Modeling, simulation and experimental set-up of a renewable ...

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Modeling, simulation and experimental set-up of a renewable hydrogen-based domestic microgrid L. Valverde a, F. Rosa a, A.J. del Real a,*, A. Arce b, C. Bordons b a b

Energy Engineering Department, School of Engineering, University of Seville, 41092 Seville, Spain System Engineering and Automation Department, School of Engineering, University of Seville, 41092 Seville, Spain

article info

abstract

Article history:

This paper deals with domestic microgrid modeling and simulation covering some aspects

Received 6 November 2012

not fully addressed in the existing literature. Specifically, most of the reviewed generic

Received in revised form

models are suitable for long-term simulations but only considering steady-state and

18 June 2013

nominal operating conditions, which overestimate the energy outputs, hydrogen produc-

Accepted 24 June 2013

tion and system performance. More specific models are capable of capturing the accurate

Available online 27 July 2013

dynamics of each individual piece of equipment. However, their complexity leads to a high computational burden making it difficult to implement an overall system-scope model

Keywords:

including all the interconnected equipment for long-term calculations. This paper seeks to

Microgrid

rectify the problem presented by the detected lack of medium-complexity dynamic models

Experimental

of renewable systems with intermediate storage, proposing a domestic microgrid solution

Renewables

composed of photovoltaics, metal hydride hydrogen-based storage with an electrolyzer,

Hydrogen

polymeric electrolyte fuel cell (PEM-FC), and interconnections with neighbor grids and

Storage

electric vehicles. This model is validated with experimental data gathered from a pilot microgrid plant designed, built and operated by the authors, and matching simulated data closely. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Consumers typically seek more energy-efficient devices, looking for environmentally friendly systems that minimize energy consumption and therefore cost less to operate. Longterm storage of electrical energy plays an important role in achieving these goals through a more extensive use of renewable energy sources. Energy storage is a key component of current and future energy technologies. The electric battery is a well-known device for storing power, although it can only be used on a limited basis. In order to achieve long-term energy storage, electrical energy can alternatively be converted into hydrogen

through an electrolysis process. Hydrogen is converted back into electricity on demand using fuel cells, thereby providing a reliable and long-term energy storage option. This energy carrier in combination with traditional systems more than compensates for the difficulties presented by the technical and economic issues in the intermediate term. Designing, manufacturing, energy management, economic analysis and optimal sizing are critical topics where equipment modeling and simulation are relevant, all of which leads to the development of many simulation tools which aim to describe real behavior of modern power plants [1]. The complexity of the existing models depends on the application. Moreover, similar and common shortcomings were detected

* Corresponding author. E-mail addresses: [email protected] (L. Valverde), [email protected] (F. Rosa), [email protected], [email protected] (A.J. del Real), [email protected] (A. Arce), [email protected] (C. Bordons). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.113

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

in most of them. Considering the reviewed generic models of renewable energy systems, including multiple power sources and/or intermediate storage devices [2], real operation features have not been extensively discussed. Similarly, most of the generic models found in the literature do not take into account dynamics, partial-load behavior and thermal inertia, considering only steady-state or nominal operation conditions. As a result, these models overestimate the energy outputs, hydrogen production and system performance. Regarding more specific models, very accurate dynamic models of each individual piece of equipment have been proposed to date (such as those describing a polymeric electrolytic membrane (PEM) fuel cell [3], an electrolyzer [4], a battery and load [5], etc). The complexity of such models makes it difficult to implement an overall system-scope model with all the interconnected equipment because of the computational burden. Furthermore, such complex models are not practical for performing long-term calculations. This paper aims to overcome the detected lack of mediumcomplexity dynamic models of renewable systems with intermediate storage, proposing a dynamic model of a domestic microgrid integrating photovoltaic array, a PEM electrolyzer, metal hydride hydrogen-based storage, a PEM fuel cell, neighbor grid energy exchanges and an electric vehicle. This dynamic model is a trade-off between model accuracy and control-oriented implementation. As for the paper’s main contributions, an experimental pilot plant is designed and deployed in order to validate the proposed model. The experimental microgrid extends the existing portfolio of similar installed facilities in order to assess renewable reliability. The main innovation of this system is the integration of a metal hydride storage tank as a medium-size hydrogen-based storage while most of the existing similar pilot plants incorporate hydrogen storage based on gas compression. Amongst the main related test

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stations are: the Phoebus-Ju¨lich plant [6], which presents an autonomous system with a photovoltaic panel, a hydrogen electrolyzer and a fuel cell power system and is tested for large building power supply; a stand-alone renewable energy system (RES) located at the Hydrogen Research Institute facilities in Canada [7]; and the HaRI project [8] which integrates several electrical sources and loads. The paper is structured as follows: Section 2 is dedicated to the description of the microgrid under study and its experimental set-up. Section 3 describes a dynamic and controloriented model of such a microgrid. Some experimental results comparing performances of the real and simulated plant are presented in Section 4. Finally, the main concluding remarks and future work are discussed in Section 5.

2. Microgrid description and experimental set-up The microgrid under study is schematized in Fig. 1. The proposed domestic system is primarily powered by a photovoltaic array. In order to avoid power interruptions caused by the intermittency of the solar resource, an electrolyzer is placed in the main power distribution line. Then, in case of power excess, electricity is used to produce and store hydrogen. On the contrary, a fuel cell generates electricity by using the stored hydrogen when it is required. A battery pack is also incorporated in the main power distribution line in order to maintain a fixed voltage on the line, thus simplifying converter design. In this way, the designed system includes five different converters: a DC/AC converter which connects domestic appliances and neighboring grids, a bidirectional DC/ DC converter to provide and obtain power from an electric vehicle and three unidirectional DC/DC converters to adapt the photovoltaic array power, the electrolyzer power and the

Fig. 1 e Hydrogen-based, domestic microgrid.

