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Economic analysis of hybrid system consists of fuel cell and wind based CHP system for supplying grid-parallel residential load
Energy and Buildings 68 (2014) 476–487
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Economic analysis of hybrid system consists of fuel cell and wind based CHP system for supplying grid-parallel residential load Mohammad Reza Ranjbar a,∗ , Mohsen Mohammadian b , Saied esmaili b a b
Graduate University of Advanced Technology, Kerman, Iran Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran
a r t i c l e
i n f o
Article history: Received 9 February 2013 Received in revised form 23 September 2013 Accepted 1 October 2013 Keywords: Combined heat and power (CHP) Hybrid system PEM fuel cell Wind energy (WE)
a b s t r a c t An evolutionary programming based approach to evaluate the effect of combining fuel cell power plants (FCPP) and wind on the operational and performance cost is presented in this paper. The fluctuating nature of wind energy (WE) has different effects on the system constraints and operational cost. Moreover, FCPPs are able to produce both thermal and electrical energy simultaneously. Results manifest that through combining FCPP and WE in a hybrid structure for CHP systems, causes lower operational cost than that of individual units. In order to consider production cost of energy, electrical power from WE, power trade with the local grid, thermal recovery from the FCPP, start-up cost of FCPP and maintenance cost; an integrated cost model for FCPP and WE is constructed. A six-minute thermal and electrical load profiles for a residential house in Mashhad Province, Iranis engaged along with the wind speed variation to specify the best cost effective strategy. According to electrical and thermal load demand, available wind power and different tariffs for purchasing and selling electricity of local grid the operation of the FCPP system is scheduled to optimize operational cost. Encouraging results indicate feasibility of the proposed technique. © 2013 Elsevier B.V. All rights reserved.
1. Introduction By eliminating subsidized energy prices in Iran, the cost of fuel severely increases. With unsubsidized utility prices, increasing energy demand, public awareness of environmental protection and hazardous nature of fossil fuels it is no wonder that environment friendly renewable energy sources are swiftly gaining in popularity. Due to the above mentioned issues conventional energy sources are no longer considered as the solely way of supplying energy then societies try to use distributed generator systems (DG) beside conventional ones [1]. The term DG means any small-scale generation which are located near the consumer’s loads instead of being in the center or remote locations. DG’s advantages, over other systems, such as less waste of energy over long transmission [2] and being quite flexible make renewed interest in the DGs operating in parallel with the distribution networks and make hybrid systems. The term hybrid energy system is commonly used to describe a power system with more than one type of energy supplier, a generator usually powered by gas, wind, photovoltaic (PV), or hydroelectric power generator. Nowadays, the use of hybrid renewable energy systems not only due to the aforementioned advantages but also
∗ Corresponding author. Tel.: +98 9173309855. E-mail addresses: [email protected] (M.R. Ranjbar), [email protected] (M. Mohammadian), [email protected] (S. esmaili). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2013.10.003
for supplying less costly the power demand of various regions, has attracted some researchers’ attention. For example in [3] electrical demand of the biggest island of Turkey was examined to realized how it could be possible to supply that with renewable energy sources. In [4] the viability of adding wind turbines to an existing diesel plant of a remote aria in Saudi Arabia was studied. Another feasibility study is described in [5], where hybrid systems supplied by hydrogen are evaluated for applications in Newfoundland, Canada. Therein most of these studies, and also [6], hybrid electricity generation systems are often considered less costly and more reliable than systems that rely on an individual source of energy. WE sources, due to the fluctuating behavior, cannot employ as the solely source of power supply, so they should be accompanied with other energy sources such as FCPP to make less costly and more reliable source of energy [6]. Recently, the combined use of renewable energy sources, especially FCPPs are becoming increasingly fascinating [7]. Proton Exchange Membrane (PEM) fuel cells for having a lot of advantages such as: high efficiency (35–60%), low to zero emissions, quiet operation, high reliability, quick installation the ability to be placed at any site in a distribution system without geographic limitations [8–11] show great promise for use as DGs. All of these advantages lead to a deep study of this type of fuel cell for supplying residential load. So, this study at the first stage began to investigate the feasibility of adding a FCPP to the then already present local grid of a residential house in the Khvaf city, Khorasan Razavi Province, Iran. On
M.R. Ranjbar et al. / Energy and Buildings 68 (2014) 476–487
Nomenclature a,b,c Cel,pi
variables in the wind turbine power output formula purchasing electricity tariff from Grid at interval i ($) Cel,si tariff for selling electricity ($/kWh) Cf price of natural gas for FCPP ($/kWh) Cg fuel price for residential load ($/kWh) thermal energy selling price ($/kWh) Cth,s i,j,k time intervals IEL,si electric energy income ($/kWh) ITH,si thermal energy income ($/kWh) LEL,i electrical load demand at interval i (kW) Lpur electrical power purchase from grid (kW) electrical power sells to grid (kW) Lsell LTH,i thermal load demand at interval i (kW) Ltot,i total load at interval i lower limit of the ramp rate (kW) pD pU upper limit of the ramp rate (kW) minimum down-time (number of intervals) MDT MUT minimum up-time (number of intervals) Nmax maximum number of starts-stops nstart–stop number of starts-stops of FCPP maximum limit of generating power (kW) Pmax Pmin minimum limit of generating power (kW) PFC,i FCPP electrical power productions at interval i (kW) Pth,i thermal recovered energy from FCPP Pth-storage,i thermal energy saving at interval i Pth-storage thermal energy saving at the end of day Prat rated electricity output power (kW) PWE,i WE electrical power production at interval i (kW) part load ratio PLR rTE,i thermal to electrical ratio at interval i the length of time interval (h) T toff FCPP off time (h) FC cooling time constant (h) Vcut-in cut in wind speed (m/s) Vcut-out cut out wind speed (m/s) Vi wind speed at interval i (m/s) Vrat rated wind speed (m/s) ˛ hot startup cost ($) cold startup cost ($) ˇ i fuel cell electrical efficiency (%) st,th thermal storage efficiency (%)
the second stage the viability of adding wind energy to the current utility system and FCPP is investigated. The combination of FCPP and WE systems in the form of combined heat and power (CHP) system can be considered as a potential choice to satisfy electrical and thermal demand of residential house. In such kind of system, wind turbine output power is considered as a negative load and is added to the residential load. Since WE systems have low to zero operating cost so in this paper WE unit always is operated at its full capacity. Thermal and electrical energy generations by FCPP should be optimized by a robust management strategy in a way to minimize the total cost with regard to satisfy constraints. In order to determine the optimal FCPP thermal and electrical output power a genetic algorithm is used. Finally, the algorithm will determine when the FCPP to be ON or OFF, by considering the different tariffs for electricity, constraints of FCPP, and minimization of total cost. For acquiring more information about economical aspect of fuel cell the following references are suggested [8–10,12–15]. In order to find the optimal output power from FCPP at the presence of constraints an economic model has been introduced in [8,9]. The
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model of these two articles just considers the feasibility of trading energy with grid, and the usage of thermal recovery from FCPP. In [10] the amount of the stored hydrogen is also included to the model. In this paper the model of above mentioned papers has been extended to integrate WE. Not only do the tariffs for selling and buying electricity from the local grid are not constant but also they vary according to the time of using electricity and volume of demand. Different strategies such as selling electric power to the local grid or residential consumer, saving thermal energy, and etc. for managing the output power of FCPP and WE units can be defined. In the paper following strategies are used; in the first strategy thermal recovery from FCPP is neglected and the thermal load is supplied by natural gas. If the recovered thermal energy is less than the thermal load, the difference between these two items can be supplied by using natural gas otherwise surplus recovered thermal energy, second strategy, can be sold to other neighborhoods and third strategy can be stored and reused later based on system economics. The effect of adding WE unit to the FCPP and local grid has been proposed in fourth through sixth strategies. The remaining part of the paper is organized as follows: Section 2 gives a complete structure of the system besides the type of FC and WE unit which are used in this study. Formulation of economic model is presented in Section 3. The solution methodology and GA algorithm with its parameter adjustments are explained in Section 4. Test results and conclusions are discussed in Sections 5 and 6, respectively.
2. System configuration and energy units 2.1. System configuration The diagram of a WE–PEM fuel cell hybrid energy system connected to grid is indicated in Fig. 1. The system is constituted of wind energy turbine, local grid, heat pump, PEM fuel cell stack and load unit.
