a hybrid optimization model of biomass trigeneration...
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A Hybrid Optimization Model of Biomass Trigeneration System Combined with PitThermal Energy Storage
Dominkovic, Dominik Franjo; Cosic, B.; Bacelic Medic, Z.; Duic, N.
Published in:Energy Conversion and Management
Link to article, DOI:10.1016/j.enconman.2015.03.056
Publication date:2015
Document VersionPeer reviewed version
Link back to DTU Orbit
Citation (APA):Dominkovic, D. F., Cosic, B., Bacelic Medic, Z., & Duic, N. (2015). A Hybrid Optimization Model of BiomassTrigeneration System Combined with Pit Thermal Energy Storage. Energy Conversion and Management, 104,90-99. https://doi.org/10.1016/j.enconman.2015.03.056
1
A hybrid optimization model of biomass trigeneration system combined 1
with pit thermal energy storage 2
3
D. F. Dominković 4
Faculty of Mechanical Engineering and Naval Architecture 5
University of Zagreb, Zagreb, Croatia 6
e-mail: [email protected] 7
8
B. Ćosić* 9
Faculty of Mechanical Engineering and Naval Architecture 10
University of Zagreb, Zagreb, Croatia 11
e-mail: [email protected] 12
address: I. Lučića 5, 10 000 Zagreb, Croatia 13
phone number: +385 98 168 81 49 14
15
Z. Bačelić Medić 16
iC artprojekt ltd, Croatia 17
Varaždin, Zagreb, Croatia 18
e-mail: [email protected] 19
20
N. Duić 21
Faculty of Mechanical Engineering and Naval Architecture 22
University of Zagreb, Zagreb, Croatia 23
e-mail: [email protected] 24
25
2
ABSTRACT 26
27
This paper provides a solution for managing excess heat production in trigeneration and thus, 28
increases the power plant yearly efficiency. An optimization model for combining biomass 29
trigeneration energy system and pit thermal energy storage has been developed. Furthermore, 30
double piping district heating and cooling network in the residential area without industry 31
consumers was assumed, thus allowing simultaneous flow of the heating and cooling energy. 32
As a consequence, the model is easy to adopt in different regions. Degree-hour method was 33
used for calculation of hourly heating and cooling energy demand. The system covers all the 34
yearly heating and cooling energy needs, while it is assumed that all the electricity can be 35
transferred to the grid due to its renewable origin. The system was modelled in Matlab© on 36
hourly basis and hybrid optimization model was used to maximize the net present value 37
(NPV), which was the objective function of the optimization. Economic figures become 38
favourable if the economy-of-scale of both power plant and pit thermal energy storage can be 39
utilized. The results show that the pit thermal energy storage was an excellent option for 40
storing energy and shaving peaks in energy demand. Finally, possible switch from feed-in 41
tariffs to feed-in premiums was assessed and possible subsidy savings have been calculated. 42
The savings are potentially large and can be used for supporting other renewable energy 43
projects. 44
45
Keywords: trigeneration, seasonal storage, optimization, biomass, feed-in tariff, feed-in 46
premium 47
48
49
50
3
51
1. INTRODUCTION 52
53
Worldwide demand for energy is increasing; as a consequence fossil fuel resources are 54
becoming more and more expensive, in the same time making renewable energy resources 55
more competitive. The European Union has adopted 20-20-20 targets until 2020, which 56
means increased energy efficiency by 20%, reduced greenhouse gas emissions by 20% and 57
reaching a 20% share of renewable in total energy generation [1]. In the EU’s 2030 58
framework for climate and energy policies presented in January 2014, continuing progress 59
towards a low-carbon economy is expected [2]. The most important objective by 2030 is to 60
reduce the greenhouse gas emissions by 40% below the 1990 level, while increasing the 61
renewable energy share to at least 27%. In order to achieve this target, improvements in the 62
energy efficiency are needed. 63
64
One good example in improving energy efficiency throughout the year is combined 65
production of electricity, heating and cooling energy in trigeneration [3]. At the same time, 66
using biomass as a fuel for the trigeneration power plant increases the renewable energy share 67
in the overall production mix. Rentizelas et al. [4] provide an optimization model for energy 68
supply based on multi-biomass trigeneration, covering peak demand with a biomass boiler. 69
Puig-Arnavat et al. [5] assessed different trigeneration configurations based on biomass 70
gasification. A Borsukiewicz-Godzur et al. [6] calculated results for three variants of 71
combined heat and power (CHP) biomass plants. A techno-economic assessment of biomass 72
fuelled trigeneration system was made by Huang et al. [7]. Recently, Wang et al. [8] 73
published a paper dealing with multi-objective optimization of a combined cooling, heating 74
and power system driven by solar energy. Zhao et al. [9] analyzed the energy efficiency level 75
4
for a station in China, which uses a trigeneration system. Although this is still a small-scale 76
trigeneration system, used for a single building, interesting economic figures have been 77
achieved, i.e. simple pay-back time of the additional investment was 5.47 years. There are 78
also papers dealing with micro-trigeneration system such as Angrisani et al. [10], where a 79
trigeneration system on a small-scale is assessed. Nevertheless, Kilkiş [11] developed a model 80
for the net-zero exergy district development for a city in Sweden, which among other units 81
includes a CHP plant with district heating and cooling system. 82
83
In the simultaneous generation of electricity, heating and cooling energy, the system should 84
be optimized to follow heating energy demand in order to achieve maximum efficiency of the 85
useful energy being utilized. Please note here that due to the renewable nature of the biomass 86