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fuel cell power requirements, respectively. The electric car also works as an electrical storage element for the system. Moreover, the aforementioned domestic microgrid is connected to other neighboring grids to exchange energy according to demand. The experimental set-up is shown in Fig. 2 and is located at the University of Seville facilities (Spain). The main characteristics of the pilot plant devices are listed in Table 1. The photovoltaic array is emulated by a programmable electronic power source which permits system behavior simulation under different weather conditions. Analogously, another programmable electronic load simulates the domestic power demand. The electric car power exchanges and the interconnection among other grids are also simulated by combining both the programmable power source and the load. This configuration makes the simulation of different power inputs and outputs more flexible. The hydrogen installation consists of a 1 kW PEM electrolyzer, a metal hydride storage tank and a PEM fuel cell system. Hydrogen purification systems are not required since the electrolyzer produces high purity hydrogen. The hydrogen is stored on a LaNi5 metal hydrides alloy storage tank with a 7 Nm3 storage capacity. Since heat is required to release the hydrogen storage content, a cooling/heating system is incorporated to the test bench. Finally, a 1.5 kW PEM fuel cell completes the hydrogen installation. As for auxiliary devices, the system includes electrovalves and a safety nitrogen circuit. All the electronic devices are connected to a 48-VDC bus supported by a 24-monoblock battery pack of advanced leadacid batteries with a C120,bt ¼ 367 Ah capacity. For the sake of simplicity, the performance of the DC/DC converter, which connects the photovoltaic array to the main 48-VDC bus, is emulated by the programmable power source and the DC/DC and DC/AC converters, which connect the electric vehicle, domestic loads and external grids to the bus, are mimicked by the programmable power load. Regarding the microgrid Supervisory Control and Data Acquisition (SCADA) system, an M-340 programmable logic control (PLC) is installed as the main plant control platform. The controller is provided with data acquisition cards in order to communicate with the programable load and power source,

Fig. 2 e View of the experimental set-up.

Table 1 e Microgrid equipment. Component Electronic power source Electronic load PEM electrolyzer Metal hydride storage PEM fuel cell Pb-acid battery pack Water purification PLC DC/DC converters

Rated capacity

Manufacturer

6 kW

POWERBOX

2.5 kW 0.23 Nm3/h 7 Nm3, 5 barg

AMREL HAMILTON-STD LABTECH

20 Nl/min @ 1.5 kW C120,bt ¼ 367 Ah 3 l/h @ 15 MU M340-Canbus 1.5 kW, 1 kW

MES-DEA EXIDE MILLIPORE SCHNEIDER WINDINERTIA

the plant devices and sensors. The communication between the DC/DC converters and the PCL is performed employing the Canbus communication protocol. The resulting pilot plant configuration is shown in Fig. 3.

3.

Microgrid modeling

A practical and accurate dynamic model of the complete domestic microgrid is developed and presented in this section. Avoiding modeling ancillary devices (such as the securityerelated nitrogen circuit), the proposed interconnected model comprises the following devices: photovoltaic (PV) array, battery pack, electrolyzer, metal hydride storage tank, PEM fuel cell, neighbor grids and electric vehicle. This kind of system represents multiephysic domains and its dominant characteristic times are shown in Table 2. Electrical dynamics, which are various orders of magnitude lower than the dominant dynamics, will thus be neglected.

3.1.

Photovoltaic array model

In the literature, we have found several models which predict the power output of photovoltaic panels. Most of these models require measurement of radiation and cell temperatures and are based on three different methodologies [9]: temperature and radiation scaling of reference measurements; interpolation of IeV curves; and electrical circuit modeling. The first approach implies a very simple formulation which is directly derived from the manufacturer’s datasheets. However, the model only predicts the maximum power by scaling a reference power value with the radiation and temperature measurements [10]. The interpolation of IeV curves [11] calculates the electrical output of all the operating points along a measured IeV curve that are not usually provided by the manufacturers. Therefore, the lack of information makes this approach difficult to implement. The electric circuit models consider solar cells as an equivalent electric circuit with radiation and temperature dependent components. The most widely used equivalent circuit is composed of five parameters. For convenience, this formulation is adopted in this work resulting in the following relationship: IPV

  i V þ I $R h VPV þIPV $RS PV PV S aPV 1  ¼ IL  Idiode $ e ; RSH

(1)

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Fig. 3 e Pilot plant configuration.

where IPV is the PV cell current, VPV is the PV cell voltage, IL is the photocurrent, Idiode the diode reverse saturation current, aPV the modified ideality factor, RS the series loss resistance and RSH the shunt loss resistance. The factor aPV can be expressed for one individual cell as: aPV ¼

ndiode $k$TPV ; q

(2)

where ndiode is the diode ideality factor, k the Boltzmann constant (1.3806  1023 J/K), TPV the cell temperature (Kelvin) and q the electron charge (C). Despite the fact that the five PV model parameters (aPV, IL, I0, RS and RSH) are not provided by manufacturers, there are several different methods employed to estimate such parameters using the parameters commonly provided in PV datasheets, which are: maximum power voltage, VPV,max, maximum power current, IPV,max, open-circuit voltage, VPV,0, short-circuit current, ISC, short-circuit current temperature coefficient, aISC, and open-circuit voltage temperature coefficient, bVPV,0. Again, the simplest methods are based on parameter reduction resulting in poor accuracy while methods

Table 2 e Time constant orders of the microgrid equipment dominant dynamics. Dynamic effect PV-field temperature PEM electrolyser temperature Metal hydride temperature PEM fuel cell temperature Battery time response

