## 行政院國家科學委員會專題研究計畫 成果報告

### 植栽圍籬對低層建築風力通風之影響－非均一孔隙率之探 討

### 研究成果報告(精簡版)

### 計 畫 類 別 ： 個別型

### 計 畫 編 號 ： NSC 97-2410-H-216-007-

### 執 行 期 間 ： 97 年 08 月 01 日至 98 年 07 月 31 日 執 行 單 位 ： 中華大學景觀建築學系

### 計 畫 主 持 人 ： 張瑋如

### 報 告 附 件 ： 出席國際會議研究心得報告及發表論文

### 處 理 方 式 ： 本計畫可公開查詢

### 中 華 民 國 98 年 10 月 28 日

**Modulation of Cross Ventilation in a Residential ** **Building Using a Porous Hedge **

### Wei Ru Chang

^{* }

### and Cheng Li Cheng

^{** }

* Keywords*：

*Passive control, Porous hedge, Cross*

*ventilation, Porosity*

**ABSTRACT **

The present paper has performed a three- dimensional numerical model to study the cross ventilation in a residential building. Examined are the effects of porous hedge placed ahead of the building, and focused are the physical procedures governing air movement during the cross ventilation. The ratio of the space between the hedge and the building to the hedge height is fixed at L/h=2.0, while the hedge porosity is varied from η=0 to 1.0. Detailed information about the mean velocity, pressure, and turbulent kinetic energy is provided to illustrate how the porous hedge affects the cross ventilation in a building of two-side openings. It is found that the porous hedge could modify the mean and turbulent flow structures behind it, and thus alter the cross ventilation of the building.

Three types of cross ventilation can be characterized from the results presented, i.e., backward cross ventilation, null ventilation, and forward cross ventilation, respectively. Results further show that the distribution of volume-averaged turbulent kinetic energy has a local minimum value at about the null ventilation conditions.

**INTRODUCTION **

In a naturally ventilated building, the indoor air is renewed with the outdoor air using wind and/or buoyancy forces. The passive scheme not only improves indoor air quality and thermal comfort [1, 2]

but also, when applied properly, leads to a significant reduction of energy consumption in ventilating the buildings [3]. Most importantly, it can avoid the Sick Building Syndrome caused by poor design of active ventilation systems. The combination of the above merits establishes the natural ventilation as the best solution for improving the microenvironment.

Consequently, the study of natural ventilation has gained more and more attention in recent years [1-5]

### .

In a typical cross-ventilated building, wind- pressure differences along the facade create a natural air exchange between indoor and outdoor spaces. The ventilation rate depends on the strength and direction of wind forces and the resistance of the airflow path [6].

Direct introduction of outdoor air by wind forces, however, does not necessarily ensure a comfortable indoor environment because it gives no control over undesirable airflow patterns. If the cross ventilation of a building is poorly designed, even with an plenty of wind resources, the period during which windows can be left open is often limited due to uncomfortable wind intrusion. To control wind-driven airflow patterns and thus improving the indoor microclimate, a passive scheme using windbreaks such as forests, nets, and hedges has been employed to modify the cross-ventilation in a building [7]. The porous hedges act not only a shelter from a strong wind [8, 9] but also a regulator to channel airflow properly to ventilate a building. The objective of the present work is to extend the author’s 2-D work [7] to develop a 3-D numerical model to study the cross ventilation in a building that are controlled passively by using a porous hedge.

A successful design of wind-driven cross ventilation requires the detailed information of airflow and pressure distributions in and around buildings. The physical processes of wind-driven cross ventilation are

*Paper Received July, 2008. Revised February, 2009, Accepted April, *
*2009. Author for Correspondence: W.R. Chang *

** **Assistant Professor,*^{, }*Department of Landscape Architecture, Fu Jen *
*Catholic University, Taipei County, 24205, Taiwan, R.O.C., Email: *

*rubyweiru@gmail.com, *
* *

***** Professor, Department of Architecture, National Taiwan University *
*of Science and Technology, Taipei 106,Taiwan ROC. *

J. CSME Vol.30, No.5 (2009)

complex, and predicting the ventilation rates is difficult.

Although full-scale measurements for a building site can provide reliable data, the experiment is time consuming and hard to control. In addition, the discrete data are not informative enough. In most cases, the experimental data obtained from one building site may not be extended to another because of different weather data and building surroundings [5]. An alternative approach to study the cross ventilation in buildings is the computational fluid dynamics (CFD) technique.

The CFD technique is becoming popular due to its informative results and low labor and equipment costs.

In the present study three-dimensional CFD model is developed to study the cross ventilation in a building that are controlled passively by using a porous hedge.

The effect of the hedge porosity on the airflow characteristics in and around a residential building is examined. The phenomena of cross ventilation in the building are discussed from the detailed distributions of mean fluid flow, turbulent kinetic energy, and pressure distributions. The computational procedure, adopted for the evaluation of such a three-dimensional turbulent flow, is based on the solution of the governing equations for the dependent variables (such as three velocity components, the pressure and the turbulent kinetic energy) by means of the finite volume technique [10, 11]. The airflow is assumed to be steady and turbulent, which is described through the well-known k-ε turbulence model. It has been proven to be able to simulate quite well the mean flow and turbulent kinetic energy of a long, porous hedge standing on flat ground [12-14]. In addition, the k-ε model has an advantage of saving computing time, and thus has become the most widely used CFD method in many industrial applications. This is the reason why the model is employed in the present paper in resolving the problem mentioned above.

**THE MODEL **

A schematic drawing illustrating the airflow around
a residential building along with a porous hedge is
shown in Fig. 1. The origin of the coordinate system is
set at the rear edge of the porous hedge. The airflow is
from left to right. The porous hedge of height h is
placed ahead of the building. The distance between the
front edge of the building and the rear edge of the
porous hedge is 2h (L). The dimensions of the interior
space of the building are 2h by 3h by h (length by width
by height). The windward and leeward walls have a
**window of size 0.5h by h. Both windows are open that **
allows of cross ventilation in the building.

**Governing equations The ** airflow studied is

considered as three-dimensional, steady, isothermal, incompressible and turbulent. The fundamental equations governing the motion of the above flow are the averaged Navier-Stokes equations, and the continuity equation, which can be expressed as:

(1)

(2)

(3)

The turbulent fluxes of momentum ( ) are
important terms that govern the turbulent diffusion and
need to be specified by certain turbulence models in
order to fulfill the closure of the equation set. A number
of turbulence models, ranging from simple algebraic
models to second-moment closure models, have been
developed in the past decades. For simplicity, the
*standard k-*ε model is used in closing the equation set.