being considered, electricity generated has preference when supplying to the grid and thus, it 87
is considered that all the electricity can be transferred to the grid at anytime. On the other 88
hand, the feed-in-tariff for electricity is the most important income for investors in 89
trigeneration power plant. In order to be eligible to receive feed-in-tariff, minimum overall 90
yearly power plant efficiency has to be reached. One way of achieving high, relatively 91
constant heat demand is to use dryers for reducing the moisture content in biomass. Currently, 92
legislation in Croatia allows this, but it is questionable if it will be allowed in the future as it is 93
not the most efficient way of using the heat energy. According to Härkönen [12], after 94
reaching the equilibrium moisture, which will happen naturally, after a required period of time 95
when exposed to the outside air, heat of desorption increases linearly as the moisture content 96
is getting lower. The biomass in Croatia is delivered to the power plant with up to 30% of 97
moisture, after which the heat needed for drying biomass increases significantly by reducing 98
the moisture content in biomass. Moreover, the increased size of wood significantly increases 99
energy consumption in dryers and drying can become unprofitable as shown by 100
5
Gebreegziabher et al. [13]. Thus, the drying will not be considered as an option to utilize heat 101
in this paper. As a consequence of not having a constant heat consumer, seasonal thermal 102
energy storage will be incorporated in the optimization model in order to deal with the peak 103
demand, as well as with large differences in heating and cooling energy demand throughout 104
the seasons. 105
106
Currently in Croatia, for the system being assessed, only feed-in tariffs for cogeneration 107
power plants or biomass electric power plants would be applicable, while the feed-in tariffs 108
for trigeneration systems do not exist. Both options are at the same level for the capacities 109
being considered in this paper. However, feed-in-tariff for the pit thermal energy storage 110
(PTES) would be of great significance for the economic feasibility of investment. Krajačić et 111
al. [14] provided an overview of potential feed-in-tariffs for different energy storage 112
technologies. For the system being assessed, the triple tariff, as discussed in Lund and 113
Andersen [15], would be significantly supportive towards the economic viability of the 114
chosen system. Furthermore, neither a feed-in-tariff for district heating and cooling network is 115
available in Croatia. As shown in Rezaie and Rosen [16], district heating in densely populated 116
regions would be a favourable investment compared to low-density residential areas. 117
However, in this case study, a neighbourhood consisting of family houses was considered. 118
119
Nevertheless, the importance of seasonal heat storage in a future sustainable energy system in 120
Croatia was assessed by Krajačić et al. [17]. Without seasonal heat storage, critical excess in 121
electricity production, as well as intermittency of wind power plants production, will be 122
difficult to deal with. 123
124
6
Up to now, most papers have dealt with the solar thermal energy coupled with the seasonal 125
energy storage [18-22]. Raine et al. [23] optimized combined heat and power production for 126
buildings using a heat storage. However, storage volumes in two different scenarios had 127
volumes of only 600 m3 and 350 m
3. Thus, these were not large-scale seasonal storages. 128
Rezaie et al. [24] assessed exergy and energy efficiencies of a seasonal hot water storage 129
combined with solar collectors and boilers. When there is no instant need for heating energy, 130
it can be stored in the large-scale pit thermal energy storage and used later when there will be 131
need for the heating energy. In Mangold [25], it is shown that the economy-of-scale is 132
significant till water storage volumes of 50,000 m3. Moreover, according to Energo 133
Styrelsen’s publication [26], the economy-of-scale for the low capacity range is quite 134
considerable. 135
136
The novel approach in this paper is a combination of large scale seasonal pit thermal energy 137
storage and biomass trigeneration power plant. The model will be developed in order to make 138
the most of economy-of-scale. Moreover, in order to develop the model which can be easily 139
replicated, only residential buildings will be considered as heat consumers. From the demand 140
side point of view this is the worst case for covering the heating and cooling load throughout 141
the year as there is no constant need for heating or cooling energy. 142
143
Furthermore, the guidance for the design of renewables’ support schemes [27] has been issued 144
by the European Commission. Feed-in-premiums, variable or fixed, were given preference 145
over feed-in-tariffs. Under the feed-in tariff, power plants do not trade any electricity on the 146
market; they rather receive a fixed amount of subsidy per energy unit of generated electricity. 147
On the other hand, under both variable and fixed feed-in premiums, power plant trades the 148
electricity generated on the market, on top of which it receives a premium, which should 149
7
fairly compensate the costs of generating the energy from the renewable energy sources. In 150
the case of fixed feed-in premium, there is a larger risk placed on an investor, as the amount 151
of subsidy on top of the market price is fixed. In the case of variable feed-in premium, a lower 152
risk is imposed on the investor as the total amount of income per unit of energy generated is 153
guaranteed to the investor and known in advance. Variable premium changes as the price on 154
the market changes, keeping the total income per unit of energy generated constant. In both 155
