid, and V 0 and E0 must be determined. When using definitions from graph theory, this problem can be described as follows: A tree G0 ¼ ðV 0 ,E0 Þ, that P P connects all nodes in B and where v A V 0 pðvÞ þ e A E0 pðeÞ is maximal must be found. Because B consists of all of the nodes that belong to the optimal heat network, B is set as B ¼ fv0 g before optimization. Node v0, which represents the biogas plant, is part of the optimal grid, and the profitable heat customers V 0 DV\fv0 g must be determined by the optimization model. Pipeline optimization is a common challenge in various areas of industrial production, such as the oil industry and also chemical engineering. Brimberg (2000) examines the optimization of oil pipelines between a given set of offshore platforms and onshore wells that must be connected to a port. He models this problem using mixed integer programming and determines the optimal network configuration and sizes of pipes to minimize construction costs. In Section 6, the network design problem is modeled as a mixed integer program (MIP), but because Steiner tree problems are NPhard, it is unlikely that an efficient algorithm with a polynomial running time will be found (Garey and Johnson, 1979). Nevertheless, it is possible to analyze problem instances, which are not too large and depict realistic bioenergy villages. In Section 7, the model is applied to a village that contains 44 potential heat customers.

5.2. Graph theory and theoretical modeling 6. Mixed integer program To economically optimize a local heating network, the optimal course of the grid and which of the potential heat customers should be connected to the grid must be determined. Therefore, heating networks are theoretically described using graph theory. The notation of this decision problem as a weighted Steiner tree problem is introduced in the following paragraphs (Uhlemair et al., 2010): A connected, undirected graph G ¼ ðV,EÞ with the set of nodes of V ¼ fv0 ,v1 , . . . ,vn g and the set of edges of eij A E is assumed. Edge eij represents the link between node vi and node vj, and the function pe : E-R is given, which assigns the NPV pe ðeij Þ to each edge eij A E. In addition, pv : V-R is a function that assigns the

In this section, a mixed integer program (MIP) is used to economically optimize the capacity of biogas plants and distribution systems (i.e., heating network) for bioenergy villages. The advantage of modeling a problem as a MIP is that common methods exists (e.g., Branch and Bound or LP relaxation) to solve the problem. To model the MIP, the graph G ¼ ðV,EÞ is transformed into the directed graph G ¼ ðV,AÞ, which replaces each undirected edge eij A E with two directed edges eij and eji. The edge weighting function remains unaltered, i.e., pe ðeij Þ ¼ pe ðeji Þ, and the Steiner tree that must be determined is described by G0 ¼ ðV 0 ,A0 Þ.

H. Uhlemair et al. / Int. J. Production Economics 147 (2014) 62–72

The objective function maximizes the overall NPV, which consists of the NPVs of a biogas station with capacity ck, the heat customers vi and the pipeline segments eij that must be installed. In addition, the CHP bonus pkwk ðkWhth Þ for externally used heat has been added to the objective function. For modeling, the following variables are used according to Uhlemair and Geldermann (2011): ( 1, if vi A V 0 \ V\fv0 g, heat customer : X i ¼ 0, else; 9X 0 9 :¼ number of nodes in V 0 \fv0 g ( 1, if eij A A0 , pipeline : Y ij ¼ 0, else; f ij :¼ amount of flow on edge eij ( 1, if capacity ck is installed; capacity : Z k ¼ 0, else:

67

energy, which is measured in kWh. This variable is used to generate a flow to every heat costumer who, according to the model, is connected to the grid (Xi ¼1). Constraint 7 generates this flow for every connected heat customer, and constraint 8 verifies that for every flow fij on edge eij, a pipeline segment Yij is actually installed. In this paper, it is assumed that only a single biogas station is installed (constraint 10), and constraint 9 allows for a ‘negative demand’ for the CHP biogas station. Thus, the biogas station is the supplier of energy. Constraint 11 requires that no biogas station is installed that requires more biomass than what is locally available to operate at a full load. Constraint 12 ensures that the CHP biogas facility produces enough heat for all heat customers in the coldest month of the year, which is assumed to be January, when 17% of the yearly heat demand is needed. Constraints 13 through 16 are integers and non-negativity constraints.

