An optimization model for multi-biomass tri-generation
energy supply
A.A. Rentizelas*, I.P. Tatsiopoulos, A. Tolis
Department of Mechanical Engineering, Sector of Industrial Management and Operational Research,
National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou 15780, Athens, Greece
article info
Article history:
Received 12 May 2008
Accepted 14 May 2008
Published online 10 August 2008
Keywords:
Biomass
Modelling
Optimization
Bioenergy
Supply chain
Logistics
District heating and cooling
Investment analysis
Tri-generation
abstract
In this paper, a decision support system (DSS) for multi-biomass energy conversion
applications is presented. The system in question aims at supporting an investor by
thoroughly assessin g an investment in locally existing multi-biomass exploitation for
tri-generation applications (electricity, heating and cooling), in a given area. The approach
followed combines use of holistic modelling of the system, including the multi-biomass
supply chain, the energy conversion facility and the district heating and cooling network,
with optimization of the major investment-related variables to maximize the financial
yield of the investment. The consideration of multi-biomass supply chain presents
significant potential for cost reduction, by allowing spreading of capital costs and reducing
warehousing requirements, especially when seasonal biomass types are concerned. The
investment variables concern the location of the bioenergy exploitation facility and its
sizing, as well as the types of biomass to be procured, the respective quantities and the
maximum collection distance for each type. A hybrid optimization method is employed
to overcome the inherent limitations of every single method. The system is demand-
driven, meaning that its primary aim is to fully satisfy the energy demand of the
customers. Therefore, the model is a practical tool in the hands of an investor to assess
and optimize in financial terms an investment aiming at covering real energy demand.
Optimization is performed taking into account various technical, regulatory, social and
logical constraints. The model characteristics and advantages are highlighted through
a case study applied to a municipality of Thessaly, Greece.
ª 2008 Elsevier Ltd. All rights reserved.
1. Introduction
1.1. Background
Numerous studies have been performed to forecast the
contribution of biomass in the future energy supply, both at
a regional and at a global level [1,2]. All of these studies
concluded the fact that biomass usage will be increased signif-
icantly in the years to come. However, there is no consensus on
the maximum level biomass exploitation could achieve.
One of the most important barriers in increased biomass
utilisation in energy supply is the cost of the respective supply
chain and the technology to convert biomass into useful
forms of energy (electricity, heat, etc.). It is therefore natural
that many attempts have been made to date to simulate and
optimize a specific biomass supply chain on the under-
standing that significant cost reductions could originate
from more efficient logistics operations. For example, an
analytic supply chain modelling for five distinct types of
biomass was performed in Ref. [3], which concluded that
* Corresponding author. Tel.: þ30 210 7722383; fax: þ30 210 7723571.
E-mail address: arent@central.ntua.gr (A.A. Rentizelas).
Available at www.sciencedirect.com
http://www.elsevier.com/locate/biombioe
0961-9534/$ – see front matter ª 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biombioe.2008.05.008
biomass and bioenergy 33 (2009) 223–233
20–50% of biomass delivered cost is due to transporting and
handling activities. Similarly, very analytical supply chain
simulation models for forest [4], cotton [5] and Miscanthus
giganteus biomass [6] have been developed. In Ref. [7] the
cost of producing energy crops – short rotation forestry –
was investigated, using spreadsheet models, focusing mainly
on the operations of biomass production, collection and
storage. In Refs. [8,9] GIS is employed to calculate the exact
transportation distances for supplying specific amounts of
energy crop feedstock across a state, taking into account the
spatial variability in their yield.
Apart from pure simulation models, optimization has also
been used in the relevant literature. A linear programming (LP)
optimization model has been utilised [10] to optimize a cost
function including the biomass logistics activities between
the on-farm storage locations and the centrally located power
plant, construction and expansion costs of storage facilities,
as well as the cost of violating storage capacity or lost revenue
in case of biomass deficit. The authors consider the use of
ambient and covered storage and take into account the uncer-
tainty in biomass production levels. A very detailed review
concerning modelling tools for biomass supply chain and bio-
energy conversion up to the year 1999 can be found in Ref. [11],
where the author acknowledges the fact that most models
tend to deal with only one aspect of the bioenergy system.
