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CHOICE OF LOCATION FOR BIOGAS PLANTS IN GERMANY

DESCRIPTION OF A LOCATION MODULE Ruth Delzeit, Institut für Lebensmittel- und Ressourcenökonomik,

Rheinische Friedrich-Wilhelms-Universität Bonn, 12.8.2008

1 Introduction

Bioenergy is said to have a big potential in contributing to an energy-mix with regard to a

sustainable energy concept. The different effects of enhanced bioenergy use are modelled

within the project “Renewable resources and land use (NaRoLa) - Integration of bioenergy

into a sustainable energy strategy”, by linking a dynamic general equilibrium (CGE) model of

the world economy with the Regional Agricultural Environmental Information System

(RAUMIS), and RAUMIS with a location module. This location module is especially impor-

tant where transport costs are very high as is the case for maize. RAUMIS has modelled the

production area and yields for energy crops, assuming a total marketability of all produced

biomass at given producer prices and opportunity costs. This assumption is incorrect, if plants

do not emerge all-over, and thus, the results of RAUMIS need to be revised by a location

module, where the demand for maize is modelled considering economies of scale in the pro-

duction and diseconomies of scale for transportation costs.

In the agricultural sector transport costs make up an important share of overall productions

costs, and are expected to rise in the future due to rising crude oil price, tolls and environ-

mental regulations (BOYSEN et al. 2006, p. 152). In addition, input prices for the production of

bioenergy have increased considerably in the last year and are expected to rise further in the

future (V. LAMPE, 2007). If we assume that only those bioenergy plants are build or persist,

which produce bioenergy cost effectively, identifying optimal location gives important infor-

mation on where plants will be located in the long run. As these plants have an influence on

the land use, this information is important to estimate environmental effects.

An optimal location is defined as the combination of location and size that minimizes total

costs, consisting of production and transportation costs. Ceteris paribus, this is equivalent to

income or a profit maximisation. The model described here intends to give information on the

demand for maize for biogas production as this is the most important bioenergy use with high

transportation costs. This paper describes a first version of the location module which still

gives only a rough estimation of maize demand per district. The paper is organized as follows:

First, in order to derive assumptions for the location module, the system of biogas production

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and its possible pathways of usage are described. Section three gives an overview on the de-

termination of potential locations of biogas plants. Thereafter, a homogeneity index to iden-

tify impacts of land use on transport costs as well as the location module for biogas plants are

described.

2 Description of the system and evolving assumptions

The location and sizes of bioenergy plants depend on a variety of factors which show interfer-

ences: legislation, the availability of raw materials (yields and share of land, distribution of

land), production costs, the possibilities to use the produced energy, and resulting transporta-

tion costs. The first calculation is done for biogas from maize. This comprises the most sig-

nificant part of the biomass production for which transportation costs are of crucial impor-

tance.

Relevant legislation

The production of bioenergy highly depends on legislation which has important impacts on

the choice of location, and the amount of bioenergy production. The production of biomass in

Germany depends on incentives, set by the German government and the European Union.

In the case of biogas from maize, the most important legislation is the Renewable Energy

Source Act (EEG), which guarantees a feed-in tariff differentiated for different sizes of plants,

the used technology and input materials. Additionally, surcharges are granted for the exclu-

sive use of renewable primary products (RPP), the use of combined heat and power genera-

tion, and the use of new technologies.

It is intended to run two scenarios: the “reality scenario” applies the current legislation and

considers existing biogas plants. With the “scenario social planner” the concept of an enlight-

ened absolutism is applied. Here, it is assumed that all biogas plants are built from scratch (no

path dependency), and all plants, independent of their size, receive same revenues. The first

version of the model implements the second scenario.

Availability of raw material

Biogas plants can be divided into those, which are operated with 90% RPP and 10% of liquid

manure and plants which run with 90% of liquid manure and 10% RPP (see e.g. INSTITUT FÜR

ENERGETIK UND UMWELT 2005, p. 136). New plants are able to be operated with RPP only,

which makes modelling easier in a first step. Thus, it is assumed that biogas plants are run

solely with energy maize, which is in practice the most used crop for input.

