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A versatile system for offshore energy conversion including diversified storage
Energy 48 (2012) 566e576
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Energy journal homepage: www.elsevier.com/locate/energy
A versatile system for offshore energy conversion including diversified storage D. Fiaschi*, G. Manfrida, R. Secchi, D. Tempesti Dipartimento di Energetica “Sergio Stecco”, Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 July 2012 Received in revised form 2 October 2012 Accepted 3 October 2012 Available online 7 November 2012
Offshore applications allow to exploit different renewable energy sources (wave, wind, solar) that are complementary each other, due to their statistical yearly distributions. In this paper, we discuss an offshore platform for energy production from renewable energy sources coupled with three energy storage systems. The proposed offshore platforms uses a Compressed Air Energy Storage (CAES) to timely shift the electricity production from the demand. The performance of the system related to a north Tyrrhenian Sea location was evaluated by a simulation model developed integrating three different software packages (Matlab, EES, TRNSYS). The system was designed to produce 564 kWh on the 2 h a day where peak electricity demand takes place. The results showed that the system is able to produce 177,000 kWh per year. This offshore power plant is conceived for local users (tourist resorts, villages), especially if placed in small or medium islands, wishing to qualify for extensive use of renewable energy. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Offshore CAES Solar energy Microturbine Energy storage Wave energy
1. Introduction Renewable energy sources (RES) are often characterized by: a) a low Energy density b) a highly stochastic nature. However, some of the most variable RES (wave, wind) have statistical distributions with winter peaks which are to some extent complementary to others, like solar radiation. The offshore applications are particularly appealing, as the situation allows to combine these three different energy sources. In the specific case, the Mediterranean climate is attractive, because extreme events e which often lead to destruction of exposed structures e are rare and their intensity is anyway lower of what is encountered in the open ocean applications. In order to be most effective, the power plant island should include one or more energy storage systems, which allow to shift electricity production from demand, as for these energy sources production often takes place when the electricity demand is low, or vice-versa. Thinking of an off-shore application, it was considered to store energy by two complementary systems: a) a Compressed Air Energy Storage (CAES) using a submerged reservoir, working in isobaric natural conditions provided by the hydrostatic under-sea pressure gradient. b) a hot rock bed for energy storage/recovery unit (RBES) from/to the compressed air flows. * Corresponding author. Fax: þ39 055 4224137. E-mail address: daniele.fiaschi@unifi.it (D. Fiaschi). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.006
The renewable energy collected from wind, wave or solar radiation is stored and its value is enhanced using natural gas. The combustion gases are expanded in a commercial micro gas turbine, with limited design modifications (in practice, the air compressor is cut out from the shaft). The application is thought as a possible pilot plant to be proposed to small local users, such as tourist resorts, wishing to qualify for extensive use of renewable energy. 2. System description and working principle The system has a variable configuration according to the operation mode. In the storage mode (SM), the layout is described in Fig. 1. A wave energy conversion device (WECD) is the heart of the system: here, the Wave Dragon [1e6] solution was considered as one of the most advanced and adaptable to multiple-renewable energy systems. The WECD platform (Figs. 2e5) can be designed to host a photovoltaic (PV) solar array system, and a set of small vertical-axis wind turbines can be integrated on the offshore platform (4 in the present case). The three RES produce each a DC power output, which is the input to a variable-frequency inverter (VFI); this last is connected to an AC electric motor driving an air compressor. A battery pack (BP) was also added upstream the VFI, so minimizing the waste of collected energy. The air compressor is a commercial screw unit which can operate at variable speed from 18 to 75 kW. Air is stored at a delivery pressure of 10 bar, corresponding to
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Fig. 3. Offshore platform, close-up view (rendering).
All the equipments considered in the system are available on the market (wind turbine [7], PV arrays [8], VFI, compressor [9], micro gas Turbine [10], battery [11]) or as a prototype needing limited adaptation (Wave Dragon [1e6]). For the present case, a commercial TURBEC micro gas turbine with a nominal power of 100 kW was considered. The compressor is disconnected so that the turbine power output is raised to 280 kW, which is the peak-load power value of the reference plant.
Fig. 1. System layout, storage mode.
a CAES reservoir depth of 100 m. Before being stored, compressed air is cooled in the RBES, which works as a sensible heat energy storage device. After the RBES, the compressed air stream is further cooled in a sea water heat exchanger (SWHE): it enters then the submerged CAES reservoir from the top, where it displaces the water which is initially filling the vessel. In the production mode (PM), the system layout is changed to that of Fig. 6. The compressed air flows to the turbine, emptying the CAES vessel and reducing the stored pressure energy. The SWHE is by-passed; and before being sent to the turbine, compressed air flows through the RBES, takes a fraction of stored heat and raises its temperature. In this way, a lower natural gas consumption in combustion chamber is achieved. Finally, a pressure regulator adjusts the pressure at the nominal value at the inlet of the combustion chamber of the gas turbine (4.5 bar). In principle, it is possible to use the cold pressurized air for the gas turbine cooling flows, thus some adjustments to the engine cooling flow rates can be proposed.
3. Estimate of wave energy The wave energy was estimated following traditional spectral decomposition methods applied in wave energy conversion studies. According to Piscopia et al. [12], the spectra of Italian sea is characterized by a significant wave height greater than 1.0 m that can be fitted quite satisfactorily using the single peak JONSWAP spectrum with a peak enhancement factor (g) of about 2.4:
h i 2 S f ¼ bJ $H1=3 $DTP4 $f 5 $exp 1:25ðDTP $f Þ4 $ " # ðDTP $f 1Þ2 exp 2s2
(1)
g
where
bJ ¼
0:0624 0:230 þ 0:0336g 0:185ð1:9 þ gÞ1 $½1:094 0:01915$ln g h
DTP yDT1=3 = 1 0:132ðg þ 0:2Þ0:559 s¼
i
sa : f fp sb : f fp
The specific energy of the waves can be expressed as:
E ¼
2 r$g$Hmo
16
¼ r$g$
ZN Sðf Þdf :
(2)
0
Of direct interest is the wave energy flux transported by the wave:
J ¼ E$cg :
Fig. 2. Offshore platform, top view (rendering).
(3)
where cg is the wave group velocity, which for deep water can be expressed as:
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Fig. 4. Offshore platform, top view.
cg ¼
g$DT g ¼ : 4p 4p$f
(4)
For a real sea wave, the wave energy flux can be expressed by the wave spectral distribution:
J ¼ r$g$
ZN
2 r$g2 $DTj $Hmo cg f S f df ¼ : 64p
(5)
0
The latter was applied to two historical data sets of wave height/ period measurements available in the North Tyrrhenian Sea, with the results summarized in Table 1, that were calculated using a Matlab code developed for the specific purpose [13]. After this calculation, it was decided to focus on the La Spezia location, because e even if the average wave energy flux is a low 3.1 kW/m e the location is attractive as there are several potential users nearby. 4. Scaling down the wave energy conversion device The performance data of the WECD were adapted from Ref. [1]. The original device was designed for operation under much more intensive seas (J ¼ 24 kW/m), while a working prototype is undergoing tests in conditions of quiet sea (J ¼ 0.4 kW/m). In order to scale down the performance, Froude number similarity rules were applied, leading to an estimated productivity (with J ¼ 3.1 kW/m) of 1 GWh/year. The main WECD data are summarized in Table 2, related to the size shown in Figs. 4 and 5; it corresponds to what can be built in shipyards available near to harbors.