Several authors have included in their biomass supply
chain modelling efforts also the bioenergy conversion facility,
generating electricity and/or heat. The results from using two
biomass-to-electricity conversion technologies, a C/ST (fluid-
ized bed combustion with steam turbine) and G/CC (fluidized
bed gasification with combined gas–steam cycle), were
compared in Ref. [12], concluding that 56–76% of the total
system operational costs are due to the biomass logistics,
thus indicating the potential for cost reduction. Similarly,
a comparative economic evaluation of various bioenergy
conversion technologies was performed in Ref. [13], using
a comprehensive biomass-to-electricity and ethanol model
(BEAM). In Ref. [14] a detailed cotton-stalk supply chain model
that employs an LP optimization for the biomass delivery
scheduling was presented. This model was applied for
centralized (electricity) and decentralized combined heat
and power (CHP) power plant scenarios. A GIS-based model
to estimate the potential for electricity production from
multiple agricultural residues was developed in Ref. [15].
However, the authors do not focus explicitly on the
implications of using multiple biomass sources on logistics
and warehousing costs. In a similar vein, a technoeconomic
assessment of a biomass power plant is performed in
Ref. [16], using a mixture of many biomass types. The authors
focused mainly on reducing the biomass logistics costs, and
more specifically, on eliminating biomass warehousing needs
by performing a two-stage optimization: firstly, the CHP
power plant location is determined to minimize the transpor-
tation distance and secondly, dynamic programming optimi-
zation is employed to identify the optimum biomass fuel mix.
None of the abovementioned models is designed to tackle
the most practical problem, which concerns satisfying
a currently existing energy demand (electricity and/or heat).
Rather, these models mostly aim at determining (and some
of them optimizing) the cost of biomass logistics and its
energy conversion, while at the same time assuming that
the energy generated will be exploited. Nevertheless, this
assumption is very optimistic in real life conditions, where it
is extremely difficult to find an existing heat or electricity
demand that would perfectly match the economically inter-
esting biomass potential calculated by these models. In
a practical case, one should first identify a suitable application
for the biomass-to-energy facility and then examine the
economic potential of exploiting the locally existing biomass
types with the objective of satisfying real energy demand.
Few models of this kind have been developed, one of them
presented in Ref. [17], where a biomass supply chain of two
fuels (namely, straw and reed canary grass) is simulated for
use in district heating applications. This discrete event simu-
lation model aimed at satisfying a daily average heating
demand load and the authors concluded that a 15–20% cost
reduction can be achieved when using two biomass types
instead of one, due to increased efficiency of the biomass
supply chain. A similar approach, but only for one biomass
type, was adopted in Ref. [18] to determine an economic
energy supply structure, covering existing heating demand
with district heating network. The problem was formulated
as an MILP (mixed-integer linear programming) optimization
using a dynamic evaluation of economic efficiency, and binary
operators to determine whether to construct or not a district
heating network, a heating plant or a co-generation plant.
Finally, a combination of GIS, mathematical modelling and
optimization for energy supply at a regional level from forest
biomass was recently presented in Ref. [19]. The system in
question attempted to partially satisfy locally existing heat
and electricity needs. The model developed employs GIS to
calculate the transportation cost from all potential biomass
collection points to all potential CHP plant locations. Then,
optimization is performed regarding the optimal sizing of
the power plant (defining which kind of energy to produce
for the specific area), and biomass collection and harvesting
scheduling.
1.2. Objectives
The model presented in this paper aspires to combine various
advanced features, to form a practical decision support
system (DSS) for investment analysis and optimization of
a bioenergy conversion investment. The major characteristics
of the model are
1. Multi-biomass supply chain. The model is able to incorporate
parametrically a large number of biomass types. The
outcome indicates, among other results, which biomass
types and at which quantities should be selected to opti-
mize the financial yield. The multi-biomass approach leads
to increased efficiencies in the biomass supply chain,
especially when biomass types with high seasonality are
concerned, according to several researchers [16,17,20].