variable and fixed premiums, one part of the income for the investor is received from the 156
market, reducing the total subsidy needed to be paid off by the governmental body or agency. 157
158
As Croatia has implemented feed-in-tariffs as a renewables’ support scheme, this paper will 159
also estimate levels at which feed-in-premiums, both variable and fixed, should be set to in 160
order to replace the current mechanism. At the end of 2013, seven countries in the EU28 were 161
using feed-in premiums or combination of feed-in premiums and other supporting schemes 162
[28]. Other common supporting schemes are green certificates and tenders. So far, feed-in 163
systems proved to be more efficient than the green certificates [29]. Potential savings in 164
expenditure on subsidies by the government, by adopting feed-in premiums, were assessed, 165
too. 166
2. METHODOLOGY 167
2.1. Problem definition 168
169
An investor who decides to invest funds wants to maximize profit. In a trigeneration power 170
plant the crucial role for maximizing income is the generated electricity sold at a price set by a 171
feed-in-tariff. Consequently, the best way to maximize profit would be to produce as much 172
electricity as possible. On the other hand, technically, the system is driven by heat demand in 173
order to maximize efficiency. In order to satisfy both economic and technical targets, the 174
8
feed-in-tariff eligibility is usually constrained by a minimum overall efficiency of the power 175
plant. In Croatia, the minimum average yearly efficiency needs to be above 50% [30] in order 176
to receive the maximum feed in tariff, while some other examples include Austria (60%), 177
Greece (65%) and Ireland (70%) [31]. Taking this into account, the model is possible to be 178
adopted and used in many European countries. In order to have a constant electricity 179
production, while still having an overall efficiency above the minimum allowed level, a 180
relatively constant heat demand is needed. However, as it is shown that the heat demand has a 181
strong seasonal pattern, especially in housing dwellings [32] and [33], there is a need to 182
develop a model which will offset high seasonality. Thus, the scope of this paper is to answer 183
the research question: “How should a district heating and cooling (DHC) system, including a 184
biomass fired CHP plant, absorption chillers and a PTES, be dimensioned in order to 185
maximize the NPV depending on system efficiency requirements for feed-in tariff 186
eligibility?”. 187
188
The system efficiency is defined by the ratio of usefully delivered energy and the total fuel 189
consumption (in this case biomass). Term usefully delivered energy covers all the electricity 190
delivered to the electrical grid, no matter what the demand for the electricity in the specific 191
area is, and heating and cooling energy consumed by the end-consumers (households). 192
Consequently, heat stored in the thermal energy storage and later used by the consumers is 193
considered as a usefully delivered energy. 194
2.2. Model description 195
196
The model optimizes the sizes of the seasonal thermal storage, the biomass power plant and 197
the absorption units which are subject to different constraints. The decision maker can set the 198
targeted overall efficiency of the power plant. The first target of the system is to fully cover 199
9
the heating and cooling energy demand. As a consequence, seasonal energy storage, besides 200
storing energy in periods with lower demand, shaves peaks in heating energy demand for 201
periods with higher demand, which usually occur during the winter season. This means that a 202
peak boiler is not necessary in the system. It is assumed that all the electricity produced in the 203
power plant can be sold to the network for the price specified by the feed-in-tariff. The 204
produced heat can be used for district heating, district cooling by using absorbers, or stored in 205
the energy storage. The three main system components are the biomass power plant, absorbers 206
and the seasonal pit thermal energy storage (PTES). 207
208
209
Figure 1. The scheme of the modelled system 210
211
The interactions within the systems can be easily understood by studying the following logic 212
tree: 213
214
10
215
Figure 2. A logic tree representation of the decisions made by the technological system 216
217
To sum up, the system presented will cover all the heating and cooling energy demand by the 218
consumers in the considered area, as well as produce a significant amount of electricity, 219
which will be transferred to the electrical grid, no matter what the generation amount equals 220
to. 221
2.3. Biomass power plant 222
223
The biomass power plant size is calculated, taking into account the heating and cooling 224
demand. As the model is heat driven, the electricity generating capacity follows the heat 225
consumption throughout the year. As an average biomass power plant has the availability of 226
approximately 90%, the model calculates the part of the year with the lowest energy demand 227
where the biomass power plant is shut down for maintenance. During this period the 228
heating/cooling demand is completely covered by the seasonal energy storage. 229
2.4. Heating and cooling demand 230
231
11
Heating and cooling demand are calculated by using degree hours, based on hourly 232
temperatures valid for the considered location. Yearly heating and cooling energy 233
consumption per m2 has to be assumed by the decision maker for the specific location. The 234
district heating and cooling network consist of double piping each, thus, allowing 235
simultaneous cooling and heating energy flow. This is of great importance during the summer, 236
when the demand for cooling energy exists due to high temperatures, as well as for the 237
heating energy for the domestic hot water (DHW) preparation. Moreover, this also allows the 238