2.2. Fuel cell unit PEM stands for polymer electrolyte membrane or proton exchange membrane. Advantages of PEM fuel cells can be mentioned as: their high efficiency compared to other energy conversion devices [16], low operation temperature cause to reach the operation point rapidly and allows rapid start-up [17], inexpensive materials than high temperature fuel cells [18]. PEMs can be made extremely thin and the thinner the polymer electrolyte the higher the conductance and lower the ohmic resistance losses. Therefore this type of fuel cell presently receives the most attention among all kind of fuel cells. Hence, in this paper 6.3 kW PEM fuel cell power is used. When FCPP works at full load it can produces thermal energy as much as electrical energy [19]. In order to manage excess thermal or electrical energy, it is vital to have a robust management strategy. In PEM FCPP, due to the lower operating temperature, thermal recovery from the stack is abandoned so, thermal energy is just recovered from the reformer where the temperature goes up to about 360 ◦ C. Hot water and space heating considers as thermal load in this paper and adds to electric loads of PEM FCPP. The thermal load is satisfied by using the recovered thermal energy from the FCPP and, if necessary, by using of natural gas. On the basis of the difference between the thermal load and the recovered thermal energy and supplying electrical load by FCPP or WE, six different strategies can be defined. In the first three strategies the only source of electrical energy supplier is grid connected PEM FCPP, while in the other strategies WE unit is added
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Fig. 1. System configuration of the proposed hybrid energy system.
Table 1 Technical parameters of XCO2 wind turbine.
The constants, a, b and c can be determined by the Eq. (2)
Power
Value
Unit
Rated power Cut in wind speed Rated wind speed Cut out wind speed
6 4.5 12.5 16
kW m/s m/s m/s
a=
vcut−in (vcut-in + vrat ) − 4vrat ((vcut-in + vrat )/2vrat )3
(vcut-in + vrat )2 3
b=
c =
4(vcut-in + vrat ) ∗ ((vcut-in + vrat )/2vrat ) − (3vcut-in + vrat ) (vcut-in + vrat ) 2 − 4((vcut-in + vrat )/2vrat )
to the source of electrical energy supplier and operates at its full capacity.
2
3
(2)
(vcut-in + vrat )2
3. Formulation of economic model 2.3. Wind energy unit A XCO2/6 kW wind energy unit is used to change wind energy to electric power. In order to protect the turbine from damage a turbine’s cut-out and cut-in speed are determined by the manufacturer. The cut-in speed is the point where the turbine starts to generate electricity from turning. The cut-out point shows the boundary of speed that denotes how fast the turbine can spin before reach to danger zone. Hence, some sort of brake mechanism are used to prevent the turbine from reaching to this danger zone. Technical information of the utilized turbine is available on the internet [20] and is given in Table 1. 2.3.1. Electric output power of the wind turbine The electric output power of the wind turbine, PWE,i at interval i with respect to wind speed vi can be calculated as below [21,22]:
pWE,i =
⎧ 0 ≤ vi < vcut-in 0 ⎪ ⎪ ⎪ ⎨ prat (a + b · vi + c · vi 2 ) vcut-in ≤ vi < vrat prat ⎪ ⎪ ⎪ ⎩ 0
⎫ ⎪ ⎪ ⎪ ⎪ ⎬
vrat ≤ vi < vcut-out ⎪ ⎪ vi ≥vcut-out
⎪ ⎪ ⎭
(1)
The mathematical representation of the cost optimization problem consists of the overall operational cost and the total system income, subject to operational and system constraints can be specified as follows: Objective function = Min
m
(
i
j
costj −
incomek )
(3)
k
Subject to: P min ≤ PFc,i ≤ P max
(4)
PFC,i − PFC,i−1 ≤ Pu
(5)
PFC,i−1 − PFC,i ≤ PD
(6)
on (Ti−1 ) − MUT (Ui−1 − Ui )≥0
(7)
off
(Ti−1 − MDT )(Ui − Ui−1 )≥0
(8)
nstart−stop ≤ N max
(9)
The first term of (1) represents the overall operational-cost, which is completely discussed in Section 3.1, while the second term is the total system income relating to daily income from the sale of excess thermal and electrical energy.
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Part load ratio (PLR) is used to determine efficiency and thermal to electrical ratio [19]. These are calculated in two categories by considering PLR as follow: For PLRi < 0.05
(10)
i = 0.2716, rTE,i = 0.6801
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to increase, on average, 25% over the 20-year life of the various wind machines [23]. Average values of O&M costs are $0.027/kWh. Therefore, formula for O&M cost used in this paper is (19). 240
CO&M = (0.027)
PWE,i ∗
i=1
6 min 60 min
(19)
For PLRi ≥0.05 i = 0.9033 × PLR5i − 2.9996 × PLR4i + 3.6503 × PLR3i − 2.0704 × PLR2i + 0.4623 × PLRi + 0.3747 rTE,i =
1.0785 × PLR4i
− 1.9739 × PLR3i
+ 1.5005 × PLR2i
(11)
− 0.2817 × PLRi + 0.6838
3.1. System cost component 3.2. System incomes components Cost of fuel: Cost of fuel for producing electrical energy by the FCPP: Cfuel,i = cf T
240 PFC,i i=1
i
(12) IEL,Si = T
Purchased electrical energy cost: Electrical energy purchased from grid when FCPP is the only supplier of demand energy.
240
CEL,pi = T
cel,pi max(Lel,i − PFC,i , 0)
240
cel,pi max(Lel,i − PFC,i − PWE,i , 0)
IEL,Si = T
240
240
cel,si max(PFC,i + PWE,i − Lel,i , 0).
(21)
If the surplus recovered thermal energy is stored and reused and FCPP be the solely source of supplying energy, income of selling surplus electrical energy give as: 240
cel,si max(PFC,i − 0.2 max(Pth,i − Lth,i , 0) − Lel,i , 0)
i=1
Electrical energy purchased from local grid for storing surplus thermal energy when FCPP supply demand energy. CEL,pi = T
(20)
i=1
(14)
i=1
cel,si max(PFC,i − Lel,i , 0)
At the presence of WE unit, surplus electrical energy income will be calculated as follows: IEL,Si = T
Electrical energy purchased from grid at the presence of both FCPP and WE unit. In this situation WE unit acts like a negative load.
240 i=1
(13)
i=1
CEL,pi = T
Selling surplus electrical energy: Surplus electrical energy sold by FCPP is calculated as follows:
(22) With integrating WE and FCPP (22) will change to (23):
cel,pi max(Lel,i + 0.2 max(Pth,i − Lth,i , 0) − PFC,i , 0)
i=1
(15)
IEL,Si = T
240
cel,si max(PFC,i +PWE,i −0.2 max(Pth,i − Lth,i , 0) − Lel,i , 0)
i=1
(23)
Electrical energy purchased from local grid for storing surplus thermal energy when WE unit is added to supply electricity power.
Surplus thermal energy incomes: If recovered thermal energy from FCPP is more than thermal load the surplus can be sold to other neighborhoods.
240
CEL,pi = T
cel,pi max(Lel,i + 0.2max(Pth,i − Lth,i , 0)
i=1
− PFC,i − PWE,i , 0)
(16)
ITH,Si = cth,si T
240
max(pthi − Lthi , 0)
(24)
i=1
Term of 0.2max(Pth,i − Lth,i , 0) illustrates requested electrical energy for storing surplus thermal energy. Gas cost for purchasing thermal energy: Gas cost can be added to the cost function if thermal load is more than recovered thermal energy and it is calculated as follow: CGas,pi = cg T
240
If the surplus recovered thermal energy is stored and reused, income of selling the saving of thermal energy at the end of day give as. ITH,Si = cth,si Pth-storage st,th
(25)
4. An overview of genetic algorithms max(Lth,i − Pth,i , 0)
(17)
i=1
Startup and maintenance cost: Csup = ˛ + ˇ(1 − e−(toff /) )
(18)
Cost of wind unit: Although wind O&M cost trends had been decreasing for the expansion in overall wind farm size, it cannot be negligible. High O&M costs associated with generators, gearboxes and drive trains. In fact, O&M costs are not fix and estimated
As genetic algorithms software is the most widely used for purposes of optimization, to optimize the fitness function (3) a genetic algorithm is used. Since six minute time interval is used, 240 variables are defined for 24 h. Linear equalities and inequalities (Eqs. (4)–(11)) with their bounds are also defined. A double vector population type is used to specify the type of the input to the fitness function. Population size, which specifies how many individuals there are in each generation, is selected 450. In order to create the initial population a uniform function is used that creates a random
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Fig. 2. Complete flowchart of the proposed method.
