**3. Fuel economy evaluation by numerical analysis**

#### **3.1 Mathematical modeling**

#### **Technique 1**


The numerical resolution of the problem consists in finding the roots of the state variables which ensures the equilibrium of the system.

#### **For an operation without CAES**

276 Modeling and Optimization of Renewable Energy Systems

**function of Type Reference** 

equation

equation [37]

equation [37]

equation [37]

equation [37]

equation [30]

equation [37]

equation [37]

equation [37]

equation [30]

**3. Fuel economy evaluation by numerical analysis** 

<sup>1</sup> *<sup>p</sup> p Q*<sup>0</sup> , *comp* Thermodynamic

*<sup>T</sup>*<sup>1</sup> *po o* , , *<sup>T</sup> <sup>p</sup>*<sup>1</sup> Thermodynamic

<sup>2</sup> *<sup>p</sup> Q pTN comp* ,,, 1 1 *comp* Thermodynamic

*<sup>T</sup>*<sup>2</sup> *Q pTN comp* ,,, 1 1 *comp* Thermodynamic

<sup>3</sup> *<sup>p</sup> Qcomp* , *<sup>p</sup>*<sup>2</sup> Thermodynamic

*T*<sup>3</sup> *Qcomp* , , *p*2 2 *T* Empirical model [37]

*Qcomp ppN* 2 3 , , *comp* Cartography [30]

*comp ppN* 2 3 , , *comp* Cartography [30]

*vol Neng* Empirical model [37, 39]

*T*<sup>4</sup> *TQ Q* 3 int , , *fuel* Empirical model [37]

*Pfric Neng* Empirical model [45]

*Qturb ppN* 4 5 , , *turb* Cartography [30]

*turb ppN* 4 5 , , *turb* Cartography [30]

The numerical resolution of the problem consists in finding the roots of the state variables

*ind Q Q* int , *fuel* Empirical model [37, 39,40]

*comp* Thermodynamic

*vol* Thermodynamic

*fric* Thermodynamic

*turb* Thermodynamic

*Qexh Q Q* int , *fuel* Thermodynamic

**3.1 Mathematical modeling** 

**State variable Can be expressed as a** 

*Pcomp Q pTp comp* ,,,, <sup>223</sup>

*Pout Q P fuel ind* , ,

*Pturb Q pTp turb* ,,,, <sup>445</sup>

which ensures the equilibrium of the system.

*Q*int *p T* 3 3 , ,

**Technique 1** 

The unknown variables are *QQ N* int , , ,, *fuel comp p p* 3 4 and the equilibrium equations are the following:

balance equation of the crankshaft:

The power supplied by the engine must be equal to the resistant power:

$$P\_{out} = P\_{load}$$

balance equation of the turbocharger torque

The torque supplied by the turbine must be equal to the necessary torque to drive the compressor:

$$P\_{comp} = P\_{turb}$$

balance equation of the turbocharger speed

The speed of the turbine and the compressor are equal:

$$N\_{comp} = N\_{turb}$$

intake aire continuity

*Q Q comp* int

exhaust air continuity

$$Q\_{turb} = Q\_{exh}$$

#### **For an operation with CAES**

The unknown variables are *QQ N* int , , ,,, *fuel comp ppp* <sup>034</sup> and the equilibrium equations are the same as previous five equations in addition to the sixth following equation:

Optimal Air-to-Fuel ratio

$$\frac{Q\_{\text{int}}}{Q\_{\text{fuel}}} = 53$$

#### **Technique 2**

Main equations are issued from the mass and heat conservation as well as the ideal gas assumptions [6, 13]. The application of the first law or thermodynamics and the perfect gas law to the control volume results in the differential equation 1 [13] that drives all the thermodynamic transformations.

$$d\left(m \cdot \mu\right) = -P \cdot dV + dq\_{\text{walls}} + dq\_{\text{comb}} + h\_T \cdot dm\_{\text{int}} + h\_{\text{ech}} \cdot dm\_{\text{exh}} + h\_{\text{fuel}} \cdot dm\_{\text{fuel}} \tag{1}$$

Optimal Design of an Hybrid Wind-Diesel System with

Fig. 7. Schema of Diesel engine main components

Compressed Air Energy Storage for Canadian Remote Areas 279

Fig. 8. Variation Characteristic curves of the compressor given by the manufacturer [30].