5. Sizing the solar PV and wind energy conversion devices For the solar PV and wind energy conversion devices, it was decided to use directly the weather data and component library available in TRNSYS; this calculation environment was also selected for running the year-round simulation of the overall system. The PV system is based on high-quality mono-crystal silicon modules, each of which is rated for a peak power of 350 W. The whole PV system is sized for an overall power of 75 kWe, under the worst conditions for average radiation, which are obtained in referred to the average radiation data the month of January. Thus, the system is able to collect from PV at least about 1/3 of the nominal 600 kWh/day needed for air compression. In summer, the whole system runs solely on PV, while during winter the contribution of wave energy is significant. The PV system is built with 234 modules arranged in 9 * 26 stacks (series/parallel), with a rated voltage of 600 VDC. Each row of modules is tilted at an angle of 45 from the horizontal, and is 3.6 m distant from the preceding/ following row, in order to avoid significant shading. The PV platform is 12 m high, has a diameter of 35 m and an overall surface area of about 960 m2. The platform can rotate in order to adjust the orientation of PV modules toward the sun, independently of wave and wind direction. Wind energy is only complementary for the location here considered, as the average wind speed is a low 5 m/s. However, wind can be an important contribution in rare conditions of low radiation and flat sea. For the wind turbines, considering the need of avoiding shading on the PV arrays and the requirement of
Fig. 5. Offshore platform, front view.
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Fig. 6. System layout, production mode.
a limited tower height, it was decided to consider the installation of vertical-axis units, with a nominal power rating of 3 kW at a wind speed of 12 m/s [7]. Each of the 4 wind turbines has a diameter of 3 m and is mounted on a 16 m height pole. The distance among the turbines is sufficient to avoid interference, according to current wind farms swept area/distance design rules. 6. Sizing of the energy storage systems 6.1. RBES
related to phase transition (needing pressurized operation). With respect to phase change energy storage, an RBES can operate at variable temperature and e working with air, a perfect gas which enthalpy depends only on temperature e this allows to reach higher final temperatures after heat recovery [14]. An RBES is basically built around a vessel containing a packed bed of solids of given nominal size (Fig. 7). A model for the RBES can be built according to Ref. [15], based on two differential equations:
rf cpf 3
The rock bed energy storage (RBES) is a key component of the system. As the air is heated during compression when operating in the SM, it is important that a high fraction of the flow enthalpy is recovered as heat, which must be used for air pre-heating in the PM. A rock bed system is an attractive device for sensible heat storage. In fact, it is much less expensive e for a fixed heat capacity e of a liquid heat storage system (requiring a secondary loop and a large and well-insulated reservoir), and it does not present any trouble Table 1 Calculated wave energy from 3-h historical data in two locations of the north Tyrrhenian Sea. N
Wave meter location
Number of data
Number of years
Missing data
Average wave energy flux (kW/m/year)
1 10
Alghero La Spezia
47638 41935
17.9 16.5
4733 (9%) 6343
13.1 3.1
dTf dT þ Gcpf f ¼ h Tr Tf dt dx
(6)
dTr ¼ h Tf Tr dt
(7)
rr cpr 1 3
In the present case, a cylindrical geometry was considered, neglecting the effects of radial heat conduction (well-insulated vessel). In order to solve the set of differential equations, a finiteTable 2 Main dimensional data for the WECD. Ramp width, m Arm length, m Freeboard crest height, m Tank volume, m3 Number of turbines Turbine unit rated power, kW Turbine rotor diameter, m
52 56 1.8 750 14 25 0.67
570
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rr cpr 1 3
Fig. 7. Rock bed energy storage (schematic).
difference approach was adopted, dividing the length L in Nx sections, and using a suitable internal time interval for time evolution of the RBES:
Dx ¼
L ; Nx
Dt ¼
Dte
(8)
Nt
From the numerical point of view, the solution of Eqs. (6) and (7) is not subjected to a stability criterion of the CFL type. However, it is recommendable that the internal spatial discretization and time step are chosen in a suitable way, in order to allow a detailed description of the RBES system, without increasing too much the number of variables. Eqs. (6) and (7) are then discretized in a timeforward scheme as follows (i ¼ 1,. Nx; j ¼ 1,. Nt):
rf cpf 3
h i h i Tf i; j Tf i; j 1 it h i h D ¼ h Tr i; j Tf i; j
þ Gcpf
h i h i Tf i; j Tf i 1; j
Dx
(9)
ðTr ½i; j Tr ½i; j 1Þ ¼ h Tr i; j Tf i; j Dt
(10)
In the present case, the TRNSYS simulation is run with an external time step of 1 h ¼ 3600 s: accordingly, Nt ¼ 10 (Dt ¼ 360 s) was chosen; and the length of the RBES was set at 2.5 m, with Nx ¼ 10 and thus Dx ¼ 0.25 m. The RBES is a cylinder of 7.5 m3, where the 60% of the volume is filled with rocks of typical diameter of 0.012 m. The weight of the rocks is approximately 12,000 kg. The differential equations are solved in an internal time loop by a dedicated program written in EES, which is called by the TRNSYS main program, taking care of the external (major) time advancement. The initialization, storage and visualization of data of the RBES are performed through a MATLAB routine called by TRNSYS. A typical output of the temperature profile during an internal TRNSYS time step is shown in Figs. 8 (for SM) and 9 (for PM). Once the initial and boundary conditions are loaded for each TRNSYS time step, this procedure is able to calculate the temperature profile in space and time across the RBES, both in the SM and in the PM. 6.2. CAES Referring to the SM, after exiting the RBES the air stream is cooled down to a final temperature which is mainly depending on the rock bed temperature Tr(Nx, t). During the final period of the SM, Tr can reach values close to the compressor exit temperature Tce; anyway, as the volume of the CAES vessel is fixed, and its pressure is fixed by the hydrostatic gradient on the sea bed, in order to store as much mass of air as possible it is necessary to further cool down the air stream. This is done in a sea water heat exchanger (SWHE); it is important to notice that this heat is not recovered, but rather lost to
Fig. 8. Example of RBES temperature profile calculation (a, rock; b, fluid); 13th hour simulation of November 20; last storage mode simulation time step of the day.
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Fig. 9. Example of RBES temperature profile calculation (a, rock; b, fluid); 17th hour simulation of November 20; first production mode simulation time step of the day.
the environment (sea water). The SWHE was sized as a countercurrent heat exchanger, and its gross surface area (A ¼ 7 m2 in this case) was determined assuming sea water at 20 C and the design value of the exit temperature Tfo fixed at 30 C. The SWHE works with a constant sea water flow rate: accordingly, with a variable inlet temperature Tri(Nx, t), the actual final value of Tfo (together with the warm water temperature) was calculated using the NTU-Efficiency correlations provided by EES, thereby considering the complete off-design operation of the heat exchanger. Actually, the value of Tfo is maintained very close to the design value, having chosen a sufficiently large heat transfer surface. The volume sizing of the CAES vessel derived from the fundamental system assumptions:
1) Duration of the production mode (2 h/day); 2) Design flow rate of the turbine (mfT ¼ 0.79 kg/s). From these assumptions and from the calculation of density for a compressed air storage temperature of 30 C, the CAES vessel volume was determined as 500 m3. If the chosen air compressor operates at full load (75 kW, with a fluid flow rate mfC ¼ 0.197 kg/s), it needs 8 h to fill completely the CAES vessel. Thus, with the proposed RES conversion system (integrating three different energy sources), daily cycles of system operation can be achieved for the largest fraction of the year. The TRNSYS simulation allows the prediction of the time history of the different forms of energy storage of the system (thermal
Fig. 10. Amount of energy generated from RES over the representative four-days period.