initial population with a uniform distribution. For removing the effect of the spread of the raw scores a scaling function should be defined, so in this paper rank function is used. Rank function scales the raw scores based on the rank of each individual, rather than its score. The rank of an individual is its position in the sorted scores. For example the rank of the fittest individual is 1, the next fittest is 2, and so on. Appropriate parents based on their scaled values from the fitness scaling function for the next generation should be selected. Therefore stochastic uniform is used as selection function, and lays out a line in which each parent corresponds to a piece of the line of length proportional to its expectation. The algorithm moves along the line in the same size steps, one step for each parent. At each step, the algorithm allocates a parent from the section it lands on. The first step is a uniform random number less than the step size. Reproduction determines how the genetic algorithm creates children at each new generation. This process consists of the number of elite, crossover and mutation fraction. In the paper elite count has been set to 20 while crossover and mutation have been set to 0.8 and 0.2 respectively. Crossover combines two parents to form a new child, for the next generation. Scattered crossover is applied in the article. The crossover at first creates a random binary vector then selects the genes by the help of this vector, where an element of the vector is 1 a gene will be selected from the first parent, otherwise it will be selected from the second parent, and finally combines the genes to form the child. For example: p1 = [a
b c d
e
f
g h ], p2 = [1
Random crossover vector = [ 1 0 Child = [ a 2 3 d
e
6 7 h]
0
2 3 4 5 6 7 8]
1 1 0
0 1]
In order to enable the genetic algorithm to search a broader space a uniform mutation function is used. It has two-step process, in the first step the algorithm picks out a fraction of the vector entries of an individual for mutation, where each entry has the same probability as the mutation rate of being mutated. In the second step, the algorithm replaces each selected entry by a random number selected uniformly from the range for that entry. Given the population size as a vector of length 450, algorithm should create a movement of individuals between subpopulations which is called migration. In migration every so often, related to interval control, the best individuals from one subpopulation replace the worst individuals in another subpopulation. A forward migration with 20 intervals is used. That is the nth subpopulation migrates into the (n + 1) th subpopulation and migration between subpopulations takes place every 20 generations. In order to control the number of individuals move between subpopulations a fraction of 0.2 is defined. For instance if individuals migrate from a subpopulation of 50 individuals into a population of 100 individuals and Fraction is 0.2, 10 individuals (0.2 × 50) migrate. Individuals that migrate from one subpopulation to another are copied; they are not removed from the source subpopulation. After all of aforementioned process a set of stopping criteria, which are related to the number of generations, time and fitness limit, are determined to allow the algorithm to terminate. Eventually fitness and constraint functions in serial form are evaluated. Serial form means the fitness and constraint functions are evaluated separately at each member of a population. Flowchart of extended GA based solution methodology is displayed within Fig. 2. 5. Case study In order to supply residential load seven different cases are tested. For the base case residential load demand is supplied by
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Table 2 Tariff of trading electrical energy with local grid. Time (h)
0–6
6–8
9
10–11
12–16
17
18–19
20
21
22
23
Purchasing tariff Selling tariff
0.05 0.03
0.07 0.05
0.09 0.07
0.1 0.07
0.11 0.08
0.13 0.09
0.14 0.1
0.17 0.14
0.15 0.1
0.1 0.07
0.07 0.05
Table 3 FCPP and genetic algorithm parameters. Maximum limit of generating power, Pmax (kW) Minimum limit of generating power, Pmin (kW) Hot start-up cost, ˛ ($) Cold start-up cost, ˇ ($) The fuel cell cooling time constant, (h) Minimum up-time, MUT (number of intervals) Minimum down-time, MDT (number of intervals) Lower limit of the ramp rate, pD (kW) Upper limit of the ramp rate, pu (kW) Length of time interval, T (h) Maximum number of starts-stops, Nmax Maximum number of evolutionary generation Number of individuals Fuel price for residential load, cg ($/kWh) Price of natural gas for FCPP, cf ($/kWh) Thermal energy selling price cth,s ($/kWh) Thermal storage efficiency, st,th (%)
6.3 0.0 0.05 0.15 0.75 2 2 0.5 0.4 0.1 5 5000 450 0.6 0.4 0.4 90
Although, Iran is one of the richest countries in the field of renewable energy sources, in the past decade just a little portion of its produced electricity derived from renewable energy sources (exclude hydro), recently authorities have given desirable attention to the potentials of renewable energy systems [24]. According to preliminary studies [24] by the Iranian renewable energy organization (SUNA), Iran’s mountainous terrain are characterized by unique wind corridors and are able to produce at least 6500 MW energy. Iranian government has committed, on its fifth five-year economic development plan (2010–2015), to generate 1650 MW of wind energy by March 2014. So, Iranian residents can rely on renewable energy sources of Iran, especially wind, to supply their demands. In this article to prove this assertion wind speed data of Khvaf city in Khorasane-Razavi Province have been used. Location of Khvaf with wind speed data and the electric output power of XCO2 turbine, after placing data to (1), are shown in Figs. 4–6 respectively. 5.1. Test and results
local grid. In the first three cases a grid connected PEM FCPP is used to supply residential load. Electricity trading tariffs are shown in Table 2. Data for PEM FCPP with GA parameters and thermal energy trading tariffs are given in Table 3. In the last three cases a 6 kW XCO2 wind turbine is added to the complex. In each case (except base case) GA defines optimal electricity output power of the FCPP with respect to consider electricity trading tariffs, thermal and electrical load, FCPP constraints and electric output power of wind turbine. As Table 2 shows selling price at all the time is cheaper than purchasing price then it encourages grid to buy electricity from FCPP. Electrical and thermal residential load are depicted, in Fig. 3. When FCPP runs, thermal energy is produced as a by-product besides electrical energy. After recovering this energy we must be sure it will be used by neighbors. Hence in order to encourage them to use this energy, its price should be lower than other ways of supplying thermal energy. So, as it is obvious from Table 2, thermal energy selling price with FCPP is considered lower than fuel price for residential load.
The suggested model has been applied to a 6 kW wind energy unit and 6.3 kW FCPP, which are grid-parallel that supply a residential house. A load profile of Khavaf city with a peak of 6.3 kW is used to simulate six minute load profile of the residential house. The space heating and winter hot water usage is considered as the thermal load profile for residential house in Khavaf, Khorasane Razavi. The electrical load is used along with the thermal load profile to simulate total six minute operation of the WE unit and FCPP. The necessary parameters are given in Tables 2 and 3. Base case: In this case both electrical and thermal load are supplied through the local grid and natural gas, respectively. Base case shows the cost of supplying residential load without considering the FCPP and WE unit. In this test case daily cost of supplying both thermal and electrical energy will lead to 17.0693$. Case 1: In this case a combination of FCPP and local grid is used to supply just electrical load. Recovering of thermal energy from FCPP is neglected. The amount of FCPP power generation is depicted in
Fig. 3. Electrical and thermal load.
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Fig. 4. Location of Khvaf in Iran.
Fig. 7 and the difference between this generation and load demand has been supplied from local grid which is shown in Fig. 8. As Fig. 7 shows, during 0–11 purchasing electricity tariff from grid is too low then the management strategy order FCPP to be off and supply electrical load from local grid so in this period the shape of Fig. 8 is exactly like electric load profile. In this strategy daily cost of supplying both thermal and electrical energy has a reduction of 0.9293$ so total cost in this case for one day is 16.14$. This strategy can result in a save of 339.1965$ per a year. Case 2: In this case thermal energy is recovered from FCPP as a by-product. It means that in addition to use of electrical output power from FCPP its recovering thermal energy is also used for supplying residential thermal load. If the recovered thermal energy is less than thermal load the lack can be compensate by using natural gas otherwise surplus recovered thermal energy is being sold to other neighbors. Electrical load and power generation are shown in Fig. 9 while electrical energy trade with local grid is shown in Fig. 10. Thermal load and recovered thermal energy are depicted in Fig. 11. A robust management strategy should consider different transient changes in FCPP production. This transient change can cause different conditions in electricity trade whit local grid. Therefore, the FCPP generation can be divided into 5 parts. As Fig. 9 shows,
Fig. 5. Wind speed changes at Khvaf in 24 h of a day at 10 min elevation.
Fig. 6. Electric output power of XCO2 turbine.
