**3.2 Wind model**

126 Fossil Fuel and the Environment

 T

Total Fc Fc *.*dt *.*

the engine, 'kW\_A' is the rating of the electric generator, 'Fc' is the total fuel consumed in kg (lbs), 'dt' is the simulation time-step, and 'T' is the simulation period. The fuel consumed in kg (lbs) is obtained by multiplying the fuel consumption rate of kg/hr (lbs/hr) by the simulation time-step 'dt' (given in hours), and the total fuel consumption in kg (lbs) is

When two or more DEGs supply the load, it is important that the DEGs operate optimally.

1. The electrical generator (Fig. 3) and diesel engine (Fig. 4) performance curves are used

4. The point of intersection of the two curves is the optimal point of operation for DEG 2.

5. If the two curves do not intersect, the optimal point is taken as 0. This situation implies

Fig. 5 shows the overall fuel consumption curves for the two DEGs and the optimal point of operation for DEG 2. In order to avoid premature mechanical failures, it is important that DEGs operate above a particular load (generally 40% of rated). The long-term operation of DEGs at light loads leads to hydrocarbon built-up in the engine, resulting in high maintenance cost and reduced engine life (Malosh & Johnson, 1985). If the optimal point is

> DEG 1 DEG 2

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>100</sup> <sup>0</sup>

Load (%)

The following steps are performed to find the optimal point of operation for DEG 2.

*.*

to determine overall fuel consumption for the given load profile.

3. The fuel consumption for each DEG is noted at different load points.

that DEG 1 is efficient throughout the operating range of the load.

less than 40% load, it is adjusted so that DEG 2 operates at or over 40% load.

Optimal point for DEG 2

Beyond this point DEG 1 is more efficient than DEG 2.

where ' Fc *.*

obtained by integrating the term ' F <sup>c</sup>

2

Fig. 5. Optimal point of operation for DEG 2.

4

6

8

10

Fuel consumed (Lbs/hr)

12

14

16

18

2. The load on the DEGs is varied from 0 to 100%.

0

' is the fuel consumption rate in kg/hr (lbs/hr), 'Leng' is the percentage load on

dt' over the period of the simulation.

(4)

The *Wind Model* block calculates the total power available from the wind turbines based on the power curve. The power curve gives the value of the electrical power based on the wind speed. The wind turbine used in this simulation is the 15/50 Atlantic Orient Corporation (AOC). Fig. 6 shows the power curve for the 15/50 AOC wind turbine generator (AOC, 2007). This block calculates the power available from the WTGs depending on the speed of wind based on a look-up table (Table 1).

The wind model block also calculates the second law efficiency of the WTG. The second law efficiency of the WTG is given as

$$
\eta\_{\text{secondlaw}} = \frac{\text{actual power}}{\text{max possible power}} \tag{5}
$$

where 'ηsecond\_law' is the second law efficiency of the WTG, 'actual\_power' is the actual power output from the WTG and 'max\_possible\_power' is the maximum possible power output from the WTG.

Fig. 6. Power curve for 15/50 Atlantic Oriental Corporation WTG [13].

The actual power of the wind turbine is obtained from the manufacturer's power curve and the maximum possible power is obtained from the Betz formula described in (Patel, 1999) as

$$\mathbf{P}\_{\text{max}} = \frac{1}{2} \rho \mathbf{A} \mathbf{V}^3 \times \begin{pmatrix} 0.59 \end{pmatrix} \mathbf{P}\_{\text{max}} \tag{6}$$

where 'Pmax' is the maximum possible power, 'ρ' is the density of air taken as 1.225 kg/m3 (0.076 lb/ft3) at sea level, 1 atmospheric pressure i.e. 101.325 kPa (14.7 psi), and a temperature of 15.55°C (60°F), 'A' is the rotor swept area in m2 (ft2), 'V' is the velocity of wind in m/s (miles/hour), and the factor '0.59' is the theoretical maximum value of power

Energy-Efficient Standalone Fossil-Fuel Based

from the PV array.

manufacturer's data sheet.

model can be used for cold region applications.