Characteristic time O(102) O(102) O(103) O(102) O(101)

s s s s s

that give accurate results require the solution of highly nonlinear system equations. There are some iterative methods that can be used to estimate these parameters from the manufacturer’s data, using simplifications in the equation-solving procedure, such as the fast-convergence method proposed in Ref. [12]. The five parameters depend mainly on the instantaneous absorbed radiation (S ) and the PV module temperature (TPV), and can be expressed by the following equations: aPV ¼ aPV;ref

IL ¼

TPV ; TPV;ref

(3)

  S  IL;ref þ aISC TPV  TPV;ref ; Sref 

Idiode ¼ Idiode;ref

RSH ¼

TPV TPV;ref

Sref RSH;ref ; S

RS ¼ RS;ref ;

3 h1  Eg;ref Eg i  e k TPV;ref TPV ;

(4)

(5)

(6) (7)

where the subscript ref refers to variables corresponding to Standard Test Conditions (STC) and Eg is the material band gap energy [13]. S denotes the instantaneous absorbed radiation, Tamb is the ambient temperature and nmod is the total number of PV modules composing the PV array. The instantaneous absorbed radiation can be easily obtained by a number of diverse sensors while the PV module temperature (which strongly affects the overall PV performance) is a more complicated variable to measure directly. The main reason is that each PV module needs a corresponding temperature sensor. As a result, the most common

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way to predict the cell temperature is by using the Normal Operating Cell Temperature, TNOC, which is provided by the PV module manufacturer as presented in Ref. [14]. The electrical dynamics for PV modules are much faster than the dominant dynamics presented in Table 2 and are thus implicitly neglected in Equation (1). Nevertheless, thermal dynamics are on the order of other dominant dynamics presented in Table 2 and cannot be ignored in the model. Therefore, the PV module temperature, TPV, is modeled as a function of the ambient temperature, Tamb, and the instantaneous solar irradiance, S, and can be approximated through the following differential equation: dTPV 1 1 S TPV þ Tamb þ ðTNOC  293:15Þ : ¼ 300 300 2400 dt

(8)

Even though the above equation implies some simplifications (such as uniform temperature in the panel and negligible radiative exchanges), the predicted temperatures match the experimental data closely for the purposes of the integrated model discussed in this paper. The PV array modeled herein is composed of 20 ISF-150 modules manufactured by ISOFOTON. The corresponding data provided by the manufacturer is presented in Table 3 as well as the five parameters calculated using the fastconvergence method proposed in Ref. [12]. Fig. 4 (a) shows the representative IeV and PeV curves for a single module at a given absorbed radiation and module temperature. The power delivered by the PV array is calculated as: PPV ¼ nmod $IPV $VPV :

H2 OðliquidÞ þ

1 electrical /H2 ðgasÞ þ O2 ðgasÞ: energy 2

The reaction can be divided into the following: 2H2 O/4Hþ þ 4e þ O2 ðanodeÞ; 4Hþ þ 4e /2H2 ðcathodeÞ: The electrolyzer modeled is operated in current mode, which means that a current is applied to the stack and then a differential of potential, Vez, is reached according to the expression given by Ref. [15]: Vez ¼ Vez;0 þ Vetd þ Vez;ohm þ Vion ;

(10)

where Vez,0 is the reversible potential, Vetd is the electrode overpotential, Vez,ohm is the ohmic overvoltage and Vion is the ionic overpotential. Hence, the voltage drop is a sum of four terms that can be drawn through the following expressions: Vez;0 ¼ 1:23  0:9 103 ðTez  298Þ þ 2:3

 RTez  2 ln pH2 ;ez $pO2 ;ez ; 4F (11)

Vetd ¼



  RTez RTez dB 1 1 iez 1 1 iez sinh sinh iez þ RI iez ; þ þ 2 iao 2 ico F F sB (12)

(9)

As can be seen in Fig. 4 (a), there is a maximum power value for the PV module, PPV,max. Power electronic devices are designed to run PV systems at around this value, PPV,max. Thus, it is assumed in this paper that PV systems work all the time around this operating point. Fig. 4 (b) and (c) depict the effect of different absorbed radiation levels and ambient temperatures on the module’s IeV curve.

3.2.

two electrodes separated by an electrolyte. In the pilot plant, the electrolyte is a proton exchange membrane. The electrochemical reactions can be expressed by:

Electrolyzer

An electrolyzer uses the electrolysis principle to split water into hydrogen and oxygen applying a high current through

Table 3 e ISOFOTON 150 datasheet and equivalent five model parameters. Datasheet parameter VPV,max IPV,max VOC ISC aISC bVOC

Value 18.5 (V) 8.12 (A) 22.6 (V) 8.70 (A) 0.003654 (A/K) 0.072998 (V/K)

Five model parameters aPV IL Idiode RS RSH

Value 0.6326 8.7324 2.5642$1015 0.2458 65.9544

sB ¼ ð0:005139l  0:00326Þ e1268 ð303Tez Þ ; 1

1

(13)

where Tez is the electrolyzer stack temperature, R is the ideal gas constant, F is the Faraday’s constant, pH2 ;ez is the hydrogen partial pressure, pO2 ;ez is the oxygen partial pressure, iez is the electrolyzer current density, iao is the anode current density, ico is the cathode current density, dB and sB are the thickness and conductivity of Nafion 117 electrolyte and l is the membrane water content. The last two terms of Equation (10) can be grouped as: Vez;ohm þ Vion ¼

dB Iez ; Aez sB

(14)

where Aez is the electrolyzer effective area. Equation (12)e(14) are related to the electrolyzer polarization curve. The real coefficients presented in these equations were obtained from the technical brochure and by fitting experimental data from the electrolyzer SPE HAMILTON-STD. The parameters are summarized in Table 4. Fig. 5 (a) shows a comparison between the voltage measured in the plant and the simulated voltage, under varying current conditions. _ H2 ;ez , The hydrogen flow rate produced by the electrolyzer, m can be directly obtained from the electrolyzer current as: _ H2 ;ez ¼ nez m

Iez ; F

(15)

where Iez is the stack current, nez is the number of electrolyzer cells and F is the Faraday constant. The validation of this equation with experimental data is presented in Fig. 5 (b).