model to be adopted by industrial consumers, as it is possible to provide both heating and 239
cooling energy simultaneously. 240
241
Calculated total heating energy for space heating, DHW preparation, as well as the cooling 242
energy demand is shown in Figure 3. The DHW distribution has been adopted from the 243
ASHRAE standard [34]. 244
245
246 247
Figure 3. Heating and cooling energy demand for the city of Osijek 248
249
0
5000
10000
15000
20000
25000
30000
1
25
9
51
7
77
5
10
33
12
91
15
49
18
07
20
65
23
23
25
81
28
39
30
97
33
55
36
13
38
71
41
29
43
87
46
45
49
03
51
61
54
19
56
77
59
35
61
93
64
51
67
09
69
67
72
25
74
83
77
41
79
99
82
57
85
15
kW
hour DHW demand Heating energy demand Cooling energy demand
12
2.5. Absorbers 250
251
Absorbers in the system are driven by the heat generated from the biomass power plant. They 252
can be driven directly by the produced heat in power plant or by the heat stored in the 253
seasonal energy storage. Absorbers were preferred, compared to adsorbers, because they have 254
a lower investment cost. As it is predicted that the water in the seasonal storage will be stored 255
with temperatures between 85oC and 90
oC, the predicted LiBr-H2O single effect absorbers are 256
able to work properly [35] and [36]. 257
2.6. Seasonal energy storage 258
259
Pit thermal energy storage (PTES) was chosen for the seasonal heat energy storage mostly 260
due to low investment cost. Water as a storage media is a well-developed solution and so far, 261
the only mature technology for large volume storages. According to [37], PTES are the largest 262
thermal energy storages being built. Typical efficiency of such storage is between 80% and 263
95%, depending on the temperature level in the storage [26]. As economy-of-scale after 264
volume of 50,000 m3 does not apply, it is possible to build a few PTES instead of one if the 265
storage volume in the model becomes very large. 266
267
The average yearly efficiency of the seasonal thermal energy storage in this model is set to 268
80% and is independent of the time that the heat is stored. This simplification is valid as the 269
seasonal storage is mostly used for the storage of the heat during the longer period of time, 270
which can be used as a reference for calculating the average efficiency of the storage. 271
Moreover, for such large capacities, as it is the case with this model, the surface-to-volume 272
ratio declines rapidly, which significantly reduces a heat exchange surface on the walls of the 273
13
storage. Thus, picking a lower average efficiency from the efficiency span reported in the 274
literature [26] is a valid assumption. 275
3. OPTIMIZATION MODEL 276
3.1. Optimization variables 277
278
Three independent variables determined by the optimization model are: 279
elP - electricity generating capacity of the biomass trigeneration power plant in kWe. 280
The heat capacity ( elP ) is proportional to the electricity generating capacity, following 281
assumed fixed heat-to-power ratio. 282
VS - volume of the storage in m3 283
AP - capacity of the absorber unit(s) in kW 284
285
3.2. Objective function 286
287
Maximizing net present value for the project lifetime, during which feed-in-tariff is assumed 288
as guaranteed, was the objective in the optimization model. Although a biomass power plant 289
has a much longer lifetime, this assumption was introduced in order to reduce vagueness 290
about the future electricity price predictions. The optimization model also calculates the 291
internal rate of return (IRR) and the simple pay-back period in order to provide enough inputs 292
for the decision making process. The NPV function is: 293
294
14
, , , ,
h c el OM Bf OM Bv OM DHCn OM S fB
B A DHCN S
NPV I I I E E E E E D
Inv Inv Inv Inv
( 1 ) 295
296
where all the future annual income and expenditure values are multiplied by a discount 297
coefficient D: 298
299
1
1t
Di
( 2 ) 300
301
where i is the discount rate and t is the project lifetime. 302
3.2.1. Income 303
304
There are three income items in the model; revenues from electricity, heating and cooling 305
energy sales. As the power plant needs to satisfy all the need for heating and cooling energy, 306
it can be assumed that all the heating and cooling energy need for the district considered is 307
sold from this power plant. Income from the heat sales during the one year Ih equals: 308
309
8760
1
h P j
j
I h h
( 3 ) 310
311
where hP is the price of kWh of heat, hj is the hourly value of heat demand (kWh) throughout 312
the year. 313
314
Ic is the income from the sales of cooling energy: 315
15
316
8760
1
c P j
j
I C c
( 4 ) 317
318
where CP is the price of kWh of the cooling energy and cj is the hourly value of the cooling 319
demand (kWh) throughout the year. 320
321
Iel is the income from the sales of electricity: 322
323
8760
1
el P j pp
j
I E e e
( 5 ) 324
325
where EP is the price of kWh of electricity, ej is the hourly value of electricity production 326
(kWh) and epp is the power plant's own electricity consumption throughout the year. 327
3.2.2. Expenditure 328
329
There are five expenditure items; fixed and variable operating and maintenance cost of the 330
biomass power plant, operating costs of district heating and cooling network and thermal 331
energy storage and cost of fuel, which is biomass in this case. 332
333
,OM BvE is the expenditure on variable O&M: 334
335
8760
,
1
OM Bv j
j
E V e
( 6 ) 336
16
337
where V is the variable cost of O&M (€/kWhe). 338
339
,OM BfE is the expenditure following fixed O&M cost: 340
341
,OM Bf elE F P ( 7 ) 342
343
where F is the fixed yearly O&M cost (€/kWe). 344
345
,OM DHCnE is the O&M cost of district heating and cooling network: 346
347
,OM DHCnE Z N ( 8 ) 348
349
where Z is the number of dwellings in a district considered and N is the cost of yearly network 350
maintenance (€/dwelling). 351