**3.5 Fuel consumption and emissions** 

the generator and the total cost of fuel in USD are calculated as

**3.4 Battery model** 

of the battery bank.

and

Hybrid Power Systems Employing Renewable Energy Sources 129

T PV PV 0

where 'PPV' is the power obtained from the PV array (kW), 'ηpv' is the efficiency of the solar collector, 'ins' is the solar insolation (kWh/m2/day), 'A' is the area of the solar collector/kW, 'PV' is the rating of the PV array (kW), and EPV is the total energy obtained

The efficiency of the solar collector is obtained from the manufacturer. The data sheets for the solar panels manufactured by Siemens and BP are available in Appendix 4 of (Agrawal, 2006). The solar insolation values are available from the site data or can be obtained by using the solar maps from the National Renewable Energy Laboratory website (NREL GIS Solar Maps, 2007). The area of the solar collector depends on the number of PV modules and the dimensions of each module. The number of PV modules depends on the installed capacity of the PV array and the dimensions of each PV module are obtained from the

In the Simulink® model, the battery bank is modeled so that it acts as a source of power, rather than back-up power. The battery model block controls the flow of power to and from the battery bank. A roundtrip efficiency of 90% is assumed for the battery charge and discharge cycle. The battery model incorporates the effect of ambient temperature as described in (Winsor & Butt, 1978) into the hybrid power system model. Therefore, the

The life of the battery bank depends on the depth of discharge and the number of charge discharge cycles. In the Simulink® model the battery bank is modeled so that it acts as a source of power rather than back-up power. Therefore, the depth of discharge of the battery-bank is assumed between 95% and 20% of the rated capacity. This higher depth of discharge reduces the number of battery operating cycles for the same energy output. It should be noted that the number of battery cycles plays a more significant role in the life

The *Calculate Other Parameters* block calculates parameters like the total kWhrs/gallon supplied by the generator, the fuel consumed in lbs, the fuel consumed in gallons, the total cost of fuel in USD, the amount of CO2 emissions, the amount of particulate matter (PM10) emissions, and the amount of NOx emissions. For example, the kWhrs/gallon supplied by

> Gen C

kWhr kWhrs/gallon F (10)

Total cost (USD) F \*cost/ <sup>C</sup> gallon , (11)

E P .dt , (9)

coefficient of the rotor (Cp) or theoretical maximum rotor efficiency which is the fraction of the upstream wind power that is captured by the rotor blade. It should be noted from (6) that the wind power varies with the cube of the air velocity. Therefore, a slight change in wind speed results in a large change in the wind power.


Table 1. Look-Up Table for the 15/50 AOC Wind Turbines

The air density 'ρ' can be corrected for the site specific temperature and pressure in accordance with the gas law

$$
\rho = \frac{\mathbf{p}}{\mathbf{R}\mathbf{T}} \tag{7}
$$

where 'ρ' is the density of air, 'p' is the air pressure, 'R' is the gas constant, and 'T' is the temperature.

#### **3.3 PV model**

The PV model block calculates the PV power (kW) and the total PV energy (kWh) supplied by the PV array using the following equations.

$$\mathbf{P}\_{\rm PV} = \mathbf{r}\_{\rm pv} \,\mathrm{\*}\mathbf{\hat{r}rs} \,\mathrm{\*}\mathbf{A}^{\ast}\mathbf{P} \mathbf{V} \,\tag{8}$$

and

$$\mathbf{E}\_{\rm PV} = \prod\_{0}^{\rm T} \mathbf{P}\_{\rm PV} . \mathbf{dt} \,, \tag{9}$$

where 'PPV' is the power obtained from the PV array (kW), 'ηpv' is the efficiency of the solar collector, 'ins' is the solar insolation (kWh/m2/day), 'A' is the area of the solar collector/kW, 'PV' is the rating of the PV array (kW), and EPV is the total energy obtained from the PV array.

The efficiency of the solar collector is obtained from the manufacturer. The data sheets for the solar panels manufactured by Siemens and BP are available in Appendix 4 of (Agrawal, 2006). The solar insolation values are available from the site data or can be obtained by using the solar maps from the National Renewable Energy Laboratory website (NREL GIS Solar Maps, 2007). The area of the solar collector depends on the number of PV modules and the dimensions of each module. The number of PV modules depends on the installed capacity of the PV array and the dimensions of each PV module are obtained from the manufacturer's data sheet.