2. Tri-generation with district heating and cooling (DHC). Tri-
generation is the generation of three types of energy
products, namely, electricity, heat and cooling, from one
plant. Recent technological advancements and cost
reductions of absorption chillers have made tri-generation
more attractive. Tri-generation combined with DHC
biomass and bioenergy 33 (2009) 223–233224
network is of great interest for relatively warm climates,
because a significant extension of the ‘‘operational time
window’’ of such a network may be realized, as opposed
to traditional district heating applications. The proposed
model is the only model in the biomass-to-energy literature
that investigates the attractiveness of tri-generation
applications.
3. Demand-driven model. The simulation and optimization
model’s objective is to satisfy a specific heating and cooling
demand. Therefore, it is more appropriate for use as a DSS
for a potential investor that has identified an energy market
and wishes to examine the financial attractiveness of satis-
fying this specific market with biomass than most of the
currently existing resource-focused models.
4. System-wide modelling and optimization. Optimization is
applied to the whole bioenergy system and not only to
one of its constituents, thus ensuring that the global
optimum design and operational characteristics for the
system are identified.
The DSS presented in this paper aims to provide the
investor with optimal answers concerning the following
investment issues:
Which is the best location to establish the biomass-
to-energy facility?
Which is the optimal relative size of the base-load CHP unit
and the peak-load boiler?
Which amount of each locally available biomass type
should be used and from where should it be collected?
For the purposes of this study optimality is perceived in
terms of investment analysis criteria, which is eventually
the main interest of every investor. However, certain techno-
logical, legislative and social constraints restrict the set of the
feasible solutions from which the optimal one is identified.
2. System structure
2.1. Problem definition
An investor, either a private entity or a regional authority, has
identified a small- to medium-scale heating and cooling
demand that could be fully supplied by exploiting locally
existing biomass. The investor wishes to assess the profit-
ability of constructing and operating a bioenergy conversion
unit to satisfy this energy demand, motivated partly by the
current legislation concerning renewable energy investments
in Greece that offers large subsidy on investment.
2.2. Brief model description
The model simulates the operation of a system comprising of
the biomass supply chain, the bioenergy conversion plant and
the DHC network that will supply the final customers with the
energy products needed. The decision maker may decide
which of the locally available biomass types will be included
for consideration in the model. The ultimate objective of the
whole system simulation is to fully satisfy the thermal and
cooling demand in the financially most efficient manner.
Thus the system operates at a heat-match mode. Heat
produced by the CHP unit and the biomass boiler may be
used for heating purposes or it may be transformed to cooling
using absorption chillers. The electricity produced is sold at
the national grid at prices that are determined by the Greek
Regulatory Authority for Energy (RAE).
The system may be broadly classified into three subsys-
tems: biomass supply chain, bioenergy conversion facility
and DHC system.
2.3. Biomass supply chain
The biomass supply chain may be further disaggregated into
biomass harvesting, loading, transportation, unloading,
handling and warehousing operations. A more detailed aspect
of the subsystems and their interrelationships follows.
2.3.1. Harvesting and loading
The model requires as input the price of biomass including the
purchasing and the loading cost. The reason for this assump-
tion is that any kind of biomass may be parametrically
included in the model by entering some of the most important
characteristics such as density (bulk), moisture (wet and
dried), heating value (wet), etc. It is practically impossible
though to have information about the various collection and
loading methods that may be used in connection to every
possible biomass type. Therefore, in order to secure the
universality and the flexibility of the model, collection and
loading costs are included in the biomass price.