7. Application Accordingly, the objective function is described as: 0 ! m n n X X X Z X th @ pc ðck ÞZ k þ pv ðvi ÞX i þ pe ðeij ÞY ij þpkwk el di X i -max: eij A A

i¼1

k¼1

Zth i ¼ 1

ð6Þ The constraints are: n X

f ji 

j¼1

n X

f ij ¼ X i

8i ¼ 0, . . . ,n,

ð7Þ

8ij : eij A A,

ð8Þ

j¼1

9V9Y ij Z f ij X 0 r0, m X

ð9Þ

Z k ¼ 1,

ð10Þ

k¼1 m X

ck Z k r Zel

k¼1

bð1gÞ

r 1X

dl¼1

al bl ,

m n Zth X 0:17 X th ck Z k Z d X, 31  24 i ¼ 1 i i Zel k ¼ 1

ð11Þ

ð12Þ

X i A f0,1g

8i ¼ 1, . . . ,n,

ð13Þ

Y ij A f0,1g

8ij : eij A A,

ð14Þ

Z k A f0,1g

8k ¼ 1, . . . ,m,

ð15Þ

f ij Z 0

8ij : eij A A:

In the following case study, three farmers are planning to install a single biogas plant with a CHP station in their village. The structure of the village, which includes the optimal grid of the heat pipelines and 44 potential heat customers, is shown in Fig. 3. Nodes 45–50 represent possible junctions of the grid and do not correspond to a household or other heat recipient. The farmers cultivate energy crops on 90 ha of their arable land. In addition, approximately 1800 m3 of liquid manure from cattle and swine is available each year. Different types of crops (e.g., maize, triticale, wheat and rye) can be cultivated on equal shares of the arable land and can be rotated within the available fields. Liquid manure accounts for 30% of the substrate, and the residual 70% of the substrate is made of ensilaged energy crops. According to Table 3 in Section 4, one ton of this substrate mixture results in approximately 0:0327 kWel of installed power. The overall heat demand of the 44 households amounts to 1032 MWh per year. The potential heat customers consist of private single-, semi- or multi-family houses and the local pub. It is expected that the biogas facility runs at a full load for 8000 h per year, its electrical efficiency is 35%, and its thermal efficiency is 45%. It is assumed that only 50% of the thermal energy that is generated in the CHP biogas plant can be used externally, the residual heat is needed for internal consumption during the fermentation process (35%), and 15% of the entire thermal energy is expected to be lost. For optimization, the Xpress software was used. In Fig. 3, the optimal heating network for this village with its 44 potential heat biogas plant

21

connected heat recipients

ð16Þ

22 20

unconnected potential heat customers

14

optimal heating grid

18 13

potential heat pipelines

pc ,pv ,pe ,pkwk net present values ðhÞ th

di bl

Zel Zth d

al b

g

heat demand of object i (kWh/year) amount of biomass l (t/year) electrical engine efficiency (%) thermal engine efficiency (%) operating duration (h/year) energy in biomass l (kWh/t) maximum of externally usable thermal energy (%) loss of thermal energy in the heating network (%)

12

17

11 2

46 10

9

1 8

15

7 3

45 6 16

5 4

25 26

44 41

27 28 24

43

34 48

35

29 23

The MIP modeling that is used here is similar to that of network flow problems (Hamacher and Klamroth, 2006). The variable fij reflects the flow of energy in the network, but it is not required that this variable represents the actual amount of

47

19

36 42

33

30

50

31 32 38

37

49

40 39

Fig. 3. Optimal course of the heating network with limited biomass availability.