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Data on the production of energy-maize per district and yields are gained by RAUMIS. Dif-

ferences of land use and yield of energy-maize determine number and size of plants which is

discussed in detail in the next section. The availability of raw material per district determines

the potential number of plants there. Additionally, a silage loss of 8% is included.

Transportation costs

Maize needs to be cut on the field and be transported to the biogas plant. The storing of maize

can be central at the biogas plant or de-central in the field. The RAUMIS model contains costs

for the harvesting by a chaffing machine and the transport to a plat form next to the field.

Costs for the first three km are therewith covered. For the capacity class of 100 kW no addi-

tional transportation costs need to be included in the model. Thus, in the location module it is

assumed that costs emerge to transport maize from a plat form next to the field to the biogas

plant.

The transportation costs consist of a constant parameter for loading and unloading the trans-

portation unit per ton. In addition, costs per distance are added, whereby distance depends on

the transported amount of maize (depending on the size of a plant), maize yields, the share of

agricultural crop land, and the distribution of crop land within districts (see section 4). Addi-

tionally, the distance is multiplied by a factor of 1.33 in order to respect that streets do not

occur in straight bee-line distances.

After the fermentation process residues are brought back to the field. In the current version of

the model, transport of residues as well as transports for fertilizers and chemicals are ne-

glected, but are planned to be included in an improved version.

Production costs for crude biogas

Production costs of biogas are divided into variable costs, which consist of costs for raw ma-

terial, costs for maintenance and repair, labour, insurance, operating staff, and parasitic en-

ergy, and fixed costs (fixed capital), which include total investment costs, a discount rate of

6%, and a useful live expectancy of 16 years.

Data on production costs were collected from a study of URBAN ET AL. (2008) and expert in-

terviews for four capacity classes, which are oriented towards the availability of data and

thresholds for subsidies. Capacity classes are 100kW, 500kW, 1000kW and 2000kW. The

crude biogas can be used by different pathways of usage, which generate different processing

costs.

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Multi-use options for biogas

The current legislation favours two pathways of usage for the produced crude biogas:

Direct production of electricity in block heat power plants

In Germany, the major technology is block heat power plants (BHPP) with combustion en-

gines, combined with a generator. Currently, the produced biogas is almost entirely used for a

direct production of electricity in motor-BHPP (INSTITUT FÜR ENERGETIK UND UMWELT 2005,

p. 75). Additionally, the BHPP modules contain a heat exchanging device, for recovering heat

from exhaust gas, cooling water and lubricating oil cycle, hydraulic advices for heat-

distribution and electrical switchgear and controlling units for electricity distribution and

regulation of the BHPP (FACHAGENTUR NACHWACHSENDE ROHSTOFFE 2006, p. 101). A 500

kWh biogas plant produces 3.484.732 kWh of electricity and 2.647.861 kWh/a heat at 8000

operating hours (FACHAGENTUR NACHWACHSENDE ROHSTOFFE 2005). Electric efficiency is

the sum of thermal and electrical energy, and usually is 80-90% (FACHAGENTUR NACH-

WACHSENDE ROHSTOFFE 2006, p. 104).

Combined Heat Generation (CHG) is the simultaneous production of power (e.g. electricity)

and heat (FACHAGENTUR NACHWACHSENDE ROHSTOFFE 2006, p.19). It is assumed that with

rising prices for raw materials only those biogas plants persist, which use combined heat

power generation, as additional revenue from heat sales and subsidies can be acquired. For the

produced heat, suitable heat sinks (demand for heat) need to be developed.

In the model, this pathway embraced the production costs for crude biogas, costs for the

BHPP and costs for a heat net for the decentred use the produced heat. Due to the de-central

production of heat, utilization degrees of 0% for capacities of 100kWh, and 50% for 500kWh

are presumed. Processing costs are adopted from URBAN ET AL. (2008).

