Microturbogas cogeneration systems for distributed generation: Effects of ambient temperature on global performance and components’ behavior

Applied Energy 124 (2014) 17–27

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Microturbogas cogeneration systems for distributed generation: Effects of ambient temperature on global performance and components’ behavior F. Caresana a,⇑, L. Pelagalli a, G. Comodi a, M. Renzi b a b

Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy Libera Università di Bolzano, Facoltà di Scienze e Tecnologie, Piazza Università, 539100 Bolzano, Italy

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Electrical power reduces with

temperature, heat recovery remains almost constant.  Thermal-to-electrical power ratio increases with ambient temperature.  Not only the density of sucked air decreases but also its volumetric flow.  Putting a limit to shaft speed causes TIT to decrease with ambient temperature.  Power reduction with ambient temperature more than doubles that of great GTs.

a r t i c l e

i n f o

Article history: Received 12 June 2013 Received in revised form 5 February 2014 Accepted 25 February 2014 Available online 20 March 2014 Keywords: Microgas turbine Cogeneration Distributed energy generation Ambient temperature influence Performance correction factors

a b s t r a c t Microturbines (MGTs) are a relatively new technology that is currently attracting a lot of interest in the distributed generation market. Particularly interesting is their use as backup source for integrating photovoltaic panels or/and wind turbines in hybrid systems. In this case the sensitivity to ambient conditions of the MGT adds to that of the renewables and the knowledge of the effects of ambient conditions on its performance becomes a key subject both for the sizing of the energy system and for its optimal dynamic control. Although the dependence of medium/large gas turbines performance on atmospheric conditions is well known and documented in literature, there are very limited reports available on MGTs and they regard only global parameters. The paper aims at filling this lack of information by analyzing the ambient temperature effect on the global performance of an MGT in cogeneration arrangement and by entering in detail into its machines’ behavior. A simulation code, tuned on experimental data, is used for this purpose. Starting from the nominal ISO conditions, electrical power output is shown to decrease with ambient temperature at a rate of about 1.22%/°C, due to a reduction of both air density and volumetric flow.

⇑ Corresponding author. Tel.: +39 071 220 4765; fax: +39 071 220 4770. E-mail address: [email protected] (F. Caresana). http://dx.doi.org/10.1016/j.apenergy.2014.02.075 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

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F. Caresana et al. / Applied Energy 124 (2014) 17–27

Meanwhile, thermal to electrical power ratio increases at a rate of about 1.30%/°C. As temperature increases compressor delivers less air at a lower pressure, and the turbine expansion ratio and mass flow reduce accordingly. With the in-use control system the turbine inlet temperature reduces at a rate of 0.07%/°C with respect to its ISO condition value. Ó 2014 Elsevier Ltd. All rights reserved.

Nomenclature c C h J K LHV LMTD m _ m p P Q Q_ S t T TIT TOT b

g _ M

q x X

specific heat capacity [J kg1 K1] torque [N m] specific enthalpy [J kg1] inertial momentum [kg m2] heat exchange coefficient [W m2 K1] low heating value [J kg1] Logarithmic Mean Temperature Difference [K] mass [kg] mass flow [kg s1] pressure [Pa] power [W] volume flow [m3 s1] heat transfer rate [W] heat exchange surface area [m2] time [s] temperature [K] turbine inlet temperature [K] turbine outlet temperature [K] compression/expansion ratio [–] efficiency [–] corrected mass flow [m s K0.5] density [kg m3] angular speed [s1] corrected speed [rpm K0.5]

Subscripts a air

1. Introduction With an electrical power output ranging from 25 kW to 500 kW, Microturbines (MGTs) are a relatively new technology that is currently attracting a lot of interest in the distributed generation (DG) market [1–4]. The DG concept, recently in expansion as a result of deregulation of electric utility, consists in using generators sized from kW to MW at load sites instead of using traditional centralized generation units sized from 100 MW to GW [5]. Since DG energy sources lie close to the final users, they reduce electrical transport losses with respect to the central station generators, and make thermal energy recovery profitable both in energy-related and in economic terms. In the future probably the DG generation will be based basically on renewable DG sources but the short-term solution in the path to the widespread of this concept seems to be the use of hybrid generation sets consisting of a mix of renewable and conventional sources, and an energy storage system. As backup source for integrating renewable energy sources in hybrid systems, apart from microturbines, reciprocating engines (ICE) and fuel cells (FC) have been proposed [6–11]. FCs are probably the most promising technology but they are still too costly and less reliable with respect to the others. MGTs are generally preferred to ICEs [8,12] thanks to their high power density, low environmental impact in terms of pollutants, low operation and maintenance (O&M) costs and multi fuel

amb aux c cc d e eq exh f fin fr g H2O in is out r t th w

ambient auxiliary compressor combustion chamber dispersed electrical equivalent exhausts fuel final friction electric generator water inlet, initial isentropic outlet recuperator turbine thermal wall

Abbreviations/acronyms CHP combined heat and power DG distributed generation MGT microgas turbine RHE recovery heat exchanger

capability, even if it they are less efficient in generating electricity [13]. Depending on parameters such as grid availability, cost of grid supplied electricity, and meteorological conditions in the application site, DG hybrid systems can be either in stand-alone or in grid-parallel configuration. In particular DG using microturbines is a typical solution for stand-alone, on site applications remote from power grids. Other applications are devoted to combined heat and power generation (CHP), peak shaving, standby power generation, reliability increase, power boost capacity, cost of energy decrease, and pollutant emission reduction [4]. As renewable energy systems have an unpredictable nature and dependence on weather and climatic conditions, in order to obtain electricity reliably and at an economical price from a hybrid system, its design must be optimal in terms of operation and component selection [14–17]. For a given location, the optimum sizing of each component requires a detailed analysis of various site-dependent variables such as solar radiation, wind speed, and ambient temperature and of their relation to the performance of the components of the system. When optimum sizing has been achieved attention has to be paid to the dynamic behavior of the system in order to assure power quality, without voltage unbalance and voltage fluctuations [12]. At this respect, one concern in using MGTs in hybrid systems is their sensitivity to ambient conditions that adds to that of the renewables. Thus the knowledge of the effects of ambient