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22500 20000
Energy (kWh)
17500 PV Panels
15000
Wind Turbines
12500
Idraulic Turbines
10000 7500 5000 2500 Ju ly Au gu st Se pt em be r O ct ob er No ve m be De r ce m be r
Ju ne
ay M
Ap ril
Ja nu ar y Fe br ua ry M ar ch
0
Month Fig. 11. Monthly sum of energy generated by each RES.
full load and speed): in this case, the compressor is stopped, and the available renewable energy is stored in the batteries; 2) when power produced by RES exceeds the nominal rated power of the compressor (75 kW); 3) when the gas turbine/RBES/CAES assembly is working in the PM, in order to accumulate briefly renewable energy which would otherwise be wasted.
energy stored in RBES and pressure energy in CAES vessel). In SM, an increase of both forms of stored energy can be observed, with a maximum of 0.5 GJ of compressed air energy and about 5 GJ of thermal energy in RBES. 6.3. Battery pack The battery pack is used both as an auxiliary storage device, and as a backup system:
7. Performance evaluation
6.3.1. BP as backup system The battery pack is designed to supply the complete absence of energy production from RES for a period of three consecutive days; thus, considering a maximum discharge level of the battery at 50% of its capacity, the total energy autonomy is 3600 kWh (¼12.96 GJ). The overall voltage of the battery pack was chosen at 240 V. The battery pack is also useful to reduce the time needed to fill the CAES vessel, when the energy produced by RES is not enough to power the compressor at the nominal rated power (75 kW).
As a volumetric (screw) compressor is used, the machine was assumed to be able of providing a constant pressure over a reasonable range of rotational speed, according to manufacturer’s data [9]. The main variable changing with actual working conditions (i.e. off-design) is flow rate, provided that the operating range for rotational speed is matched (20%e100%). The compression is simulated assuming a given value of the compressor efficiency, and applying traditional non-isentropic flow relations [16]. A constant discharge pressure is guaranteed by the hydrostatic pressure gradient on the sea bed. Solar radiation, wind velocity, ambient temperature for the location of Pisa (Italy) were taken from the weather data library available in TRNSYS. Data sets of wave height/period measurements available in the north Tyrrhenian Sea were used to determine wave energy through the equations described in Section 3. Since it is supposed to install the power plant in the north Tyrrhenian Sea at a distance of approximately
6.3.2. BP as auxiliary storage device There are significant cases in which the batteries are systematically used as a storage device (recharging):
Power (kW), State of charge (%)
1) when the power produced by RES is less than the minimum power needed for compressor activation (18 kW over 75 kW at 300 275 250 225 200 175 150 125 100 75 50 25 0 -25 -50 -75
Battery State of Charge Power from Gas turbine Total power to compressor Power to (>0) or from (<0) battery Power to compressor from RES
0
12
24
36
48
60
72
84
96
Simulation Hour Fig. 12. Evolution of power parameter and battery state of charge in typical NovembereDecember 4 days simulation.
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Fig. 13. Example of stored energy profile (thermal energy and pressure energy) for a simulation period of four days (November 20e24).
10 km from the shores near Pisa, we can assume that there will be a slight difference between the weather data, taken from Pisa, and the real location of the power plant. In fact, while solar radiation and ambient temperature can be considered quite similar for both locations, the wind velocity could be a little different. However, wind energy gives a very small contribution to the overall energy produced by the system due to the very small wind power capacity installed. Thus, we can conclude that using the weather data for Pisa leads only to slight underestimation of the wind energy produced. It was initially chosen to simulate the system over a 4 days time period. This allows to include several operating cycles (SM and PM), and to clearly represent the behavior of all the involved parameters. The periods simulated are selected among those representing 80% of the year, in terms of climate conditions and energy generated from RES. The discriminating parameter for the selection of these periods is the energy generated from RES which directly activates the compressor: in fact, the duration of the air compression phase is mostly affected by this parameter. By dividing a year in 91 periods of 4 days and by summing the energy generated by the RES in all periods, it is possible to calculate the cumulative curve of the energy produced by RES. Then, we neglected the 4-days periods where the energy produced by RES is lower than the value corresponding to 10% on the cumulative curve, or higher than the value corresponding to 90%. Thus, we were able to identify the 4-days periods which represent the 80% cases of yearly energy produced by RES. In Fig. 10, some representative periods are shown, with their amount of energy generated from RES directly provided to the compressor. In the same figure, a subdivision of the year in 5 parts is
573
shown: these periods correspond to different productions of RES that typically occur during the different seasons of the year. As shown in Fig. 11, the monthly amount of energy generated by each of the three sources varies depending on the season: in winter months, the production from wave energy is greater than solar energy (or much greater, like in November and December, where it reaches 18,000 kWh/month), whereas from May to October an opposite trend is observed (with peak photovoltaic production of over 22,000 kWh in July). Through the graphical output of TRNSYS, the time history of the following parameters can be verified: 1) Power generated by each RES. 2) Power directly provided to the compressor. 3) Power to or from battery. 4) Power produced by gas turbine (in PM). 5) Battery charge level. 6) Thermodynamic properties of air at all cycle points (temperature, density, volumetric) and mass flow rate. 7) Conditions in the storage vessel (volume of air, pressure energy). It is also possible to verify the fuel consumption of the gas turbine at every PM time step and the related thermodynamic performance. The days from 20 to 24 of November are considered representative of system performance in November and December; Fig. 12 shows the evolution of the first five previously mentioned parameters. As energy is mostly produced by the WECD, the power generated by RES has a largely variable trend (dotted-blue line). However, differently from the summer period, when energy is mainly produced by PV, the compressor is powered also during the night. Power generated by RES is never sufficient to compress all the air flow rate which can be daily stored, therefore energy is taken from the BP (black line). Starting from a full charge condition, at the end of the simulation period, the BP charge decreases to 79%, with 2370 kWh provided to the compressor by the BP. Also in this time period, the compressor system is thus able to store the air flow rate necessary to daily activate the turbine for 2 h. The related energy production is 568 kWh/day (red line). The time history of energy storage during a 4-days period can be verified by means of the simulation model (see Section 6.2). Pressure energy (GJ) of the stored compressed air at every simulation time step is defined as:
EP ¼ ðVCA $PCA Þ=10; 000
(11)
While the thermal energy stored in the RBES at every simulation time step is:
800.0 700.0 Air out of compressor Air out of RBES in SM Air out of SWHE Air out of RBES in PM
Temperature (°K)
600.0 500.0 400.0 300.0 200.0 100.0 0.0 0
12
24
36
48
60
72
84
96
Simulation hour Fig. 14. Evolution of compressed air temperature in a typical NovembereDecember 4 days simulation.
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Fig. 15. Annual simulation: monthly energy to compressor and fraction supplied from RES and batteries.