Gas induction and production of electricity in BHPP

Biogas can be inducted into the gas grid, using qualitatively high processed biogas. This

method is applied in pilot projects already. It is assumed that it becomes technically mature

within the modelling time frame of the project (2020) and is thus included in the location

module. The possibility of induction depends on several standards and legislation, as well as

on the technical and economic side on the gas net at hand with different gas qualities and gas

pressures.

The costs for induction of gas in possible districts of gas induction are included in the model,

as well as costs for the BHPP. Again, costs are taken from URBAN ET AL. (2008).

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The model chooses the cost effective pathway for each capacity and sums up the evolving

processing costs. The same pertains to different revenues from heat sale, gas induction and

electricity induction.

3 Pre-selection of potential locations

In our initial model we assume that no plants exist in the baseline year 2003. In the “social

planner” scenario, the initial location of plants will already be determined by the Location

Module. We assume that this will not make a difference in 2020. In order to determine a

maximal amount of plants, first, districts with more than 500/km2 habitants were excluded, as

no biogas production is possible in urbanized areas due to availability of raw material and

restrictions in building laws. For the choice of location (independent of the size) it is assumed,

that the availability of raw materials and the usage of the produced energy (gas injection and

heat sink) are the most important factors for location a biogas plant. Using a Geographical

Information System (GIS) these potential locations are identified using an analysing tool.

Maize areas

As in RAUMIS climatic data and data on soil are not explicitly modelled, in a first step we

tried to identify areas advantageous for maize cultivation regarding heat sums and water

availability using a spatial analysis tool of GIS.

To determine thresholds for advantageous areas of maize cultivation, an expert interview was

held with representatives of the German Maize Committee. According to the experts of the

German Maize Committee no areas can be classified to be advantageous or disadvantageous

for maize cultivation, as different varieties of maize are bred which are well adapted to differ-

ent natural conditions. Thus, a pre-selection of relevant areas according to availability of

maize could not be realized.

Areas with heat sinks

It is assumed that CHG is needed for cost efficiency. Currently, most biogas plants do not

have a concept for usage of produced heat. Further, most existing plants have been con-

structed in areas with poor possibilities for heat disposal (BREMER ENERGIE INSTITUT 2007, p.

1). A study of the BREMER ENERGY INSTITUT (2007) examined possibilities for heat disposal,

which are technically and economically feasible. All of these possibilities assume an existing

plant can be improved or heat can be used after a plant is constructed. With existing data the

amount of heat sinks cannot be assessed on a district level.

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Another option for heat disposals are heating networks and bigger heat users like swimming

pools, retirement homes, schools etc. Based on this, the heat demand is still prohibitively dif-

ficult to estimate for each district, as there are different kinds (e.g. full-day/half-day), and

sizes of buildings and therewith different demands on heat.

Thus, we decided to calculate potential heat demand for each district using data offered by the

German Federal Ministry of Economy and Technology (2006) on heat relevant energy use.

The results were then compared with produced heat by biogas plants. They indicate that, in

theory, in all districts heat demand exceeds potential heat produced by biogas plants. Realiz-

ing that this is a very rough estimation of heat demand, during expert consultation no better

method on district level could be detected.

Areas of gas injection

In order to determine districts with suitable gas pipelines for the injection of biogas, studies

from the INSTITUT FÜR ENERGETIK UND UMWELT (2005) and ARBEITSGEMEINSCHAFT WUP-

PERTAL INSTITUT, FRAUNHOFER GESELLSCHAFT-UMSICHT, GASWÄRME-INSTITUT ESSEN

(2007), and URBAN ET AL. (2008) were reviewed. Following a study on the structure of the gas

grid, the gas grid can be assumed to cover on average 85% of Germany, but an assessment of

numbers of municipalities, which are suitable for an induction of biogas is not possible with

this information as a direct induction is dependant on the location of induction, the structure

of the gas grid and consumers at hand (INSTITUT FÜR ENERGETIK UND UMWELT 2005, p. 115).