352
,OM SE is the O&M cost of storage: 353
354
,OM S VE U S ( 9 ) 355
356
where U is the O&M price of the yearly storage maintenance (€/m3). 357
358
fBE is the expenditure on fuel (biomass): 359
17
360
8760
1
1 1fB j
jd el
E B eh
( 10 ) 361
362
where B is the price of biomass (€/ton), hd is the lower calorific value of biomass (kWh/ton) 363
and ηel is the electrical efficiency of the power plant. 364
3.2.3. Investment 365
366
The overall investment consists of four parts; investment in the biomass power plant, in 367
absorption chillers, in district heating and cooling networks and in the pit thermal energy 368
storage. Investment in the biomass power plant BInv is calculated as follows: 369
370
B inv elInv B P ( 11 ) 371
372
where invB is the price of investment per power plant capacity (€/kWel). 373
374
AInv is the price of investment in absorption chillers: 375
376
1A inv peakInv A C
COP ( 12 ) 377
378
where invA is the price of investment per absorption capacity (€/kW), peakC is the peak 379
demand for cooling energy (kW) and COP is the coefficient of performance of the absorption 380
units. As mentioned before, the model predicted that all the cooling energy needs to be 381
18
satisfied from this power plant, thus the needed capacity of absorption units is equal to peak 382
cooling demand divided by the coefficient of performance, which was set in this model to 0.7. 383
384
Investment in the district heating and cooling network DHCNInv is calculated as follows: 385
386
DHCN invInv N Z ( 13 ) 387
388
where invN is the investment per dwelling (€/dwelling). In this model invN was used from Ref. 389
[38]. 390
391
Investment in the pit thermal energy storage SInv : 392
393
S inv VInv S S ( 14 ) 394
395
where invS is the price of storage investment (€/m3), which was implemented in this model 396
from Ref. [26]. 397
3.3. Constraints 398
399
The heat demand in every hour j throughout the year needs to be covered, either by biomass 400
power plant production, by heat stored in PTES, or by both sources of heat: 401
402
, ,VB j S j jh h h ( 15 ) 403
404
19
where ,B jh is the hourly heat production in the biomass power plant and
,VS jh is the heat taken 405
from PTES on an hourly basis. 406
407
Heat used in the absorption units needs to cover the cooling demand in every hour j 408
throughout the year: 409
410
, ,
1VB j S j jh h c
COP ( 16 ) 411
412
The sum of the heat production capacity of the biomass power plant and the heat from the 413
storage that can be taken has to be larger or equal to peak heat demand: 414
415
1
3600el V w p S peakP HTP S c T h ( 17 ) 416
417
where HTP is the heat-to-power ratio, w is the density of water (kg/m3),
pc is the specific 418
heat capacity of water (kJ/(kgK)), T is the difference in temperature of stored water and the 419
design temperature of the dwellings’ heating systems (K), S is the efficiency of the PTES 420
and peakh is the peak heat demand (kW). 421
422
The cooling energy peak demand needs to be covered in the same manner as the heating 423
energy peak demand: 424
425
1
3600el V w p S peakP HTP COP S c T COP c ( 18 ) 426
20
427
Storage volume size has to be able to store all the heating energy which needs to be taken at 428
certain time from the PTES: 429
430
,
1 1 1 13600
VS sum V
p S
h Sc T
( 19 ) 431
432
where ,VS sumh is the sum of heating energy which needs to be taken from the storage in the 433
longest period of time where average biomass heat production rate is lower than heat demand 434
(under the term “heat demand”, “cooling energy demand” is also assumed, which is the same 435
in this model except COP coefficient which needs to be taken into account). 436
437
18760el av X
el
e h P B
( 20 ) 438
439
where e and h present the produced electricity and heat demand during one year of power 440
plant operation, el is the electrical efficiency of the power plant, avB is the availability of the 441
biomass power plant and X is the minimum overall efficiency power plant needs to have to 442
be eligible to receive subsidy. 443
3.4. Optimization method 444
445
A hybrid optimization method was used to optimize this problem. As this is a non-linear 446
problem, a Genetic Algorithm and fmincon were used in Matlab©. The Genetic Algorithm 447
has been recently applied in several papers for the optimization of the energy systems, such as 448
21
in optimization of low-temperature district heating network [39]. It is a useful optimization 449
method, which approaches to a global optimum very fast because it generates a population of 450
points at each iteration, instead of a single point at each iteration in a classical algorithm [40]. 451
However, it converges relatively slowly when it reaches a solution close to the global 452
optimum. Thus, after Genetic Algorithm, fmincon starts and finds a minimum of the 453
constrained nonlinear multivariable function [40]. However, fmincon needs to have a good 454
initial point in order to end up in the global optimum instead of a local optimum. Thus, hybrid 455
programming optimization method has proven to be very effective for this type of problem. 456
4. CASE STUDY: the City of Osijek 457
458
The model was applied to a district in the city of Osijek. Osijek is one of the four largest cities 459
in Croatia. 2000 dwellings with 200 m2, with an average spacing of 10 meters between each 460
of them were assumed. In Croatia, the yearly average heating energy consumption is rather 461
high and 160 kWh/m2 of heating energy per annum was assumed. In order to be eligible for 462
the feed-in support, in Croatia, overall yearly efficiency of the power plant has to be above 463
50% [30]. Biomass moisture is considered to be relatively constant at 30% as this is the usual 464
case in Croatia. Input data for the case study are presented in Table 1. 465
466
467
468
469
470
471
472
473
22
Table 1. List of data used in case study 474
475
amount unit ref.