The correlation between the mean turbulent kinetic
*energy k and the dissipation rate of turbulence *ε is
expressed by the following equations:

(4)

(5)

where ν*t* is the turbulent diffusivity, and the
*Kronecker symbol. The transport equations for k and *
ε* are *

### (6) (7)

**Figure 1 Schematic drawing of the wind-driven**

**cross ventilation around the building.**

Porous hedge Windward window Leeward window

The model constants are also the standard values for wind-tunnel flows:

*C**µ**=0.09, C*ε1*=1.44, C*ε2=1.92,σ*k*=1.0, and σ^{ε}=1.3 [15]

The Darcy’s law describes the flow momentum within the porous hedge, i.e.,

(8) where η is the porosity of the hedge, representing the volume occupied by the pores, to the total volume of the porous solid. The permeability κ is a quantity of the surface area to volume ratio of the porous matrix. The last term in the above equation represents the Darcy’s drag imposed by the pore walls on the fluid within the pores, and usually results in a significant pressure drop across the porous solid.

**Grid creation and boundary As shown in Fig. 2, a **
half-sphere computational domain is employed to
simulate the fluid flow characteristics around the hedge
and building. In general, the fluid flow around the
building and the porous hedge is changed significantly.

Therefore, a fine mesh of high spatial resolution is created around these regions so that an accuracy prediction may be obtained. A total of 1,376,900 unstructured control cells are generated from the whole computational domain. Additional runs for a coarser mesh (1,590,000 cells) and a finer mesh (1,000,000 cells) are obtained by checking grid independence. A comparison of the results of the 1,376,900-cell mesh and the 1,590,000-cell mesh shows that the maximum discrepancy in the mean velocity profiles is 0.05 percent. This change is so small that the accuracy of the solutions on a 1,376,900-cell mesh is already satisfactory.

At the inlet of the computational domain (the upstream quarter sphere), a uniform velocity is imposed.

At the downstream section (the downstream quarter sphere), the averaged pressure is chosen as the reference pressure. There is no standard method for setting the turbulence kinetic energy and the dissipation rate in the free stream. In the present simulation, we assume 0.5% turbulence intensity in the free stream.

*Thus, k and *ε* at the inlet section can be calculated. All *
solid boundaries, such as ground and building walls, we
use non-slip conditions in conjunction with the wall
functions.

**The solution method ** In the simulation
processes, the highly coupled, nonlinear, partial
differential equations are discretized into a set of linear
algebraic equations by using the finite volume
discretization method [16-18]. Then, they are solved by
iterative solutions on each control cell, defined over the
computational domain. A balance between source terms,
convention and momentum fluxes is evaluated by the

continuity equation at the faces of each cell. The estimation of diffusion fluxes at the cell faces is obtained by a centered approximation, while the first order upwind approximation is adopted for the advection terms. The pressure-velocity linkage is solved via the SIMPLER algorithm [19].

**RESULTS AND DISCUSSION **

**Verification of the model** Before the subsequent
discussion about the computational results, it is
important to validate present numerical procedure and
data by comparing the present results with those in
previous works. Figure 3 shows a comparison of mean
*velocity ratios in x (U/U*h*) and z (W/U*h) directions
between the present predictions and the previous
experiments [12]. In this plot, the hedge porosity is
fixed at η=0.7, and the axial station selected for
comparison is at h/2 behind the hedge. It is seen that
both the experimental and simulated results reveal a
forward velocity behind the hedge, meaning that there
is no flow recirculation. Moreover, both results show a
*rather uniform distribution of U/U*_{h}* for 0.1<z/h<0.9, *
where the maximum discrepancy is less than 10%. In
the previous experiments, however, a large variation of
*U/U*h* and W/U*h* occurs at the elevation 0.9<z/h<1.0, *
where turbulence is significant due to the strong shear
flow. In general, the above comparisons are satisfactory
to confirm that the present numerical procedure is
adequate and the present numerical results reliable.

**Detailed fluid flow A comparison of mean-flow **
patterns around the building between the hedge-free
case and the solid-hedge case is shown in Figs. 4 and 5.

**Figure 2 Mesh distributions on the **
**computational domain. **

J. CSME Vol.30, No.5 (2009)

Figure 4 distributes the mean-velocity vectors on the
planes cutting across the middle of the computational
*module (y=0), whereas Fig. 5 visualizes the mean-flow *
traces around the building. Figures 4 (a) and 5 (a) are
the hedge-free cases, while Fig. 4 (b) and 5 (b) are the
results that the solid-hedge is placed ahead of the
building. The above results serve as a reference to
examine the effect of porous hedge on the cross
ventilation in the building.

It is seen from Fig. 4 (a) that the hedge-free case has a forward airflow that ventilates the building as it traverses through a sudden contracting and expanding channel. When a solid hedge stands ahead of the building (Fig. 4 (b)), the airflow is deflected significantly when it approaches the solid hedge, and then separates from the upstream salient of the solid hedge. The relatively low pressure behind the solid hedge (will be shown later) induces the airflow upstream. It thus forms a flow recirculation behind the solid hedge that ventilates the building reversely, with a backward airflow from the leeward window to the windward window.

A particle trace is helpful in visualizing the
mean-flow structures in a flow domain. It represents
well the trajectory of a massless particle moving in a
*fluid. In Fig. 5, four particles are released at points of (x, *
*y, z) = (6, 0, 2.75), (-1, 0, 2.75), (-1, 4, 1.5), and (-1, -4, *
1.5), respectively, and then move through the flow
domain. Each trace is shown by a curve together with
the velocity vectors. The color mapping is also
provided to illustrate the velocity magnitude along the
trace. It is seen from these figures that the trace #1 of
the hedge-free case penetrates the building directly
from the windward window to the leeward window. In
contrast, the trace #1 of the solid-hedge case circulates
the particle round the building. It enters the building
from the leeward window, then exits from the building
via the windward window, and finally turns upward and
moves downstream over the building roof. Traces #3
and 4 of the hedge-free case impinge on the front wall
of the building directly, while those of the solid-hedge
case are deflected by the solid hedge and pass the
building laterally.

As the discussion of Figs. 4 and 5, the flow structure around the building is strongly affected by the solid hedge. Therefore, before discussing the effect of porous hedge on the ventilated airflow in the building, it is important to understand the mean velocity distribution ahead of the building, which is regarded as the inlet/outlet conditions of the ventilated building.