#### **3.2 Results and analysis**

#### **Technique 1**

We suppose in this numerical application that the used engine possesses a capacity of 5 l and turns at a regime of 1500 rotations per minute. Thus, the results obtained by the optimization are presented in Figures. 9-11. In conventional operation, the ratio air/fuel decreases with the load to reach in full load at the neighborhood of the stoichiometry as shown in Figure 9. For any requested torque lower than 120 Nm, we obtain an Air-to-Fuel ratio higher than 53, which means that there is no provision of the use of compressed air. Once the torque exceeds 120 N m, the turbocharger cannot ensure the quantity of necessary air to have an optimal air/fuel ratio. The engine then works in the zone of interest of operation with compressed air. Figure 10 shows the necessary inlet pressure of the compressor to operate the engine at its maximum efficiency thanks to the compressed air. Indeed, in the absence of CAES, the inlet pressure of the compressor is constant and equal to 1 bar, which is shown by the red curve ("Without Compressed Air"). The CAES allows feeding of the compressor at a chosen pressure to achieve the exact necessary air flow for maximum performance (efficiency). In our case, this pressure varies between 1 bar at very low regimes and 2.6 bars at full load. An adapted strategy for checking the valve relaxation of compressed air would achieve that balance. Finally, Figure 11 shows the reduction in fuel consumption which is brought about by the compressed air. This reduction in fuel consumption grows with the load to peak to 50% fuel saving at 800 Nm

*u T x*, *<sup>i</sup>* Thermodynamic tables [54]

*h T x*, *<sup>i</sup>* Thermodynamic tables [54]

walls *dq TT N gas walls en* , , *<sup>g</sup>* Empirical model [55]

delay *TPN gas* , , *gas eng* Chemical model [56,57]

*dm PP TA in out in* , ,, Thermodynamic model [56,57]

We suppose in this numerical application that the used engine possesses a capacity of 5 l and turns at a regime of 1500 rotations per minute. Thus, the results obtained by the optimization are presented in Figures. 9-11. In conventional operation, the ratio air/fuel decreases with the load to reach in full load at the neighborhood of the stoichiometry as shown in Figure 9. For any requested torque lower than 120 Nm, we obtain an Air-to-Fuel ratio higher than 53, which means that there is no provision of the use of compressed air. Once the torque exceeds 120 N m, the turbocharger cannot ensure the quantity of necessary air to have an optimal air/fuel ratio. The engine then works in the zone of interest of operation with compressed air. Figure 10 shows the necessary inlet pressure of the compressor to operate the engine at its maximum efficiency thanks to the compressed air. Indeed, in the absence of CAES, the inlet pressure of the compressor is constant and equal to 1 bar, which is shown by the red curve ("Without Compressed Air"). The CAES allows feeding of the compressor at a chosen pressure to achieve the exact necessary air flow for maximum performance (efficiency). In our case, this pressure varies between 1 bar at very low regimes and 2.6 bars at full load. An adapted strategy for checking the valve relaxation of compressed air would achieve that balance. Finally, Figure 11 shows the reduction in fuel consumption which is brought about by the compressed air. This reduction in fuel consumption grows with the load to peak to 50%

 

function of Type Reference

Kinematic equation [56,57]

, , <sup>0</sup> *delay* Empirical model [56,57]

State variable Can be expressed as a

*V*

comb *dq*

**3.2 Results and analysis** 

fuel saving at 800 Nm

**Technique 1** 

Fig. 7. Schema of Diesel engine main components

Fig. 8. Variation Characteristic curves of the compressor given by the manufacturer [30].

Optimal Design of an Hybrid Wind-Diesel System with

Fig. 11. Comparison of the fuel consumption.

regarding intake and exhaust conditions.

**Detailed parametric study at BMEP = 10 bars** 

 Turbocharged mode with compressed air cooling; CAES charged mode with an intake temperature of 25°C; CAES charged mode with an intake temperature of -50°C.