Power plant availability 0.9 [26]
Biomass price 38.5 €/ton [41]
Lower calorific value (30%
moisture)
3,500 kWh/ton [42]
η power plant total 0.89 [26]
ηel 0.3 [26]
HTP ratio 1.97 [26]
η storage 0.8 [26]
Storage temperature 90 oC [26]
invB 3,600 €/kWe [26]
invA 400 €/kW [43]
invN 8,150 €/dwelling [38]
invS 56 €/m3 [44]
Plant own electricity
consumption
6%
Discount rate 7%
Feed-in-tariff 0.156 €/kWhe [30]
COP 0.7 [43]
Design temperature for heating 21 oC
Design temperature for cooling 26 oC
F 29 €/kW per annum [26]
23
V 0.0039 €/kWh [26]
N 75 €/dwelling per annum [38]
U 0.39 €/m3 per annum [26]
Ph 0.0198 €/kWh
PC 0.0198 €/kWh
Project lifetime 14 years
476
Three case studies were conducted, with minimum yearly average power plant efficiencies of 477
50%, 65% and 75%, respectively. The first number was chosen in order to represent a current 478
situation in Croatia, where the minimum yearly efficiency needed, in order to be eligible for 479
the maximum feed-in tariff is more than 50%. The 65% efficiency was chosen in order to 480
represent the situation where the efficiency level currently used in Greece would be adapted 481
to the Croatian system. The last efficiency, amounting to 75%, was chosen in order to 482
represent a possible future stringent measures adopted in order to reduce inefficient use of 483
energy even more. A sensitivity analyses were performed and the influence of the biomass 484
price on overall results was investigated. The second parameter that was checked in the 485
sensitivity analyses was the reduced heat and cooling demand due to increased thermal energy 486
savings which resulted after applying a better insulation. Many programs of improving 487
insulation properties are being carried out in Croatia, where the government supports the 488
investment up to 47% [45]. Thus, in this case a shift from energy class E to energy class C 489
was assumed. 490
5. RESULTS AND DISCUSSION 491
5.1. Case study 1 492
493
24
In this case study, with the minimum yearly power plant efficiency of 50%, all economic 494
indicators are good and this investment would be profitable for the investor. The NPV equals 495
to 39,630,000 €, IRR is 15.0% and the simple pay-back time is 5.72 years. Optimal capacity 496
of the power plant is 14,675 kWe. The results would be even better if a higher heat price could 497
be achieved, but it was decided to use the cheaper than best alternative approach in order to be 498
certain that customers would shift to a new heat supply option. The storage size in this case 499
would be 30,350 m3. The heat from the storage in this case is only used during the time when 500
the biomass power plant is not producing heat due to regular yearly maintenance work. In 501
Figure 4 the use of storage for peak energy demand can be seen. 502
503
504
Figure 4. Operation of the system in the case study 1 505
506
One could argue here that the PTES is not a necessary component of the system, since it is 507
rarely used. A possible substitute could be a small back-up hot water boiler. However, this is 508
not the case as it can be seen from the calculation in the Table 2. It is important to keep in 509
mind that the heating energy stored in the PTES and later used by the consumers is considered 510
as usefully delivered energy by the cogeneration plant system. If the small back-up boiler 511
would be used instead of the seasonal storage, the amount of heat used from PTES now would 512
0
500
1.000
1.500
2.000
2.500
3.000
3.500
0
5.000
10.000
15.000
20.000
25.000
30.000
35.000
13
46
69
11
03
61
38
11
72
62
07
12
41
62
76
13
10
63
45
13
79
64
14
14
48
64
83
15
17
65
52
15
86
66
21
16
55
66
90
17
24
67
59
17
93
68
28
18
62
6
MW
h
kWh
hour
Electricity production [kWh] Heating energy production [kWh]
Absorption units production [kWh] Storage energy content [MWh]
25
be released into the air. Thus, the total yearly efficiency, calculated as explained in the section 513
2.1., would drop below 50%. In order to tackle this issue, the cogeneration plant should be 514
resized and lower its capacity in order to stay above the efficiency requirements for the feed-515
in tariff eligibility. 516
517
Table 2. Comparison of the two technologies in the district heating system 518
Peak
biomass
boiler
PTES
Efficiency 0.97 0.8
Investment 100 €/kW 56 €/m3 €/kW
Maximum load 7,873 7,873 kW
Total heat needed 2,397,000 2,397,000 kWh
Calorific value of the wood 3,500 - kWh/t
Wood needed 706 - t
Price of fuel 39 - €/t
Total cost of fuel 27,182 - €/year
Total investment cost 787,330 1,699,600 €
Variable cost 27,557 11,836 €/year
Yearly amortization of investment 56,238 121,400
Yearly cost (including amortized
investment) 110,977 133236
€/year
Avoided income of feed in tariff 93,714 - €/year
Savings using the PTES instead of peak
boiler
71,455 €/year
26
519
As it can be seen from the table, although running the biomass boiler instead of PTES, in the 520
case with the minimum yearly efficiency of 50%, is cheaper from the investment point of 521
view, the option with the PTES is a better choice in the system organized in this way, as it 522
enables the larger capacity of the cogeneration power plant to be installed in the first place, 523
which contributes to the better economic indicators in overall. Increasing the minimum yearly 524
efficiency to higher levels, this saving becomes larger and larger. 525
5.2. Case Study 2 526
527
Although the economic indicators in this case are slightly less favourable from the investor’s 528
point of view compared to the case study 1, it is nevertheless still economically feasible 529
investment. In this case, in which the minimum yearly efficiency is set to 65%, a current 530
efficiency level set by legislation in Greece, the NPV of the project amounts to 15,320,000 €, 531
IRR is 11.5% and the simple payback time equals 6.78 years. Optimal capacity of the 532
cogeneration plant is 8,270 kWe. 533
534
535