Table 3 Annual simulation: monthly amount of energy to compressor and fraction supplied from RES and batteries. Month
January February March April May June July August September October November December
ET ¼
Energy to compressor (monthly value)
Fraction from RES
Fraction from battery
(kWh)
(kWh)
(%)
(kWh)
(%)
12653.0 14067.0 14750.6 17678.7 14832.4 17514.5 18628.3 18092.6 16536.7 12483.3 16788.4 15287.0
7902.3 8467.0 9986.7 12695.4 12021.5 12802.0 15390.1 13669.5 11814.1 9325.7 12744.2 11606.6
62.5 60.2 67.7 71.8 81.0 73.1 82.6 75.6 71.4 74.7 75.9 75.9
4750.8 5600.0 4763.9 4983.4 2811.0 4712.5 3238.3 4423.1 4722.6 3157.6 4044.2 3680.4
37.5 39.8 32.3 28.2 19.0 26.9 17.4 24.4 28.6 25.3 24.1 24.1
Nx X Ar $x$rr $cpr i¼1
10
$ðTr ½i Ta Þ
(12)
The time history of the stored energy for the simulation period is shown in Fig. 13. In the PM, the air temperature is raised from the storage value (300 K) up to 550 K through the RBES (Fig. 14). The simulation code calculates the fuel flow rate (Mng) required
in the combustion chamber to reach the design maximum temperature (1223 K) at the turbine inlet. Hence, it is possible to calculate the thermodynamic efficiency (hT) of the cycle, defined as:
hT ¼
Wtb ETng
(13)
The results of the simulation of 4-days periods, representing the 80% of the annual conditions, showed that the system is able to produce 560 kWh a day. However, if the simulations are carried out for a period longer than 4 days, the results are strictly affected by the sizing of the battery pack. The simulations showed that the BP is undersized, which leads to the following consequences: - If the energy produced by the RES is too low for a period longer than 4 days, in the SM the system is not be able to store enough air to activate the turbine (winter time); - On the contrary, the BP is not able to store all the energy produced by the RES when it is too high for a long period (summer time). The simulation of the system over a whole year leads to a more accurate description of system behavior. However, it is important to notice that such simulation takes into account weather conditions
Fig. 16. Annual simulation: monthly energy generated by gas turbine, and difference with theoretical energy production.
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Table 4 Annual simulation: monthly generated energy, natural gas consumption and thermodynamic efficiency. Month
Energy produced (monthly value)
Theoretical energy production
Difference between actual and theoretical production
(kWh)
(kWh)
(kWh)
January February March April May June July August September October November December
11563.3 13259.3 13821.5 16651.4 13818.9 16368.0 17498.1 17215.0 15515.0 11837.3 15237.6 14099.6
17546.0 15848.0 17546.0 16980.0 17546.0 16980.0 17546.0 17546.0 16980.0 17546.0 16980.0 17546.0
5982.7 2588.7 3724.5 328.6 3727.1 612.0 47.9 331.0 1465.0 5708.7 1742.4 3446.4
belonging to 20% of the conditions previously defined as not meaningful. The BP is fully charged at the beginning of the simulation period (i.e. 1st January), but, differently from the simulation of a 4-days period, the results are affected by the fixed BP discharge depth (50% allowed). Fig. 15 shows that the BP provides an important fraction of the overall energy to the compressor. The fraction of this energy fed by the RES ranges from 60.2% in February to 82.6% in July (Table 3). Consequently, the yearly energy output from the gas turbine in PM is less than the theoretical energy output estimated assuming that the gas turbine works for 2 h a day at full load (i.e. 564 kWh/day, see Fig. 16). The results show that the most penalized months are January and October, respectively with an energy production deficit of 34% and 32.5%, that lead to an overall reduction of about 6000 kWh (Table 4). From April to September, indeed, the energy produced by the system is close to the theoretical full load value, with an average difference of 6% in 6 months (Table 4). The highest value of natural gas consumption is in July (3722 Nm3), due to the longest working time of gas turbine (Table 4). Given the natural gas mass flow, using Eq. (13) it is possible to evaluate the thermodynamic efficiency of the system, which reaches an yearly average value of 47.6%. Thus, the system is able to provide a yearly production of 177,000 kWh, which is 14% less than the energy production estimated with the activation of the gas turbine 2 h a day. 8. Conclusions In this paper an offshore power plant using RES and three different energy storage systems (CAES, BP and RBES) was presented and investigated. The sizing of the system was based on weather data (solar radiation, wind and wave energy, ambient temperature) of typical north Tyrrhenian sea climate. Annual performance of the system was simulated by a TRNSYS model linked to Matlab and EES subroutines. The system was simulated over 4-days time intervals, chosen among those representing 80% of the year, in order to assess the behavior of the different parameters of the system. In addition, a simulation over a whole year was carried out in order estimate the overall system performance. This showed an yearly energy production potential of about 177,000 kWh. Acknowledgements Arch. Federico Farsetti is gratefully acknowledged for the help he gave us in doing renderings of Figs. 2 and 3.
Natural gas consumption
Thermodynamic efficiency (hT)
(%)
(Sm3)
(%)
34.1 16.3 21.2 1.9 21.2 3.6 0.3 1.9 8.6 32.5 10.3 19.6
2404.6 2783.8 2887.3 3542.6 2868.7 3474.3 3722.8 3656.5 3248.9 2405.7 3223.0 2917.7
47.9 47.5 47.7 46.9 48.0 47.0 46.9 46.9 47.6 49.1 47.1 48.2
References [1] Knapp W, Frigaard P, Kofoed JP. Wave Dragon. Wave power plant using low-head turbines. In: Proc. of Hidroenergia 2004, European wave energy conference, Cork Ireland; 27.05.2004. [2] Frigaard P, Tedd J, Kofoed JP, Friis-Madsen E. 3 years experience with energy production on the Nissum Bredning Wave Dragon Proto Type, CA-OE Workshop, Lisbon; Nov. 2006. [3] Frigaard P, Kofoed JP. Power production experience from Wave Dragon prototype testing in Nissum Bredning: 2003 to 2005. Hydraulics and Coastal Engineering No. 34. Department of CIVIL Engineering, Aalborg University; 2005. [4] Kofoed JP, Frigaard P. The Dragon of Nissum Bredning. Renewable Ocean Energy 2009;4(4). [5] Kofoed JP, Frigaard P, Friis-Madsen E, Sørensen HC. In: Sayigh AAM, editor. Prototype testing of the wave energy converter wave Dragon, World Renewable Energy Congress VIII (WREC 2004). Elsevier Ltd; 2004. [6] Wave Dragon Web site, http://www.wavedragon.net; 2005. [7] Vertical axis wind turbine, EN-ECO Skyline S-30, http://www.en-eco.com/; 2010. [8] SunPower E18/305, http://www.sunpowercorp.it/downloads/sp_305Ewh_it_ a4_ds_w.pdf; 2010. [9] Fiac Air compressor AIRBLOK SD 100, http://www.fiac.it; 2009. [10] Turbec gas turbine T100Power, http://www.turbec.com; 2006. [11] Sunerg lead acid battery OPzS Solar 420, http://www.sunergsolar.com; 2010. [12] Piscopia R, Inghilesi R, Panizzo A, Corsini S, Franco L. Analysis of 12-year wave measurements by the Italian Wave Network. In: Proc. 28th ICCE conference; 2002. p. 121e33. Cardiff. [13] Vicinanza D, Cappietti L, Contestabile P. Assessment of Wave Energy around Italy, Journal of Coastal Research SI 64. Proceedings of ICS2011, Poland, ISSN: 0749-0208, pp. 613e17. [14] Ercan Ataer O. Storage of thermal energy. In: Abdullah Gogus Yalcin, editor. Energy storage systems. Encyclopedia of Life Support Systems (EOLSS), developed under the Auspices of the UNESCO. Oxford, UK: Eolss Publishers, http://www.eolss.net; 2006. [15] MacPhee David, Dincer Ibrahim. Thermal modeling of a packed bed thermal energy storage system during charging. Applied Thermal Engineering March 2009;29(4):695e705. [16] Dixon SL. Fluid mechanics and thermodynamics of turbomachinery. 4th ed. Boston: Butterworth-Heinemann; 1998.