**Technique 2** 

injection advance:

Compressed Air Energy Storage for Canadian Remote Areas 281

In our study, we have chosen to focus on three operating modes to study the impact of

For the CAES charged mode temperatures, we know that a temperature drop will inevitably occur when expanding the CAES from storage pressure to intake pressure. However, it is possible to heat the intake air before admitting it using engine's cooling system or exhaust temperature recovery. We have chosen not to work below intake temperature of -50°C because it is the range of minimum external temperature that can be met in northern areas. Below this temperature, we need to investigate if the Diesel engine remains operational which exceeds the purpose of this study. These operating modes are not the only ones to be studied, but they were chosen to increase our understanding of the Diesel engine behavior

In order to understand its behavior, we will provide a complete analysis of the variation of the thermodynamic cycle and its efficiency, depending on the control parameters (intake pressure, intake temperature, exhaust pressure and injection advance) for a fixed load corresponding to a BMEP of 10 bars. Figure 13 illustrates the effect of intake pressure and exhaust pressure on specific fuel consumption of the engine at a BMEP of 10 bars for a fixed intake temperature of 298K and a fixed injection advance of 6 degrees. As we can observe, increasing intake pressure and reducing exhaust pressure highly reduces fuel consumption.

Fig. 9. Comparison of the (air/fuel) ratio.

Fig. 10. Comparison of the pressure at compressor inlet..

Fig. 11. Comparison of the fuel consumption.

#### **Technique 2**

280 Modeling and Optimization of Renewable Energy Systems

Fig. 9. Comparison of the (air/fuel) ratio.

Fig. 10. Comparison of the pressure at compressor inlet..

In our study, we have chosen to focus on three operating modes to study the impact of injection advance:


For the CAES charged mode temperatures, we know that a temperature drop will inevitably occur when expanding the CAES from storage pressure to intake pressure. However, it is possible to heat the intake air before admitting it using engine's cooling system or exhaust temperature recovery. We have chosen not to work below intake temperature of -50°C because it is the range of minimum external temperature that can be met in northern areas. Below this temperature, we need to investigate if the Diesel engine remains operational which exceeds the purpose of this study. These operating modes are not the only ones to be studied, but they were chosen to increase our understanding of the Diesel engine behavior regarding intake and exhaust conditions.

#### **Detailed parametric study at BMEP = 10 bars**

In order to understand its behavior, we will provide a complete analysis of the variation of the thermodynamic cycle and its efficiency, depending on the control parameters (intake pressure, intake temperature, exhaust pressure and injection advance) for a fixed load corresponding to a BMEP of 10 bars. Figure 13 illustrates the effect of intake pressure and exhaust pressure on specific fuel consumption of the engine at a BMEP of 10 bars for a fixed intake temperature of 298K and a fixed injection advance of 6 degrees. As we can observe, increasing intake pressure and reducing exhaust pressure highly reduces fuel consumption.

Optimal Design of an Hybrid Wind-Diesel System with

decreased:

already 180 bar.

Compressed Air Energy Storage for Canadian Remote Areas 283

We present some qualitative explanations for this improvement, which will be completed with data in the rest of this paragraph. Actually, two main reasons are behind the fuel consumption reduction when the intake pressure is increased and exhaust pressure

 The scavenging work, called also "the low pressure cycle work", increases and turns out to be positive (motor). That is added to the work provided by the high pressure cycle and reduces fuel consumption. In a classic turbocharged Diesel, intake pressure is slightly lower than exhaust pressure; the scavenging work is slightly negative and

 The high-pressure cycle efficiency increases with pneumatic hybridization thanks to higher fresh air quantity. This improvement is mainly due to lower thermal losses, due to the reduction of combustion temperature resulting from less fuel burned from one side, and higher air density (therefore higher calorific capacity) from the other side. As mentioned before, the maximum pressure allowed in the cylinder limits the amount of intake pressure. Figure 14 shows the variation of the maximum cylinder pressure as a function of the intake and exhaust pressures. We observe the maximum cylinder pressure is almost not affected by exhaust pressure but varies linearly with intake pressure with a high slope of about 40 to 1. With a 4 bars intake pressure, the maximum cylinder pressure reaches

Fig. 14. Maximum gas pressure variation with intake and exhaust pressures, for a fixed

The second potential limitation that we have investigated is the exhaust temperature. Actually, exhaust valve has a threshold in terms of gas temperature not to be exceeded. As we can observe in Figure 15, the exhaust temperature is lower when intake pressure is

intake temperature of 25°C, at BMEP = 10 bars

requires more fuel for the same total work of the thermodynamic cycle.