Figure 6 shows the effect of the hedge porosity on the
*axial velocity (U) at the mid-station (x/h=1.0) between *
the porous hedge and the building on the symmetric
*plane of the computational module (y=0). It is seen that *
due to the blockage effect, the axial velocity decreases
with decreasing the hedge porosity from η =1.0 to 0.4.

At η = 0.2, a part of airflow moves upstream indicating that a flow reversal exits behind the porous hedge, which is like that of solid hedge (η = 0).

Focus is now put on the effect of porous hedge on
the cross ventilation in the building. Figure 7 compares
the distributions of mean-velocity vectors on the plane
cutting across the middle of the computational module
*(y=0) of various hedge porosities, i.e., *η = 0.2, 0.4, 0.6
and 0.8. The corresponding pressure distributions on
the plane are also provided in Fig. 8. Obviously, the
cross ventilation resulting from these four porosities are
quite different. At the highest porosity of η = 0.8 (Figs.

7 (a) and 8(a)), the high pressures near the windward
window results in a strong airflow into the building. It
traverses directly through the building like that of the
hedge-free case (Fig. 4 (a)). When the porosity
decreases to η =0.6 (Fig. 7 (b)), the strength of forward
ventilated airflow is reduced due to a higher blockage
of the porous hedge (Fig. 6). Meanwhile, the pressure
difference between two windows is lessened (Fig. 8
**Figure 3 Comparison of the present predictions **

**with previous works. **

(b)). As the hedge porosity further decreases to η =0.4 (Fig. 7 (c)), clearly, the indoor airflow is stagnant almost and the indoor pressures are rather uniform (Fig.

8 (c)). At the lowest hedge porosity of η = 0.2 (Fig.

7(d)), the backward airflow ventilates the building from the leeward window to the windward windows by the adverse pressure gradient in the building (Fig. 8(d)). It is similar to that of the solid hedge, which is dominated by the flow recirculation (Fig. 5 (b)) behind the solid hedge [20].

Figure 9 further shows the effect of the hedge
porosity on the pressure distribution along the elevation
*of z/h=0.58 on the symmetric plane of the *
*computational module (y=0). The solid and dashed *
curves represents the results of the solid-hedge (η = 0)
and hedge-free (η = 1.0) cases, respectively. It is
observed that the pressure for the hedge-free case
(dashed curve) increases before encountering the
building due to the blockage effect, decreases to a local
minimum in the building, then bumps up and down,
and finally recovers, after the lowest point, to normal

**(a) Hedge-free case **

**(b) Solid-hedge case (**η^{=0) }

**Figure 4 Comparison of mean-flow velocity **
**vectors at the sectional plane cutting across the **
**middle of the computational domain (y=0). **

**(a) Hedge-free case **

**(b) Solid-hedge case (**η^{=0) }

**Figure 5 Particle traces around the building for **
**the hedge-free and solid-hedge cases. **

**Figure 6 Axial mean velocity (U) distributions at ****the mid-station (x/h=1.0) between the porous ****hedge and the building on the module symmetric **
**plane (y=0). **

trace#4(-1,-4,1.5) trace#3(-1,4,1.5)

trace#2(-1,0,2.75) trace#1(6,0,2.75)

trace#4(-1,-4,1.5)

trace#3(-1,4,1.5)

trace#2(-1,0,2.75) trace#1(6,0,2.75)

J. CSME Vol.30, No.5 (2009)

* (a) *η

**=0.8**

* (b) *η

^{ =0.6 }* (c) *η

**=0.4**

* (d) *η

**=0.2**

**Figure 7 Effect of hedge porosity on the **
**distributions of mean-flow velocities on the **
**mid-plane (y=0) of the building. **

* (a) *η

^{ =0.8}* (b) *η

**=0.6**

* (c) *η

**=0.4**

* (d) *η

^{ =0.2 }**Figure 8 Effect of hedge porosity on the pressure **
**distributions on the mid-plane (y=0) of the ****building. **

level. It is further seen that the pressure for the solid-hedge case (solid curve) drops significantly as the airflow across the solid hedge. A relatively low pressure occurs in the region between the solid hedge and the building, which is attributed to the flow reversal [21].

When the porous hedge is placed ahead of the building, the pressures around the hedge and the building are ranged between the solid-hedge case and the hedge-free case. It is interesting to note that the pressures inside the building for η = 0.4 (dotted line) are rather uniform, meaning that the driving force for the cross ventilation is missing. This confirms the results displayed in Fig. 7 (c) showing a stagnant air inside the build.

It is concluded from the above discussion that the cross ventilation inside the building is strongly affected by the hedge porosity. The ventilation in the building can be characterized by thee categories, i.e., the backward cross ventilation (η = 0.2), null ventilation (η

~0.4), and the forward cross ventilation (η* = 0.6, and *
0.8), respectively.

**Ventilated airflow rate **

Figure 10 shows the
effect of porous hedge on the ventilated airflow rate
through the building. The abscissa of the plot is the
hedge porosity, and the ordinate is the airflow rate ratio
between the porous-hedge case and the hedge-free case,
i.e.,
(9)

The magnitude of the ventilated airflow rate ratio can
represent the shelter effect by the porous hedge. The
*smaller the absolute value of Se is, the higher the *
shelter effect of the porous hedge becomes. It is seen
from Fig. 10 that the ventilated airflow rate ratio
becomes negative as the porosity is lower than 0.37. It
indicates adverse ventilation from the leeward window
to the windward window. After η>0.37, the ventilated
airflow rate ratio increases with increasing the hedge
porosity. It can be illustrated by the velocity vectors
shown in Fig. 7 and the pressure distributions shown in
Fig. 8. Therefore, it is concluded that a critical hedge
porosity at about η* = 0.37 which results in null *
ventilation in the building. It is interested to note that
the present critical hedge porosity is higher than that
obtained for the previous study [7]. This may be
attributed to the present 3-D results accounted for the
lateral-flow effect that did not consider in the previous
2-D work. Figure 11 further shows the effect of the
hedge porosity on the volume-averaged turbulent
kinetic energy in the building. The volume-averaged
kinetic energy is represented as the following form,

(10)
**Figure 9 Pressure distributions at the elevation of **

**z/h=0.58 along the flow direction on the ****symmetric plane (y=0) of the computational ****domain. **

**Figure 10 Effect of the hedge porosity on the **
**ventilated airflow rate across the building. **

**Figure 11 Effect of the hedge porosity on the **
**volume-averaged turbulent kinetic energy in the **
**building. **

J. CSME Vol.30, No.5 (2009)

It is seen that the value of is high for the both the strong forward ventilation and adverse ventilation. A valley of the curve is found around the null ventilation.