List of symbols A: surface, m2 cg: wave group velocity, m/s cp: constant pressure specific heat, J/(kg K) D: diameter, m EP: pressure energy, GJ ET: thermal energy, GJ E: wave specific energy, KJ/m2 F: frequency, 1/s g: gravitational constant, m/s2 G: specific surface flow rate, kg/(s m2) h: volumetric heat transfer coefficient, W/(m3 K) H: wave height, m J: wave energy flux, kW/m L: length, m M: mass, kg m: mass flow rate, kg/s N: number of steps
576 P: pressure, bar S: spectral amplitude, m2s t: time, s T: temperature, C x: distance, m DT: wave period, s V: volume, m3 W: generated energy, kWh bJ: JONSWAP spectrum parameter g: peak enhancement factor of JONSWAP spectrum 3 : void fraction (RBES) h: efficiency r: density, kg/m3 s: JONSWAP spectrum parameter Acronyms BP: battery pack CAES: compressed air energy storage CFL: CouranteFriedrichseLambert PM: production mode PV: photovoltaic RBES: rock bed energy storage RES: renewable energy system
D. Fiaschi et al. / Energy 48 (2012) 566e576 SM: storage mode SWHE: sea water heat exchanger VFI: variable-frequency inverter WECD: wave energy conversion device Subscripts 1/3: third of higher waves a: ambient CA: compressed air ce: compressor exit (fluid) e: external loop (TRNSYS) f: fluid fC: fluid, compressor fT: fluid, turbine m0: spectrum zero-moment ng: natural gas P: peak p: platform r: rock bed t: time T: thermodynamic tb: turbine x: space (x direction)
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A versatile system for offshore energy conversion including diversified storage D. Fiaschi*, G. Manfrida, R. Secchi, D. Tempesti Dipartimento di Energetica “Sergio Stecco”, Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 July 2012 Received in revised form 2 October 2012 Accepted 3 October 2012 Available online 7 November 2012
Offshore applications allow to exploit different renewable energy sources (wave, wind, solar) that are complementary each other, due to their statistical yearly distributions. In this paper, we discuss an offshore platform for energy production from renewable energy sources coupled with three energy storage systems. The proposed offshore platforms uses a Compressed Air Energy Storage (CAES) to timely shift the electricity production from the demand. The performance of the system related to a north Tyrrhenian Sea location was evaluated by a simulation model developed integrating three different software packages (Matlab, EES, TRNSYS). The system was designed to produce 564 kWh on the 2 h a day where peak electricity demand takes place. The results showed that the system is able to produce 177,000 kWh per year. This offshore power plant is conceived for local users (tourist resorts, villages), especially if placed in small or medium islands, wishing to qualify for extensive use of renewable energy. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Offshore CAES Solar energy Microturbine Energy storage Wave energy
1. Introduction Renewable energy sources (RES) are often characterized by: a) a low Energy density b) a highly stochastic nature. However, some of the most variable RES (wave, wind) have statistical distributions with winter peaks which are to some extent complementary to others, like solar radiation. The offshore applications are particularly appealing, as the situation allows to combine these three different energy sources. In the specific case, the Mediterranean climate is attractive, because extreme events e which often lead to destruction of exposed structures e are rare and their intensity is anyway lower of what is encountered in the open ocean applications. In order to be most effective, the power plant island should include one or more energy storage systems, which allow to shift electricity production from demand, as for these energy sources production often takes place when the electricity demand is low, or vice-versa. Thinking of an off-shore application, it was considered to store energy by two complementary systems: a) a Compressed Air Energy Storage (CAES) using a submerged reservoir, working in isobaric natural conditions provided by the hydrostatic under-sea pressure gradient. b) a hot rock bed for energy storage/recovery unit (RBES) from/to the compressed air flows. * Corresponding author. Fax: þ39 055 4224137. E-mail address: daniele.fiaschi@unifi.it (D. Fiaschi). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.006
The renewable energy collected from wind, wave or solar radiation is stored and its value is enhanced using natural gas. The combustion gases are expanded in a commercial micro gas turbine, with limited design modifications (in practice, the air compressor is cut out from the shaft). The application is thought as a possible pilot plant to be proposed to small local users, such as tourist resorts, wishing to qualify for extensive use of renewable energy. 2. System description and working principle The system has a variable configuration according to the operation mode. In the storage mode (SM), the layout is described in Fig. 1. A wave energy conversion device (WECD) is the heart of the system: here, the Wave Dragon [1e6] solution was considered as one of the most advanced and adaptable to multiple-renewable energy systems. The WECD platform (Figs. 2e5) can be designed to host a photovoltaic (PV) solar array system, and a set of small vertical-axis wind turbines can be integrated on the offshore platform (4 in the present case). The three RES produce each a DC power output, which is the input to a variable-frequency inverter (VFI); this last is connected to an AC electric motor driving an air compressor. A battery pack (BP) was also added upstream the VFI, so minimizing the waste of collected energy. The air compressor is a commercial screw unit which can operate at variable speed from 18 to 75 kW. Air is stored at a delivery pressure of 10 bar, corresponding to
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Fig. 3. Offshore platform, close-up view (rendering).
All the equipments considered in the system are available on the market (wind turbine [7], PV arrays [8], VFI, compressor [9], micro gas Turbine [10], battery [11]) or as a prototype needing limited adaptation (Wave Dragon [1e6]). For the present case, a commercial TURBEC micro gas turbine with a nominal power of 100 kW was considered. The compressor is disconnected so that the turbine power output is raised to 280 kW, which is the peak-load power value of the reference plant.
Fig. 1. System layout, storage mode.
a CAES reservoir depth of 100 m. Before being stored, compressed air is cooled in the RBES, which works as a sensible heat energy storage device. After the RBES, the compressed air stream is further cooled in a sea water heat exchanger (SWHE): it enters then the submerged CAES reservoir from the top, where it displaces the water which is initially filling the vessel. In the production mode (PM), the system layout is changed to that of Fig. 6. The compressed air flows to the turbine, emptying the CAES vessel and reducing the stored pressure energy. The SWHE is by-passed; and before being sent to the turbine, compressed air flows through the RBES, takes a fraction of stored heat and raises its temperature. In this way, a lower natural gas consumption in combustion chamber is achieved. Finally, a pressure regulator adjusts the pressure at the nominal value at the inlet of the combustion chamber of the gas turbine (4.5 bar). In principle, it is possible to use the cold pressurized air for the gas turbine cooling flows, thus some adjustments to the engine cooling flow rates can be proposed.
3. Estimate of wave energy The wave energy was estimated following traditional spectral decomposition methods applied in wave energy conversion studies. According to Piscopia et al. [12], the spectra of Italian sea is characterized by a significant wave height greater than 1.0 m that can be fitted quite satisfactorily using the single peak JONSWAP spectrum with a peak enhancement factor (g) of about 2.4:
h i 2 S f ¼ bJ $H1=3 $DTP4 $f 5 $exp 1:25ðDTP $f Þ4 $ " # ðDTP $f 1Þ2 exp 2s2
(1)
g
where
bJ ¼
0:0624 0:230 þ 0:0336g 0:185ð1:9 þ gÞ1 $½1:094 0:01915$ln g h
DTP yDT1=3 = 1 0:132ðg þ 0:2Þ0:559 s¼
i
sa : f fp sb : f fp
The specific energy of the waves can be expressed as:
E ¼
2 r$g$Hmo
16
¼ r$g$
ZN Sðf Þdf :
(2)
0
Of direct interest is the wave energy flux transported by the wave:
J ¼ E$cg :
Fig. 2. Offshore platform, top view (rendering).