F. Caresana et al. / Applied Energy 124 (2014) 17–27

conditions on the MGT performance is a key subject both for the sizing of the energy system and for its optimal dynamic control. Actually, when weather rapidly changes, assuring good power quality from a local grid consisting of photovoltaic panels or/and wind turbines aided by MGTs is a non-trivial problem. The dependence of medium/large GTs performance on atmospheric conditions is well known and documented in literature, whilst studies dealing with microturbines are scarce. One of the first researchers to carry out a comprehensive study on the impact of atmospheric conditions on GTs performance was EI-Hadik [18] who concluded that the ambient temperature has the greatest effect, a 1 °C temperature growth causing a reduction of around 0.6% in power and of around 0.18% in efficiency. He argued that the effect on power could be explained with the reduction of air density at nearly constant volumetric flow. Also Kakaras et al. [19] reported that the gas turbine output and efficiency are strong functions of the ambient air temperature. He said that, depending on the gas turbine type, power output is reduced by a percentage between 5 and 10 percent of the ISO-rated power output (15 °C) for every 10 °C increase in ambient air temperature. At the same time the specific heat consumption increases by a percentage between 1.5% and 4%. Chaker and Meher-Homji [20] reported that gas turbine output is a strong function of the ambient air temperature with power output dropping by 0.54–0.9% for every 1 °C rise. They also affirmed that aeroderivative gas turbines exhibit even a greater sensitivity to ambient conditions. Mohanty and Paloso [21] presented that by increasing the inlet air temperature from the ISOrated condition to a temperature of 30 °C, would result in a 10 percent decrease in the net power output. For gas turbine of smaller capacities, this decrease in power output can be even greater. The fact that power output drop with temperature is greater in small gas turbines is also reported by Amell and Cadavid [22], that said that in small gas turbines not only density but also volumetric flow decreases with temperature. As for MGTs, there are very limited reports available regarding the effect of the inlet air temperature on its basic performance [23–27] and they regard only global parameters without entering in details in the plant components behavior. In particular only Basrawi et al. [23] investigated the effect of the inlet air temperature on the performance of a MGT with cogeneration system arrangement. Employing a model based on experimental results, they found that when ambient temperature increased, electrical efficiency decreased but exhaust heat recovery increased. They also found that when ambient temperature increased exhaust heat recovery to mass flow rate and exhaust heat to power ratio increased. The authors of the present paper have already approached the problem in [28] using artificial neural networks (ANNs) to describe the electrical performance of a MGT. The results of that investigation, based on experimental data acquired from a manufacturer’s test bed, were used for sensitivity analysis of the machine behavior in different ambient conditions evidencing that the electrical efficiency is not significantly affected by air pressure and relative humidity, but it is strongly air temperature-dependent; the higher the temperature the lower the efficiency. The present work extends the analysis to MGTs in cogeneration arrangement and, thanks to a simulation code tuned on experimental data, enters in detail into the machines’ behavior, showing how their working characteristics change with ambient temperature. As a result, corrections of the cogeneration unit performances with ambient temperature are provided. The organization of the paper is as follows. Section 2 presents the assumptions used to model the MGT-CHP components. Section 3 presents the comparison between the numerical results

19

obtained and the experimental data available. Section 4 reports the performance charts of the MGT-CHP at different ambient temperatures. Finally, conclusions are given in Section 5. 2. Materials and method 2.1. The MGT-CHP unit The machine chosen for the analysis was a Turbec T100 PH based on a regenerative Brayton cycle; it is a more recent version of the one investigated by Colombo et al. [29] and features an embedded fuel compressor. The unit is fired with natural gas in a combustor of the lean-premixed-low-emission type. The Turbec Company [30] declares that, in ISO 2314 conditions [31], and at the nominal rotational speed of 70,000 rpm, the machine produces 100 kW of electrical power with an efficiency of 30%; the combustion products exit the turbine at a temperature of 645 °C, cross the regenerator, and enter the recovery heat exchanger (RHE) at 270 °C. The RHE is a counter-flow type designed for a water mass flow rate of 2 l/s and temperatures of 50 °C and 70 °C at the inlet and outlet, respectively. At these nominal conditions stated thermal power production is 155 kW, with a thermal efficiency of 47%. According to its datasheet the machine can safely work at ambient inlet temperature from 25 °C to 40 °C with a maximum power of 120 kW. An electrically driven bypass valve fitted along the RHE inlet manifold can divert some of the exhaust gases to the chimney to regulate the thermal power recovered. In practice, demand is represented by user-set values of electrical power and fluid temperature at the RHE outlet, and by selection of the operating mode (electrical or thermal priority). In the electrical priority mode the MGT produces the electrical power required by the user, and the fluid temperature is kept at the set-point through regulation of bypass valve opening. In the thermal priority mode the bypass valve is closed and all the exhausts pass through the RHE to produce thermal power. The temperature of the hot fluid is kept at its set-point by variations in the amount of electricity produced; the user-selected electrical power value is a threshold. Electrical priority mode operation with the bypass valve closed is equivalent to operation in the thermal priority mode. 2.2. Modeling of the MGT-CHP unit In the following the theory and methods at the basis of the analysis are resumed. First of all the general assumptions are reported, then a dedicated paragraph is devoted to each of the main components of the CHP unit. 2.2.1. General assumptions Although the analysis object of the present work required only stationary data, some hints on dynamic modeling are reported throughout the text. In fact the code was developed also for future applications in dynamic modeling of hybrid systems. Each component was modeled through an ad hoc block written in Matlab–Simulink code. A control was synthesized to govern the transition from a working point to another in accord with the Turbec T100-PH logic, i.e. changing the amount of fuel fed to the MGT combustion chamber in order to keep constant the temperature at the turbine outlet. In particular in electrical priority mode the control consists of three regulators, the first keeps the turbine exhaust temperature as close as possible to 917 K by changing the electrical power, the second changes the fuel mass flow until the power calculated