Thus, in a GIS-analysis, districts with access to gas pipelines were selected, and for those the

option of gas induction was included into the model.

4 Development of the homogeneity index for districts using spatial autocorre-lation

The distance a transportation unit has to cover to deliver maize from a platform in the field to

the biogas plant depends not only on the yields but also on the distribution of land within a

district. Therefore, a homogeneity index for districts using spatial autocorrelation has been

developed. In order to include the homogeneity or heterogeneity of land use into the term for

transportation costs, districts are analysed using the GIS tool spatial autocorrelation.

Data for the analysis is based on CORINE database and was calibrated for the CAPRI model,

and the data is joined to a GIS shapefile.

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What is spatial autocorrelation? Spatial autocorrelation is determined both by similarities in position, and by similarities in

attributes (GUJARATI 2003, p. 89), which means that it deals simultaneously with similarities

in the location of spatial objects and their attributes, in our case the share of arable land. Spa-

tial autocorrelation gives answers to question like: are values randomly distributed over the

features, or do high values tend to cluster? Are high values surrounded by high values and low

values surrounded by low values? (GUJARATI 2003, p.348).

Autocorrelation can be defined as “correlation between members of a series of observations

ordered in time or space” (KENDALL AND BUCKLAND 1971, p. 8). Observations in time relate

to e.g. time series data, and observations in space to cross-sectional data or spatial data. In the

classical model of autocorrelation it is assumed that the disturbance term relating to any ob-

servation is not influenced by the disturbance term relating to any other observation. If there

is such dependence there is autocorrelation (GUJARATI 2003, p. 442). Compared to autocorre-

lation, spatial autocorrelation is more complicated as the correlation has two dimensions and

is bi-directorial. Respective measures are obtained by expressing spatial similarity in one ma-

trix and values similarity in the other, whereby different indices for spatial association yield

different measures of value similarity (ANSELIN 1995, p. 98). Spatial autocorrelation can be

examined by using local or global measures.

For testing spatial autocorrelation Global Moran's I and Local Moran's Ii are the most com-

monly used test statistics for spatial autocorrelation in univariate map patterns or in regression

residuals (TIEFELSDORF 2002). Global spatial statistics mean that procedures are applied to the

complete region under study (GETIS & ORD, 1992, p. 189) and require measurements from all

or many geo-referenced points in the sample (ORD & GETIS, 1995, p. 286). The global spatial

autocorrelation assumes homogeneity, and yields only one statistic to summarize the whole

study area. Moran’s I indicates general properties of the pattern of attributes and distinguishes

between positive and negative autocorrelated patterns (LONGLEY ET AL. 2005, p. 348). For the

problem at hand the Global Moran's I is applied, as the study areas (districts) are relatively

small and one value of heterogeneity per district is searched for. The correlated attribute is the

share of agricultural crop area.

Global Moran's I

Definition Global Moran’s I is a translation of non-spatial correlation measures to a spatial context, and

is calculated from:

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where the numerator is the covariance term with i and j (two areal units), x is the data value in

each unit, x the overall value of x, and wij is the proximity of location between point i and j.

By calculating the product of the unit’s differences from x , the extend to which they vary

together is determined. The product is positive, if both xi and xj lie on the same side (above or

below) of the mean. It is negative, if the sides they are positioned are different, and the value

depends on the difference from the overall value to the unit’s values. These covariance terms

are multiplied with wij which switches each possible covariance on or off depending on

(MITCHELL 2005, p. 121, ORD & GETIS 1995, p. 289)

Application in GIS Spatial autocorrelation can be positive, if features that are similar in location are also similar

in attributes and negative when features which are close together in space tend to be more

dissimilar in attributes than features which are further apart (GUJARATI 2003, p.88). Pattern of

spatial autocorrelation can be divided into three groups. The pattern is random, if features are

located independently, and all locations are equally likely. It is clustered if some locations are

more likely than others, and the presence of one feature may attract others to its vicinity. If the

presence of one feature may make others less likely in its vicinity, the pattern is called dis-

persed (GUJARATI 2003, p. 347).