(3)
where cg is the wave group velocity, which for deep water can be expressed as:
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Fig. 4. Offshore platform, top view.
cg ¼
g$DT g ¼ : 4p 4p$f
(4)
For a real sea wave, the wave energy flux can be expressed by the wave spectral distribution:
J ¼ r$g$
ZN
2 r$g2 $DTj $Hmo cg f S f df ¼ : 64p
(5)
0
The latter was applied to two historical data sets of wave height/ period measurements available in the North Tyrrhenian Sea, with the results summarized in Table 1, that were calculated using a Matlab code developed for the specific purpose [13]. After this calculation, it was decided to focus on the La Spezia location, because e even if the average wave energy flux is a low 3.1 kW/m e the location is attractive as there are several potential users nearby. 4. Scaling down the wave energy conversion device The performance data of the WECD were adapted from Ref. [1]. The original device was designed for operation under much more intensive seas (J ¼ 24 kW/m), while a working prototype is undergoing tests in conditions of quiet sea (J ¼ 0.4 kW/m). In order to scale down the performance, Froude number similarity rules were applied, leading to an estimated productivity (with J ¼ 3.1 kW/m) of 1 GWh/year. The main WECD data are summarized in Table 2, related to the size shown in Figs. 4 and 5; it corresponds to what can be built in shipyards available near to harbors.
5. Sizing the solar PV and wind energy conversion devices For the solar PV and wind energy conversion devices, it was decided to use directly the weather data and component library available in TRNSYS; this calculation environment was also selected for running the year-round simulation of the overall system. The PV system is based on high-quality mono-crystal silicon modules, each of which is rated for a peak power of 350 W. The whole PV system is sized for an overall power of 75 kWe, under the worst conditions for average radiation, which are obtained in referred to the average radiation data the month of January. Thus, the system is able to collect from PV at least about 1/3 of the nominal 600 kWh/day needed for air compression. In summer, the whole system runs solely on PV, while during winter the contribution of wave energy is significant. The PV system is built with 234 modules arranged in 9 * 26 stacks (series/parallel), with a rated voltage of 600 VDC. Each row of modules is tilted at an angle of 45 from the horizontal, and is 3.6 m distant from the preceding/ following row, in order to avoid significant shading. The PV platform is 12 m high, has a diameter of 35 m and an overall surface area of about 960 m2. The platform can rotate in order to adjust the orientation of PV modules toward the sun, independently of wave and wind direction. Wind energy is only complementary for the location here considered, as the average wind speed is a low 5 m/s. However, wind can be an important contribution in rare conditions of low radiation and flat sea. For the wind turbines, considering the need of avoiding shading on the PV arrays and the requirement of
Fig. 5. Offshore platform, front view.
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Fig. 6. System layout, production mode.
a limited tower height, it was decided to consider the installation of vertical-axis units, with a nominal power rating of 3 kW at a wind speed of 12 m/s [7]. Each of the 4 wind turbines has a diameter of 3 m and is mounted on a 16 m height pole. The distance among the turbines is sufficient to avoid interference, according to current wind farms swept area/distance design rules. 6. Sizing of the energy storage systems 6.1. RBES
related to phase transition (needing pressurized operation). With respect to phase change energy storage, an RBES can operate at variable temperature and e working with air, a perfect gas which enthalpy depends only on temperature e this allows to reach higher final temperatures after heat recovery [14]. An RBES is basically built around a vessel containing a packed bed of solids of given nominal size (Fig. 7). A model for the RBES can be built according to Ref. [15], based on two differential equations:
rf cpf 3
The rock bed energy storage (RBES) is a key component of the system. As the air is heated during compression when operating in the SM, it is important that a high fraction of the flow enthalpy is recovered as heat, which must be used for air pre-heating in the PM. A rock bed system is an attractive device for sensible heat storage. In fact, it is much less expensive e for a fixed heat capacity e of a liquid heat storage system (requiring a secondary loop and a large and well-insulated reservoir), and it does not present any trouble Table 1 Calculated wave energy from 3-h historical data in two locations of the north Tyrrhenian Sea. N
Wave meter location
Number of data
Number of years
Missing data
Average wave energy flux (kW/m/year)
1 10
Alghero La Spezia
47638 41935
17.9 16.5
4733 (9%) 6343
13.1 3.1
dTf dT þ Gcpf f ¼ h Tr Tf dt dx
(6)
dTr ¼ h Tf Tr dt
(7)
rr cpr 1 3
In the present case, a cylindrical geometry was considered, neglecting the effects of radial heat conduction (well-insulated vessel). In order to solve the set of differential equations, a finiteTable 2 Main dimensional data for the WECD. Ramp width, m Arm length, m Freeboard crest height, m Tank volume, m3 Number of turbines Turbine unit rated power, kW Turbine rotor diameter, m
52 56 1.8 750 14 25 0.67
570
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rr cpr 1 3
Fig. 7. Rock bed energy storage (schematic).
difference approach was adopted, dividing the length L in Nx sections, and using a suitable internal time interval for time evolution of the RBES:
Dx ¼
L ; Nx
Dt ¼
Dte
(8)
Nt
From the numerical point of view, the solution of Eqs. (6) and (7) is not subjected to a stability criterion of the CFL type. However, it is recommendable that the internal spatial discretization and time step are chosen in a suitable way, in order to allow a detailed description of the RBES system, without increasing too much the number of variables. Eqs. (6) and (7) are then discretized in a timeforward scheme as follows (i ¼ 1,. Nx; j ¼ 1,. Nt):
rf cpf 3
h i h i Tf i; j Tf i; j 1 it h i h D ¼ h Tr i; j Tf i; j
þ Gcpf
h i h i Tf i; j Tf i 1; j
Dx
(9)
ðTr ½i; j Tr ½i; j 1Þ ¼ h Tr i; j Tf i; j Dt
(10)
In the present case, the TRNSYS simulation is run with an external time step of 1 h ¼ 3600 s: accordingly, Nt ¼ 10 (Dt ¼ 360 s) was chosen; and the length of the RBES was set at 2.5 m, with Nx ¼ 10 and thus Dx ¼ 0.25 m. The RBES is a cylinder of 7.5 m3, where the 60% of the volume is filled with rocks of typical diameter of 0.012 m. The weight of the rocks is approximately 12,000 kg. The differential equations are solved in an internal time loop by a dedicated program written in EES, which is called by the TRNSYS main program, taking care of the external (major) time advancement. The initialization, storage and visualization of data of the RBES are performed through a MATLAB routine called by TRNSYS. A typical output of the temperature profile during an internal TRNSYS time step is shown in Figs. 8 (for SM) and 9 (for PM). Once the initial and boundary conditions are loaded for each TRNSYS time step, this procedure is able to calculate the temperature profile in space and time across the RBES, both in the SM and in the PM. 6.2. CAES Referring to the SM, after exiting the RBES the air stream is cooled down to a final temperature which is mainly depending on the rock bed temperature Tr(Nx, t). During the final period of the SM, Tr can reach values close to the compressor exit temperature Tce; anyway, as the volume of the CAES vessel is fixed, and its pressure is fixed by the hydrostatic gradient on the sea bed, in order to store as much mass of air as possible it is necessary to further cool down the air stream. This is done in a sea water heat exchanger (SWHE); it is important to notice that this heat is not recovered, but rather lost to
Fig. 8. Example of RBES temperature profile calculation (a, rock; b, fluid); 13th hour simulation of November 20; last storage mode simulation time step of the day.