**CONCLUDING REMARKS **

A three-dimensional numerical model has been
performed to examine the effect of porous hedge on the
cross ventilation in a residential building. The porosity
of the porous hedge is varied from η*=0 to 1.0. Results *
reveal that placing a porous hedge ahead of the building
is an effective scheme to modify the cross ventilation
by altering the airflow patterns. The cross ventilation
inside the building is strongly dependent of hedge
porosity. The shelter effect of the porous hedge can be
enhanced by decreasing the hedge porosity. An inverse
cross-ventilation of the building can be found for low
hedge porosity. From the results presented, it can be
characterized as the backward cross ventilation for η* < *

0.37, null ventilation for η* ~ 0.37, and the forward *
cross ventilation for η* > 0.37, respectively. Results *
further show that the distribution of volume-averaged
turbulent kinetic energy has a local minimum value at
about the null ventilation conditions.

**ACKNOWLEDGMENT **

This research was sponsored by the National Science Council of Taiwan under contract no. NSC 97-2410-H-216-007.

**REFERENCES **

[1] Hunt, G.R., Linden, P.F., The fluid mechanics of natural ventilation-displacement ventilation by buoyancy-driven flows assisted by wind, Building and Environment 1999; 34: 707-720.

[2] Aynsley R. Estimating summer wind driven natural ventilation potential for indoor thermal comfort. Journal of Wind Engineering and Industrial Aerodynamics 1999; 83:515–25.

[3] Lu, W.Z., Lo, S.M., Fang, Z., Yuen, K.K., A preliminary investigation of airflow field in designated refuge floor, Building and Environment 2001; 36: 219-230.

[4] Li, Y., Delsante, A., Natural ventilation induced by combined wind and thermal forces, Building and Environment 2001; 36: 59-71.

[5] Chen, Z.D., Li, Y., Buoyancy-driven displacement natural ventilation in a single-zone building with three-level openings, Building and Environment 2002; 37: 295-303.

[6] Chang, W.R., Effect of porous hedge on the cross ventilation in a residential building, Building and

Environment, 2006; 41: 549-556.

[7] Hwang, J.J., Dynamic Modeling of a Wind Hydrogen System, Journal of the Chinese Society of Mechanical Engineers, 2009; 30: 221-227.

[8] Hwang, J.J., Liou, T.M., Augmented Heat- Transfer in a Rectangular Channel with Permeable Ribs Mounted on The Wall, Journal of Heat Transfer, 1994; 116: 912-920

[9] Hwang, J.J., Liou, T.M., Heat-Transfer in a Rectangular Channel With Perforated Turbulence Promoters Using Holographic- Interferometry Measurement, International Journal of Heat and Mass Transfer, 1995; 38: 3197-3207

[10] Hwang, J.J., Lai, D.Y., Three-dimensional mixed convection in a rotating multiple-pass square channel, International Journal of Heat and Mass Transfer, 1998; 41: 979-991.

[11] Hwang, J.J., Chen, C.K., Savinell, R.F., Liu, C.C., Wainright, J., A three-dimensional numerical simulation of the transport phenomena in the cathodic side of a PEMFC, Journal of Applied Electrochemistry, 2004; 34: 217-224.

[12] Boldesa, U., Colmana, J., Maranon Di Leo, J., About the penetration of a horizontal axis cylindrical vortex into the nearby downwind region of a vertical porous fence, Journal of Wind Engineering and Industrial Aerodynamics 2003;

91: 859-872.

[13] Packwood, A.R., Flow through porous fences in thick boundary layer: comparisons between laboratory and numerical experiments, Journal of Wind Engineering and Industrial Aerodynamics 2000; 88: 1-24.

[14] Wilson, J.D., Numerical studies of flow through a windbreak, Journal of Wind Engineering and Industrial Aerodynamics 1985; 21: 119-154.

[15] Launder, B.E., Spalding, D.B., The numerical computation of turbulent flow, Computer Methods in Applied Mechanics and Engineering 1974; 3:

269-289.

[16] Hwang, J.J., Chen, P.Y., Heat/Mass Transfer In Porous Electrodes of Fuel Cells, International Journal of Heat and Mass Transfer, 2006; 49:

2315-2327.

[17] Chao C.H., Effect Local Thermal Non- Equilibrium on Porous Electrode In Fuel Cells, Journal of the Chinese Society of Mechanical Engineers, 2007; 28: 275-287.

[18] Hwang, J.J., Full Coverage of Two-Phase Transports In a Porous Electrode of a PEM Fuel Cell, Journal of the Chinese Society of Mechanical Engineers, 2008; 29: 195-205.

[19] Patankar, S.V., Numerical Heat Transfer and Fluid Flow 1980, Hemisphere, Washington, DC.

[20] Hwang, J.J., Liou, T.M., Heat Transfer and

Friction in a Low-Aspect-Ratio Rectangular Channel with Staggered Perforated Ribs on Two Opposite Walls, Journal of Heat Transfer, 1995;

117: 843-850

[21] Hwang, J.J., Cheng, C.S., Augmented Heat Transfer In a Triangular Duct by Using Multiple Swirling Jets, Journal of Heat Transfer, 1999; 121:

683-690.

## 運用多孔隙圍籬調節住宅 建築風力通風之研究

### 張瑋如

天主教輔仁大學景觀設計學系

### 鄭政利

國立台灣科技大學建築系

### 摘 ** 要 **

本文運用三維數值模型探討兩面開窗住宅建物 之風力通風狀況，主要在研究設置於建物前之多孔 隙率圍籬對於穿越氣流之影響，包括平均速度、壓 力與紊流動能強度之變化。圍籬建物間距離與圍籬

高度之比固定為L/H=2.0，而圍籬孔隙率變化為η=0

到 1.0。研究結果顯示，多孔隙圍籬會影響穿越建物 的氣流結構，進而改變建物室內外的通風型態。本 研究歸納出三種典型的通風模式，分別為「逆向通 風」、「無通風」，以及「正向通風」。研究亦發 現在無通風狀態下體積平均紊流動能強度會達到相 對最低值。