Figure 5. Operation of the system in the case study 2 536
0
500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
0
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
1
29
3
58
5
87
7
11
69
14
61
17
53
20
45
23
37
26
29
29
21
32
13
35
05
37
97
40
89
43
81
46
73
49
65
52
57
55
49
58
41
61
33
64
25
67
17
70
09
73
01
75
93
78
85
81
77
84
69
MW
h
kWh
hour Electricity production [kWh] Heating energy production [kWh]
Absorption units production [kWh] Storage energy content [MWh]
27
537
In Figure 5, it can be noted that, compared to the case study 1, PTES here is used extensively 538
during the high demand for heating energy during the winter time, as well as during the 539
maintenance time. 540
541
This case study shows that the PTES could be used for shaving peak energy demands instead 542
of the oversized cogeneration power plants that are now used in Croatia. Secondly, the 543
economic indicators show that a shift in legislation from minimum efficiency to be eligible 544
for the feed-in-tariff from 50 to 65% would not cause a risk to the economic performance of 545
the project. 546
5.3. Case study 3 547
548
In this case, with the minimum overall yearly power plant efficiency of 75%, the economic 549
indicators are vague for an investor. The NPV is 78,972 €, IRR is 7.0% and the simple 550
payback time is 8.73 years. Optimal capacity of the power plant is 6,590 kWe. 551
552
553
Figure 6. Operation of the system in the case study 3 554
0
2.000
4.000
6.000
8.000
10.000
12.000
14.000
0
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
13
14
62
79
40
12
53
15
66
18
79
21
92
25
05
28
18
31
31
34
44
37
57
40
70
43
83
46
96
50
09
53
22
56
35
59
48
62
61
65
74
68
87
72
00
75
13
78
26
81
39
84
52
MW
h
kWh
hour
Electricity production [kWh] Heating energy production [kWh]
Absorption units production [kWh] Storage energy content [MWh]
28
555
The storage size in this case is much larger with a volume of 159,220 m3. It can be seen in 556
Figure 6 that the storage is used more often than in previous cases. In some parts during the 557
winter, the total amount of heat taken from the PTES is more than two and a half times larger 558
than the heat produced in the biomass power plant at the same time. Thus, in this case the 559
seasonal energy storage significantly contributes to the overall power plant efficiency, as it 560
significantly shaves a peak demand. During the regular yearly maintenance work, heat is 561
provided from the seasonal energy storage in the same manner as in the case study 1. 562
5.4. Comparison of the figures in the different case studies 563
564
In Table 3 all the important results are listed for easier comparison of the case studies’ 565
optimization results. 566
Table 3. Results of case studies 567
568
Case study 1 Case study 2 Case study 3
Power plant capacity 14,675 kWe 8,270 kWe 6,590 kWe
Storage size 30,350 m3 53,310 m
3 159,220 m
3
Absorption units size 7,910 kW 7,910 kW 7,910 kW
NPV 39,630,000 € 15,320,000 € 78,972 €
IRR 15.0% 11.5% 7.0%
Simple pay-back time 5.72 years 6.78 years 8.73 years
Total investment cost 73,990,000 € 52,211,000 € 52,094,000 €
Share of storage in
total investment
2.3% 5.7 % 17.1%
29
Share of absorbers in
total investment
4.3% 6.1% 6.1%
Share of biomass
cogeneration plant in
total investment
71.4% 57.0% 45.5%
Share of DHC
network in total
investment
22% 31.2% 31.3%
569
As it can be seen from the results, the overall investment in the first case study is higher than 570
the overall investments in the second and third case studies. This occurs because of a higher 571
biomass power plant capacity in the first case; the biomass power plant in the first case has a 572
14.4% higher share in total investment than in the second case and 24.9% higher compared to 573
the third case. In the second and the third case, the total investment is roughly the same. 574
However, in the third case investment in the cogeneration plant is lower, while the investment 575
cost of the PTES is much higher compared to the second case. It is interesting to assess shares 576
of different constituents in the total investment. The district heating and cooling network has a 577
significant share in all the cases, although significantly larger in the second and third case 578
compared to the first one. This difference in the DHC network costs share occurs (although 579
costs are the same in absolute terms in all the cases) because the overall investment in the first 580
case is approximately 42% larger compared to the second and the third case. 581
5.5. Comparison of fixed and variable feed-in-premiums 582
583
When comparing the feed-in-tariff and electricity prices on Nordpool for the year 2013 584
(because Croatia does not have its own electricity spot market), it was calculated that the 585
30
fixed feed-in-premium should be set at 0.113 €/kWh in order to remain the same yearly 586
subsidy level as it is the case now. In the case of the variable feed-in-premium (where the 587
total revenue per kWh of electricity would remain the same as with the feed-in-tariff), 76% of 588
the electricity income would come from the feed-in-premium and 24% would be earned on 589
the spot market. Thus, in the case of switching from feed-in tariffs to feed-in premiums, 590
yearly subsidy expenditures would decrease for 24%, as these funds would be obtained from 591
the electricity market itself. This is a significant amount of savings that could then be used for 592
further renewable energy subsidies. 593
594
Prices below zero, where the feed-in-premium could not be received, are very rare, while 595
prices on the spot market above the feed-in-tariff did not occur at all during 2013. Thus, hours 596
in which the power plant would not be eligible for the feed-in-premium do not play a 597
significant role. For the case study 1, these two feed-in-premium options are shown in Figures 598
7 and 8. 599
600
601
602