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Fig. 9. Example of RBES temperature profile calculation (a, rock; b, fluid); 17th hour simulation of November 20; first production mode simulation time step of the day.
the environment (sea water). The SWHE was sized as a countercurrent heat exchanger, and its gross surface area (A ¼ 7 m2 in this case) was determined assuming sea water at 20 C and the design value of the exit temperature Tfo fixed at 30 C. The SWHE works with a constant sea water flow rate: accordingly, with a variable inlet temperature Tri(Nx, t), the actual final value of Tfo (together with the warm water temperature) was calculated using the NTU-Efficiency correlations provided by EES, thereby considering the complete off-design operation of the heat exchanger. Actually, the value of Tfo is maintained very close to the design value, having chosen a sufficiently large heat transfer surface. The volume sizing of the CAES vessel derived from the fundamental system assumptions:
1) Duration of the production mode (2 h/day); 2) Design flow rate of the turbine (mfT ¼ 0.79 kg/s). From these assumptions and from the calculation of density for a compressed air storage temperature of 30 C, the CAES vessel volume was determined as 500 m3. If the chosen air compressor operates at full load (75 kW, with a fluid flow rate mfC ¼ 0.197 kg/s), it needs 8 h to fill completely the CAES vessel. Thus, with the proposed RES conversion system (integrating three different energy sources), daily cycles of system operation can be achieved for the largest fraction of the year. The TRNSYS simulation allows the prediction of the time history of the different forms of energy storage of the system (thermal
Fig. 10. Amount of energy generated from RES over the representative four-days period.
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22500 20000
Energy (kWh)
17500 PV Panels
15000
Wind Turbines
12500
Idraulic Turbines
10000 7500 5000 2500 Ju ly Au gu st Se pt em be r O ct ob er No ve m be De r ce m be r
Ju ne
ay M
Ap ril
Ja nu ar y Fe br ua ry M ar ch
0
Month Fig. 11. Monthly sum of energy generated by each RES.
full load and speed): in this case, the compressor is stopped, and the available renewable energy is stored in the batteries; 2) when power produced by RES exceeds the nominal rated power of the compressor (75 kW); 3) when the gas turbine/RBES/CAES assembly is working in the PM, in order to accumulate briefly renewable energy which would otherwise be wasted.
energy stored in RBES and pressure energy in CAES vessel). In SM, an increase of both forms of stored energy can be observed, with a maximum of 0.5 GJ of compressed air energy and about 5 GJ of thermal energy in RBES. 6.3. Battery pack The battery pack is used both as an auxiliary storage device, and as a backup system:
7. Performance evaluation
6.3.1. BP as backup system The battery pack is designed to supply the complete absence of energy production from RES for a period of three consecutive days; thus, considering a maximum discharge level of the battery at 50% of its capacity, the total energy autonomy is 3600 kWh (¼12.96 GJ). The overall voltage of the battery pack was chosen at 240 V. The battery pack is also useful to reduce the time needed to fill the CAES vessel, when the energy produced by RES is not enough to power the compressor at the nominal rated power (75 kW).
As a volumetric (screw) compressor is used, the machine was assumed to be able of providing a constant pressure over a reasonable range of rotational speed, according to manufacturer’s data [9]. The main variable changing with actual working conditions (i.e. off-design) is flow rate, provided that the operating range for rotational speed is matched (20%e100%). The compression is simulated assuming a given value of the compressor efficiency, and applying traditional non-isentropic flow relations [16]. A constant discharge pressure is guaranteed by the hydrostatic pressure gradient on the sea bed. Solar radiation, wind velocity, ambient temperature for the location of Pisa (Italy) were taken from the weather data library available in TRNSYS. Data sets of wave height/period measurements available in the north Tyrrhenian Sea were used to determine wave energy through the equations described in Section 3. Since it is supposed to install the power plant in the north Tyrrhenian Sea at a distance of approximately
6.3.2. BP as auxiliary storage device There are significant cases in which the batteries are systematically used as a storage device (recharging):
Power (kW), State of charge (%)
1) when the power produced by RES is less than the minimum power needed for compressor activation (18 kW over 75 kW at 300 275 250 225 200 175 150 125 100 75 50 25 0 -25 -50 -75
Battery State of Charge Power from Gas turbine Total power to compressor Power to (>0) or from (<0) battery Power to compressor from RES
0
12
24
36
48
60
72
84
96
Simulation Hour Fig. 12. Evolution of power parameter and battery state of charge in typical NovembereDecember 4 days simulation.
D. Fiaschi et al. / Energy 48 (2012) 566e576
Fig. 13. Example of stored energy profile (thermal energy and pressure energy) for a simulation period of four days (November 20e24).
10 km from the shores near Pisa, we can assume that there will be a slight difference between the weather data, taken from Pisa, and the real location of the power plant. In fact, while solar radiation and ambient temperature can be considered quite similar for both locations, the wind velocity could be a little different. However, wind energy gives a very small contribution to the overall energy produced by the system due to the very small wind power capacity installed. Thus, we can conclude that using the weather data for Pisa leads only to slight underestimation of the wind energy produced. It was initially chosen to simulate the system over a 4 days time period. This allows to include several operating cycles (SM and PM), and to clearly represent the behavior of all the involved parameters. The periods simulated are selected among those representing 80% of the year, in terms of climate conditions and energy generated from RES. The discriminating parameter for the selection of these periods is the energy generated from RES which directly activates the compressor: in fact, the duration of the air compression phase is mostly affected by this parameter. By dividing a year in 91 periods of 4 days and by summing the energy generated by the RES in all periods, it is possible to calculate the cumulative curve of the energy produced by RES. Then, we neglected the 4-days periods where the energy produced by RES is lower than the value corresponding to 10% on the cumulative curve, or higher than the value corresponding to 90%. Thus, we were able to identify the 4-days periods which represent the 80% cases of yearly energy produced by RES. In Fig. 10, some representative periods are shown, with their amount of energy generated from RES directly provided to the compressor. In the same figure, a subdivision of the year in 5 parts is
573
shown: these periods correspond to different productions of RES that typically occur during the different seasons of the year. As shown in Fig. 11, the monthly amount of energy generated by each of the three sources varies depending on the season: in winter months, the production from wave energy is greater than solar energy (or much greater, like in November and December, where it reaches 18,000 kWh/month), whereas from May to October an opposite trend is observed (with peak photovoltaic production of over 22,000 kWh in July). Through the graphical output of TRNSYS, the time history of the following parameters can be verified: 1) Power generated by each RES. 2) Power directly provided to the compressor. 3) Power to or from battery. 4) Power produced by gas turbine (in PM). 5) Battery charge level. 6) Thermodynamic properties of air at all cycle points (temperature, density, volumetric) and mass flow rate. 7) Conditions in the storage vessel (volume of air, pressure energy). It is also possible to verify the fuel consumption of the gas turbine at every PM time step and the related thermodynamic performance. The days from 20 to 24 of November are considered representative of system performance in November and December; Fig. 12 shows the evolution of the first five previously mentioned parameters. As energy is mostly produced by the WECD, the power generated by RES has a largely variable trend (dotted-blue line). However, differently from the summer period, when energy is mainly produced by PV, the compressor is powered also during the night. Power generated by RES is never sufficient to compress all the air flow rate which can be daily stored, therefore energy is taken from the BP (black line). Starting from a full charge condition, at the end of the simulation period, the BP charge decreases to 79%, with 2370 kWh provided to the compressor by the BP. Also in this time period, the compressor system is thus able to store the air flow rate necessary to daily activate the turbine for 2 h. The related energy production is 568 kWh/day (red line). The time history of energy storage during a 4-days period can be verified by means of the simulation model (see Section 6.2). Pressure energy (GJ) of the stored compressed air at every simulation time step is defined as:
EP ¼ ðVCA $PCA Þ=10; 000
(11)
While the thermal energy stored in the RBES at every simulation time step is:
800.0 700.0 Air out of compressor Air out of RBES in SM Air out of SWHE Air out of RBES in PM
Temperature (°K)
600.0 500.0 400.0 300.0 200.0 100.0 0.0 0
12
24
36
48
60
72
84
96
Simulation hour Fig. 14. Evolution of compressed air temperature in a typical NovembereDecember 4 days simulation.