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a) 200

15 IPV

IPV,max

PPV

I

PV

100

PPV (W)

(A)

10

5

0

0

5

10

15

V

PV

b) 10

(V)

c)

S

8

(A) PV

6 4

T

amb

6 4

I

I

PV

(A)

8

2

2 0

0 25

20

0

5

10

15

20

25

0

0

5

10

VPV (A)

15

20

25

VPV (V)

Fig. 4 e (a) IeV and PeV curves for the 150 ISOFOTON module; (b) radiation effects on the IeV curve and (c) ambient temperature on the IeV curve.

A lumped capacitance thermal dynamic model is used to predict the electrolyzer temperature. Next equations can be obtained from the overall energy balance: Cez;t

dTez ¼ Q_ gen  Q_ loss  Q_ cool ; dt

(16)

where Cez,t is the overall thermal capacity of the electrolyzer, Q_ gen is the heat produced by the stack, Q_ loss is the heat delivered to the environment and Q_ cool is the heat removed by the cooling system. The heat generated in the stack is a product of the thermodynamic irreversibility in the electrolysis process and can be approximated by:

_ T ð1  Vtm Þ : Q_ gen ¼ W

(17)

The heat generated depends on the electrolyzer power _ T , and on the so-called thermoneutral poconsumption, W tential, Vtn, which is a point when the electrolysis reaction becomes an exothermic reaction. The following expressions are used to calculate the thermoneutral potential: Vtn ¼ Vhv þ

   1:5 psat 4:29 104 þ 40:76 Tez  273 2F pez  psat  0:066ðTez  273Þ2

Vhv ¼ 1:4756þ2:252104 ðTez 273Þþ1:52108 ðTez 273Þ2 ; 8096:23 Tez

(19)

Table 4 e Model parameters for the PEM electrolyzer.

psat ¼ e13:669

Param.

where Vhv is the higher-high-value voltage, psat is the vapor partial pressure, pez is the electrolyzer pressure and Tez is the electrolyzer temperature. The wasted heat is a sum of the effects of radiation and convection losses. Heat losses can be expressed as:

Aez pH2 ;ez pO2 ;ez iao ico dB sB l Cez,t

Comments Stack area Partial pressure Partial pressure Anode current density Cathode current density Membrane thickness Membrane conductivity Membrane water content Thermal capacity

Value 2

212.5 cm 6.9 bar 1.3 bar 1.06316 A/cm2 13 A/cm2 178 mm 0.14 S/cm 21 molH2/molSO3 402400 J/K

;

(18)

Cez;t ðTez  Tamb Þ: Q_ loss ¼ sez;t

(20)

(21)

where sez,t is the electrolyzer time constant identified by means of an experimental procedure presented in Ref. [16].

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10.75

60

10.25

40

9.75

9.25

Hydrogen production (Nl/min)

b)

Simulated data Experimental data Current profile 0

100

200

400

500

600

700

800

0

Time (s) 3 2.5 2 1.5 1 Simulated data Experimental data

0.5 0

1

10

20

30

40

50

60

Electrolyzer stack current (A)

c)

Electrolyzer temperature (K)

300

20

Current profile (A)

Stack Voltage (V)

a)

294

Vfc ¼ Vfc;0  Vact  Vfc;ohm  Vconc ;

(22)

where Vfc,0 is the open circuit voltage. Vact is related to the activation losses which prevail at lower current densities. At a latter stage, as current density rises, ohmic losses, Vfc,ohm, become the main actor. When the current density reaches its highest values, at a maximum power level, concentration overvoltage, Vconc, causes a quick voltage drop due to internal inefficiencies when reactant consumption is high. Following the procedure described in Refs. [3], it is possible to obtain an analytical relation of the polarization curve of a PEM fuel cell from experimental data. Specifically, a 1.5 kW MES-DEA fuel cell was successfully characterized and implemented in the pilot plant emulator by the following equation:        Vfc ¼1:046 þ0:003 Tst T0st þ0:244 0:5ln pO2 ;fc þln pH2 ;fc |fflffl{zfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

293 292

Vfc;0

291 290

equations (whose dynamics can be neglected), fluid dynamics and thermal dynamics. As regards the static electrochemical model, the voltage supplied by a fuel cell is evaluated by curves that present cell voltages, Vfc, versus the current density:

Model Experimental 0

100

200

300

400

500

600

700

DVfc =DTst

DVfc =Dpfc

  ist ð1þ8:001Þ 0:066 1exp 0:299$ifc 0:028$ifc ; 0:013 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} Vact

Vfc;ohm

Time (s)

Fig. 5 e (a) Comparison of the model and experimental electrolyzer voltage for different currents; (b) Measured and simulated hydrogen output flow; (c) Simulated and measured stack temperature.

As for the cooling heat, the hypothesis of an ideal cooling system coupled with the electrolyzer is adopted herein, allowing the system to be able to remove any excess heat. Fig. 5 (c) shows the thermal dynamic validation for a current profile.

3.3.