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Fig. 7. Supplying electrical loads by combination of FCPP and local grid.
Fig. 8. Purchasing electricity from local grid.
Fig. 9. Electrical load and generation.
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Fig. 10. Electrical power trade with local grid.
from 0:00 to 6 that management strategy ordered FCPP to be off because purchasing electricity from local grid, during this period, is more economical than generating power by FCPP then in this period electrical load supplied by local grid and recovered thermal energy is zero. Start-up cost can be another factor that management strategy considered to keep the fuel cell off. From 6 to 10 the optimum power generation, according to management strategy is to supply electrical load by FCPP. Sometimes supplying thermal load just by generating extra power from FCPP is not cost-effective, unless the excess power generation will be sold to local grid and thermal load supplied by natural gas. 10 AM to 1 PM is the time period that this operation may take place since electricity price is almost high. Fortunately in the period generated power from FCPP is more than residential electrical demand so surplus electrical power can be sold to local grid by a lower price. The actiondepends on management strategy, maybe supplying thermal load or electricity tariffs be factors for the operation. During the time period 1 PM to 5 PM (780–1020 min), generated electrical power by FCPP is just for supplying electrical load. In this period excess recovered thermal energy is sold to the neighbors. From 5 PM to 0:00, trading electrical power with local grid take place while not only does
FCPP cannot sell thermal energy, but also need to buy natural gas to supply thermal load. In this case daily cost of energy supplying is equal to 14.5385$ it means a 2.5308$ reduction in each day that result in 923.7420$ saving per year. So, this strategy is more effective than the previous strategy. Case 3: This case is like the second case except that surplus recovered thermal energy from FCPP is stored and reused at the end of the day. If the recovered thermal energy is less than thermal load, thermal load is supplied by thermal reservoir otherwise it will be stored and sold to other neighbors at the end of the day. Both FCPP power generation and recovered thermal energy will be like Figs. 9 and 11 in case 2 respectively. Since our desire is supplying residential load, unlike case 2 surplus recovered thermal energy between 13 and 16 h of Fig. 11, is stored and reused at the end of the day unless recovered energy is less than thermal load. Daily cost of supplying energy in this case is equal to 14.5334$ so daily cost reduction will be 2.5359$. Total yearly saving is equal to 925.6035$. The effect of using FCPP as a DG system for supplying residential demand is being analyzed. The results prove that recovering thermal energy is the most effective strategy. Although storing surplus
Fig. 11. Thermal load and generation.
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Fig. 12. FCPP and WE power generation with electrical load.
Fig. 13. Electrical trading with grid.
Fig. 14. FCPP and WE power generation with electrical load.
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Fig. 15. Electricity trading with local grid.
thermal energy is seems to be more affordable than case 2, it is not viable for residential use since storing thermal energy needs higher technology and expensive equipment. Now the effect of integrating WE unit to pervious system and making a hybrid system is examined. Case 4: By adding another source of energy to the case 1, case 4 is forming. In this case, in addition to the FCPP unit the model is tested in using a total capacity of 6 kW WE unit, which is operated at its full capacity all the time. Wind speed data, Fig. 5, and WE unit data, Table 1, are used to calculate power output of WE unit for the three remaining cases. WE unit can affect the amount of power generated by FCPP and in turn changes the answers. FCPP power generation with electrical load and sum of output power of DGs is shown in Fig. 12. In this case thermal recovery is neglected and thermal load supplied by natural gas. Electricity trading with local grid is depicted in Fig. 13. Total cost in this case is 11.4886$ so from the result and [6] it is obvious that hybrid systems can cause lower cost than a single-supply systems. Case 5: After integrates WE unit to the model of case 2 the model of this case will generate. Since WE unit act as a negative load FCPP need to produce lower energy to supply residential load and the
less it (FC) works the lower it produces thermal energy. Electrical load and WE power generation plus FCPP power generation are depicted in Fig. 14. Electricity trading with local grid is shown in Fig. 15. Fig. 16 shows thermal recovery from FCPP. Total cost of this case, which is incomparable with case 2, is 9.3626$. It is evident from Fig. 15 that integrated generation system causes to buy less electrical energy than the first three cases, and also the system sells excess electrical energy most of the time. This excess electrical energy is high during the low thermal load according to Figs. 15 and 16. Case 6: In this case the priority is to supply thermal load by recovered thermal energy from FCPP then by natural gas. If thermal recovery is more than thermal load, surplus recovered thermal energy is stored and reused at the end of the day. But if the recovered thermal energy is less than thermal load, thermal load is supplied from thermal reservoir and natural gas. Hybrid system power generation and trading electricity with local grid in the case are the same as case 5 and have been depicted in Figs. 14 and 15 respectively. As Fig. 16 shows thermal recovery from FCPP just around 14 can be stored so preparing apparatus to save just a little amount of thermal energy would not be cost effective. Therefore
Fig. 16. Thermal recovery.
M.R. Ranjbar et al. / Energy and Buildings 68 (2014) 476–487 Table 4 Cost of each case. Case number
Total cost ($/24 h)
Base case Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
17.0693 16.1400 14.5385 14.5334 11.4886 9.3926 9.7519
total cost in this case should be higher than case 5 and it is 9.7519 so the fifth case is the best case among all of the cases as it is obvious from Table 4. 6. Conclusion The integration of WE and FCPP system in an economic model which consist of power trade with the local grid with different tariffs and thermal recovery from FCPP is introduced in this paper. The paper suggests practical concepts regarding operational cost modeling of the system. Six test cases were evaluated using a residential load profile of Khavaf city in Khorasane Razavi Province, Iran. In the first three cases the fuel cell power plant supplies electrical and thermal power as solely DG system but in the last three cases WE unit is added to the complex and based on the available power from WE unit, the fuel cell power plant supplies both electrical and thermal power to the residential demand. Base on wind speed and low-cost wind turbine energy production, WE unit runs at full capacity most of the time. The main factor that affects the operation of the FCPP is thermal load. For instance some times, based on the system economics, FCPP inclines to generate electrical energy more than the electric load during high thermal consumption periods and produces low electrical energy during low thermal periods. Test results on a 6.3 kW fuel cell power plants and 6 kW WE unit indicate the feasibility of the suggested approach and its potential to find the optimal power output from the FCPP subject to the connected constraints and WE unit power. References [1] T. Zhou, B. Franc¸ois, Energy management and power control of a hybrid active wind generator for distributed power generation and grid integration, IEEE Transactions on Industrial Electronics 58 (1) (2011) 95–104.