The data concerning the biomass existing in the region
examined come from the National Statistical Service of Greece
(NSSG). Statistical data have been gathered concerning the
total area that each cultivation type occupies in each munici-
pality (which is the highest level of detail available). The data
have been processed with GIS software and they have been
connected to the longitude and latitude of the centroid of
each geographical ‘‘parcel’’, i.e. municipality. Therefore, it is
assumed that biomass produced in a specific parcel is
available at the centroid of the parcel, for transportation
calculations. The area occupied with each cultivation type is
multiplied by a biomass yield ratio, which signifies the
expected biomass yield per area unit and a residue availability
ratio, denoting the percentage of the residue that may be
considered available for energy production purposes. These
ratios are considered fixed for the whole region examined.
2.3.2. Transportation
Transportation is performed by standardized transportation
vehicles. The alternative use of farmer-owned tractors and
platforms has not been considered, as they may be unavail-
able for a long period of use. The transportation vehicles
required for each time period are contracted from a trucking
company. The type of vehicle assumed is truck with trailer,
according to Ref. [6], with maximum load 25 tons and
maximum volume 120 m
3
. The average travel speed is
assumed to be 50 km h
1
loaded and 60 km h
1
unloaded
and it is operated by one driver.
Transportation costs are a function of the transportation
distance and the time required for the transportation vehicle
biomass and bioenergy 33 (2009) 223–233 225
to make a return trip. The transportation distance is
calculated for every potential location of the bioenergy
conversion facility during the optimization procedure, by clas-
sifying the available biomass into co-centric rings (annuluses)
with user-defined breadth. The transportation distance is
then calculated as the radius of the circle dividing the annulus
into two annuluses of equal area, multiplied by a tortuosity
factor (2
1/2
), similarly to Ref. [17]. Time spent by the transpor-
tation vehicle includes, apart from pure transportation return
trip time, the loading and unloading standing time. Maximum
transportation distance is user-defined and is set to 40 km for
the case study. Biomass of each type is assumed to be
collected and transported in a linear pattern during its entire
harvesting period.
2.3.3. Unloading and warehousing
Biomass is transported from the fields immediately to the
centralized warehouse which is attached to the bioenergy
conversion facility. The warehouse is of closed type, according
to Ref. [14]. This layout offers the possibility of drying the
biomass using exhaust heat from the bioenergy facility, thus
avoiding biomass quality degradation and minimizing the
loss of material during storage. For this reason, material loss
is assumed to be negligible [10,14].
Unloading is performed by using wheel loaders (hereafter
denoted as ‘‘Outside loaders’’) which carrie the biomass into
the warehouse. Loaders of the same type are used for biomass
handling and movement to the conveyor belt (hereafter
denoted as ‘‘Inside loaders’’) that transfer the fuel to the adja-
cent power plant. The simulation model calculates the appro-
priate number of inside wheel loaders and their number is
rounded towards infinity. The inside loaders are purchased
and owned by the bioenergy facility and any excess capacity
is used for moving the biomass from the transportation vehi-
cles to the warehouse. When this is not adequate, extra loaders
are contracted only for the period that biomass is available for
collection. The same type of loaders is assumed to be able to
handle all potential biomass types with only minor attachment
changes. For this reason, the investment cost of the loaders is
increased by 10%. Each loader is operated by one driver.
It is assumed that the warehouse will always hold
a minimum safety stock to ensure that biomass will have
dried adequately before it is used and to avoid a potential
unreliability of the bioenergy conversion facility towards the
final DHC customers due to fuel shortage.
2.4. Bioenergy conversion plant
The bioenergy conversion plant consists of a centralized base-
load CHP unit and a heat peak-load biomass boiler. Heat
generated may be used for district heating purposes as well
as for district cooling using absorption chillers. The relative
size of the CHP unit and the boiler is not pre-defined, as is
the usual practice in similar cases, but is calculated by the
optimization module taking into account several constraints.
The inclusion of a biomass boiler is a necessity for numerous
reasons: it can cover peak heat loads with low investment cost
and it may additionally serve as a backup heat supplier in case
of an unexpected damage in the base-load unit. Moreover, the
boiler may generate the heat required even when the base-
load unit is out of commission for maintenance. Therefore,
a higher reliability of the system towards the final heat and
cooling customers is ensured.