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F. Caresana et al. / Applied Energy 124 (2014) 17–27

from the first regulator reaches the reference value and eventually the third regulator changes the exhaust bypass valve position until the temperature of the hot fluid reaches its set-point. In thermal priority mode only two regulators are needed, the first, as in electrical priority mode, keeps the turbine exhaust temperature as close as possible to 917 K by changing the electrical power, the second regulator changes the fuel mass flow until the temperature of the hot fluid reaches its set-point, the electrical power comes as consequence. In steady state conditions, regardless the machine working point and the control priority mode:

T exh

t out

¼ TOT ¼ 917K

ð1Þ

During transients the mass accumulation effects are neglected; in particular at any instant the mass flow of exhausts exiting the combustion chamber and entering the turbine is the sum of the air mass flow delivered by the compressor and the fuel mass flow fed in the combustion chamber:

_ exh ¼ m _ aþm _f m

ð2Þ

As the machine is of the single shaft type, the compressor, the turbine and the electric generator have the same rotational speed at any instant of time:

x ¼ xc ¼ xt ¼ xg

Fig. 1. Compressor map. The area enclosed by the dotted line is enlarged in Fig. 8.

ð3Þ

The MGT machines are modeled as quasi-stationary components and static maps, based on manufacturer’s data, are used to describe their behavior. The heat exchangers are modeled to account for time dynamics; however, at this stage of the research, greater emphasis is placed on the accuracy of steady state values than on transient behavior and thus the heat flow between the fluids is modeled by using the classic Logarithmic Mean Temperature Difference (LMTD) law. Experimental data, collected on an ad hoc test-bed [32], have been used to tune the coefficients of the correlations used in the model, in particular for: - pressure drops in the plant components; - heat exchangers characteristics; - friction torque and group rotational inertia. Air and exhausts characteristics are evaluated by means of analytical correlations [33] that are used: - to obtain enthalpy once known temperature, this correlation is indicated through the text as h = fh(T) - and to evaluate the final point of an isentropic expansion or compression process once known the initial point and the pressure ratio, the use of this correlation is indicated through the text as Tfin = fis(Tin, b). The details of the correlations are reported in Appendix A. 2.2.2. Compressor The parameters of interest for the compressor are: inlet pressure pc_in, inlet temperature Tc_in, angular speed xc, air temperature at the outlet port Tc_out, air pressure at the outlet port pc_out, air _ a , isentropic efficiency gis_c, and power Pc. mass flow m The key assumption for modeling this component is that the fluid-dynamic processes taking place in the machine are much faster than the rate of change in its thermodynamic boundary conditions. Thus the machine is modeled as a stationary component and a static map, based on manufacturer’s data, is used. Fig. 1 resumes the compressor performance reporting the machine isentropic efficiency gis_c, and the corrected speed

c ffi _ c ¼ m_ c Xc ¼ pxffiffiffiffiffiffiffi as a function of corrected mass flow M pc in

Tc

pffiffiffiffiffiffiffiffiffi T c in

in

and compression ratio bc ¼ ppc

. _ c , bc, the third and the machine Given two values out of Xc, M isentropic efficiency can be derived from the map. The enthalpy at the compressor outlet and the power it requires are: out

c in

hc

out

¼ hc

in

_ a ðhc Pc ¼ m

þ

out

hc

out is

 hc

gis c

 hc in Þ

in

ð4Þ ð5Þ

with

hc

in

¼ fh ðT c in Þ

ð6Þ

and the isentropic temperature and enthalpy at the compressor outlet evaluated as:

Tc

out is

¼ fis ðT c in ; bc Þ

ð7Þ

hc

out is

¼ fh ðT c in ; bc Þ

ð8Þ

The real temperature at the compressor outlet is then evaluated solving the equation:

hc

out

 fh ðT c

out Þ

¼0

ð9Þ

2.2.3. Combustion chamber The parameters of interest for the combustion chamber are: air _ a , air temperature at the chamber inlet Tcc_in, air presmass flow m _ f , exhausts mass sure at the chamber inlet pcc_in, fuel mass flow m _ exh , exhausts temperature at the chamber outlet Tcc_out, and flow m exhausts pressure at the chamber outlet pcc_out. Accumulations of mass and energy in the chamber are neglected, and the pressure losses are taken as proportional to air flow rate. _ f is calculated by a proportional–integral The fuel mass flow m control block in order to reach the set point for electrical power (electrical priority) or water temperature at the RHE outlet (thermal priority). Combustion chamber inlet pressure and temperature are taken equal to the respective values at the recuperator outlet:

T cc

in

¼ Ta

r out

ð10Þ

pcc

in

¼ pa

r out

ð11Þ

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F. Caresana et al. / Applied Energy 124 (2014) 17–27

The mass conservation Eq. (2) and the energy balance equation are used to evaluate the enthalpy of the exhausts at the chamber outlet:

hcc

out

¼

_ a hcc m

with hcc

in

in

_ f ðhf þ LHVÞ  Q_ d þm _ exh m

¼ fh ðT cc in Þ

cc

ð12Þ

out

 fh ðT cc

out Þ

¼0

ð14Þ

2.2.4. Turbine The parameters of interest for the turbine are: inlet pressure pt_in, inlet temperature TIT, angular speed xt, outlet temperature _ exh , isentropic effiTOT, outlet pressure pt_out, exhausts mass flow m ciency gis_t, and power output Pt. Turbine inlet pressure and temperature are taken equal to the respective values at the combustion chamber outlet:

pt

in

¼ pcc

TIT ¼ T cc

ð15Þ

out

out

¼ ht

with ht

in

in

þ gis t ðht

¼ fh ðTITÞ

in

 ht

out is Þ

out is

¼ fis ðTIT; bt Þ

out is Þ

ð20Þ

The real temperature at the turbine outlet TOT, is found by solving the equation:

ht

out

 fh ðTOTÞ ¼ 0

_ exh ðht Pt ¼ m

ð21Þ

in

 ht

out Þ

ð22Þ

2.2.5. Recuperator The inputs for this modeling block are: exhausts inlet temperature Texh_r_in, exhausts inlet pressure pexh_r_in, exhausts mass flow _ exh , air inlet temperature Ta_r_in, air inlet pressure pa_r_in, and air m _ a . The outputs are: exhausts outlet temperature mass flow m Texh_r_out, exhausts outlet pressure pexh_r_out, air outlet temperature Ta_r_out, and air outlet pressure pa_r_out. The main relations used in the model are summarized below. Heat losses through the ducts between turbine and recuperator and between compressor and recuperator are neglected, thus the temperature of exhausts and air at the recuperator inlet are:

T exh Ta

r in

r in

¼ TOT

¼ Tc

ð23Þ ð24Þ

out

_ exh ðhexh Q_ exh r ¼ m

ð18Þ

ð19Þ

r in

 hexh

r out Þ

ð25Þ

A fraction er of it is acquired by air:

_ a ðha Q_ a ¼ er Q_ exh r ¼ m

r out

 ha

r in Þ

ð26Þ

and the remains are dispersed in ambient:

Q_ d r ¼ ð1  er Þ Q_ exh

ð27Þ

r

Q_ a can also be expressed as the product of the heat exchange surface area Sr, the global heat exchange coefficient Kr, and the logarithmic temperature difference LMTDr:

Q_ a ¼ ðKSÞr LMTDr

ð17Þ

and the isentropic temperature and enthalpy at the turbine outlet evaluated as:

Tt

¼ fh ðT t

The heat flux transferred by the exhausts is:

ð16Þ

out

Like the compressor, the turbine is modeled as a stationary component and a static map is used to describe its behavior. Fig. 2 resumes the turbine performances reporting the isentropx ffiffiffiffit ffi pic efficiency gis_t and the corrected pffiffiffiffiffiffiffi speed Xr ¼ TIT as a function of _ t ¼ m_ exh TIT and expansion ratio b ¼ pt in . corrected mass flow M t pt in pt out The pressure at the turbine outlet is calculated adding to ambient pressure the pressure drop of the exhausts through the recuperator and the RHE. _ t , bt, the third and the machine Given any two values out of Xt, M isentropic efficiency can be derived from the map. The exhausts’ outlet enthalpy is:

ht

out is

The power the compressor requires is:

ð13Þ

The heat power losses Q_ d cc are modeled as proportional to the difference between the chamber mean temperature and ambient temperature. The temperature at the chamber outlet Tcc_out is calculated by solving the equation:

hcc

ht

ð28Þ

For a counter-flow arrangement:

LMTDr ¼

DT 2  DT 1   ln DDTT 21

with

DT 1 ¼ T exh DT 2 ¼ T exh

r;out r;in

 Ta

 Ta

r in

r out

ð29Þ

The air and exhausts temperatures at the recuperator outlet are related to the respective enthalpies by means of the correlations of [33] reported in Appendix A:

ha

r out

hexh

¼ fh ðT a

r out

r out Þ

¼ fh ðT exh

r out Þ

ð30Þ ð31Þ

The product (KS)r is modeled as a function of the exhausts mass flow. Air pressure at the recuperator inlet pa_r_in is taken equal to that at the compressor outlet, that at the outlet pa_r_out is calculated taking into account of a pressure drop function of air mass flow.

Fig. 2. Turbine map. The area enclosed by the dotted line is enlarged in Fig. 9.