(23) where ifc ¼ Ifc/Afc denotes the current density, Afc ¼ 61 cm2 is the effective membrane area of the cells composing the stack and T0st ¼ 296K being the nominal operating temperature. Fig. 6 shows the polarization (IeV) curve corresponding to the PEMFC as well as the influence of the oxygen pressure inside the stack and the stack temperature on this curve. As mentioned in Ref. [3] hydrogen pressure can be assumed to be constant. The thermal dynamics are formulated through an energy balance accounting for the energy produced by the water formation reaction, H_ reac , the energy supplied in the form of electricity, Pelec, the amount of heat evacuated by radiation, Q_ rad , and both natural and forced convection, Q_ conv :

PEM fuel cell mst Cst

There have been many PEM fuel cell models in the literature developed in the last 20 years. Earlier models, such as [17], presented an empirical polarization curve based on calculated coefficients, as some recent papers [18] have shown. In Refs. [19], an extended equation with a larger number of parameters was proposed, improving the formulation of the polarization curve dependence on the fuel cell stack temperature and hydrogen partial pressures. As the polarization curve had initially been based solely on the steady-state case, recent research has considered the fluid dynamics inside the stack, taking transient behavior into account. Some authors have proposed complex multidimensional studies [20,21]. Although these contributions are very useful for fuel cell design, they do require large computational calculations. Thus, simplified one-dimensional time dependent models are more suitable for control purposes and long-term simulations, such as those presented in Refs. [3,19,22]. Such simplified dynamic models are composed mainly of three modules: electrochemical

Vconc

dTst ¼ H_ reac  Pelec  Q_ rad  Q_ conv ; dt

(24)

where mst is the fuel cell stack mass and Cst is the average heat capacity of the system. The enthalpy flow rate, H_ reac , is calculated as: _ H2 DhH2 þ m _ O2 DhO2  m _ H2 O h0f ;H2 O DhH2 O ; H_ reac ¼ m

(25)

  DhH2 ¼ Cp;H2 Tst  T0 ;

(26)

  DhO2 ¼ Cp;O2 Tst  T0 ;

(27)

  DhH2 O ¼ Cp;H2 O Tst  T0 ;

(28)

h0f ;H2 O

where is the mass specific enthalpy of vapor formation and Cp;H2 , Cp;O2 and Cp;H2 O are the specific heats of hydrogen, oxygen and vapor respectively, T0 is the reference temperature for the enthalpy. The hydrogen consumption can be calculated from the following stoichiometric balance:

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With respect of the fluid dynamics, the most important variable is the cathode oxygen pressure, PO2 ;fc since anode hydrogen pressure, PH2 ;fc , can be assumed to be constant. The oxygen pressure is given by the compressor located upstream from the cathode channel. In order to simplify the model, the following equation has been obtained by linearizing the fluid dynamic models presented in Ref. [3]. A Ist vs PO2 ;fc expression has thus been obtained:

a)

60 Simulated data Experimental data

55

st

V (V)

50 45 40 35

dpO2 ;fc ¼ 12:10 pO2 ;fc þ 0:09 Ist : dt

30 25

0

10

20

30

40

50

Finally, Table 5 includes the parameter values for the PEMFC under study.

c)

60

60

p

O ,st

T

st

50

2

Vst (V)

Vst (V)

50 40 30

3.4.

40 30

0

20

40

60

20

0

20

Ist (A)

40

60

Ist (A)

Fig. 6 e (a) PEM-FC polarization curve; (b) Oxygen pressure effects on the polarization curve; (c) and stack temperature effects on the polarization curve.

Ist ¼ Ifc ; _ H2 ;fc;cons ¼ m

(29) Ist : 2FAfc

(30)

Energy yielded in the form of electricity is: Vst ¼ nst Vfc ;

(31)

Pst ¼ Vst Ist ;

(32)

Pst being the stack power, Vst the stack voltage and Ist the stack current. Radiation heat exchanged is modeled as shown below, where εst is the emissivity, s ¼ 5.678$108 Wm2 K4 is the Stefan-Boltmann constant and Arad is the radiation exchange area:   Q_ rad ¼ εst sArad T4st  T4amb :

(37)

70

Ist (A)

b)

20

60

11679

(33)

The convective term is composed of two others, one of them corresponding to the natural convection heat, Q_ nat , and the other, to the forced convection heat, Q_ forc . In each case, the convective heat transfer coefficients (hnat and hforc) are different, just as the exchange areas Anat and Aforc are different, since natural convection takes place in the fuel cell lateral walls and forced convection occurs across the internal cell walls due to the installed fan. Q_ conv ¼ Q_ nat þ Q_ forc ;

(34)

Q_ nat ¼ hnat Anat ðTst  Tamb Þ;

(35)

Q_ forc ¼ hforc Aforc ðTst  Tamb Þ:

(36)

Metal hydride tank

Metal Hydride (MH) tanks are a very suitable solution for hydrogen storage in stationary power plants achieving high energy storage densities. A simplified model of a LaNi5 alloy of 7 Nm3 capacity is used to analyze the cyclical absorption-desorption processes. The metal hydrides’ hydrogen absorption, also referred to as a refueling process, is governed by an exothermic reaction. The heat released causes an increase in the bed temperature and a reduction in the absorption rate. The inverse process, the desorption process, requires a heating fluid in order to sustain the reaction [23]. The MH bed has been modeled as a zero-dimensional system to allow a realistic but simplified description of the complex reactions inside this alloy. The model includes two separate blocks for absorption and desorption processes. Thus, the equations must be separately tailored for each process. Mass and energy balance equations have been studied and validated in several previous works as [24]. The mass balance for the refueling process is: _ H2 ;in ¼ εMH fvbed m

dr dqH2 ;a þ ð1  εMH Þf rs vbed ; dt dt

(38)

where εMH is the porosity of MH powder, f is the volume ratio of the heat transfer equipment volume to the total bed volume, vbed is the bed volume, r is the hydrogen gas density, rs is the MH density and qH2 ;a is the absorbed hydrogen weight fraction. In our system, the hydrogen absorbed in the MH is equal to the hydrogen produced by the electrolyzer. The refueling process produces heat removed by a cooling

Table 5 e PEM-FC model parameters. Parameter

Value

Dimension

mst Cst εst Arad Anat Aforc hnat hforc

5 1100 0.9 0.1410 0.0720 1.2696 14 19.65

kg Jkg1 K1 e m2 m2 m2 WK1 m2 WK1 m2

11680

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

fluid. This heat can be calculated through the next energy balance:

Table 6 e Metal hydride tank model parameters.