Fig. 12. Direct injection Diesel engine simplified thermodynamic model.

Fig. 13. Fuel consumption as a function of intake and exhaust pressures, for a fixed intake temperature of 25°C at BMEP = 10 bars

Fig. 12. Direct injection Diesel engine simplified thermodynamic model.

Fig. 13. Fuel consumption as a function of intake and exhaust pressures, for a fixed intake

temperature of 25°C at BMEP = 10 bars

We present some qualitative explanations for this improvement, which will be completed with data in the rest of this paragraph. Actually, two main reasons are behind the fuel consumption reduction when the intake pressure is increased and exhaust pressure decreased:


As mentioned before, the maximum pressure allowed in the cylinder limits the amount of intake pressure. Figure 14 shows the variation of the maximum cylinder pressure as a function of the intake and exhaust pressures. We observe the maximum cylinder pressure is almost not affected by exhaust pressure but varies linearly with intake pressure with a high slope of about 40 to 1. With a 4 bars intake pressure, the maximum cylinder pressure reaches already 180 bar.

Fig. 14. Maximum gas pressure variation with intake and exhaust pressures, for a fixed intake temperature of 25°C, at BMEP = 10 bars

The second potential limitation that we have investigated is the exhaust temperature. Actually, exhaust valve has a threshold in terms of gas temperature not to be exceeded. As we can observe in Figure 15, the exhaust temperature is lower when intake pressure is

Optimal Design of an Hybrid Wind-Diesel System with

exhaust pressure of 1 bar, at BMEP = 10 bars

exhaust pressure of 1 bar, at BMEP = 10 bars

Compressed Air Energy Storage for Canadian Remote Areas 285

Fig. 16. Fuel consumption as a function of intake pressure and temperature, for a fixed

Fig. 17. Maximum gas pressure function of intake pressure and temperature, for a fixed

increased or exhaust pressure is decreased. Therefore, exhaust temperature will not limit the pneumatic hybridization.

After the analysis of the effect of intake and exhaust pressures for a fixed intake temperature and fixed injection advance, we illustrate (Figure 16) the effect of intake temperature and pressure on fuel consumption, for a fixed exhaust pressure of 1 bar and a fixed injection advance of 6 degrees. Fixing exhaust pressure to 1 bar assumes that the turbocharger is already by-passed. Fuel consumption is reduces as intake temperature lowers. As will be shown later with additional data, reducing intake temperature for the same intake pressure will reduce heat losses as well and improve cycle efficiency because the global gas temperature is lower (higher air density and lower initial cycle temperature).

Regarding maximum cylinder pressure, we observe in Figure 17 that reducing the intake temperature for the same intake pressure increases the maximum cylinder pressure. This is due to higher air quantity admitted. Therefore the maximum intake pressure we can reach is lower for low intake temperature. For example, at -50°C intake temperature, the maximum cylinder pressure reaches 180 bars for an intake pressure of 3.2 bars, which is 0.8 bars lower than the limitation at +25°C intake temperature.

Fig. 15. Exhaust gas temperature function of intake and exhaust pressures, for a fixed intake temperature of 25°C, at BMEP = 10 bars

increased or exhaust pressure is decreased. Therefore, exhaust temperature will not limit the

After the analysis of the effect of intake and exhaust pressures for a fixed intake temperature and fixed injection advance, we illustrate (Figure 16) the effect of intake temperature and pressure on fuel consumption, for a fixed exhaust pressure of 1 bar and a fixed injection advance of 6 degrees. Fixing exhaust pressure to 1 bar assumes that the turbocharger is already by-passed. Fuel consumption is reduces as intake temperature lowers. As will be shown later with additional data, reducing intake temperature for the same intake pressure will reduce heat losses as well and improve cycle efficiency because the global gas

Regarding maximum cylinder pressure, we observe in Figure 17 that reducing the intake temperature for the same intake pressure increases the maximum cylinder pressure. This is due to higher air quantity admitted. Therefore the maximum intake pressure we can reach is lower for low intake temperature. For example, at -50°C intake temperature, the maximum cylinder pressure reaches 180 bars for an intake pressure of 3.2 bars, which is 0.8 bars lower

Fig. 15. Exhaust gas temperature function of intake and exhaust pressures, for a fixed intake

temperature is lower (higher air density and lower initial cycle temperature).

than the limitation at +25°C intake temperature.

temperature of 25°C, at BMEP = 10 bars

pneumatic hybridization.

