**3.1 DEG and fuel consumption model**

The DEG consists of two parts: the electric generator and the diesel engine. The electric generator model consists of the efficiency curve that describes the relationship between the electrical efficiency and the electrical load on the generator. Fig. 3 shows a typical electrical efficiency curve for an electric generator. The fuel curve for a diesel engine describes the amount of fuel consumed depending on the engine load. A typical diesel engine fuel curve is a linear plot of load versus fuel consumption as shown in Fig. 4.

Fig. 2. PV-wind-diesel-battery hybrid power system model.

A fourth order polynomial fit for the electrical efficiency curve as a function of the generator electrical load 'Lgen' at unity 'ηel' and 0.8 'ηe2' power factor is used. The actual load on the electric generator is converted to its percentage value by dividing the actual load by the electric generator rating and multiplying by 100. This operation is performed so that the

A general model block diagram for the wind-PV-diesel-battery hybrid power system is shown in Fig. 2. The model is based on previous work with a PV-diesel-battery system (Wies, et al., 2005a) & (Wies, et al., 2005b), and a wind-diesel battery system (Wies, et al., 2005c). The basic model blocks in Fig. 2 and their subsystems are described in detail in Chapter 2 of (Agrawal, 2006). The model consists of nine different subsystems contained in blocks. The electrical energy sources in the model include DEGs, subsystems are described in detail in Chapter 2 of (Agrawal, 2006). The model consists of nine different subsystems contained in blocks. The electrical energy sources in the model include DEGs, WTGs, a PV array, and a battery bank. Currently, the Simulink® model performs a long term performance analysis including the environmental impact calculations of the hybrid power system under consideration. The different inputs required include the annual load and power factor profile, the annual wind speed for the WTGs, the annual insolation profile for the PV array, the annual ambient air temperature in which the power system is operating,

Some basic information about the DEG, Fuel Consumption, Wind, PV, and Battery

The DEG consists of two parts: the electric generator and the diesel engine. The electric generator model consists of the efficiency curve that describes the relationship between the electrical efficiency and the electrical load on the generator. Fig. 3 shows a typical electrical efficiency curve for an electric generator. The fuel curve for a diesel engine describes the amount of fuel consumed depending on the engine load. A typical diesel engine fuel curve

A fourth order polynomial fit for the electrical efficiency curve as a function of the generator electrical load 'Lgen' at unity 'ηel' and 0.8 'ηe2' power factor is used. The actual load on the electric generator is converted to its percentage value by dividing the actual load by the electric generator rating and multiplying by 100. This operation is performed so that the

the kW ratings of the generators, and the kW rating of the battery bank.

is a linear plot of load versus fuel consumption as shown in Fig. 4.

Fig. 2. PV-wind-diesel-battery hybrid power system model.

subsystem models are provided in the following sections.

**3.1 DEG and fuel consumption model** 

**3. Simulation model** 

same efficiency equations are independent of the rating of the electric generators. The values for the electrical efficiency ηel of the generator and the mechanical load 'Leng' on the engine for any given power factor 'pf' are determined using linear interpolation as follows:

$$
\eta\_{\rm el} = \eta\_{\rm el2} + \left(\frac{(\eta\_{\rm el1} \text{ - } \eta\_{\rm el2})}{0.2} \ast (\text{pf - } 0.8)\right) \tag{1}
$$

$$\mathcal{L}\_{\text{eng}} = \frac{\mathcal{L}\_{\text{gen}}}{\eta\_{\text{el}}} \tag{2}$$

Fig. 3. Typical efficiency for an electric generator.

Fig. 4. Typical fuel consumption curve for DEG.

The linear fit for the diesel engine fuel curve is given as

$$\dot{\mathbf{F}}\_{\mathcal{C}} = 0.5 \,\mathrm{\*} \left( \mathbf{L}\_{\mathrm{eng}} \,\, \mathrm{\*} \frac{\mathrm{kW}\_{-} \,\mathrm{A}}{100} \right) - 0.44 \,\tag{3}$$

and

Energy-Efficient Standalone Fossil-Fuel Based

wind based on a look-up table (Table 1).

efficiency of the WTG is given as

output from the WTG.

**3.2 Wind model** 

Hybrid Power Systems Employing Renewable Energy Sources 127

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

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

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

actualpower

maxpossiblepower (5)

secondlaw

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

<sup>1</sup> P V 0.59 P

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

<sup>3</sup>

max

<sup>2</sup> *max* (6)

$$\text{Total F}\_{\text{c}} = \bigcap\_{0}^{\text{T}} \text{F}\_{\text{c}}.\text{dt} \tag{4}$$

where ' Fc *.* ' is the fuel consumption rate in kg/hr (lbs/hr), 'Leng' is the percentage load on 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 obtained by integrating the term ' F <sup>c</sup> *.* dt' over the period of the simulation.

When two or more DEGs supply the load, it is important that the DEGs operate optimally. The following steps are performed to find the optimal point of operation for DEG 2.


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

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