 ð1  εMH Þ ð1  εMH Þ dTMH qH2 ;a rs Cv;g þ rs Cp;s rCv;g þ εMH εMH dt

Parameter

where Cv,g is the specific heat of H2 gas at constant volume, Cp,s is the MH specific heat at constant volume, Ua is the overall heat transfer coefficient for absorption, Acs is the heat transfer area, TMH is the MH temperature, Tc is the cooling water _ H2 ;in is the hydrogen supply mass flow rate. temperature and m The hydrogen desorbed in the process is calculated from the mass conservation balance. For our system, the hydrogen desorbed is equal to the hydrogen injected to the fuel cell: _ H2 ;out ¼ εMH fvbed m

dr dqH2 ;d  ð1  εMH Þf rs vbed ; dt dt

(40)

qH2 ;d being the desorbed hydrogen weight fraction. The hydride cools down during the desorption process. Thus, the system is heated in order to maintain the appropriate conditions for the desorption process. The energy balance for the desorption case can be evaluated as:  ð1  εMH Þ ð1  εMH Þ dTMH qH2 ;d rs Cv;g þ rs Cp;s rCv;g þ εMH εMH dt ð1  εMH Þ dqH2 ;d Acs ¼  Ud rs DHd ðTMH  Th Þ εMH dt εMH fvbed  _ H2 ;out pMH m þ ; r εMH fvbed

(41)

where Ud is the overall heat transfer coefficient for desorption, _ H2 ;out is the hydrogen Th is the water heating temperature and m output flow rate. The hydrogen content in the MH alloy at equilibrium conditions can be drawn from the equilibrium pressure on a Pressure-Composition-Temperature (PCT) curve (or PressureComposition-Isotherm (PCI) curve) [25]. Note that the equilibrium pressure is highly dependent on temperature as given by Van’t Hoff law [26]. Absorption reaction kinetics for LaNi5eH2 hydrides can be suitably described by the expression [27]:     RTEa dqH2 ;a pMH  MH ¼ Ca e ln  qH2 ;a;max  qH2 ;a : dt pMH Analogously, the desorption case results in: 

 dqH2 ;d ¼ Ca e dt

RTEa

MH

  pMH  pMH  ln qH2 ;d;max  qH2 ;d ; pMH

3.5.

Battery pack model

In the present work, a dynamic lumped model for the Leadacid battery pack is calibrated based on [28,29]. The model

a)

Simulated data

(43)

where pMH is the pressure in the metal hydride bed, pMH represents the equilibrium pressure, Ca is the Arrhenius rate constant and Ea is the activation energy. Table 6 shows the parameters for the metal hydride tank. Experimental and simulation results are compared for the absorption and desorption processes. Specifically, Fig. 7 (a) illustrates the storage system response for the absorption mode with a constant pressure. The hydrogen content on the metal hydride tank rises very fast at the beginning of the

Experimental data

4.5 4 3.5 3 2.5 2

(42)

0.55 3240 kg/m3 1.2174 %w/w 20.4 J/mol K 419 J/mol K 1.1453 m2 1 100.5 J/mol K 21.18 KJ/nik 59.187 1/s 30800 J/mol 966.1980 W/m2 K 833.144 W/m2 K

process which results in a rapid temperature rise and a reduction in the hydrogen absorption rate as seen in Fig. 7 (b). On the other hand, the desorption model is validated by performing a constant hydrogen demand from the fuel cell. The auxiliary heating system heats the hydride with hot water (40e70  C) in order to enhance the desorption process, and its strong dependence on the hot water inlet temperature should be borne in mind. The effect of increasing the fluid temperature and desorption flow rate is represented in Fig. 8 (a), while the thermal dynamic validation for such a desorption case is shown in Fig. 8 (b).

Tank pressure (bar)

(39)

εMH rs qH2 ;max Cv,g Cp,s Acs f DS Ea Ca DH Ud Ua

0

1000

2000

3000

4000

5000

6000

7000

8000

5000

6000

7000

8000

Time (s)

b) Bed temperature (K)

ð1  εMH Þ dqH2 ;a Acs ¼  Ua rs DHa ðTMH  Tc Þ εMH dt εMH fvbed  _ H2 ;in pMH m þ ; r εMH fvbed

Value

305

300

295

290

0

1000

2000

3000

4000

Time (s)

Fig. 7 e (a) Comparison between model simulation and experimental absorption process at constant pressure (4.5 barg) and (b) Model bed temperature and experimental during charging process.

11681

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

a)

Simulated data

Table 7 e Battery model parameters.

Experimental data

Tank pressure (bar)

8

Parameter C120,bt Vbt,0 Kbt Abt Bbt

6 5 4 3

367 Ah 51.58 V 0.006215 V 11.053 V 2.452 Ah1

2 1

0

500

1000

1500

2000

2500

Zt

Time (s)

Bed temperature (K)

b)

Cout;t ¼

Ibt dt:

330

Analogously, for the discharging process the internal voltage is:

320 315

Vbt;int ¼ Vbt;0  Kbt

310

C120;bt C120;bt I þ Kbt Cout;t Cout;t þ 0:1C120;bt bt C120;bt  Cout;t

þ Abt eBbt Cout;t ;

305 0

500

1000

1500

2000

2500

Time (s)

Fig. 8 e (a) Comparison between model simulation and experimental desorption process at constant pressure (4.5 barg) and (b) Model bed temperature and experimental during charging process.