### 行政院國家科學委員會補助國內專家學者出席國際學術會議報 告

### 2009年 7月 31 日 報告人姓

### 名

### 張瑋如

### 服務機構 及職稱

### 中華大學景觀建築系 助理教授

### 時間 會議 地點

### 98/07/19~98/07/23 美國舊金山Westin St.

### Francis飯店

### 本會核定 補助文號

### NSC 97-2410-H-216-007

### 會議 名稱

### (中文) 第三屆國際永續能源會議

### (英文) ASME 3rd International Conference on Energy Sustainability 發表

### 論文 題目

### (中文)

### (英文) Dynamic Modeling Of A Wind Hydrogen System

### 參加1.會議經過

### 第 三 屆 國 際 永 續 能 源 會 議 (ASME 3rd International Conference on Energy Sustainability) 於美國舊金山的Westin St. Francis飯店舉行，平行會議有Heat Transfer 2009與InterPACK’2009。 會議時間為98年7月19日至23, 本人於7月月16日出發搭乘華航 晚上班機飛往舊金山。

### 從2006開始每年由美國機械工程師學會(ASME)主辦的國際永續會議，今年是第三 屆。 根據大會資料顯示，此次大會有來自全世界三十餘國及地區，總計超過五百人與 會。 參與會議的人員有35%是來自工業界與政府機構的R&D人員，而65% 則是來自一 般學術或研究機構的研發人員。 從國家來區分，與會人員有58%是來自美國本土，其 餘42%則是來自世界各地。

### 本次大會共安排了兩場聯合會議專題講座 （Joint Conference Keynote Address) 、四 場大會專題演講（Energy Sustainability Conference Plenary Address)、以及一場 Yellot Award獲獎者演講 。第一場聯合會議專題講座是由美國國家再生能源實驗室 (National Renewable Energy Laboratory, NREL)主任Dr. Dan Arvizu所主講的“Frontiers of Research in Renewable Energy”，第二場則是GE（General Electric Corporation)資深副總裁 Mr.

### Mark M. Little所主講的“Advanced Energy Systems and Sustainability”；四場大會專題

### 所主講的“Efficient Use of Our Natural Gas Resources -An Important Component of Energy Sustainability”、由Chevron Energy Technology Co.資深計畫工程師 Dr. Trevor Demayo 所主講的”How Can We Measure Energy System Sustainability?”、以及由University of Minnesota的Professor Jane Davidson 所主講的“Solar After Dark: Storage Options”；而 Yellot Award的得主的Professor Aldo Steinfeld (ETH Zurich)的演講題目則是”Fuels from Sunlight, Water, and CO2”。除了上述專題演講外，會場同時有各種潔淨能源設備與相 關之量測器材展示，內容相當豐富。

### 本次會議共計有280篇論文發表，共分成二十五項子題，依論文特性分成21個場次 同時進行。本人文章發表時間為第二天（20日）下午 ，約有三十幾人與會聆聽，由於 本篇論文是首度完成再生氫能系統動態模擬論文，引起在場與會人員相當大的回響，演 講後的討論氣氛極為熱絡，問答不斷，由於時間不足，會後還到場外交換心得、互贈論 文，受益匪淺。

### 與會2. 與會心得

### 本會議是因應目前全球發展潔淨能源技術所召開的學術研討會，會場同時來自全世 界各先進國家的潔淨能源產品與技術之展示，這種大規模展覽會與矸討會結合的方式，

### 是一項趨勢，國內會議也逐漸往這個趨勢發展，參與此次會議受益良多，感觸亦深，最 重要的還是要再一次強調學術與產業結合的重要性，台灣的產業要升級一定要有強大的 學術研究能力當基礎，否則只是空談，而台灣所召開的學術研討會目前也有與產業密切 結合的相同趨勢，兩者互相配合、齊力並進，才能夠提昇台灣科技競爭力 。

### 最後感謝國科會提供經費補助，使本人能順利參加本會議。

### 3.考察參觀活動(無是項活動者省略)

### 無 4.建議

### 新能源的研發已是必然趨勢，其中燃料電池的應用在國際間即受到相當的重視，

### 建議國內相關環境規劃設計產業亦能投入研發行列

### 5.攜回資料名稱及內容

### (1) (1)2010ASME Heat Transfer與Energy Sustainability徵文通告。

### (2) (2)會議手冊乙份。

### (3) (3)親自拍攝展覽會照片乙批。

### 6.其他

### 無

**ES2009-90221 **

**DYNAMIC MODELING OF A WIND HYDROGEN SYSTEM **

**J. J. Hw ang/Department of Greenergy **
**Technology, National Univ ersity of Tainan, **

**Taiw an **

**W.R. Chang/Department of Landscape **
**Architecture, Chung-Hua Univ ersity, Taiw an **

**ABSTRACT **

Dynamic behaviors of an integrated wind hydrogen system have been modeled mathematically. It is based on a combination of fundamental theories of mechanics, thermodynamics, mass transfer, fluid dynamics, and empirical electrochemical relationships. The model considers wind hydrogen system to be composed of three subsystems, i.e., a wind generator, an electrolyzer, and a hydrogen tank. An additional pressure switch model is presented to visualize the hydrogen storage dynamics under a constant outflow condition.

Validation of the wind hydrogen model system is evaluated according to the measured data from the manufacturer’s data.

Then, using wind power as the primary energy input and hydrogen as energy storage simulated the power system.

Finally, flow and electrical characteristics and efficiencies of each subsystem as well as the entire system are presented and discussed. The present model will integrate with fuel cell systems to realize the stand-alone renewable power generator in the future work.

**INTRODUCTION **

The environmental impact of burning fossil fuels and their inevitable depletion have led to a growing interest in renewable energy sources. These sources of energy can no longer be overlooked, because of the need to achieve sustainable development and compliance with the provisions of the recently enforced Kyoto protocol. Wind energy, for example, is available almost everywhere. It can be harnessed to provide electricity at some of the lowest costs available for new generation [1]. Coupling wind turbines to hydrogen-generating

electrolyzers has the potential to provide low-cost, environmentally friendly distributed generation of hydrogen in addition to electricity [2-10]. In this way, hydrogen generation can be a pathway for wind generation to contribute directly to reducing the dependence on fossil fuels. The objective of the present paper is to develop a simulation model that effectively predicts the dynamic behaviors of a wind hydrogen system that comprises subsystems including a wind generator, an electrolyzer, and a hydrogen tank. The integrated model is implemented by using Simplorer simulation platform. The effects of constant hydrogen consumption are examined to demonstrate the transient dynamic behaviors at the standby conditions of a wind hydrogen fuel cell (WHFC) system. It also verifies the effectiveness of the proposed management approach for operation of the integrated wind hydrogen system.