Spatial relationships are conceptualized by defining how the distance is measured. Using e.g.

“Inverse distance” the impact of one feature on another feature decreases with distance. It is

possible to define a “fixed distance band”, including every feature with a specific distance

into the analysis, and excluding features outside the critical distance (MITCHELL 2005, p.

135ff). The neighbourhood the Global Moran’s I statistics is applied is based on a distance

which can be specified by the user.

Deriving a factor for spatial autocorrelation For each district a Global Moran’s I statistics is calculated using the following specifications.

In the analysis of distribution of arable land within districts, “fixed distance band” with a dis-

tance of 10000m is used. Thus, all attributes within a neighbourhood of 10km are included

into the calculation.

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In order to derive a factor for spatial autocorrelation from the Global Moran’s I, it is assumed

that a Moran’s Index of 0.9- 1, which denotes total homogeneity among the attributes results

in a factor of 1, with is multiplied to driving distances (and thus transportation costs). In case

of a dispersed distribution of the attributes (Moran’s Index of -1), transportation costs are

doubled (see Table 1).

Moran Factor Moran Factor

0.9-1 1 -0.1 1.55

0.8-0.9 1.05 -0.2 1.6

0.7-0.8 1.1 -0.3 1.65

0.6-0.7 1.15 -0.4 1.7

0.6-0.5 1.2 -0.5 1.75

0.40.5 1.25 -0.6 1.8

0.3-0.4 1.3 -0.7 1.85

0.2-0.3 1.35 -0.8 1.9

0.1-0.2 1.4 -0.9 1.95

0-0.1 1.45 -1 2

0 1.5

Table 1: Deriving a transportation factor from Moran's I Index

As the Moran’s I index does not consider the value of attributes (clustering of high or low values), and additional factor includes the values of shares of arable land.

Deriving a factor for share of land use Based on the same data, for each district the overall share of arable land on the total land area

is calculated. The data is available for raster cells of one square kilometre, but as raster cells

with equal attributes are merged in the data base, they show high variations in size. Thus, the

overall share per district is weighed according to the size of each raster cell.

The resulting share of arable land on total land per district is converted into a factor by divid-

ing the maximum available share (100%) by the calculated share. The driving distance for a

district with 50% of arable land is therefore doubled, whereas distances in a district with 10%

of arable land are multiplied with a factor of 10.

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5 Description of the location module

For the version “social planner”, the model is formulated to sequentially locate facilities

which maximise profits in each region. In each sequence or step, the optimal size of a plant is

calculated, and the used amount of maize for the capacity is subtracted from the available

amount of maize of the former sequence for the next step. For each step “current” prices, ca-

pacities, and districts are applied.

Objective function

, , , ,max ( ) ) (( * * )* )cl cl cl cp cl u cl cl cl k ck ck kcl CL cp CP u U k K cl CL ck CK

x r v p q f km zη α β σ∈ ∈ ∈ ∈ ∈ ∈

= − − − − − +∑ ∑ ∑ ∑ ∑ ∑

Indices / Sets:

l…L: class of capacities (100, 500, 1000, 2000kW)

u…U: pathways for usage

p…P: price for maize

k…K: districts

s…S: steps

Subsets:

op…OP: optimal size in regions (k,l)

cs…CS: current step (s)

cl…CL: current class of capacity

cp…CP: current price

ck…CK: current region

Given data/ Parameters:

rcl sum of revenues per produced kWh (in € per year)

vcl: variable production costs (€/kWh per year) with service and maintenance, staff, insurance, parasitic energy

,cp clη : input costs (maize)

rev feed in prices for electricity (in €/kWh per year)

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heatcl subsidy for usage of heat (in €/kWh per year)

fcl: fixed costs (in € per year) with mechanical technology,

investment costs, interest

pcl,u processing costs for different pathways per produced kWh (in €/kWh per year) qcl: production output of j at capacity l (in kWh per year)