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customers is shown, and the optimal capacity of the biogas plant is 175 kWel . Furthermore, a NPV of 829 915h can be realized for the objective function. Therefore, this bioenergy project can be valued as economically profitable for the investigated planning horizon of 20 years. Dashed lines and white dots indicate network segments and potential heat customers that are not connected to the optimal grid. Only 21 objects can be connected to the optimal grid, and 3 of these are merely grid junctions that do not demand heat. The available biomass is not sufficient to supply all households with heat, although it would be economically profitable to connect several other potential heat customers to the grid. To secure the heat supply for cold days, a capacity of 367 kWel or 472 kWth would be necessary when it is assumed that 17% of the annual heat demand is needed in January and only half of the generated heat can be used externally [2  1032MWhth  0:17= ð31  24 hÞ  472 kWth ]. When considering the abovementioned assumptions, approximately 7857 tons of energy crops [0:7  367 kWel =ð0:0327 kWel =tÞ] must be cultivated on 170 ha of arable land each year, and approximately 3366 m3 of liquid manure must be available [0:3  367 kWel =ð0:0327 kWel =tÞ]. To generally secure the heat supply (e.g., for technical breakdowns) or for extremely cold days of the year, an additional heating station must be installed. A station using wood chips, if available, and an oil-based peak-load boiler is possible add-on facilities. When assuming capacities of 200 kWth for a heating station that utilizes wood chips and 420 kWth for the peak-load boiler, further investments of approximately 250,000h must be ¨ 2010). The number of hours a year that this considered (Thran, additional heating station should be in operation must be determined. Furthermore, whether the station should only be used for security reasons, or if it should supply heat on a permanent basis such as the biogas plant, must also be decided. This decision certainly depends on the local possibilities to produce wood chips and the general availability of biomass. Currently, this decision has not been incorporated in the optimization model. The willingness to be a part of the bioenergy project and receive locally generated heat is also an important consideration. For different reasons, some people may prefer to use other heat sources. However, others may want to receive locally generated heat, even if their connection to the grid is not economically profitable for the operating company. If a household is located far outside of the village, the costs for installing a pipeline might be higher than the revenues that would be obtained from selling heat to those villagers. Nevertheless, some benefit to the entire bioenergy project could be obtained if some unprofitable heat customers were also incorporated. Excluding villagers who would like to receive local bioenergy could endanger the entire spirit of local bioenergy projects and lead to a cessation of the project (Ruppert, 2008). The optimization model is designed to calculate an optimal solution for different scenarios regarding the willingness of people to receive locally generated bioenergy. To analyze the effects on the net present value and the layout of the grid, four different scenarios for the hypothetical village are presented in the following paragraphs. The influence of biomass availability is not considered in these scenarios and it is assumed that all households can be supplied with heat. The results are shown in Fig. 4. In scenario (a), all villagers are willing to participate in the project, but only the economically profitable households are connected to the optimized grid. The plant to be installed has a capacity of 500 kWel and is able to supply all connected households with heat even during winter. This scenario leads to a maximum NPV of 1,387,520h, which is the highest possible NPV for this village and can be seen as a benchmark for the other scenarios. Because the NPV is positive, the investment is profitable when considering a planning horizon of 20 years.

The case where all households must be connected to the grid is presented in scenario (b). All variables of the households Xi are set to 1 (connected) before the algorithm begins. Doing so leads to a NPV of 1,373,280h, which is slightly lower than in scenario (a) but is still positive and economically profitable. The same principle is also applied to the remaining scenarios. First, the assumptions are integrated into the model. Subsequently, the algorithm begins and calculates the optimal solution based on those assumptions. In scenario (c), eight households i do not want to be connected (Xi ¼ 0), but all of the other households j must be connected (X j ¼ 1). In scenario (d), the same villagers as in scenario (c) do not want to be connected (Xi ¼0), and the optimization model determines whether to connect the other villagers (X j A f0,1g). In scenario (d), the algorithm separates the economically profitable heat customers from the other households who want to be connected. The NPVs of the last two scenarios are 1,214,810h and 1,229,050h, respectively, and are still profitable, but are less than the optimal solution. In all cases, a 500 kWel plant has been installed because it has the highest NPV of all plants, and no restrictions concerning the availability of biomass have been made. All of the scenarios show a positive NPV; therefore, all investments are profitable when assuming that 30% liquid manure is used in the substrate mixture, which considerably reduces the substrate costs. This finding also implies that, in reality, these scenarios would be much less profitable in regions where no liquid manure is available. In the optimal solution, four objects are not connected to the grid, and when comparing scenarios (c) and (d), those four households also create the difference in NPV. When comparing scenarios (b) and (c), it becomes obvious that the NPV is much higher when all of the villagers are connected to the grid than if eight of them are excluded. This occurrence must not be interpreted as that those eight must be persuaded to take part in the grid. Alternatively, it should be seen as a chance to reduce, ex-post, some initial costs such as the connection fee or the price per kWh of heat when generating a higher NPV by connecting all objects instead of excluding a portion of them. Many further interpretations of the results of this scenario analysis are possible, and the results can be discussed and used to support negotiations and decision making.