An important issue arising is the implications of the multi-
biomass approach adopted by the model, on the technology of
the biomass CHP plant. It is a fact that the various existing
bioenergy conversion technologies present a different ability
to handle biomass types with varying characteristics. Some
technologies are more flexible in biomass characteristics varia-
tion (e.g. fluidized bed combustion) as opposed to others (e.g.
pyrolysis),and sometypes of biomass have very similar charac-
teristics whereas othersmay havetotally different.Sinceinthis
model every biomass type may be parametrically inserted, it is
assumed that the user of the model will have the responsibility
to choose the appropriate biomass conversion technology that
will be tolerant enough to the characteristics variations of the
biomass types under consideration, and he will keep this in
mind when determining and inputting the investment, opera-
tional and maintenance cost of the CHP plant.
An electricity transmission line is constructed from the
CHP plant to the nearest grid connection point. The transmis-
sion line is assumed to be a straight line between the two
points, which is normally the case.
2.5. District heating and cooling system
The absorption chillers are installed at the bioenergy
conversion facility. They operate with heat from the CHP
unit and/or the biomass boiler and they are chosen among
commercially available models. Each chiller is connected to
its own cooling tower to allow independent operation – for
increased efficiency in partial load. The capacity of the bioen-
ergy conversion plant is determined by the maximum of heat-
ing or cooling demand load, taking also into account the DHC
network losses.
The DHC network to be constructed consists of a double
pre-insulated steel pipeline (forward and return); therefore,
it cannot accommodate simultaneous heat and cooling trans-
fer. As a result, the periods of heat and cooling demand must
not overlap and consequently this type of network is suitable
mainly for space heating and cooling applications, where
simultaneous need for heat and cooling is rare. However,
the model is easily customizable and may accommodate other
applications, like industrial process heat or cooling, even
when the two types of energy are needed simultaneously.
The pipeline is designed for the maximum medium flow,
either cold (8
C) or hot water (up to 120
C). It is therefore
obvious that the cooling capacity of a certain pipe is signifi-
cantly lower than its heating capacity for the same medium
flow. The pipeline is assumed to be a straight line between the
bioenergy conversion facility and the customer location, which
is usual in this type of pipelines. Apart from the main pipeline,
a distribution network needs to be constructed if domestic
space heating and cooling applications are considered.
3. Optimization model
The simulation and the optimization model were developed in
Matlab
ª
by Mathworks.
biomass and bioenergy 33 (2009) 223–233226
3.1. Optimization variables
The independent variables that describe the system and are
determined by the optimization method are the following:
P
MT
: the thermal capacity of the base-load CHP plant (MW).
The electrical capacity of the plant (P
ME
) is proportional to
the thermal capacity, as a fixed power-to-heat ratio (PHR)
is assumed.
P
B
: the thermal capacity of the peak-load biomass boiler
(MW).
Xb
i
: the total amount of the ith biomass type to be procured
each year (tons of wet biomass).
VW
0
: the initial yearly biomass inventory (m
3
). This variable
is necessary, as the calculations are based on a rolling
horizon framework, similarly to Ref. [10].
X
PL
and Y
PL
: the optimum location (geographical coordi-
nates) to construct the bioenergy facility (km).
3.2. Objective function
The objective function to be maximized is the net present value
(NPV) of the investment for the project’s lifetime. NPV was
chosen not only because it is the most frequently used invest-
ment appraisal criterion in co-generation plant investments
[21], but also as it is considered theoretically superior to other
criteria [22]. The model calculates also the values of other
investment criteria for the optimum solution found (IRR, pay
back period), but the optimization process is based on NPV.