Fig. 16. Fuel consumption as a function of intake pressure and temperature, for a fixed exhaust pressure of 1 bar, at BMEP = 10 bars

Fig. 17. Maximum gas pressure function of intake pressure and temperature, for a fixed exhaust pressure of 1 bar, at BMEP = 10 bars

Optimal Design of an Hybrid Wind-Diesel System with

106

from turbocharged mode to CAES charged mode.

0

2

4

6

8

10

Pressure [Pa]

12

14

16

18 x 106

Pressure - Logarithmic [Pa]

107

108

Compressed Air Energy Storage for Canadian Remote Areas 287

mode and positive for CAES charged modes. We also notice that the scavenging work in CAES+25°C is slightly higher than the one in CAES-50°C because intake pressure is higher.

> Turbo charged +25°C CAES charged +25°C CAES charged -50°C

> Turbo charged +25°C CAES charged +25°C CAES charged -50°C

10-5 10-4 10-3 <sup>105</sup>

Volume - Logarithmic [m3]

We notice in Figure 20 the high increase of the maximum cylinder pressure when moving

0 1 2 3 4 5 6

Volume [m3]

Fig. 20. P-V diagram at BMEP=10 bars, for different charging modes

x 10-4

Fig. 19. log P-log V diagrams at BMEP=10 bars, for different charging modes

The last parameter studied is the Injection Advance (IA) which is responsible of Start of Combustion (SOC) angle. Actually, there is an optimal advance that reduces the fuel consumption to a minimum, for every condition of intake pressure, intake temperature and exhaust pressure. The reasons are:


For the simplification of the study, the AID was not modeled and the effect of the SOC angle is directly studied and set to its optimal value. Figure 18 illustrates the effect of SOC angle on fuel consumption, for the three chosen operating points. We observe that the optimal SOC angle for turbocharged mode is 6 degrees, for CAES charged at 25°C mode is 7 degrees and for CAES charged at -50°C mode, is 9 degrees. It is important to note that increasing injection advance to reduce fuel consumption, increases the maximum cylinder pressure, and therefore decreases the maximum intake pressure. In that case, the fuel consumption may increase instead of decreasing, but the global efficiency is better because less compressed air is consumed.

Fig. 18. Effect of SOC angle on fuel consumption, at BMEP = 10 bars, for different charging modes

The thermodynamic cycles of the chosen operating points are illustrated in Figures 19 and 17. All three operating modes are working at optimal SOC angles and therefore optimal IA.

Figure 19 illustrates the P-V diagram plotted in a logarithmic scale. It is interesting to analyze the low-pressure cycle called also the scavenging cycle. We notice that the pneumatic work witch is the area of the scavenging cycle is near zero for turbo-charged

The last parameter studied is the Injection Advance (IA) which is responsible of Start of Combustion (SOC) angle. Actually, there is an optimal advance that reduces the fuel consumption to a minimum, for every condition of intake pressure, intake temperature and

 The Auto-Ignition Delay (AID) depends of the intake conditions and so does the SOC because it is simply equal to the difference between the IA and the AID. It is important to have a SOC angle nearly before the Top Dead Center (TDC) in order to have good

 The thermal loss depends of the intake temperature and pressure and the cylinder pressure profile changes consequently. To have optimal cycle efficiency, the SOC needs

For the simplification of the study, the AID was not modeled and the effect of the SOC angle is directly studied and set to its optimal value. Figure 18 illustrates the effect of SOC angle on fuel consumption, for the three chosen operating points. We observe that the optimal SOC angle for turbocharged mode is 6 degrees, for CAES charged at 25°C mode is 7 degrees and for CAES charged at -50°C mode, is 9 degrees. It is important to note that increasing injection advance to reduce fuel consumption, increases the maximum cylinder pressure, and therefore decreases the maximum intake pressure. In that case, the fuel consumption may increase instead of

decreasing, but the global efficiency is better because less compressed air is consumed.