Vbt being the battery voltage, Vbt,int the battery internal voltage and Ibt the battery current. The internal voltage for the battery charging process is: Vbt;int ¼ Vbt;0  Kbt þ Abt e

C120;bt C120;bt I  Kbt Cout;t C120;bt  Cout;t bt C120;bt  Cout;t

Bbt Cout;t

;

(45)

70 Simulated data Experimental data Battery current (A)

60 50

PV power supply (W)

(44)

a)

Domestic power demand (w)

Vbt ¼ Vbt;int þ Ri Ibt ;

3000

2000

1000

0

10

0

1

2

3

4

5

6

7

8

9

10

12

Time (hour)

Fig. 9 e Comparison between battery experimental voltage and battery model voltage while a discharging test is carried out.

1

2

3

4

5

6

7

8

5

6

7

8

5

6

7

8

Time (hours)

1500

1000

Electric vehicle demand (W)

20

0

b)

40 30

(47)

where Vbt,0 is a constant voltage, Ibt is the battery current filtered by a first-order filter, Abt is the exponential zone amplitude, Bbt represents the exponential zone inverse time constant, Kbt is the polarization constant, Cout,t is the extracted capacity and C120,bt is the maximum battery capacity. The model parameters are obtained through the experimental test shown in Fig. 9 and listed in Table 7. The battery response time is estimated to be 31 s.

uses an internal resistance, Ri, and a controlled voltage source to mitigate the battery’s exponential behavior. The battery voltage is expressed as:

0

(46)

0

325

300

Voltage (V)

Value

7

500

0

0

1

2

3

4

Time (hours)

c) 600

400

200

0

0

1

2

3

4

Time (hours)

Fig. 10 e (a) PV array power supply; (b) domestic demand profile; (c) and electric vehicle demand.

11682

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

a)

Simulated data 800 600 400 200 0 800 600 400 200 0

600 400 200 0

0

1

2

3

Electrolyzer Power (W)

800 800 600 600 400 200 400 0

5

6

7

−1000

500 0 −500

1

2

3

4

5

6

7

8

5

6

7

8

Time (hours)

b) 54 52 50 48 46

0

1

2

3

4

5

6

7

8 44

Time (hours)

0

1

2

3

4

Time (hours)

Fig. 12 e (a) Power exchanges with neighbor grids and (b) DC bus voltage.

0.55 0.405 0.4 0.395 0.39 0.385

0.5 0.59 0.45

0.58

0.4 0.57 0.35

0

1

4 2

5 3

4

5

6

7

8

Time (hours)

Fig. 11 e (a) PEM fuel cell operation; (b) electrolyzer operation; (c) and hydrogen storage performance.

4.

−500

500

0

200 0

0

1000

−1000

8

800 600 400 200

c) H inventory level (kg) 2

4

Experimental data

1500

1000

Time (hours)

b)

Simulated data

1500

Grid power (W)

800

Bus voltage (V)

Fuel cell Power (W)

1000

a) 2000

Experimental data

Experimental results

The microgrid mathematical description is validated through this section with the experimental results gathered from the pilot plant set-up previously described in Section 2. The experiment comprises 8 h of continuous operation. Therefore, the domestic power demand profile, the electric vehicle charging profile and the photovoltaic power availability shown in Fig. 10 are applied to the mathematical model and the pilot plant. As seen, the power demand is mainly concentrated on two periods (midday and late afternoon). The power supplied from the photovoltaic array is concentrated during the first half of the day and with some variability. Finally, the electric car consumes power from the domestic microgrid in the latter half of the simulated day. The power plant generators track the domestic power profile with the support of the fuel cell. Hydrogen is generated by the electrolyzer when power supply exceeds the demand. The hydrogen stock is the result of both processes: reduction of hydrogen storage when the fuel cell operates and increase when the electrolyzer is utilized. The activation of the electrolyzer and the fuel cell is regulated by the well-known control strategy known as “control by hysteresis band” [30,31]. Fuel cell and electrolyzer on-off switching thresholds depend on the battery state of charge (SOC). If, for example, the SOC goes below a certain value (i.e. 45% in this work), the fuel cell is activated until the SOC is recovered (a value of 50% was selected herein) and the fuel cell is switched off. If, on the

other hand, the SOC goes above a certain value (75% in this work), the electrolyzer is switched on until the batteries are depleted and the SOC goes below a certain threshold (70%). Fig. 11 (c) compares the experimental and simulated hydrogen stock while Fig. 11 (a) and (b) show the fuel cell and the electrolyzer utilization respectively. The comparison exhibits a good fit between experimental and simulated data. As power exchanges with neighbor grids are allowed, the proposed domestic microgrid imports power when its own sources are not capable of tracking its demands (mainly, domestic appliances and electric vehicle consumption). Contrarily, power export occurs when there is an energy excess. Both cases occur in the implemented experiment as observed in Fig. 12 (a). The exported power exhibits positive values while imported power presents negative values. Fig. 12 (b) shows the resulting voltage of the DC bus. The DC voltage varies notably during the first stage when the battery exchanges power and remains constant after the 5.6 h test when the battery is not working. This is explained by the availability of the solar resource during the first stage of the day and the lack of PV power on the second stage, when the power demand is still present. This leads to the battery discharging to the minimum limit. Note that, at this time the FC and the grid start to supply power in order to satisfy the loads (household and electric vehicle) and prevent an excessive battery discharge.