2.2.6. Recovery heat exchanger (RHE) The inputs to this modeling block are: exhausts inlet temperature Texh_RHE_in, exhausts inlet pressure pexh_RHE_in, exhausts mass _ exh , water inlet temperature T H2 O in , and water mass flow flow m _ H2 O . m The outputs of the block are: exhausts outlet temperature Texh_RHE_out, exhausts outlet pressure pexh_RHE_out, water outlet temperature T H2 O out , and thermal power transferred from the exhausts to water Q_ H O ¼ P th . 2

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F. Caresana et al. / Applied Energy 124 (2014) 17–27

Unlike the recuperator, the water–gas heat-exchanger is modeled as a dynamic component. In fact the heat capacity of water in the exchanger cannot be neglected being its mass significantly higher than the mass of the air or of the exhausts contained in the recuperator and its specific heat almost four times as high. In a dynamic approach the heat exchanger pipe and fins heat capacity can be considered by adding in the energy balance equation an equivalent mass of water calculated as:

mH2 O

eq

¼ mw

cw c H2 O

ð32Þ

with mw and cw respectively the mass and the specific heat capacity of the material of which the exchanger walls are done. The heat power transferred by the exhausts is:

Q_ exh

RHE

_ exh ðhexh ¼m

RHE in

 hexh

RHE out Þ

ð33Þ

A fraction 1  eRHE of it is dispersed in ambient:

Q_ d

RHE

¼ ð1  eRHE ÞQ_ exh

ð34Þ

RHE

and the main part goes to the water and the exchanger walls, as shown by the following dynamic relationship:

eRHE Q_ exh RHE ¼ ðmH2 O þ mH2 O eq ÞcH2 O

dT H2 O dt

out

þ Q_ H2 O

ð35Þ

The heat power transferred to water is:

_ H2 O cH2 O ðT H2 O Q_ H2 O ¼ m

out

 T H2 O in Þ

ð36Þ

with cH2 O averaged in the temperature range and:

Q_ H2 O ¼ ðKSÞH2 O LMTDH2 O

ð37Þ

As in the case of the regenerator a counter-flow model is used, with an heat exchange coefficient function of the exhausts’ mass flow.

LMTDH2 O ¼

DT 2  DT 1   ln DDTT 21

with

DT 1 ¼ T exh DT 2 ¼ T exh

RHE out RHE

 T H2 O

in  T H2 O

in

out

ð38Þ

Again the relationship between enthalpy and temperature of the exhausts is given by the correlation fh(T) in Appendix A. The steady state solution is obtained when in Eq. (35) dT H O out 2 ¼ 0. dt 2.2.7. Shaft The inputs to the block are: turbine power Pt, compressor power Pc, electrical power output Pe, and auxiliary power Paux. The output of the block is the shaft rotational speed x, that is found by solving the torques’ balance equation:

dx J ¼ C t  C c  C e  C fr  C aux dt

Ct ¼ Cc ¼ Ce ¼

Pc

compressor torque

x Pe

torque absorbed by the alternator

x

C aux ¼ C fr

turbine torque

x

Paux

x

3. Experimental validation To verify the model, the outputs of the code have been checked against experimental data collected on a test-bed (developed by Turbec in collaboration with Università Politecnica delle Marche) used by Turbec technicians mainly for end-line-tests [32]. The test-bed, whose scheme is reported in Fig. 3, is provided with an hydraulic system for thermal power dissipation designed to simulate a broad range of thermal demands. It consists of two separate circuits thermally interconnected by a plate heat exchanger. The primary circuit contains the water circulating through the turbine RHE, while the secondary circuit contains a water–glycol mixture that discharges the heat to the outside air by circulating through an air cooler. The water circuit is provided with a volumetric flow meter and with two Pt100 temperature sensors at the RHE inlet and outlet. Valves V1 and V2 in the water circuit allow flow rate regulation through the RHE. V1 is only manually operated, whereas V2 -which keeps the water temperature at the RHE outlet at its set-point- can also be controlled remotely by a PID. The pneumatic mixing valve V3, installed in the secondary circuit to keep the water temperature at the RHE inlet at its set-point, is automatically driven by a PID controller. All measurement instruments and control signals are managed by means of a PLC connected to a PC (for more details see [32]). Tests were carried out throughout all the year, and from the available data it was possible to extract cases differing only for ambient temperature. In particular medium data of the relevant machine performances were derived for 8 °C and 30 °C with pamb ¼ 101 kPa, same thermal load conditions, Q H2 O ¼ 2l s1 , T H2 O in ¼ 50  C, and same regulation mode (thermal priority i.e. exhaust bypass valve closed). For each working point the thermal power recovered and the electrical, thermal and total efficiency of the unit were evaluated as:

Pth ¼ qH2 O Q H2 O cH2 O ðT H2 O P

ge ¼ _ e mf LHV P

gth ¼ _ th mf LHV

out

 T H2 O in Þ

ð40Þ

ð41Þ

ð42Þ

ð39Þ

with the torques acting on the shaft calculated as:

Pt

The steady-state solution is found when in Eq. (39) Ct  Cc  Ce  Cfr  Caux = 0, i.e. ddtx ¼ 0 .

torque absorbed by the auxiliaries

friction torque

Friction torque is modeled as a function of shaft rotational speed. The torque Caux takes into account for the power needed to drive the auxiliaries, the main being the natural gas compressor.

P þP

th gtot ¼ _ e ¼ ge þ gth mf LHV

ð43Þ

The comparison with the simulated results is shown in Fig. 4. The electrical efficiency at 8 °C is about 30% at 100 kW and declines to an average of 26% at 40 kW. Taking into account inlet and exhaust duct pressure losses, these values are consistent with those stated in the manufacturer’s data sheet [30]. At 30 °C of ambient temperature the MGT electrical performance decrease. A maximum electrical power of about 80 kW is reached with and electrical efficiency of around 27%, and at 40 kW electrical efficiency declines to about 24%. In the common range of electrical power (40–80 kW), recoverable thermal power and total efficiency are greater at 30 °C, electrical efficiency is instead greater at 8 °C. The numerical curves are in good agreement with the experimental points and, in particular, the influence of ambient temperature is well captured by the model.