Figure 7. Hourly revenue with the variable feed-in-premium, case study 1 603
0
500
1000
1500
2000
2500
1
33
8
67
5
10
12
13
49
16
86
20
23
23
60
26
97
30
34
33
71
37
08
40
45
43
82
47
19
50
56
53
93
57
30
60
67
64
04
67
41
70
78
74
15
77
52
80
89
84
26
Tota
l rev
enu
e [€
]
hour
Variable feed-in premium Revenue from market sales
31
As it can be seen, for electricity market prices in the year 2013 on Nordpool, the modelled 604
biomass power plant would be eligible to receive premium in all hours except those when 605
maintenance was in progress. 606
607
608
Figure 8. Hourly revenue with the fixed feed-in-premium, case study 1 609
610
Similar to the case with the variable feed-in-premium, the power plant would be eligible to 611
receive the premium in all hours except when maintenance work was in progress. Like in the 612
previous case, subsidy funds account for 76% of the income from selling the electricity, while 613
24% of income is earned on the electricity market. However, in the case with the fixed feed-614
in-premium, risk for an investor would be higher than in the case with the variable feed-in-615
premium because of the vagueness of the future electricity market price predictions. 616
5.6. Sensitivity analyses 617
618
In the sensitivity analyses, the impact of a significant increase in the biomass price was 619
checked, as well as the impact of improved thermal insulation. A different biomass price for 620
0
500
1000
1500
2000
2500
3000
3500
1
33
8
67
5
10
12
13
49
16
86
20
23
23
60
26
97
30
34
33
71
37
08
40
45
43
82
47
19
50
56
53
93
57
30
60
67
64
04
67
41
70
78
74
15
77
52
80
89
84
26
Tota
l rev
enu
e [€
]
hour
Revenue from fixed feed-in premium Revenue from market sales
32
the case of Croatia, according to difference in transportation distances, was assessed by 621
B.Ćosić et al. [41]. 622
623
624
625
Figure 9. NPV change with biomass price increase 626
627
It can be seen in Figure 9 that the biomass price significantly affects the NPV value. 628
However, in the first two cases, the NPV value is beneficial for the investor even for a 629
significant increase in the biomass price. As expected, in the third case, the NPV becomes 630
even worse than in the original case study with an increase in the biomass price. It can be 631
further noticed that the slope of curves with lower efficiencies is larger than those with higher 632
efficiencies. Thus, the NPV value is more dependant to the biomass price if the average yearly 633
efficiency is lower. This occurs because of the larger power plant capacity in the case with the 634
lower average yearly efficiency achieved, in which the biomass contributes more to the 635
overall costs. 636
637
-20000000
-10000000
0
10000000
20000000
30000000
40000000
50000000
38,5 43,5 48,5 53,5 58,5 63,5 68,5
NP
V
€/ton
50% efficiency 65% efficiency 75% efficiency
33
In the second sensitivity analysis case, the improved thermal insulation reduced the cooling 638
and heating energy demand from 160 kWh/m2 to 95 kWh/m
2 per annum (Table 4.). Pukšec et 639
al. [46] showed for the case of Croatia that significant energy savings could be expected if the 640
policy measures already implemented are properly modelled in the future energy demand. 641
642
Table 4. Results in case of reduced heating and cooling energy demand 643
644
Case study 1 Case study 2 Case study 3
Biomass power plant
capacity
8,620 kWe 4,863 kWe 3,875 kWe
Storage volume 21,230 m3 25,128 m
3 81,519 m
3
Absorption units
capacity
4,225 kW 4,225 kW 4,225 kW
NPV 16,282,290 € 2,873,014 € -5,651,591 €
645
It can be seen that the NPV is lower compared to the base case studies in all the cases. The 646
most significant decrease in NPV occurs in the first case. The NPV value in the first case 647
study decreased for significant 59% compared to the original case study. Thus, it is shown 648
that the careful planning should be carried out before deciding to invest in a power plant 649
similar to this one because the impact of reducing heating and cooling energy demand is high 650
comparing to economic indicators in two cases. If this change would be sudden, with the 651
power plant already being built, the economic indicators would be even worse, as the power 652
plant would be extremely oversized. 653
34
654
6. CONCLUSIONS 655
656
This model was developed in order to try to find a solution for the problems of efficiency in 657
the existing cogeneration power plants. Moreover, the model showed that an increase in terms 658
of the overall power plant efficiency from 50% to 65% in legislation, in order to be eligible 659
for the maximal feed-in-tariff, would not present a problem for the economic side of a project. 660
Additionally, the following conclusions can be made: 661
Increase in the overall power plant efficiency reduces the economic benefits for the 662
investor. 663
PTES is an efficient and cheap solution in combination with a biomass power plant by 664
means of peak energy demand shaving and replacing the power plant supply during 665
downtime. 666
PTES can significantly improve the overall yearly power plant efficiency. 667
Reducing the heating and cooling energy demand represents a great risk for the 668
economic indicators of the whole project. Thus, a relatively secure energy demand 669
should be envisaged at the beginning of the project in order to maximally reduce the 670
risk for the investor. 671
Increase in the biomass price is negative to the economy of the investment. 672
Economy-of-scale of both thermal energy storages and biomass power plants should 673
be utilized in order to have an economically feasible project. 674
Switching from feed-in tariffs to feed-in premiums can obtain large savings in subsidy 675
fund expenditures. 676
For the larger overall power plant efficiencies a different approach is needed in order 677
to try to reach an economically feasible solution. 678
35
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