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[2] R. Ramakumar, P. Chiradeja, Distributed generation and renewable energy systems, in: IEEE Energy Conversion Engineering Conference, 2002. IECEC’02. 2002 37th Intersociety, 2004, pp. 716–724. [3] A. Demiroren, U. Yilmaz, Analysis of change in electric energy cost with using renewable energy sources in Gökceada, Turkey: an island example, Renewable and Sustainable Energy Reviews 14 (1) (2010) 323–333. [4] S. Rehman, I. El-Amin, F. Ahmad, S. Shaahid, A. Al-Shehri, J. Bakhashwain, A. Shash, Feasibility study of hybrid retrofits to an isolated off-grid diesel power plant, Renewable and Sustainable Energy Reviews 11 (4) (2007) 635–653. [5] M. Khan, M. Iqbal, Pre-feasibility study of stand-alone hybrid energy systems for applications in Newfoundland, Renewable Energy 30 (6) (2005) 835–854. [6] S. Tichi, M. Ardehali, M. Nazari, Examination of energy price policies in Iran for optimal configuration of CHP and CCHP systems based on particle swarm optimization algorithm, Energy Policy 38 (10) (2010) 6240–6250. [7] P. Nema, R. Nema, S. Rangnekar, A current and future state of art development of hybrid energy system using wind and PV-solar: a review, Renewable and Sustainable Energy Reviews 13 (8) (2009) 2096–2103. [8] M. El-Sharkh, A. Rahman, M. Alam, Evolutionary programming-based methodology for economical output power from PEM fuel cell for micro-grid application, Journal of Power Sources 139 (1) (2005) 165–169. [9] A.M. Azmy, I. Erlich, Online optimal management of PEM Fuel cells using neural networks, IEEE Transactions on Power Delivery 20 (2) (2005) 1051–1058. [10] M. El-Sharkh, M. Tanrioven, A. Rahman, M. Alam, Impact of hydrogen production on optimal economic operation of a grid-parallel PEM fuel cell power plant, Journal of Power Sources 153 (1) (2006) 136–144. [11] M. El-Sharkh, M. Tanrioven, A. Rahman, M. Alam, Cost related sensitivity analysis for optimal operation of a grid-parallel PEM fuel cell power plant, Journal of Power Sources 161 (2) (2006) 1198–1207. [12] F. Barbir, T. Gomez, Efficiency and economics of proton exchange membrane (PEM) fuel cells, International Journal of Hydrogen Energy 22 (10) (1997) 1027–1037. [13] Y. Zoka, H. Sasaki, J. Kubokawa, R. Yokoyama, H. Tanaka, In optimal deployment of fuel cells in distribution systems by using genetic algorithms, in: IEEE International Conference on Evolutionary Computation 1995, 1996, p. 479. [14] G. Erdmann, Future economics of the fuel cell housing market, International Journal of Hydrogen Energy 28 (7) (2003) 685–694. [15] N. Srinivas, K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation 2 (3) (1994) 221–248. [16] L. Carrette, K. Friedrich, U. Stimming, Fuel cells – fundamentals and applications, Fuel cells 1 (1) (2001) 5–39. [17] A.J. Appleby, Fuel Cell Handbook, Van Nostrand Reinhold, New York, 1988, pp. 762. [18] D. Feroldi, M. Basualdo, Description of PEM fuel cells system, in: PEM Fuel Cells with Bio-Ethanol Processor Systems, IEEE, 2012, pp. 49–72. [19] M.B. Gunes, Investigation of a Fuel Cell based Total Energy System for Residential Applications, Virginia Polytechnic Institute and State University, 2001. [20] Catalogue of European Urban Wind Turbine Manufacturers www.urbanwind.net [21] R. Billinton, G. Bai, Adequacy evaluation of generation systems including wind energy, IEEE Canadian Conference on Electrical and Computer Engineering, 2002. IEEE CCECE 2002 (2002) 24–29. [22] P. Giorsetto, K.F. Utsurogi, Development of a new procedure for reliability modeling of wind turbine generators, IEEE Transactions on Power Apparatus and Systems 1 (1983) 134–143. [23] www.renewableenergyworld.com (2013). [24] http://www.suna.org.ir/
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Economic analysis of hybrid system consists of fuel cell and wind based CHP system for supplying grid-parallel residential load Mohammad Reza Ranjbar a,∗ , Mohsen Mohammadian b , Saied esmaili b a b
Graduate University of Advanced Technology, Kerman, Iran Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran
a r t i c l e
i n f o
Article history: Received 9 February 2013 Received in revised form 23 September 2013 Accepted 1 October 2013 Keywords: Combined heat and power (CHP) Hybrid system PEM fuel cell Wind energy (WE)
a b s t r a c t An evolutionary programming based approach to evaluate the effect of combining fuel cell power plants (FCPP) and wind on the operational and performance cost is presented in this paper. The fluctuating nature of wind energy (WE) has different effects on the system constraints and operational cost. Moreover, FCPPs are able to produce both thermal and electrical energy simultaneously. Results manifest that through combining FCPP and WE in a hybrid structure for CHP systems, causes lower operational cost than that of individual units. In order to consider production cost of energy, electrical power from WE, power trade with the local grid, thermal recovery from the FCPP, start-up cost of FCPP and maintenance cost; an integrated cost model for FCPP and WE is constructed. A six-minute thermal and electrical load profiles for a residential house in Mashhad Province, Iranis engaged along with the wind speed variation to specify the best cost effective strategy. According to electrical and thermal load demand, available wind power and different tariffs for purchasing and selling electricity of local grid the operation of the FCPP system is scheduled to optimize operational cost. Encouraging results indicate feasibility of the proposed technique. © 2013 Elsevier B.V. All rights reserved.
1. Introduction By eliminating subsidized energy prices in Iran, the cost of fuel severely increases. With unsubsidized utility prices, increasing energy demand, public awareness of environmental protection and hazardous nature of fossil fuels it is no wonder that environment friendly renewable energy sources are swiftly gaining in popularity. Due to the above mentioned issues conventional energy sources are no longer considered as the solely way of supplying energy then societies try to use distributed generator systems (DG) beside conventional ones [1]. The term DG means any small-scale generation which are located near the consumer’s loads instead of being in the center or remote locations. DG’s advantages, over other systems, such as less waste of energy over long transmission [2] and being quite flexible make renewed interest in the DGs operating in parallel with the distribution networks and make hybrid systems. The term hybrid energy system is commonly used to describe a power system with more than one type of energy supplier, a generator usually powered by gas, wind, photovoltaic (PV), or hydroelectric power generator. Nowadays, the use of hybrid renewable energy systems not only due to the aforementioned advantages but also
∗ Corresponding author. Tel.: +98 9173309855. E-mail addresses: [email protected] (M.R. Ranjbar), [email protected] (M. Mohammadian), [email protected] (S. esmaili). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2013.10.003
for supplying less costly the power demand of various regions, has attracted some researchers’ attention. For example in [3] electrical demand of the biggest island of Turkey was examined to realized how it could be possible to supply that with renewable energy sources. In [4] the viability of adding wind turbines to an existing diesel plant of a remote aria in Saudi Arabia was studied. Another feasibility study is described in [5], where hybrid systems supplied by hydrogen are evaluated for applications in Newfoundland, Canada. Therein most of these studies, and also [6], hybrid electricity generation systems are often considered less costly and more reliable than systems that rely on an individual source of energy. WE sources, due to the fluctuating behavior, cannot employ as the solely source of power supply, so they should be accompanied with other energy sources such as FCPP to make less costly and more reliable source of energy [6]. Recently, the combined use of renewable energy sources, especially FCPPs are becoming increasingly fascinating [7]. Proton Exchange Membrane (PEM) fuel cells for having a lot of advantages such as: high efficiency (35–60%), low to zero emissions, quiet operation, high reliability, quick installation the ability to be placed at any site in a distribution system without geographic limitations [8–11] show great promise for use as DGs. All of these advantages lead to a deep study of this type of fuel cell for supplying residential load. So, this study at the first stage began to investigate the feasibility of adding a FCPP to the then already present local grid of a residential house in the Khvaf city, Khorasan Razavi Province, Iran. On
M.R. Ranjbar et al. / Energy and Buildings 68 (2014) 476–487
Nomenclature a,b,c Cel,pi
variables in the wind turbine power output formula purchasing electricity tariff from Grid at interval i ($) Cel,si tariff for selling electricity ($/kWh) Cf price of natural gas for FCPP ($/kWh) Cg fuel price for residential load ($/kWh) thermal energy selling price ($/kWh) Cth,s i,j,k time intervals IEL,si electric energy income ($/kWh) ITH,si thermal energy income ($/kWh) LEL,i electrical load demand at interval i (kW) Lpur electrical power purchase from grid (kW) electrical power sells to grid (kW) Lsell LTH,i thermal load demand at interval i (kW) Ltot,i total load at interval i lower limit of the ramp rate (kW) pD pU upper limit of the ramp rate (kW) minimum down-time (number of intervals) MDT MUT minimum up-time (number of intervals) Nmax maximum number of starts-stops nstart–stop number of starts-stops of FCPP maximum limit of generating power (kW) Pmax Pmin minimum limit of generating power (kW) PFC,i FCPP electrical power productions at interval i (kW) Pth,i thermal recovered energy from FCPP Pth-storage,i thermal energy saving at interval i Pth-storage thermal energy saving at the end of day Prat rated electricity output power (kW) PWE,i WE electrical power production at interval i (kW) part load ratio PLR rTE,i thermal to electrical ratio at interval i the length of time interval (h) T toff FCPP off time (h) FC cooling time constant (h) Vcut-in cut in wind speed (m/s) Vcut-out cut out wind speed (m/s) Vi wind speed at interval i (m/s) Vrat rated wind speed (m/s) ˛ hot startup cost ($) cold startup cost ($) ˇ i fuel cell electrical efficiency (%) st,th thermal storage efficiency (%)
the second stage the viability of adding wind energy to the current utility system and FCPP is investigated. The combination of FCPP and WE systems in the form of combined heat and power (CHP) system can be considered as a potential choice to satisfy electrical and thermal demand of residential house. In such kind of system, wind turbine output power is considered as a negative load and is added to the residential load. Since WE systems have low to zero operating cost so in this paper WE unit always is operated at its full capacity. Thermal and electrical energy generations by FCPP should be optimized by a robust management strategy in a way to minimize the total cost with regard to satisfy constraints. In order to determine the optimal FCPP thermal and electrical output power a genetic algorithm is used. Finally, the algorithm will determine when the FCPP to be ON or OFF, by considering the different tariffs for electricity, constraints of FCPP, and minimization of total cost. For acquiring more information about economical aspect of fuel cell the following references are suggested [8–10,12–15]. In order to find the optimal output power from FCPP at the presence of constraints an economic model has been introduced in [8,9]. The
477
model of these two articles just considers the feasibility of trading energy with grid, and the usage of thermal recovery from FCPP. In [10] the amount of the stored hydrogen is also included to the model. In this paper the model of above mentioned papers has been extended to integrate WE. Not only do the tariffs for selling and buying electricity from the local grid are not constant but also they vary according to the time of using electricity and volume of demand. Different strategies such as selling electric power to the local grid or residential consumer, saving thermal energy, and etc. for managing the output power of FCPP and WE units can be defined. In the paper following strategies are used; in the first strategy thermal recovery from FCPP is neglected and the thermal load is supplied by natural gas. If the recovered thermal energy is less than the thermal load, the difference between these two items can be supplied by using natural gas otherwise surplus recovered thermal energy, second strategy, can be sold to other neighborhoods and third strategy can be stored and reused later based on system economics. The effect of adding WE unit to the FCPP and local grid has been proposed in fourth through sixth strategies. The remaining part of the paper is organized as follows: Section 2 gives a complete structure of the system besides the type of FC and WE unit which are used in this study. Formulation of economic model is presented in Section 3. The solution methodology and GA algorithm with its parameter adjustments are explained in Section 4. Test results and conclusions are discussed in Sections 5 and 6, respectively.