8. Conclusion A linear optimization model has been generated to economically optimize the production and distribution systems of bioenergy villages. Optimal solutions for the capacity of a biogas facility, for the course of the heating grid, and regarding profitable heat customers can be simultaneously generated. The willingness of people to use locally generated bioenergy was included in the optimization process. In this way, some social aspects can be taken into account. To avoid mono-cropping and crop failure, a mix of different energy crops was used, and the process of crop rotation was applied. Although the idea of crop rotation has been reflected upon, the impact of cultivating energy crops on the climate and on biodiversity must be further considered when calculating the location-specific availability of biomass. The flexibility of the model allows for a direct application to various different settings and regions. It is possible to take political and social factors into account, such as the existence of governmental grants and allowances or the refusal of a portion of the population to participate in the project. Furthermore, various aspects of different landscapes can be incorporated, such as higher investments in the heating network in hilly regions or restricted land use in the outskirts of a larger city with a higher number of potential heat customers. The model even allows

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biogas plant connected heat recipients

Connected nodes: 46 NPV 1,387,520€

Connected nodes: 50 NPV 1,373,280€

Connected nodes: 42 NPV 1,214,810€

Connected nodes: 38 NPV 1,229,050€

Fig. 4. (a) The first scenario shows the most profitable solution with 44 connected nodes. (b) In the second scenario all households are connected. (c) Eight houses do not want to receive heat, all others are connected. (d) Same scenario as in (d), but with only economically profitable heat customers connected.

4000000 3000000 2000000 1000000

fixed substrate costs

€

variable substrate costs

0

allowances -1000000

percentage of liquid manure* electrical efficiency

-2000000 -3000000 -0.5

-0.3

-0.1

0.1

0.3

0.5

percentage change (*percentage points) Fig. 5. Sensitivity analysis of a 500 kWel plant for various parameters.

for the incorporation of existing structures into the process of optimization. By adjusting the adequate binary variables and net present values of the existing facilities in the constraints, the model is able to appropriately handle these existing assets. In this way, potential expansions of the decentralized heating system can also be optimized. Therefore, the model is applicable to a wide range of planning situations and offers valuable information to all potential investment stakeholders in a district heating system that is based on the biomass. 8.1. Sensitivity analysis Because the composition and costs of the substrate for biogas plants have a major impact on the solution of the optimization

model, sensitivity analyses are performed to estimate the influence of changing parameters on the NPV of biogas plants. This analysis determines the effect of different substrate costs, allowances, capacity, efficiency, and the used percentage of liquid manure on the NPV of a biogas plant with an installed power of 500 kW that began operation in the year 2010. These results are shown in Fig. 5. The original value of each parameter is interpreted as 0%, the different functions display the effect of the altered parameters on the NPV, and all other variables remain constant. The substrate costs per ton BC kW ½h=t can be written as a function of the installed power xkW by BC kW ðxkW Þ ¼ 36:17 þ pffiffiffiffiffiffiffiffi 0:0333  xkW ½h=t. Because the plant capacities only range from 100 kW to 2 MW, the variable substrate costs per ton for the