574
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Fig. 15. Annual simulation: monthly energy to compressor and fraction supplied from RES and batteries.
Table 3 Annual simulation: monthly amount of energy to compressor and fraction supplied from RES and batteries. Month
January February March April May June July August September October November December
ET ¼
Energy to compressor (monthly value)
Fraction from RES
Fraction from battery
(kWh)
(kWh)
(%)
(kWh)
(%)
12653.0 14067.0 14750.6 17678.7 14832.4 17514.5 18628.3 18092.6 16536.7 12483.3 16788.4 15287.0
7902.3 8467.0 9986.7 12695.4 12021.5 12802.0 15390.1 13669.5 11814.1 9325.7 12744.2 11606.6
62.5 60.2 67.7 71.8 81.0 73.1 82.6 75.6 71.4 74.7 75.9 75.9
4750.8 5600.0 4763.9 4983.4 2811.0 4712.5 3238.3 4423.1 4722.6 3157.6 4044.2 3680.4
37.5 39.8 32.3 28.2 19.0 26.9 17.4 24.4 28.6 25.3 24.1 24.1
Nx X Ar $x$rr $cpr i¼1
10
$ðTr ½i Ta Þ
(12)
The time history of the stored energy for the simulation period is shown in Fig. 13. In the PM, the air temperature is raised from the storage value (300 K) up to 550 K through the RBES (Fig. 14). The simulation code calculates the fuel flow rate (Mng) required
in the combustion chamber to reach the design maximum temperature (1223 K) at the turbine inlet. Hence, it is possible to calculate the thermodynamic efficiency (hT) of the cycle, defined as:
hT ¼
Wtb ETng
(13)
The results of the simulation of 4-days periods, representing the 80% of the annual conditions, showed that the system is able to produce 560 kWh a day. However, if the simulations are carried out for a period longer than 4 days, the results are strictly affected by the sizing of the battery pack. The simulations showed that the BP is undersized, which leads to the following consequences: - If the energy produced by the RES is too low for a period longer than 4 days, in the SM the system is not be able to store enough air to activate the turbine (winter time); - On the contrary, the BP is not able to store all the energy produced by the RES when it is too high for a long period (summer time). The simulation of the system over a whole year leads to a more accurate description of system behavior. However, it is important to notice that such simulation takes into account weather conditions
Fig. 16. Annual simulation: monthly energy generated by gas turbine, and difference with theoretical energy production.
D. Fiaschi et al. / Energy 48 (2012) 566e576
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Table 4 Annual simulation: monthly generated energy, natural gas consumption and thermodynamic efficiency. Month
Energy produced (monthly value)
Theoretical energy production
Difference between actual and theoretical production
(kWh)
(kWh)
(kWh)
January February March April May June July August September October November December
11563.3 13259.3 13821.5 16651.4 13818.9 16368.0 17498.1 17215.0 15515.0 11837.3 15237.6 14099.6
17546.0 15848.0 17546.0 16980.0 17546.0 16980.0 17546.0 17546.0 16980.0 17546.0 16980.0 17546.0
5982.7 2588.7 3724.5 328.6 3727.1 612.0 47.9 331.0 1465.0 5708.7 1742.4 3446.4
belonging to 20% of the conditions previously defined as not meaningful. The BP is fully charged at the beginning of the simulation period (i.e. 1st January), but, differently from the simulation of a 4-days period, the results are affected by the fixed BP discharge depth (50% allowed). Fig. 15 shows that the BP provides an important fraction of the overall energy to the compressor. The fraction of this energy fed by the RES ranges from 60.2% in February to 82.6% in July (Table 3). Consequently, the yearly energy output from the gas turbine in PM is less than the theoretical energy output estimated assuming that the gas turbine works for 2 h a day at full load (i.e. 564 kWh/day, see Fig. 16). The results show that the most penalized months are January and October, respectively with an energy production deficit of 34% and 32.5%, that lead to an overall reduction of about 6000 kWh (Table 4). From April to September, indeed, the energy produced by the system is close to the theoretical full load value, with an average difference of 6% in 6 months (Table 4). The highest value of natural gas consumption is in July (3722 Nm3), due to the longest working time of gas turbine (Table 4). Given the natural gas mass flow, using Eq. (13) it is possible to evaluate the thermodynamic efficiency of the system, which reaches an yearly average value of 47.6%. Thus, the system is able to provide a yearly production of 177,000 kWh, which is 14% less than the energy production estimated with the activation of the gas turbine 2 h a day. 8. Conclusions In this paper an offshore power plant using RES and three different energy storage systems (CAES, BP and RBES) was presented and investigated. The sizing of the system was based on weather data (solar radiation, wind and wave energy, ambient temperature) of typical north Tyrrhenian sea climate. Annual performance of the system was simulated by a TRNSYS model linked to Matlab and EES subroutines. The system was simulated over 4-days time intervals, chosen among those representing 80% of the year, in order to assess the behavior of the different parameters of the system. In addition, a simulation over a whole year was carried out in order estimate the overall system performance. This showed an yearly energy production potential of about 177,000 kWh. Acknowledgements Arch. Federico Farsetti is gratefully acknowledged for the help he gave us in doing renderings of Figs. 2 and 3.
Natural gas consumption
Thermodynamic efficiency (hT)
(%)
(Sm3)
(%)
34.1 16.3 21.2 1.9 21.2 3.6 0.3 1.9 8.6 32.5 10.3 19.6
2404.6 2783.8 2887.3 3542.6 2868.7 3474.3 3722.8 3656.5 3248.9 2405.7 3223.0 2917.7
47.9 47.5 47.7 46.9 48.0 47.0 46.9 46.9 47.6 49.1 47.1 48.2
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List of symbols A: surface, m2 cg: wave group velocity, m/s cp: constant pressure specific heat, J/(kg K) D: diameter, m EP: pressure energy, GJ ET: thermal energy, GJ E: wave specific energy, KJ/m2 F: frequency, 1/s g: gravitational constant, m/s2 G: specific surface flow rate, kg/(s m2) h: volumetric heat transfer coefficient, W/(m3 K) H: wave height, m J: wave energy flux, kW/m L: length, m M: mass, kg m: mass flow rate, kg/s N: number of steps
576 P: pressure, bar S: spectral amplitude, m2s t: time, s T: temperature, C x: distance, m DT: wave period, s V: volume, m3 W: generated energy, kWh bJ: JONSWAP spectrum parameter g: peak enhancement factor of JONSWAP spectrum 3 : void fraction (RBES) h: efficiency r: density, kg/m3 s: JONSWAP spectrum parameter Acronyms BP: battery pack CAES: compressed air energy storage CFL: CouranteFriedrichseLambert PM: production mode PV: photovoltaic RBES: rock bed energy storage RES: renewable energy system
D. Fiaschi et al. / Energy 48 (2012) 566e576 SM: storage mode SWHE: sea water heat exchanger VFI: variable-frequency inverter WECD: wave energy conversion device Subscripts 1/3: third of higher waves a: ambient CA: compressed air ce: compressor exit (fluid) e: external loop (TRNSYS) f: fluid fC: fluid, compressor fT: fluid, turbine m0: spectrum zero-moment ng: natural gas P: peak p: platform r: rock bed t: time T: thermodynamic tb: turbine x: space (x direction)