2. System configuration and energy units 2.1. System configuration The diagram of a WE–PEM fuel cell hybrid energy system connected to grid is indicated in Fig. 1. The system is constituted of wind energy turbine, local grid, heat pump, PEM fuel cell stack and load unit.
2.2. Fuel cell unit PEM stands for polymer electrolyte membrane or proton exchange membrane. Advantages of PEM fuel cells can be mentioned as: their high efficiency compared to other energy conversion devices [16], low operation temperature cause to reach the operation point rapidly and allows rapid start-up [17], inexpensive materials than high temperature fuel cells [18]. PEMs can be made extremely thin and the thinner the polymer electrolyte the higher the conductance and lower the ohmic resistance losses. Therefore this type of fuel cell presently receives the most attention among all kind of fuel cells. Hence, in this paper 6.3 kW PEM fuel cell power is used. When FCPP works at full load it can produces thermal energy as much as electrical energy [19]. In order to manage excess thermal or electrical energy, it is vital to have a robust management strategy. In PEM FCPP, due to the lower operating temperature, thermal recovery from the stack is abandoned so, thermal energy is just recovered from the reformer where the temperature goes up to about 360 ◦ C. Hot water and space heating considers as thermal load in this paper and adds to electric loads of PEM FCPP. The thermal load is satisfied by using the recovered thermal energy from the FCPP and, if necessary, by using of natural gas. On the basis of the difference between the thermal load and the recovered thermal energy and supplying electrical load by FCPP or WE, six different strategies can be defined. In the first three strategies the only source of electrical energy supplier is grid connected PEM FCPP, while in the other strategies WE unit is added
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Fig. 1. System configuration of the proposed hybrid energy system.
Table 1 Technical parameters of XCO2 wind turbine.
The constants, a, b and c can be determined by the Eq. (2)
Power
Value
Unit
Rated power Cut in wind speed Rated wind speed Cut out wind speed
6 4.5 12.5 16
kW m/s m/s m/s
a=
vcut−in (vcut-in + vrat ) − 4vrat ((vcut-in + vrat )/2vrat )3
(vcut-in + vrat )2 3
b=
c =
4(vcut-in + vrat ) ∗ ((vcut-in + vrat )/2vrat ) − (3vcut-in + vrat ) (vcut-in + vrat ) 2 − 4((vcut-in + vrat )/2vrat )
to the source of electrical energy supplier and operates at its full capacity.
2
3
(2)
(vcut-in + vrat )2
3. Formulation of economic model 2.3. Wind energy unit A XCO2/6 kW wind energy unit is used to change wind energy to electric power. In order to protect the turbine from damage a turbine’s cut-out and cut-in speed are determined by the manufacturer. The cut-in speed is the point where the turbine starts to generate electricity from turning. The cut-out point shows the boundary of speed that denotes how fast the turbine can spin before reach to danger zone. Hence, some sort of brake mechanism are used to prevent the turbine from reaching to this danger zone. Technical information of the utilized turbine is available on the internet [20] and is given in Table 1. 2.3.1. Electric output power of the wind turbine The electric output power of the wind turbine, PWE,i at interval i with respect to wind speed vi can be calculated as below [21,22]:
pWE,i =
⎧ 0 ≤ vi < vcut-in 0 ⎪ ⎪ ⎪ ⎨ prat (a + b · vi + c · vi 2 ) vcut-in ≤ vi < vrat prat ⎪ ⎪ ⎪ ⎩ 0
⎫ ⎪ ⎪ ⎪ ⎪ ⎬
vrat ≤ vi < vcut-out ⎪ ⎪ vi ≥vcut-out
⎪ ⎪ ⎭
(1)
The mathematical representation of the cost optimization problem consists of the overall operational cost and the total system income, subject to operational and system constraints can be specified as follows: Objective function = Min
m
(
i
j
costj −
incomek )
(3)
k
Subject to: P min ≤ PFc,i ≤ P max
(4)
PFC,i − PFC,i−1 ≤ Pu
(5)
PFC,i−1 − PFC,i ≤ PD
(6)
on (Ti−1 ) − MUT (Ui−1 − Ui )≥0
(7)
off
(Ti−1 − MDT )(Ui − Ui−1 )≥0
(8)
nstart−stop ≤ N max
(9)
The first term of (1) represents the overall operational-cost, which is completely discussed in Section 3.1, while the second term is the total system income relating to daily income from the sale of excess thermal and electrical energy.
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Part load ratio (PLR) is used to determine efficiency and thermal to electrical ratio [19]. These are calculated in two categories by considering PLR as follow: For PLRi < 0.05
(10)
i = 0.2716, rTE,i = 0.6801
479
to increase, on average, 25% over the 20-year life of the various wind machines [23]. Average values of O&M costs are $0.027/kWh. Therefore, formula for O&M cost used in this paper is (19). 240
CO&M = (0.027)
PWE,i ∗
i=1
6 min 60 min
(19)
For PLRi ≥0.05 i = 0.9033 × PLR5i − 2.9996 × PLR4i + 3.6503 × PLR3i − 2.0704 × PLR2i + 0.4623 × PLRi + 0.3747 rTE,i =
1.0785 × PLR4i
− 1.9739 × PLR3i
+ 1.5005 × PLR2i
(11)
− 0.2817 × PLRi + 0.6838
3.1. System cost component 3.2. System incomes components Cost of fuel: Cost of fuel for producing electrical energy by the FCPP: Cfuel,i = cf T
240 PFC,i i=1
i
(12) IEL,Si = T
Purchased electrical energy cost: Electrical energy purchased from grid when FCPP is the only supplier of demand energy.
240
CEL,pi = T
cel,pi max(Lel,i − PFC,i , 0)
240
cel,pi max(Lel,i − PFC,i − PWE,i , 0)
IEL,Si = T
240
240
cel,si max(PFC,i + PWE,i − Lel,i , 0).
(21)
If the surplus recovered thermal energy is stored and reused and FCPP be the solely source of supplying energy, income of selling surplus electrical energy give as: 240
cel,si max(PFC,i − 0.2 max(Pth,i − Lth,i , 0) − Lel,i , 0)
i=1
Electrical energy purchased from local grid for storing surplus thermal energy when FCPP supply demand energy. CEL,pi = T
(20)
i=1
(14)
i=1
cel,si max(PFC,i − Lel,i , 0)
At the presence of WE unit, surplus electrical energy income will be calculated as follows: IEL,Si = T
Electrical energy purchased from grid at the presence of both FCPP and WE unit. In this situation WE unit acts like a negative load.