F. Caresana et al. / Applied Energy 124 (2014) 17–27

23

Fig. 3. MGT-CHP test bed.

Fig. 5. MGT-CHP plant performance chart. Fig. 4. Simulated(lines)/experimental(points) data comparison.

4. Results and discussion In this paragraph the results obtained from the developed code are used to focus on the effects of ambient temperature both on the MGT and its components performances. The thermal and electrical performances of the plant are resumed in Fig. 5 for ambient temperature in the range 25 °C to 40 °C, power in the range 40–120 kW and rotational speed up to 70,000 rpm. The chart is provided with iso-ambient temperature, iso-rotational speed, iso-electrical efficiency and iso-total efficiency lines. All iso-lines represent, as a function of electrical power, the thermal power recoverable from the exhausts with bypass valve

completely closed and water flow and inlet temperature at their nominal values, Q H2 O ¼ 2l s1 ; T H2 O in ¼ 50  C. In the considered working range electrical efficiency varies between 24% and 34%, and total efficiency between 62% and 82%. The iso-ambient temperature curves (black dashed lines) are almost straight with positive slope, the iso-speed curves (black solid lines) are almost horizontal. In point A electrical power, thermal power, rotational speed and turbine inlet temperature all reach their peak values, this occurs at an ambient temperature around 1.2 °C. Moving the working point from bottom to top along any of the iso-ambient temperature curves under that of point A (blue dashed line), electrical power rises with rotational speed reaching 120 kW;

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F. Caresana et al. / Applied Energy 124 (2014) 17–27

at this power, the lower the ambient temperature, the lower the rotational speed and the recoverable thermal power. Moving the working point from bottom to top along any of the iso-ambient temperature curves over that of point A, the maximum value of the deliverable electrical power can be found at the intersection with the maximum rotational speed line; on this line, starting from point A, as temperature increases electrical power output reduces, whilst the maximum recoverable thermal power remains almost constant. As a consequence, the thermalto-electrical power ratio increases. At a given speed, as ambient temperature increases (in Fig. 5 this means moving almost horizontally from right to left), electrical power decreases whilst thermal power remains almost unchanged, total efficiency increases whilst electrical efficiency decreases. At a given electrical power, as ambient temperature rises (in Fig. 5 this means moving upwards along a vertical line) speed and recoverable thermal power increase, again total efficiency increases whilst electrical efficiency decreases. To show the ambient temperature effects on the CHP unit working range, the cases at 0 °C and 40 °C are taken as examples and evidenced in Fig. 5 by gray shading their respective working areas. At high ambient temperature the electrical power range narrows whist that of thermal power remains almost unchanged, i.e. maximum electrical power reduces and thermal to electrical power ratio increases. For given ambient temperature, a point inside the gray zone indicates a working point with the bypass valve partially open; for a given electrical power, the more the valve opening the lower the thermal power recovered and thus thermal and total efficiency; electrical efficiency remains instead almost unchanged. As an example, consider in the Pe, Pth chart of Fig. 5 points B(60, 40) and C(80, 40), and the MGT working at 0 °C or 40 °C of ambient temperature. B is a possible working point for both ambient temperatures, whilst C is possible only for the 0 °C case (the maximum of electrical power at 40 °C is 70 kW, in fact to reach 80 kW the temperature should be 30 °C or lower). Now, considering point B(60, 40) as a working point at 0 °C, the required 60 kW of electrical power are obtained at 58,750 rpm with an electrical efficiency of 30% (as visible from point D data), but as B is not along the 0 °C iso-line the exhaust bypass valve is open to reduce thermal power from the maximum available of 85 kW (point D) to the required 40 kW, thus the CHP thermal efficiency reduces by a factor of 40/85. As electrical efficiency remains almost the same, total efficiency decreases from 72% to 50%. Considering point B(60, 40) as a working point at 40 °C, the required 60 kW of electrical power are instead obtained at

66,750 rpm with an electrical efficiency of 25.5%, also in this case the exhaust bypass valve is open to reduce thermal power from the maximum available of 135 kW (point E) to the required 40 kW, thermal efficiency now reduces by a factor of 40/135. Total efficiency decreases from 83% to 43%. In Fig. 6 the trends of electrical and thermal efficiency (in case of exhaust bypass valve closed) are reported as a function of electrical power and for different ambient temperatures. Thermal efficiency increases with ambient temperature, indicating that a greater fraction of fuel energy is discharged through the exhausts instead of being converted into mechanical work. At low temperature the increase of electrical efficiency is more than counterbalanced by the decrease of thermal efficiency and total efficiency decreases. Fig. 7 reports the percent variations with respect to 15 °C of the machine maximum electrical and thermal performances together with the trends of the principal working parameters involved. At 1.2 °C the electrical power reaches its absolute maximum and under this temperature the variations are no longer related to ambient temperature effects only (gray shaded area in figure). The mean variations per unit degree in the range 1.2–40 °C are reported in Table 1. The curves of thermal power, TIT and air volume flow are very close, as well as the curves of air mass flow and compression ratio. Electrical power decreases with temperature at a rate of about 1.22%/°C (i.e. about 1.22 kW/°C for the Turbec T100-PH standard). In fact both air mass flow and power per unit mass of air decrease; the former as a consequence of the reduction of air density and volume flow, the latter as a consequence of the reduction of compression ratio and TIT. At this respect, notice that for larger GTs there is general agreement in considering the volume flow of air independent from ambient temperature, and to attribute the reduction of air mass flow only to the variation of density [18–20], in MGTs the effect of density is actually augmented by the reduction of volume flow, as it seems to happen in smaller GTs [21,22]. Thermal power decreases much less than electrical power (about 0.10%/°C). Actually the reduction of the exhausts mass flow is partially compensated by the increment of the exhausts temperature at the RHE inlet. The thermal to electrical power ratio increases at a rate of about 1.30%/°C. Electrical efficiency reduces with temperature at a rate of about 0.51%/°C, thermal efficiency increases at a rate of about 0.70%/°C. It’s worth noting that putting an upper limit to rotational speed causes TIT to decrease with ambient temperature at a rate of about 0.07%/°C (preventing the machine from thermal stresses at high ambient temperatures).