α : costs for un and uploading (in € per t)

β : transportation costs for each km (in € per km)

kmcl,ck,k: driving distance (in km)

ckσ : Homogenity factor

bck,cp,cs: amount of maize produced in ck at cp (in tons)

bk,p: amount of maize produced in k at p (in tons)

mzprcp price for maize (in € per t/FM) mzdmcl demand for maize at l (in t/kWh) proccl,u processing of biogas netcl,u construction of net (gas or heat) CHPGcl costs for CHPG tkoutk distance between k (km) tkinck,cl driving distance within k (km) moranck factor derived from Global Morans’s I shareck factor derived from share on crop land on total land

Decision variables / Variables

zk: transported amount of maize (in tons)

x: profit

2) Side conditions

(1) ,k p kp P

b z∈

≤∑ for all p ∈ P and k∈K

(2) *1.08k lk K l L

z mzdm∈ ∈

=∑ ∑ for all k∈K and l ∈ L

(3) , , , , .k p cs k p cur kb b z l= − for all p ∈ P and k∈K

(4) , , , ,k p cur k p cscs CS

b b∈

= ∑ for all p ∈ P, k∈K and cs ∈ CS

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(5) zk ≥ 0 for all k ∈ K

(6) x > 0

where

(7) ( )cl clr rev heat= +

(8) , *cl cp cp clmzpr mzdmη =

(9) , , , CHPGcl u cl u cl u clp proc net= + +

(10) ,

mz /cl ckcl ck

dm etkin =

Π

(11) , ,( )*1,33ck cl ck cl ckkm tkin tkout= +

(12) *ck ck ckmoran shareσ =

The objective function maximises profits of plants by selecting the optimal size for each dis-

trict. In each sequence, one facility can be opened per district. Transports from other districts

are allowed but transport costs increase due to rising distances to a plant. Due to restriction in

computability, the research area Germany is subdivided into NUTS 2 level. Thus, for each

NUTS 2 region in Germany a calculation is done. Consequently, in the model maize can be

transported between different districts within the region, but no transport is possible within

different NUTS 2 regions.

Condition 1 ensures that not more maize is transported from a district to plants than is pro-

duced in that district. Input of maize and the plant‘s output (electricity) are related with condi-

tion 2. Additionally, closed plants are not provided with maize and a silage loss of 8% is con-

sidered. Constraints 5 and 6 determine the rage of value for variables.

Revenues from biogas production and processing consist of revenues for feed-in prices for

electricity and revenues from heat sale (7). These revenues are subtracted by variable and

fixed costs of the biogas production and costs for processing the biogas. Input costs (maize)

are extracted from variable costs, as they are varied in order to receive a demand function.

The processing costs (9) include upgrading to biogas of higher quality in the case of biogas

induction (procl,u), construction costs for a pipeline from a processing plant to a gas pipeline

or construction costs of a heat net (netl,u), as well as costs of a CHPG.

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Transportation costs consist of a constant term for up and unloading a transportation unit (α )

and a cost term, that depends on the driving distance ( β ). The driving distance is divided into

transports within a district (tkin) and from other districts (tkout). Tkin depends on the maize

needed for a certain capacity, and the yields of a certain district (10). A transportation matrix

which includes the mean distances between all districts is represented by tkout.

In each sequence the optimal size in each district is determined, depending on current indices

of a sequence, which correspond to the subsets. A loop is run over prices, districts, and ca-

pacities to find the best locations in the current round. The used maize by the optimal loca-

tions is sequentially subtracted from the available maize of the former sequence. The process

is stopped if the profit becomes smaller or equal to zero or if the resources are exhausted.

Thus, in the model in each step, one plant can be built in each district, and withdraws raw

materials for plants which can be built in the next step. Therewith, for different price levels of

maize the model determines the demand for maize in each district and a demand function can

be derived.

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