Figure 1 shows a typical wind hydrogen fuel cell system.

It consists of a wind generator, a pressurized alkaline electrolyzer for H2 production, a pressurized tank for H2

storage, fuel cells for H2 utilization, a secondary battery bank
for electricity energy buffer, and a DC/AC inverter for the user
load [11, 12]. Wind generators convert wind energy into
electricity. Since the large fluctuations in power are together
with the wind energy, a battery bank serves as an instantaneous
and daily energy buffer for storing the fluctuating power
coming from the wind-power generators. For an electrolyzer,
the H_{2} generation rate is proportional to the current into the
water electrolysis. For space saving and better system
performance, H_{2} will be produced and stored under high
pressure. If neither the wind generator nor the battery can
provide sufficient electricity, the fuel cell will utilize H2 to

produce electricity for the load. The fuel cell needs a DC/DC converter to transform its output voltage level to the DC bus voltage [12, 13]. Since the fuel cell cannot promptly follow a sudden load change and its output voltage changes slowly, it behaves as a constant current/power source. A microprocessor- based controller is used to monitor the status of all wind hydrogen system devices, control and protect them, and coordinate the overall system operation. In the present model, focuses are put on the wind hydrogen subsystem, as shown by a shaded block in Fig. 1. The wind generator supplies electrical energy demand of the electrolyzer for hydrogen production.

The hydrogen is then stored in a pressurized tank before needed. A pressure switch ahead of the electrolyzer controls the electrolyzer. When the hydrogen pressure is lower than the set pressure, the pressure switch keeps contact to supply the hydrogen again. If the pressure in the hydrogen tank exceeds the set threshold pressure, the pressure switch cuts off the electrolyzer. In the present simulation, the fuel cell keeps its standby conditions. Thus, a small of amount of hydrogen is consumed by the power requirement of BOPs that reduces the pressure in the H2 tank. That is the pressure switch is used to control a uniform pressure level in the hydrogen tank.

**MODELING **

**Wind generator model ** As shown in Fig. 1, the wind
generator consists of a squirrel cage induction generator
connected to the wind turbine rotor through a gearbox:

• Wind turbine: horizontal axis, three blades, and variable pitch angle.

• Transmission system: gearbox.

• Electric generator: asynchronous generator.

As the wind turbine is placed in an animate air, the amount of
power transferred to a wind turbine is directly proportional to
the density of the air (ρ*), the area swept out by the rotor (A) and *
*the cube of the wind speed (V) [14]: *

(1)

*where C**p* is the power coefficient. It is a function of the tip
*speed ratio and the blade pitch angle for pitch regulated wind *
turbines. The rotor limits the power extracted from the wind by
controlling the blade pitch angle (pitch regulated wind turbine)
to decrease the rotor aerodynamic efficiency for high wind
speeds and thus limiting the mechanical power extracted from
the wind. According to Betz' law, a wind turbine can extract at
most 59% of the energy that would otherwise flow through the
*turbine's cross section, that is C** _{p}* can never be higher than 0.59
in the above equation. The tip speed ratio λ

*is defined as*(2)

where ωr* is the angular speed of the rotor blade and R is the *
blade length. Applying the actuator disk theory [14, 15], the
rotor model provides the aerodynamic torque extracted from
the wind by the following equation
(3)

Usually the rotational speed of the wind turbine is slower than the equivalent rotation speed of the electrical network. Typical rotation speeds for a wind generators are 5-20 rpm while a directly connected machine will have an electrical speed between 750-3600 rpm. Therefore, a gearbox is inserted between the rotor hub and the generator. In the present power systems, the drive train model is usually represented by two masses [16] as shown in Fig. 2. The first mass stands for the wind turbine rotor (blades, hub and low-speed shaft), while the second mass stands for generator rotor (high-speed shaft). The equations of the model are (4) (5)

(6)
*where K*mc* and D*mc are the stiffness and damping of the
*mechanical coupling of the drive train, respectively. J*_{b}* and J*_{g}
are the inertias of the wind turbine blade and generator,
*respectively. T*_{m}* and T*_{g} are the generator mechanical torque and
the generator electrical torque, respectively.
The asynchronous machine equations, expressed in a
reference frame rotating at synchronous speed and taking
positive currents going out from the machine, are [17, 18]:
(7)
(8)

(9)

(10)

(11)

(12)

(13)

(14)
where the sub-indexes (s, r) stand for the rotor and stator
quantities, respectively, and the sub-indexes (d, q) stand for the
components aligned with the d-and q-axis in a synchronous
rotating reference frame. Variable φ represents the flux linkage,
*v the voltage and i the current. *ωs and ωg are the synchronous
*and generator rotor speed, respectively, while s is the slip *
*defined as s=(*ωs-ωg)/ωs. The electric parameters of the machine,
*R*s*, X*s*, X*m*, R*r* and X*r, stand for the stator resistance and
reactance, mutual reactance and rotor resistance and reactance,
respectively. All variables are in per unit. The parameters of the
wind generator are given in Table 1.

**Electrolyzer model ** The electrolyzer is a crucial part
in a wind hydrogen system, and the technical challenge is to
make it operate smoothly with intermittent wind energy
sources. Most of the R&D on water electrolysis related to
renewable hydrogen projects have focused on alkaline systems

still too high, and the market for small-scale H2-production units is at present day still relatively small.

An alkaline water electrolyzer consists of several electrolyzer cells connected in series. The electrolyzer model [22-25] considered here is based on the characteristics of individual cells. The calculations of the required operation voltage and the mass flow rates of hydrogen and oxygen are all done on a per cell basis, while the corresponding values for the whole electrolyzer unit are simply found by multiplying by the number of series cells. The equation that describes the behavior of the electrolyzer is:

(15)

The overpotentials represent here the surplus of electrical
voltages necessary to activate the electrode reactions and to
overcome the concentration gradients. All of the overpotentials
depend on the current density and are calculated by the same
manner of the fuel cell. According to Eq. (15), the simplified
circuit diagram of an alkaline water electrolyzer cell is
displayed in Fig. 3. The following equation expresses the
*theoretical equilibrium cell voltage V*_{OCV}* of the alkaline water *
electrolyzer under the effective working conditions, such as
temperature and pressure:

(16)

*where V*o is the reversible cell voltage at standard conditions,
, the operating pressure of hydrogen, and, , the
water vapor partial pressure.