240 i=1
(13)
i=1
CEL,pi = T
Selling surplus electrical energy: Surplus electrical energy sold by FCPP is calculated as follows:
(22) With integrating WE and FCPP (22) will change to (23):
cel,pi max(Lel,i + 0.2 max(Pth,i − Lth,i , 0) − PFC,i , 0)
i=1
(15)
IEL,Si = T
240
cel,si max(PFC,i +PWE,i −0.2 max(Pth,i − Lth,i , 0) − Lel,i , 0)
i=1
(23)
Electrical energy purchased from local grid for storing surplus thermal energy when WE unit is added to supply electricity power.
Surplus thermal energy incomes: If recovered thermal energy from FCPP is more than thermal load the surplus can be sold to other neighborhoods.
240
CEL,pi = T
cel,pi max(Lel,i + 0.2max(Pth,i − Lth,i , 0)
i=1
− PFC,i − PWE,i , 0)
(16)
ITH,Si = cth,si T
240
max(pthi − Lthi , 0)
(24)
i=1
Term of 0.2max(Pth,i − Lth,i , 0) illustrates requested electrical energy for storing surplus thermal energy. Gas cost for purchasing thermal energy: Gas cost can be added to the cost function if thermal load is more than recovered thermal energy and it is calculated as follow: CGas,pi = cg T
240
If the surplus recovered thermal energy is stored and reused, income of selling the saving of thermal energy at the end of day give as. ITH,Si = cth,si Pth-storage st,th
(25)
4. An overview of genetic algorithms max(Lth,i − Pth,i , 0)
(17)
i=1
Startup and maintenance cost: Csup = ˛ + ˇ(1 − e−(toff /) )
(18)
Cost of wind unit: Although wind O&M cost trends had been decreasing for the expansion in overall wind farm size, it cannot be negligible. High O&M costs associated with generators, gearboxes and drive trains. In fact, O&M costs are not fix and estimated
As genetic algorithms software is the most widely used for purposes of optimization, to optimize the fitness function (3) a genetic algorithm is used. Since six minute time interval is used, 240 variables are defined for 24 h. Linear equalities and inequalities (Eqs. (4)–(11)) with their bounds are also defined. A double vector population type is used to specify the type of the input to the fitness function. Population size, which specifies how many individuals there are in each generation, is selected 450. In order to create the initial population a uniform function is used that creates a random
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Fig. 2. Complete flowchart of the proposed method.
initial population with a uniform distribution. For removing the effect of the spread of the raw scores a scaling function should be defined, so in this paper rank function is used. Rank function scales the raw scores based on the rank of each individual, rather than its score. The rank of an individual is its position in the sorted scores. For example the rank of the fittest individual is 1, the next fittest is 2, and so on. Appropriate parents based on their scaled values from the fitness scaling function for the next generation should be selected. Therefore stochastic uniform is used as selection function, and lays out a line in which each parent corresponds to a piece of the line of length proportional to its expectation. The algorithm moves along the line in the same size steps, one step for each parent. At each step, the algorithm allocates a parent from the section it lands on. The first step is a uniform random number less than the step size. Reproduction determines how the genetic algorithm creates children at each new generation. This process consists of the number of elite, crossover and mutation fraction. In the paper elite count has been set to 20 while crossover and mutation have been set to 0.8 and 0.2 respectively. Crossover combines two parents to form a new child, for the next generation. Scattered crossover is applied in the article. The crossover at first creates a random binary vector then selects the genes by the help of this vector, where an element of the vector is 1 a gene will be selected from the first parent, otherwise it will be selected from the second parent, and finally combines the genes to form the child. For example: p1 = [a
b c d
e
f
g h ], p2 = [1
Random crossover vector = [ 1 0 Child = [ a 2 3 d
e
6 7 h]
0
2 3 4 5 6 7 8]
1 1 0
0 1]
In order to enable the genetic algorithm to search a broader space a uniform mutation function is used. It has two-step process, in the first step the algorithm picks out a fraction of the vector entries of an individual for mutation, where each entry has the same probability as the mutation rate of being mutated. In the second step, the algorithm replaces each selected entry by a random number selected uniformly from the range for that entry. Given the population size as a vector of length 450, algorithm should create a movement of individuals between subpopulations which is called migration. In migration every so often, related to interval control, the best individuals from one subpopulation replace the worst individuals in another subpopulation. A forward migration with 20 intervals is used. That is the nth subpopulation migrates into the (n + 1) th subpopulation and migration between subpopulations takes place every 20 generations. In order to control the number of individuals move between subpopulations a fraction of 0.2 is defined. For instance if individuals migrate from a subpopulation of 50 individuals into a population of 100 individuals and Fraction is 0.2, 10 individuals (0.2 × 50) migrate. Individuals that migrate from one subpopulation to another are copied; they are not removed from the source subpopulation. After all of aforementioned process a set of stopping criteria, which are related to the number of generations, time and fitness limit, are determined to allow the algorithm to terminate. Eventually fitness and constraint functions in serial form are evaluated. Serial form means the fitness and constraint functions are evaluated separately at each member of a population. Flowchart of extended GA based solution methodology is displayed within Fig. 2. 5. Case study In order to supply residential load seven different cases are tested. For the base case residential load demand is supplied by
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481
Table 2 Tariff of trading electrical energy with local grid. Time (h)
0–6
6–8
9
10–11
12–16
17
18–19
20
21
22
23
Purchasing tariff Selling tariff
0.05 0.03
0.07 0.05
0.09 0.07
0.1 0.07
0.11 0.08
0.13 0.09
0.14 0.1
0.17 0.14
0.15 0.1
0.1 0.07
0.07 0.05
Table 3 FCPP and genetic algorithm parameters. Maximum limit of generating power, Pmax (kW) Minimum limit of generating power, Pmin (kW) Hot start-up cost, ˛ ($) Cold start-up cost, ˇ ($) The fuel cell cooling time constant, (h) Minimum up-time, MUT (number of intervals) Minimum down-time, MDT (number of intervals) Lower limit of the ramp rate, pD (kW) Upper limit of the ramp rate, pu (kW) Length of time interval, T (h) Maximum number of starts-stops, Nmax Maximum number of evolutionary generation Number of individuals Fuel price for residential load, cg ($/kWh) Price of natural gas for FCPP, cf ($/kWh) Thermal energy selling price cth,s ($/kWh) Thermal storage efficiency, st,th (%)
6.3 0.0 0.05 0.15 0.75 2 2 0.5 0.4 0.1 5 5000 450 0.6 0.4 0.4 90
Although, Iran is one of the richest countries in the field of renewable energy sources, in the past decade just a little portion of its produced electricity derived from renewable energy sources (exclude hydro), recently authorities have given desirable attention to the potentials of renewable energy systems [24]. According to preliminary studies [24] by the Iranian renewable energy organization (SUNA), Iran’s mountainous terrain are characterized by unique wind corridors and are able to produce at least 6500 MW energy. Iranian government has committed, on its fifth five-year economic development plan (2010–2015), to generate 1650 MW of wind energy by March 2014. So, Iranian residents can rely on renewable energy sources of Iran, especially wind, to supply their demands. In this article to prove this assertion wind speed data of Khvaf city in Khorasane-Razavi Province have been used. Location of Khvaf with wind speed data and the electric output power of XCO2 turbine, after placing data to (1), are shown in Figs. 4–6 respectively. 5.1. Test and results
local grid. In the first three cases a grid connected PEM FCPP is used to supply residential load. Electricity trading tariffs are shown in Table 2. Data for PEM FCPP with GA parameters and thermal energy trading tariffs are given in Table 3. In the last three cases a 6 kW XCO2 wind turbine is added to the complex. In each case (except base case) GA defines optimal electricity output power of the FCPP with respect to consider electricity trading tariffs, thermal and electrical load, FCPP constraints and electric output power of wind turbine. As Table 2 shows selling price at all the time is cheaper than purchasing price then it encourages grid to buy electricity from FCPP. Electrical and thermal residential load are depicted, in Fig. 3. When FCPP runs, thermal energy is produced as a by-product besides electrical energy. After recovering this energy we must be sure it will be used by neighbors. Hence in order to encourage them to use this energy, its price should be lower than other ways of supplying thermal energy. So, as it is obvious from Table 2, thermal energy selling price with FCPP is considered lower than fuel price for residential load.