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various plants are between 0:333h=t and 1:489h=t. Hence, the percentage of variable costs of the biomass compared to the total cost per ton amounts to only 0.9% to 4%. This finding also explains the progression of the two substrate cost functions in Fig. 5. Both curves have a negative slope because the NPV of the plant decreases as the substrate costs increase. However, the function of fixed substrate costs is much steeper because it accounts for 98% of the total substrate costs. An increase in allowances leads to a significant rise in the NPV, and because the revenue of the biogas plant is calculated by multiplying the allowances per kWh by the effective electricity output of the plant, the curve in Fig. 5 shows a linear progression. The slope of this curve depends on the total revenue, and it will be steeper for larger plants that generate a higher revenue. An interesting point on this curve is its root at  9% because it indicates the political margin for a decrease in the allowances. Thus, a decrease in the allowances of 9% represents the threshold above which this plant, with a capacity of 500 kWel , would still be economically profitable. A potential increase in the electrical efficiency also has a positive effect on the NPV because it effectively increases the electricity output and, therefore, the generated revenue of a plant without increasing the operating costs. However, because the benchmark in this analysis is a 500 kWel biogas plant, the curve actually does not express the increase in power output but represents the decrease in substrate input that is needed to generate the same amount of electricity. For this reason, the progression of the function is not linear but has a positive and slightly decreasing slope. The last parameter to be examined in this analysis is the percentage of liquid manure that is fed into the fermenter of a biogas plant. In contrast to the other variables, the alteration of this factor is given in percentage points and is not represented by the percentage change of the variable. Because the original value of liquid manure is set to 30%, it is impossible to calculate net present values for a higher decrease than 30%. The curve of this parameter is broken at 0%, which can be explained by the granted bonus allowance for using 30% or more liquid manure in the substrate mixture to run the plant. Beyond this point the curve has an increasing slope due to the fact that each additional percentage point of liquid manure replaces a larger amount of biomass and because the total amount of used biomass increases. This displacement leads to lower substrate costs and a higher NPV when it is assumed that the liquid manure is allocated free of charge. 8.2. Amendment to the Renewable Energy Act in 2012 The Renewable Energy Act is being amended in 2012 to adjust the law to a shifting policy away from an unconditional support of renewable energies. The major goals that are to be achieved by the amendment include further development of renewable energies, an increase in cost efficiency, and a faster integration into the national energy-system and market structures (BMELV, 2011) by several different mechanisms. The first important point is the simplified allowance system. These allowances are mainly paid for the use of different substrates (see Table 5). The degression rate has been increased to 2% but is limited to the substrate specific allowances. Substrates in class I include several energy crops, whole crop silage and scrap wood. Class II includes liquid and other manure, straw, and biomass from landscape conservation. The basic allowance is paid for nearly all biomass substrates according to BMU (2001). The main requirement for all biogas plants to receive any allowance is a substrate mixture that contains at least 60% manure or at least 60% heat usage from the CHP in houses or stables or for internal

Table 5 Allowances [h ct=kWh] for substrates used in a biogas plant, which started to operate in 2012, according to BMU (2011). Equivalent power ðkWel Þ