5.

Conclusions

This paper presents a balanced mathematical model accounting for both dynamics tracking accuracy and long-term simulation. To that end, the model is complex enough to take into account system dynamics, partial-load behavior and thermal dynamics, while at the same time is simple enough

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

not to present a very high computational burden. Different equipment composing a domestic hydrogen-based microgrid has been modeled throughout the different sections of the paper. The last section is dedicated to the modeling validation, showing the experimental results obtained when testing the proposed input profiles. As shown, the model meets the main goal of accurately representing the system performance for long-term simulations. Future works will deal with control issues, and will aim to implement advanced predictive controllers for real-time operation, taking advantage of the models developed in this paper.

Nomenclature

Abt Acs Aez Afc Aforc Anat Arad Bbt Ca C120,bt Cez,t Cout,t Cp;H2 O Cp;H2 Cp;O2 Cp,s Cst Cy,g Ea Eg F IL IPV Ibt Ibt Idiode Iez Ist Kbt PPV Pst R RS RSH Ri S T0 T0st Tc Th TMH TNOC TPV Tamb

exponential zone amplitude, V heat transfer area, m2 electrolyzer effective area, cm2 fuel cell effective membrane area, cm2 fuel cell forced exchange area, m2 fuel cell natural exchange area, m2 radiation exchange area, cm2 exponential zone inverse time constant, A1 h1 Arrhenius rate constant, s1 maximum battery capacity, Ah electrolyzer thermal capacity, J/K battery extracted capacity, Ah vapor specific heat, J/(kg K) hydrogen specific heat, J/(kg K) oxygen specific heat, J/(kg K) MH specific heat at constant volume, J/(mol K) fuel cell heat capacity, J/(kg K) hydrogen gas specific heat, J/(mol K) activation energy, KJ/nik material band gap energy, J Faraday’s constant, s A mol1 photocurrent, A PV current, A battery current, A battery filtered current, A diode reverse saturation current, A electrolyzer stack current, A fuel cell stack current, A charge/discharge polarization constant, A/h PV field power, W fuel cell stack power generated, W ideal gas constant, J mol1 K1 series loss resistance, U shunt loss resistance, U battery internal resistance, U absorbed radiation, W/m2 the reference temperature for the enthalpy, K fuel cell nominal stack temperature, K cooling water temperature, K water heating temperature, K MH temperature, K normal operating cell temperature, K PV cell temperature, K ambient temperature, K

Tez Tez Tst Ud Ua VPV Vact Vbt,int Vbt Vbt Vconc Vetd Vez,0 Vez,ohm Vez Vfc,0 Vfc,ohm Vfc Vhv Vion Vst Vtn #ref aISC dB H_ reac Q_ cony Q_ cool Q_ forc Q_ gen Q_ loss Q_ nat _T W _ H2;ez m _ H2;fc;cons m _ H2;in m _ H2;out m l r rs s sB sez,t εMH εst aPV f h0f ;H2 O hforc hnat iao ico iez ifc k mst ndiode nez nmod pMH

11683

electrolyzer stack temperature, V electrolyzer temperature, K fuel cell stack temperature, K desorption heat transfer coefficient, W/(m2 K) absorption heat transfer coefficient, W/(m2 K) PV voltage, V fuel cell activation voltage, V battery internal voltage, V battery voltage, V constant voltage, V fuel cell concentration voltage, V electrolyzer electrode overpotential, V electrolyzer reversible potential, V electrolyzer ohmic overvoltage, V electrolyzer voltage, V fuel cell open circuit voltage, V fuel cell ohmic voltage, V fuel cell voltage, V electrolyzer higher-high-value voltage, V electrolyzer ionic overpotential, V fuel cell stack voltage, V electrolyzer thermoneutral potential, V variables at standard test,  shortecircuit temperature coefficient, V/K electrolyzer membrane thickness, mm the enthalpy flow rate,  convection heat, W electrolyzer cooling evacuated heat, W forced convection heat, W electrolyzer produced heat, W electrolyzer delivered heat, W natural convection heat, W W T electrolyzer power consumption, W electrolyzer hydrogen flow rate, g/h fuel cell consumed hydrogen flow, kg/s hydrogen supply flow rate, kg/s hydrogen output flow rate, kg/s membrane water content, molH2/molSO3 hydrogen gas density, kg/m3 MH density, kg/m3 Stefan-Boltmann constant, W/(m2 K4 electrolyzer membrane conductivity, S/cm electrolyzer time constant, s MH powder porosity,  fuel cell emissivity,  PV modified ideality factor,  MH volume ratio,  vapor formation mass specific enthalpy, W/kg forced heat transfer coefficient, W/K m2 natural heat transfer coefficient, W/(K m2) electrolyzer anode current density, A/cm2 electrolyzer cathode current density, A/cm2 electrolyzer current density, A/cm2 fuel cell current density, A/cm2 Boltzman constant, J/C fuel cell stack mass, kg diode ideality factor,  number of electrolyzer cells,  number of PV modules,  metal hydride bed equilibrium pressure, bar

11684

pH2;fc pH2;ez pMH pO2;fc pO2;ez pez psat q qH2;a=d;max qH2;a=d ybed

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 1 6 7 2 e1 1 6 8 4

fuel cell hydrogen partial pressure, bar electrolyzer hydrogen partial pressure, bar metal hydride bed pressure, bar fuel cell oxygen partial pressure, bar electrolyzer oxygen partial pressure, bar electrolyzer pressure, bar vapor partial pressure, bar electron charge, C maximum absorbed/desorbed hydrogen weight fraction, % w/w absorbed/desorbed hydrogen weight fraction, % w/w bed volume, m3

references

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