The ohmic overpotential can be represented by

(17)

*where R*_{el}* is the internal resistance of the electrolyzer, and given *
by and:

(18)

*The electrical conductivity σ*_{k} of the electrolyte KOH is given
by

(19) where is the mass concentration of potassium hydroxide.

According to the partial reactions during the electrolysis of an
alkaline solution at the cathode and the anode, the total current
*density j consists of two parts, the cathodic and anodic parts. *

(20)

*The activation overpotentials at the cathode and the anode in *
the electrolyzer are calculated using the Butler-Volmer
equations:

(21)

The production rates of hydrogen ( ) and oxygen ( ) in an electrolyzer cell can be calculated by:

(23)

where * and N**S* are the Faraday’s efficiency and number of
series cells, respectively. The operational parameters for the
**above electrolyzer are given in Table 2. **

**Pressure switch model ** In the present system, a normal
closed contact switch is employed to switch the electrolyzer on
(signal 0) and off (signal 1) depending on the hydrogen
pressure in the tank. For stability, a 2-point regulation method
is employed to control the pressure switch. The threshold
pressure and its corresponding hysteresis are 500 kPa and 20
kPa, respectively. That is when the hydrogen pressure in the
tank exceeds 500 kPa, the electrolyzer is switched off to stop
producing hydrogen. If the hydrogen pressure in the tank is
lower than 480 kPa, the pressure switch breaks contact to
electrolyzer that produces the hydrogen.

**Model scheme ** In this work, a multi-domain
simulation program Simplorer is employed to model the wind
hydrogen system. It is a quasi-steady simulation tool with a
modular structure and can offer a wide variety of algorithms to
determine characteristic values, such as average and rms values
or rise and fall time during a transient simulation. Besides
classic gradient-based algorithms, it also offers a sophisticated
genetic optimizer. Conventional manual optimization (trial and
error) can handle only a small number of parameter variations
and is useful for 2 or 3-dimensional parameter spaces. In
**contrast, Simplorer can handle higher order problems by using **
automated optimization algorithm. Therefore, a wide range of
influences can be taken into account. In addition, it is
composed of linked modules and can be integrated into other
**simulation programs (e.g., MATLAB Simulink). **

**RESULTS AND DISCUSSION **

Windpower is the only primary power source in the wind hydrogen system. It represents the inlet conditions of the present model. As shown in Fig. 4, two kinds wind dynamics are studied, i.e., uniform wind speeds (Case 1) and hill-like distributions of wind speeds (Case 2).

Figure 5 shows the dynamic behaviors of the electrolyzer and hydrogen tank of Case 1. It is seen that the wind generator with uniform wind speed starts the electrolyzer with constant voltages and currents. The electrolyzer produces the hydrogen that keeps flow rate into the tank at a high level. Meanwhile the the pressure in the hydrogen tank increases linearly due to accumulation of hydrogen. When the hydrogen pressure reaches to 500 kPa, the electrolyzer switched off to stop producing hydrogen. The hydrogen begins flowing out of the tank with a constant flow rate. It is used to provide the auxiliary

power of the standby fuel cell subsystem. Therefore, the hydrogen pressure in the tank decreases gradually. When the hydrogen pressure is reduced to 480 kPa, the electrolyzer is reactive to produce hydrogen again. The slight zigzag of pressure distribution reflects the control strategy of the pressure switch mentioned above, which keeps the pressure in the hydrogen tank in a relatively uniform level, 490 ± 10kPa.

The efficiency of the wind hydrogen system is defined the ratio of hydrogen enthalpy flow to the total windpower across the wind turbine, i.e.,

(24)

Essentially, Eq. (24) can be also represented by the production of the subsystem efficiencies, i.e., wind turbine efficiency ηtb, gearbox efficiency ηgb asynchronous generator efficiency ηag, AC/DC invertors efficiency ηac/dc, and water electrolyzer efficiency ηZER. The turbine efficiency is represented by the ratio of the mechanical power delivery by the turbine blades to the windpower input to the wind turbine, while the generator efficiency is defined as the ratio of the shaft work to the produced electrical work. The electrolyzer efficiency is defined as the ratio of the hydrogen production rate to the power requirement of the electrolyzer. Thus, the efficiency of the wind hydrogen system can be represented by

(25) Figure 6 shows the dynamics of the wind hydrogen system efficiency along with some selected subsystem efficiencies for Case 1. Except for the idle conditions, the efficiencies of turbine, generator, and electrolyzer are 43%, 77%, and 58%, respectively. The wind hydrogen system efficiency is about 19% (wind speed 5m/s).

Figures 7 and 8 respectively show the dynamics of the power outs and efficiencies of the wind generator for Case 2. It is seen that the windpower increases sharply with an increase of wind speed since the power contained in the wind is proportional to the cubic of wind speed (Eq. 1). As shown in Fig. 8, after the cut-in wind speed, the turbine efficiency slightly increases and then decreases with increasing wind speed. It has the local minimum at the peak of wind speed distributions. As for the generator, the efficiency slightly increases with increasing the wind speed.

Figure 9 shows the dynamics of the electrolyzer and the hydrogen tank. At the initial stage, the wind is too small to drive the turbine to power the electrolyzer. Therefore, the pressure in the hydrogen tank decreases gradually due to the hydrogen consumption by the standby power requirement of the fuel cell subsystem. When the wind speed increases over the cut-in speed, the generator is active by the windpower and simultaneously the electrolyzer begins to produce hydrogen.

The hydrogen pressure in the tank thus increases gradually. A sharp increase in the hydrogen production rate fills up the hydrogen tank quickly. When the pressure reaches to 500 kPa, the electrolyzer is switched off and then the hydrogen pressure in the tank is gradually decreased again. Figure 10 shows the

dynamics of the efficiency of the wind hydrogen system. The efficiencies of wind generator and electrolyzer are also included for comparison. Under the active conditions, the efficiency of present wind hydrogen system decreases with increasing ambient windpower, which is ranged from 10% to 14%.

**CONCLUSIONS **

Exploiting conservation of mass, momentum and energy in a wind hydrogen system has developed a dynamic model in this paper. The majority of the system includes wind generators, an electrolyzer, and a pressured hydrogen tank. Special attention has been given to the modeling of subsystems to clearly quantify the dynamic interactions among each part of the wind hydrogen system. The integrated model is implemented by using Simplorer simulation platform. Case studies of examining the wind-speed effects have demonstrated that the model can capture the transient dynamic behaviors of the wind hydrogen system. It also verifies the effectiveness of the proposed management approach for operation of a stand-alone wind hydrogen system, which is essential for determining control strategy to ensure efficient and reliable operation of each part of the wind hydrogen system. Furthermore, the wind hydrogen dynamic model can be integrated with fuel cell system models to design, analyze and optimize the sustainable energy systems.