Fig. 18. Effect of SOC angle on fuel consumption, at BMEP = 10 bars, for different charging

The thermodynamic cycles of the chosen operating points are illustrated in Figures 19 and 17. All three operating modes are working at optimal SOC angles and therefore optimal IA. Figure 19 illustrates the P-V diagram plotted in a logarithmic scale. It is interesting to analyze the low-pressure cycle called also the scavenging cycle. We notice that the pneumatic work witch is the area of the scavenging cycle is near zero for turbo-charged

exhaust pressure. The reasons are:

to be adjusted around its nominal value.

cycle efficiency.

modes

mode and positive for CAES charged modes. We also notice that the scavenging work in CAES+25°C is slightly higher than the one in CAES-50°C because intake pressure is higher.

Fig. 19. log P-log V diagrams at BMEP=10 bars, for different charging modes

We notice in Figure 20 the high increase of the maximum cylinder pressure when moving from turbocharged mode to CAES charged mode.

Fig. 20. P-V diagram at BMEP=10 bars, for different charging modes

Optimal Design of an Hybrid Wind-Diesel System with

Compressed Air Energy Storage for Canadian Remote Areas 289

Fig. 22. Heat flow through boundary, for different charging modes, at BMEP = 10 bars

As a synthesis of this complete study around the operating point of BMEP 10 bars, Figure 23 illustrates the reasons for fuel economy brought by CAES charged modes compared to turbocharged mode. We observe that 65% of the fuel consumption reduction from turbocharged mode at +25°C to CAES charged mode at +25°C is caused by direct pneumatic power production and 35% is caused by heat loss reduction. The heat loss reduction constitutes the only reason for the improvement from CAES charged +25°C to CAES charged -50°C mode, as the pneumatic contribution is higher in CAES+25°C mode due to higher intake pressure.

**149**

**Heat loss**

'

**Turbo charged +25°C CAES charged +25°C CAES charged -50°C** 

Fig. 23. Explanation of consumption change from a charging mode to another, at BMEP=10 bars

**reduction**

**159**

**Pneumatic**

**contribution**

**173**

**Pneumatic**

**contribution**

**216**

**Référence** 

0

50

100

**Specific Consumption [g/kW.h]**

150

200

250

**128**

**Heat loss**

**reduction**

Figure 21 and 22 illustrate respectively the T-θ diagram and heat exchange through boundaries for the three modes. We can see in Figure 21 that a significant decrease in gas temperature is obtained when moving from turbocharged mode to CAES-50°C mode passing by CAES+25°C charging mode. This temperature decrease is a result of the three following reasons:


In Figure 22, negative flow means the gas is loosing energy through boundary and positive flow means the gas is earning energy from boundary. For turbocharged mode, the flow is positive only during intake because gas temperature at this time is lower than boundaries' temperatures. During combustion, expansion and exhaust phases, the heat flow is negative causing significant loss in energy. As for the CAES charged mode at 25°C, we observe that heat loss decreases significantly comparing to turbocharged mode but the flow is still negative. In CAES charged mode at -50°C, the overall heat flow is positive therefore the system is not loosing energy, on the contrary, it is recovering thermal energy from the engine. Of course, this assumes that the engine is hot and that the CAES charged mode at -50°C occurs occasionally, after a certain time of working under standard turbocharged mode. The thermal inertia of the Diesel engine defines the minimal and maximal working time of turbocharged mode and CAES mode respectively in order to make this hypothesis valid. In case the time of operating with CAES charged mode at -50°C exceeds a certain limit, the heat flow will stabilize to meet a global value near zero which will increase the fuel consumption by a small amount.