The suggested model has been applied to a 6 kW wind energy unit and 6.3 kW FCPP, which are grid-parallel that supply a residential house. A load profile of Khavaf city with a peak of 6.3 kW is used to simulate six minute load profile of the residential house. The space heating and winter hot water usage is considered as the thermal load profile for residential house in Khavaf, Khorasane Razavi. The electrical load is used along with the thermal load profile to simulate total six minute operation of the WE unit and FCPP. The necessary parameters are given in Tables 2 and 3. Base case: In this case both electrical and thermal load are supplied through the local grid and natural gas, respectively. Base case shows the cost of supplying residential load without considering the FCPP and WE unit. In this test case daily cost of supplying both thermal and electrical energy will lead to 17.0693$. Case 1: In this case a combination of FCPP and local grid is used to supply just electrical load. Recovering of thermal energy from FCPP is neglected. The amount of FCPP power generation is depicted in
Fig. 3. Electrical and thermal load.
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Fig. 4. Location of Khvaf in Iran.
Fig. 7 and the difference between this generation and load demand has been supplied from local grid which is shown in Fig. 8. As Fig. 7 shows, during 0–11 purchasing electricity tariff from grid is too low then the management strategy order FCPP to be off and supply electrical load from local grid so in this period the shape of Fig. 8 is exactly like electric load profile. In this strategy daily cost of supplying both thermal and electrical energy has a reduction of 0.9293$ so total cost in this case for one day is 16.14$. This strategy can result in a save of 339.1965$ per a year. Case 2: In this case thermal energy is recovered from FCPP as a by-product. It means that in addition to use of electrical output power from FCPP its recovering thermal energy is also used for supplying residential thermal load. If the recovered thermal energy is less than thermal load the lack can be compensate by using natural gas otherwise surplus recovered thermal energy is being sold to other neighbors. Electrical load and power generation are shown in Fig. 9 while electrical energy trade with local grid is shown in Fig. 10. Thermal load and recovered thermal energy are depicted in Fig. 11. A robust management strategy should consider different transient changes in FCPP production. This transient change can cause different conditions in electricity trade whit local grid. Therefore, the FCPP generation can be divided into 5 parts. As Fig. 9 shows,
Fig. 5. Wind speed changes at Khvaf in 24 h of a day at 10 min elevation.
Fig. 6. Electric output power of XCO2 turbine.
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Fig. 7. Supplying electrical loads by combination of FCPP and local grid.
Fig. 8. Purchasing electricity from local grid.
Fig. 9. Electrical load and generation.
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Fig. 10. Electrical power trade with local grid.
from 0:00 to 6 that management strategy ordered FCPP to be off because purchasing electricity from local grid, during this period, is more economical than generating power by FCPP then in this period electrical load supplied by local grid and recovered thermal energy is zero. Start-up cost can be another factor that management strategy considered to keep the fuel cell off. From 6 to 10 the optimum power generation, according to management strategy is to supply electrical load by FCPP. Sometimes supplying thermal load just by generating extra power from FCPP is not cost-effective, unless the excess power generation will be sold to local grid and thermal load supplied by natural gas. 10 AM to 1 PM is the time period that this operation may take place since electricity price is almost high. Fortunately in the period generated power from FCPP is more than residential electrical demand so surplus electrical power can be sold to local grid by a lower price. The actiondepends on management strategy, maybe supplying thermal load or electricity tariffs be factors for the operation. During the time period 1 PM to 5 PM (780–1020 min), generated electrical power by FCPP is just for supplying electrical load. In this period excess recovered thermal energy is sold to the neighbors. From 5 PM to 0:00, trading electrical power with local grid take place while not only does
FCPP cannot sell thermal energy, but also need to buy natural gas to supply thermal load. In this case daily cost of energy supplying is equal to 14.5385$ it means a 2.5308$ reduction in each day that result in 923.7420$ saving per year. So, this strategy is more effective than the previous strategy. Case 3: This case is like the second case except that surplus recovered thermal energy from FCPP is stored and reused at the end of the day. If the recovered thermal energy is less than thermal load, thermal load is supplied by thermal reservoir otherwise it will be stored and sold to other neighbors at the end of the day. Both FCPP power generation and recovered thermal energy will be like Figs. 9 and 11 in case 2 respectively. Since our desire is supplying residential load, unlike case 2 surplus recovered thermal energy between 13 and 16 h of Fig. 11, is stored and reused at the end of the day unless recovered energy is less than thermal load. Daily cost of supplying energy in this case is equal to 14.5334$ so daily cost reduction will be 2.5359$. Total yearly saving is equal to 925.6035$. The effect of using FCPP as a DG system for supplying residential demand is being analyzed. The results prove that recovering thermal energy is the most effective strategy. Although storing surplus
Fig. 11. Thermal load and generation.
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Fig. 12. FCPP and WE power generation with electrical load.
Fig. 13. Electrical trading with grid.
Fig. 14. FCPP and WE power generation with electrical load.
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Fig. 15. Electricity trading with local grid.
thermal energy is seems to be more affordable than case 2, it is not viable for residential use since storing thermal energy needs higher technology and expensive equipment. Now the effect of integrating WE unit to pervious system and making a hybrid system is examined. Case 4: By adding another source of energy to the case 1, case 4 is forming. In this case, in addition to the FCPP unit the model is tested in using a total capacity of 6 kW WE unit, which is operated at its full capacity all the time. Wind speed data, Fig. 5, and WE unit data, Table 1, are used to calculate power output of WE unit for the three remaining cases. WE unit can affect the amount of power generated by FCPP and in turn changes the answers. FCPP power generation with electrical load and sum of output power of DGs is shown in Fig. 12. In this case thermal recovery is neglected and thermal load supplied by natural gas. Electricity trading with local grid is depicted in Fig. 13. Total cost in this case is 11.4886$ so from the result and [6] it is obvious that hybrid systems can cause lower cost than a single-supply systems. Case 5: After integrates WE unit to the model of case 2 the model of this case will generate. Since WE unit act as a negative load FCPP need to produce lower energy to supply residential load and the
less it (FC) works the lower it produces thermal energy. Electrical load and WE power generation plus FCPP power generation are depicted in Fig. 14. Electricity trading with local grid is shown in Fig. 15. Fig. 16 shows thermal recovery from FCPP. Total cost of this case, which is incomparable with case 2, is 9.3626$. It is evident from Fig. 15 that integrated generation system causes to buy less electrical energy than the first three cases, and also the system sells excess electrical energy most of the time. This excess electrical energy is high during the low thermal load according to Figs. 15 and 16. Case 6: In this case the priority is to supply thermal load by recovered thermal energy from FCPP then by natural gas. If thermal recovery is more than thermal load, surplus recovered thermal energy is stored and reused at the end of the day. But if the recovered thermal energy is less than thermal load, thermal load is supplied from thermal reservoir and natural gas. Hybrid system power generation and trading electricity with local grid in the case are the same as case 5 and have been depicted in Figs. 14 and 15 respectively. As Fig. 16 shows thermal recovery from FCPP just around 14 can be stored so preparing apparatus to save just a little amount of thermal energy would not be cost effective. Therefore
Fig. 16. Thermal recovery.
M.R. Ranjbar et al. / Energy and Buildings 68 (2014) 476–487 Table 4 Cost of each case. Case number
Total cost ($/24 h)
Base case Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
17.0693 16.1400 14.5385 14.5334 11.4886 9.3926 9.7519
total cost in this case should be higher than case 5 and it is 9.7519 so the fifth case is the best case among all of the cases as it is obvious from Table 4. 6. Conclusion The integration of WE and FCPP system in an economic model which consist of power trade with the local grid with different tariffs and thermal recovery from FCPP is introduced in this paper. The paper suggests practical concepts regarding operational cost modeling of the system. Six test cases were evaluated using a residential load profile of Khavaf city in Khorasane Razavi Province, Iran. In the first three cases the fuel cell power plant supplies electrical and thermal power as solely DG system but in the last three cases WE unit is added to the complex and based on the available power from WE unit, the fuel cell power plant supplies both electrical and thermal power to the residential demand. Base on wind speed and low-cost wind turbine energy production, WE unit runs at full capacity most of the time. The main factor that affects the operation of the FCPP is thermal load. For instance some times, based on the system economics, FCPP inclines to generate electrical energy more than the electric load during high thermal consumption periods and produces low electrical energy during low thermal periods. Test results on a 6.3 kW fuel cell power plants and 6 kW WE unit indicate the feasibility of the suggested approach and its potential to find the optimal power output from the FCPP subject to the connected constraints and WE unit power. References [1] T. Zhou, B. Franc¸ois, Energy management and power control of a hybrid active wind generator for distributed power generation and grid integration, IEEE Transactions on Industrial Electronics 58 (1) (2011) 95–104.
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