Fig. 6. Electrical and thermal efficiency.

Fig. 7. Percent variations with respect to nominal data.

F. Caresana et al. / Applied Energy 124 (2014) 17–27 Table 1 Influence of ambient temperature. Mean percent variation with respect to 15 °C. Percent variation with respect to 15 °C (% °C1) Electrical power Thermal power Electrical efficiency Thermal efficiency Air/exhausts mass flow Ambient air volume flow Specific power TIT Thermal to electrical power ratio Exhausts temperature at the RHE inlet

1.22 0.10 0.51 +0.70 0.45 0.12 0.80 0.07 +1.30 +0.13

Fig. 8. Compressor working points at different ambient temperature.

Fig. 9. Turbine working points at different ambient temperature.

Figs. 8 and 9 show the effect of ambient temperature on compressor and turbine respectively. The actual working points of the machines are represented in a portion of their respective maps where iso-lines of ambient temperature, electrical power, rotational speed and TIT have been drawn in addition to the iso-corrected speed lines. In the 25–40 °C ambient temperature interval, the machines’ working areas (gray shaded in the figures) are upper limited by maximum power and maximum rotational speed lines (continuous blue and continuous black lines through point A (1.2 °C and 70,000 rpm), and lower limited by minimum power lines (40 kW blue lines). On the compressor map the iso-power (blue solid lines), isoambient temperature (black dashed lines) and iso-rotational speed

25

(black solid lines) curves are almost straight lines with positive slope. Iso-power lines are the less steep and iso-speed lines the steepest. Moving the working point along a iso-ambient temperature curve (dashed black lines) from bottom to top, rotational speed and MGT power rise; with ambient temperature in the range 1.2–40 °C the maximum deliverable power can be found at the intersection with the maximum rotational speed line (70,000 rpm). At 1.2 °C and 70,000 rpm (point A in figure) the power reaches its maximum allowable value of 120 kW, and thus under this temperature the maximum rotational speed is decreased to limit power (the working point moves along the 120 kW iso-power line). Along a iso-speed curve, as temperature increases (in Fig. 8 this means moving downwards along a black solid line) the working point moves towards lower compression ratios and lower corrected flows, i.e. the compressor delivers less air at a lower pressure, as a consequence MGT power decreases. To obtain the same power as temperature rises (in Fig. 8 this means moving upwards along a blue line) the shaft rotational speed has to be increased, and thus the compressor has to work at a higher compression ratio and a higher corrected flow, delivering more mass flow at a higher pressure. As ambient temperature increases the same TIT guarantees less power and it is reached at a higher rotational speed (in Fig. 8 the working point moves along a red line from left to right). The turbine working points change accordingly to those of the compressor, as shown in Fig. 9 where iso-ambient temperature, iso-power, iso-rotational speed and iso-TIT curves are represented with the same line types used in the compressor map. Moving the working point along a iso-ambient temperature curve (dashed black lines) from bottom to top, in the range 1.240 °C, MGT power rises reaching a maximum at the intersection with the 70,000 rpm line. At 1.2 °C and 70,000 rpm (point A) power reaches 120 kW; under this temperature rotational speed is decreased to avoid exceeding the power limit. At a given rotational speed, as ambient temperature increases the working point moves towards lower expansion ratio and lower corrected mass flow (in Fig. 9 this means moving downwards along a black solid line). When the same power is requested at a higher temperature (in Fig. 9 this means moving the working point upwards along a blue line), the shaft has to rotate at a higher speed, and the expansion pffiffiffiffiffiffiffi _ t ¼ m_ exh TIT , deratio increases. In this case the corrected flow, M pt in creases, as the increase of turbine inlet pressure outweighs the increases of exhausts mass flow and TIT. On the turbine map, iso-TIT lines (solid red lines) are almost horizontal, in fact as TOT is kept constant from the machine control system and turbine efficiency does not vary significantly, the expansion-ratio remains almost unchanged when TIT is kept constant. So far, the analysis of the MGT performances has been limited within ranges where it works in normal or safe condition. In the following Figs. 10–12, the charts of Figs. 5, 8 and 9 are redrawn to evidence the MGT working areas where these limits are exceeded. The boundaries of the normal working areas, which are lightgray colored, are delimited by the lines where ambient temperature, electrical power, rotational speed, and TIT reach their respective limits. As upper limit for TIT we chose the value reached with the machine working at maximum speed and maximum power (point A in the performance charts), i.e. 1232 K. Working areas where rotational speed and power are out of bounds are evidenced in green and blue respectively. Red areas evidence working points where TIT and Pe, or TIT and rpm, or TIT

26

F. Caresana et al. / Applied Energy 124 (2014) 17–27

performance with ambient temperature would be much lower, and heat recovery would increase significantly. The reduction of electrical power consequent to an increase of temperature from 1.2 °C to 40 °C would be around 28 kW vs. 50 kW (in Fig. 10 compare points A and A2 vs. points A and A1), meanwhile thermal power would increase of about 48 kW instead of decreasing of about 6.6 kW. Rotational speed would reach 75 710 rpm at 40 °C (point C). 5. Conclusions

Fig. 10. MGT-CHP plant normal working area.