The NPV function to be maximized is
NPV ¼ðR
E
þ R
EP
þ R
H
þ R
C
þ R
G
ÞDf
I
W
I
M
I
B
I
ET
I
DH
I
C
ðA
BP
þ A
BT
þ A
W
þ A
M
þ A
B
þ A
ET
þ A
DH
þ A
C
ÞDf ð1Þ
It should be noted that the objective function calculates the
NPV before taxes. All the annual monetary amounts are multi-
plied by a discounting coefficient Df, which turns them into
present values:
Df ¼
1 ½1 þði rÞ=ð1 þ rÞ
N
i r
(2)
where i is the interest rate, r is the inflation rate and N is the
investment lifetime.
3.3. Revenues of the facility
The revenues of the facility presented here are all in annual
amounts. R
E
is the revenue from net electricity sale to the grid:
R
E
¼ C
E
ð1 n
E
Þ
X
T
t¼1
E
MEt
E
DC
!
(3)
where E
ME
¼ E
MT
PHR is the electricity produced, E
DC
is the elec-
tricity consumed in absorption chillers’ operation, n
E
is the
electricity transmission losses and t ¼ 1,.,T is the time period.
R
EP
is the electricity capacity availability reimbursement:
R
EP
¼ 12sC
PE
P
ME
(4)
where s ¼ 0.9 for biomass and C
PE
is the income from capacity
availability (V/kW).
R
H
is the revenue from heat sales:
R
H
¼ C
T
X
T
t¼1
E
HDt
(5)
where C
T
is the price of selling a thermal kWh and E
HDt
is the
heat demand of the customers in each time period t. C
T
is
proportional tothe priceofoil,asoilisinmostcasesthecompet-
itive fuel that the potential customers will be currently using.
Even if they are using another fuel, e.g. natural gas, it is always
the case that its price will be connected to the price of oil. In
this model it has been assumed that heat will be sold to the
customers at a price 20% lower than the respective price of oil.
R
C
is the revenue from cooling sales:
R
C
¼ C
C
X
T
t¼1
E
CDt
(6)
The price C
C
of a cooling kWh is assumed to be 0.036V, when
the respective variable cost of producing it using normal elec-
tric compression chillers for a typical household in Greece was
calculated to be in the range of 0.036 and 0.05V. E
CDt
is the
cooling demand of the customers in each time period t.
R
G
is the revenue from GHG emissions’ reduction trading:
R
G
¼ðG
E
þ G
T
þ G
C
ÞC
CO
2
(7)
where G
E
, G
T
and G
C
are the GHG reductions achieved from net
electricity produced and from substituting heat produced by
oil and cooling produced by electricity, respectively. C
CO
2
is
the market price of a ton CO
2
equivalent.
3.4. Expenses
3.4.1. Biomass supply chain-related expenses
A
BP
is the annual biomass purchasing and loading cost:
A
BP
¼
X
n
i¼1
Xb
i
Bpr
i
(8)
where Bpr
i
is the purchasing and loading cost of each biomass
type i ¼ 1,.,n.
A
BT
is the annual biomass transportation cost:
A
BT
¼
X
n
i¼1
X
L
l¼1
Xb
il
ðC
TDi
Ltr
l
þ C
TTi
Ttr
l
Þ (9)
The coefficients C
TD
and C
TT
represent the specific transporta-
tion cost per unit of transportation distance and per unit of
time, respectively. C
TD
is mainly affected by the fuel cost while
C
TT
by salaries, insurance, depreciation and maintenance
costs. Ltr is the trip distance and Ttr is the return trip time,
for every distance class l ¼ 1,.,L. For transportation calcula-
tions, the vehicle capacity V
C
is defined as
V
C
¼ min
f
V
CW
; V
CV
g
(10)
where V
CW
and V
CV
are the vehicle’s weight and volume
capacity, respectively.
I
W
is the warehousing equipment and loaders’ investment
cost:
I
W
¼ðE
W
C
W
þ I
L
Þ (11)
where E
W
is the warehouse area (m
2
), C
W
is the warehouse
specific investment cost (V m
2
) and I
L
is the warehousing
equipment and loaders’ investment cost (V).
biomass and bioenergy 33 (2009) 223–233 227