The extension of this study will be to fully validate the model in our future work.

**ACKNOWLEDGMENTS **

This research was partly sponsored by the National Science Council of Taiwan under contract no. NSC 95-2212-E-451-002.

**REFERENCES **

[1] Neville, R.C., “Wind Energy Conversion,” Elsevier Science, 1995.

[2] Turner J.A., Sustainable hydrogen production, Science 2004; 305:972–974.

[3] Nowotny J., Sorrell CC, Sheppard LR, Bak T. Wind- hydrogen: environmentally save fuel for the future. Int J Hydrogen Energy, 2005; 30:521–544.

[4] Schucan T.H., Case studies of integrated hydrogen energy systems, Report, IEA/H2/T11/ FR1-2000, International Energy Agency Hydrogen Implementing Agreement Task11- Integrated Systems, Operating agent:

National Renewable Energy Laboratory, Golden, Colorado, 1999.

[5] Dutton A.G., Bleijs J.A.M., Dienhart H., Experience in the design, sizing, economics, and implementation of autonomous wind-powered hydrogen production systems, Int J Hydrogen Energy, 2000; 25:705–722.

[6] Stantarelli M., Calı` M., Macagno S., Design and analysis of stand-alone hydrogen energy systems with different renewable sources, Int J Hydrogen Energy, 2004;

29:1571–1586.

[7] Vidueira J.M., Contreras A., Veziroglu T.N., PV autonomous installation to produce hydrogen via

production by water splitting with a conversion efficiency of 18%, Int J Hydrogen Energy, 2007; 32: 3248-3252 [9] Bechrakis D.A., McKeogh E.J., Gallagher P.D.,

Simulation and operational assessment for a small autonomous wind–hydrogen energy system, Energy Conversion and Management, 2006; 47: 46-59

[10] Iqbal M.T., Modeling and control of a wind fuel cell hybrid energy system, Renewable Energy, 2003; 28: 223- 237.

[11] Luque A., Marti A., Increasing the efficiency of ideal wind-power generators by photon induced transitions at intermediate levels, Physical Review Letters, 1997;

78(26): 5014-5017.

[12] Hwang J.J., Wang D.Y., Shih N.C., Lai D.Y., Chen C.K., Development of fuel-cell-powered electric bicycle, J.

Power Sources, 2004; 133: 223-228

[13] Hwang J.J., Wang D.Y., Shih N.C., Development of a lightweight fuel cell vehicle, J. Power Sources, 2005;

141:108-115.

[14] Heier, S. Grid Integration of Wind Energy Conversion Systems, John Wiley and Sons, 1998.

[15] Freris L.L., Wind energy conversion systems, Prentice Hall, 1990.

[16] Ledesma P., Usaola J., Rodrı´guez J.L., Transient stability of a fixed speed wind farm, Renewable Energy, 2003; 28: 1341–55

[17] Holdsworth L., Wu X.G., Ekanayake J.B., Jenkins N., Comparison of fixed speed and doubly-fed induction wind turbines during power system disturbances, IEE Proc Gener Transm Distrib, 2003; 150 (3): 343–52 [18] Kundur P., Power system stability and control, New York,

McGraw-Hill, 1994.

[19] Wang J.T., Savinell R.F., Simulation studies on the fuel electrode of a H2-polymer electrolyte fuel cell, Electrochimia Acta, 1992; 37(15): 2737-2745.

[20] Yamaguchi M., Shinohara T., Taniguchi H., Nakanori T.,
Okisawa K., Development of 2500 cm^{2} solid polymer
electrolyte water electrolyzer in WE-NET, Proceedings of
the 12^{th} World Hydrogen Energy Congress, Buenos Aires,
21–26 June 1998. p. 747–55.

[21] Gorgun H., Dynamic modeling of a proton exchange membrane (PEM) electrolyzer, 2006; 31: 29-38.

[22] Gerd Wedler, Lehrbuch der Physikalischen Chemie, Third Edition, VCH Publisher mbH, D-6940 Weinheim (Federal Republic of Germany), 1987.

[23] Carl Hamann, Wolf Vielstich, Elektrochemie, Third revised Edition, WILEY-VCH.

[24] Hartmut Wendt, Electrochemical hydrogen technologies, Electrochemical Production and Combustion of Hydrogen, Elsevier, 1990.

[25] Hans Dieter Baehr, Thermodynamik, Eine Einführung in die Grundlagen und ihre technischen Anwendungen, Ninth Edition, Springer Publisher 1996.

**Performance ** **Value ** **Unit **

Air density 1.229 kg/m

Number of blade 3 -

Rotor radius 2.15 m

Start-up wind speed 2.5 m/s

Cut-in wind speed 2.0 m/s

Rated power 50 kW

Rated wind speed 11 m/s

Rated rotor speed 110 rpm

Furling wind speed 12 m/s

Max. design wind speed 60 m/s

**Table 2 Parameters and coefficients of the electrolyzer **

**Parameters ** **Symbol Value ** **Unit **

Number of cells *N**s* 30 -

Cross section area of

the electrolyte *A**c* 150 cm²

Distance between

electrodes (Electrode Gap) *d**e* 0.0003 cm
Surface factor of

electrodes *f*_{air} 44.5 -

Cathodic standard

exchange current density 0.12×10^{-3} A/cm²
Anodic standard

exchange current density 0.12×10^{-6} A/cm²
Cathodic transfer

coefficient αc 0.5 -

Anodic transfer

coefficient αa 0.3 -

**Figure 1 Typical wind hydrogen fuel cell (WHFC) power **
**system. **

**Figure 2 Structure and equilibrium circuit diagram of the **
**wind generator. **

**Figure 3 Simplified circuit diagram of the water electrolysis **
**cell. **

**Figure 4 Inlet conditions of the present model, wind **
**dynamics. **

**Figure 5 Dynamic behaviors of the electrolyzer and **
**hydrogen tank for Case 1. **

**Figure 6 Efficiencies of the subsystems of the wind **
**hydrogen system for Case 1. **

**Figure 8 Efficiencies of subsystems of the wind generator **
**for Case 2. **

**Figure 9 Dynamic behaviors of the electrolyzer and **
**hydrogen tank for Case 2. **

**Figure 10 Dynamics of the efficiency of the wind hydrogen **
**system for Case 2.**