This paper focused on the effect of ambient temperature on the performance of a microturbine in cogeneration arrangement and, thanks to a simulation code, the authors entered in detail into the machines’ behavior. A performance chart has been drawn showing how the MGT working range changes with temperature in the interval 25–40 °C. The effects on global performances can be summarized as follows. A 1 °C growth of ambient temperature with respect to the 15 °C ISO-condition causes: – – – – –

Fig. 11. Compressor normal working area.

a reduction of electrical power of about 1.22%; a reduction of electrical efficiency of about 0.51%; a reduction of thermal power of about 0.10%; an increase of thermal efficiency of about 0.70%; an increase of the thermal-to-electrical power ratio of about 1.30%.

The main reason causing the decrease of electrical power is basically that already well known in literature for larger GTs, i.e. the reduction of air mass flow with temperature, however, the reduction for MGTs is almost twofold that of GTs. Actually the reduction in air volumetric flow in MGTs (about 0.12%/°C) assumes values comparable to that of density (about 0.33%/°C). This behavior is different from what generally assumed for larger GTs in which the volume flow is considered independent from ambient temperature. At this respect it is worth noting some differences: – the machines are of the radial type (vs. axial type), – TOT is kept constant (vs. constant TIT), – the plant operates on a regenerated cycle (vs. simple cycle). The global effects listed above are explained in the paper by entering in detail in the machines’ behavior, in particular it is shown that: – as temperature increases the compressor working point moves towards lower compression ratios and lower corrected flows, i.e. the compressor delivers less air at a lower pressure – the turbine behaves accordingly working at lower expansion ratio and lower corrected mass flow.

Fig. 12. Turbine normal working area.

and both Pe and rpm, are out of bounds. In dark gray areas, although speed, power and TIT would be within their normal ranges, ambient temperature is out of bounds. In fact, with ambient temperature lower than 25 °C there would be potential icing at the compressor inlet, and over 40 °C the machine power electronics would be likely to fail due to deficiencies in the cooling system. Fig. 10 data evidence that, if a control system limiting TIT instead of rpm was adopted (as common in larger GTs that work at constant rotational speed), the drop in maximum electrical

Plant performance correction factors are provided considering the in-use control system, based on limiting maximum rotational speed at constant TOT, but it is also shown that if a constant TIT control system was adopted, as common in larger GTs, the drop in electrical performance with ambient temperature would be much lower at the cost of a greater rotational speed. Appendix A. Ref. [33] gives accurate correlations for the evaluation of the characteristics of air, in particular we used the correlations

F. Caresana et al. / Applied Energy 124 (2014) 17–27

provided to calculate enthalpy from temperature and those used to calculate the final temperature of an isentropic compression or expansion once known pressure ratio and initial temperature. The correlation for calculating enthalpy (in kJ) is a third order polynomial:

hðTÞ ¼

3 X Ah ðNÞ  T N

ðA1Þ

0

with Ah(0) = 0.120740102; Ah(1) = 0.924502; Ah(2) = 0.115984 103; Ah(3) = 0.563568108. In the paper we refer at this correlation as:

h ¼ fh ðTÞ

ðA2Þ

As far as an isentropic process is concerned the calculation of the final temperature is based on the following. Starting from the evidence that for an isentropic process it can be written:

ln

  Z pfin 1 T fin dT ¼ cp R T in T pin

ðA3Þ

where R is the specific gas constant. Irvine and Liley [33] defined a function that they called ‘‘Isoentropic Pressure Function’’:

IPRðTÞ ¼

1 R

Z

T

T0

cp

dT T

ðA4Þ

and provided a correlation to approximate this function as:

! 1 1 X N IPRðTÞ ¼ AIPR ðNÞ  T þ AIPR ð2Þ  lnðTÞ R 0

ðA5Þ

with AIPR(0) = 1.386989; AIPR(1) = 0.00018493; AIPR(2) = 0.95; R = 0.287 and a correlation to evaluate temperature once known IPR(T) as:

TðIPRÞ ¼

3 X AT

IPR ðNÞ

 IPRðTÞN

ðA6Þ

0

with AT_IPR(0) = 8800.92; AT_IPR(1) = 1269.74; AT_IPR(2) = 61.9391; AT_IPR(3) = 1.0353.The use of these correlations in case of an isentropic compression or expansion are as follows: Known Tin, pin and pfin: 1 1 X IPRðT in Þ ¼ AIPR ðNÞ  T Nin þ AIPR ð2Þ  lnðT in Þ R 0

IPRðT fin Þ ¼ IPRðT in Þ þ ln

T fin ¼

3 X AT

IPR ðNÞ

  pfin pin

 IPRðT fin ÞN

! ðA7Þ

ðA8Þ

ðA9Þ

0

Combining Eq. (A7)–(A9) a function can be conceived that gives Tfin p as output, having Tin, and b ¼ pfin as inputs: in

T fin ¼ fis ðT in ; bÞ

ðA10Þ

For the sake of simplicity these correlations have been used for both air and exhausts, in fact due to the great air excess typical of regenerated machines (in our case the air mass flow is at least 110 times the fuel mass flow), the characteristics of the exhausts are very similar to those of air. References [1] Hwang Y. Potential energy benefits of integrated refrigeration system with microturbine and absorption chiller. Int J Refrig 2004;27:816–29.

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