Basic allowance

Substrate class I

Substrate class II

Liquid manure

r 150 r 500 r 750 r 5000

14.3 12.3 11 11

6 6 5 4

8 8 8 8

8 8 6 6

consumption. This requirement shall increase the energy efficiency of newly installed plants and decrease the amount of methane and other greenhouse gases that are emitted into the atmosphere by conventional methods of manure disposal. To reach this goal, small plants of up to an equivalent size of 75 kWel that are run using at least 80% liquid manure have a fixed allowance of 0:25h for every kWh; however, the possibility to combine with other allowances is not permitted. To increase biodiversity and reduce the monocropping of maize and other profitable energy crops, the mass percentage of ensilaged maize and grain that is used in the substrate mixture is limited to 60%. Another important aspect of the amendment is the incentive for the operator of a biogas plant to market the energy alone. It is possible for these individuals to sell electricity at the national energy exchange in Leipzig or through delivery contracts with private customers. If the total revenue is below the granted allowances, they will be paid the difference so that they are not subjected to worse conditions than other companies. This economic incentive also increases the willingness to establish a demand-driven production of electricity, through higher revenues for the operator. This approach for reducing the dependency on the national allowances is supported by a flexibility allowance, which is granted for biogas storage and greater generators allowing for a postponement of the production of up to 12 h. In this way, the generation of electricity can be regulated and shifted with the demand peaks of each day. These different aspects of the amendment to the Renewable Energy Act all aim for the above-mentioned goals, namely, a further development of renewable energies, higher cost efficiency, and integration into the national electricity market. To include these changes in the presented model, it must be adapted in various ways, in particular the interdependencies and the meeting of all constraints pose a challenge to the modeling. 8.3. Outlook and further research To facilitate data collection for the issue of local biomass availability, the optimization model will be connected with a Geographic Information System (GIS). One suitable GIS for the ¨ region of Lower Saxony in Germany is BioSTAR (Baubock, 2010). BioSTAR offers the possibility to determine location-specific harvest yields based on soil types and climate data, which are available through the German Weather Service.2 By predicting potential harvest yields in certain regions, it will also be possible to analyze various scenarios concerning climate change over the next 20 years. In this way, the development of climate conditions and its effects on harvest yields and substrate costs can be taken into consideration beforehand and can be included in the decision-making process. Currently, a CHP biogas plant is modeled as the only source of heat. In future research, a second heat source and a peak-load 2

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boiler will also be considered in the optimization model. As of now, additional investment costs have been mentioned but have not been integrated into the model. By doing this, the heat supply is secured for extremely cold days of the year, and a locationspecific optimal mix of different heat facilities can be calculated. In the absence of a peak-load boiler and without an additional heating station, the capacity of the biogas facility is probably too large for periods of the year with less heat demand. As a consequence, a substantial amount of heat is wasted, and a substantial amount of biomass is needed to operate at a fullload capacity throughout the year to generate enough revenue from feeding electricity into the national grid. This occurrence causes problems in terms of energy efficiency and land-use competition. However, the plants are still profitable for the operating companies, and the revenues from selling electricity exceed the opportunity costs of the wasted heat. Nevertheless, the optimization model must be improved to be able to calculate an optimal mix of base and peak load energy stations with a high overall energy efficiency. In a second step, the model can be enlarged to optimize several plants simultaneously. By taking several plants into consideration, the model optimizes the set-up of the heating system regarding installed power and the location of the plants. Location planning could be achieved using binary variables for every potential location in a discrete set, which would determine the number of plants to be built and their specific locations. Nevertheless, various problems regarding the complexity of the model must be considered. By augmenting the model to depict multiple plants, the number of constraints is also multiplied by the number of plants. Furthermore, the availability of liquid manure and other biomass must be determined, the allocation of these substrates to the various locations must be taken into consideration, and every single plant must be equipped with a suitable peak-load boiler or other heat source as a backup facility. All of these model-specific adjustments will most likely increase the runtime of the algorithm, and how the model can be scaled for regional bioenergy projects must be investigated. The mathematical implementation could pose a great challenge due to the complexity of the problem and further research will have to examine under which constraints the model is still applicable to larger problems, providing solutions in a reasonable running time.

9. Summary In this paper, a model to support the decision making during the process of planning a bioenergy village has been presented. A case study in Lower Saxony (Germany) has been executed to introduce and evaluate the different parts of the model. The production system includes the biomass supply, the initial investment for the plant, the operating costs, and the governmental grants and allowances. It is therefore possible to model various scenarios concerning biomass costs, biomass availability, plant efficiency, or the existence of subsidies. The modeling of the distribution system depicts the course of the local heating network, the location of the biogas plant, and the various households as potential heat customers. Defining the question of an optimal heating network as a Steiner tree problem and combining the production and distribution systems into one integrated MILP offers the possibility to systematically analyze the interdependencies between the connected households, the size of the biogas plant and the needed biomass. For the first time, this model allows for an economic assessment of various scenarios, an optimization of the capacity planning for a biogas plant, and the course of the district heating network.

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