Fig. 21. T-θ diagram at BMEP=10 bars, for different charging modes

Figure 21 and 22 illustrate respectively the T-θ diagram and heat exchange through boundaries for the three modes. We can see in Figure 21 that a significant decrease in gas temperature is obtained when moving from turbocharged mode to CAES-50°C mode passing by CAES+25°C

1. The higher air density resulting from the higher intake pressure and/or the lower intake temperature, leads to higher calorific capacity of the in-cylinder gas and therefore lower temperature rise for a certain heat energy released by the combustion. 2. Lower heat release resulting from lower quantity of burned fuel that reduces

3. Intake air temperature is 75°C lower for CAES -50°C that is responsible for lower

In Figure 22, negative flow means the gas is loosing energy through boundary and positive flow means the gas is earning energy from boundary. For turbocharged mode, the flow is positive only during intake because gas temperature at this time is lower than boundaries' temperatures. During combustion, expansion and exhaust phases, the heat flow is negative causing significant loss in energy. As for the CAES charged mode at 25°C, we observe that heat loss decreases significantly comparing to turbocharged mode but the flow is still negative. In CAES charged mode at -50°C, the overall heat flow is positive therefore the system is not loosing energy, on the contrary, it is recovering thermal energy from the engine. Of course, this assumes that the engine is hot and that the CAES charged mode at -50°C occurs occasionally, after a certain time of working under standard turbocharged mode. The thermal inertia of the Diesel engine defines the minimal and maximal working time of turbocharged mode and CAES mode respectively in order to make this hypothesis valid. In case the time of operating with CAES charged mode at -50°C exceeds a certain limit, the heat flow will stabilize to meet a

charging mode. This temperature decrease is a result of the three following reasons:

average gas temperature of this operating mode compared to CAES 25°C.

global value near zero which will increase the fuel consumption by a small amount.

Fig. 21. T-θ diagram at BMEP=10 bars, for different charging modes

temperature rise for CAES 25°C and CAES -50°C;

Fig. 22. Heat flow through boundary, for different charging modes, at BMEP = 10 bars

As a synthesis of this complete study around the operating point of BMEP 10 bars, Figure 23 illustrates the reasons for fuel economy brought by CAES charged modes compared to turbocharged mode. We observe that 65% of the fuel consumption reduction from turbocharged mode at +25°C to CAES charged mode at +25°C is caused by direct pneumatic power production and 35% is caused by heat loss reduction. The heat loss reduction constitutes the only reason for the improvement from CAES charged +25°C to CAES charged -50°C mode, as the pneumatic contribution is higher in CAES+25°C mode due to higher intake pressure.

Fig. 23. Explanation of consumption change from a charging mode to another, at BMEP=10 bars

Optimal Design of an Hybrid Wind-Diesel System with

40

50

100

150

200

250

Fuel Consumption [g/kWh]

300

350

400

450

for the same reasons as described in the previous paragraph.

60

80

100

Maximal cylinder pressure [bars]

120

140

160

180

Compressed Air Energy Storage for Canadian Remote Areas 291

2 4 6 8 10 12 14 16 18 20 22

CAES charged +50°C CAES charged +25°C CAES charged +0°C CAES charged -50°C Turbo charged +25°C

> CAES charged +50°C CAES charged +25°C CAES charged +0°C CAES charged -50°C Turbo charged +25°C

BMEP [bars]

2 4 6 8 10 12 14 16 18 20 22

BMEP [bars]

Fig. 26. Fuel specific consumption for different charging modes, function of engine load

Fig. 25. Maximum cylinder pressure for different charging modes, function of engine load

When comparing fuel consumption of CAES charged mode with turbocharged mode, we observe in Figure 26 that at lower loads, the reduction is higher. That is due to the more important absolute pneumatic power as intake pressure is higher, relatively to the total power of the engine. We notice also that better fuel economy for lower intake temperature

#### **Optimization result at different loads**

In this section, we will compare different charging modes on different criteria, for different operating points, after optimization. The charging modes considered are:


All CAES charged modes are operating at maximum allowable intake pressure, that is intake pressure for witch maximum gas pressure during thermodynamic cycle reaches 180 bars and at an exhaust pressure of 1 bar, while turbocharged mode operates at an intake pressure and exhaust pressure both dependant on BMEP but almost equal. All operating points are set with an optimal injection advance, the one that maximizes the cycle efficiency, even if the intake allowed pressure has to be decreased. As mentioned before, the variation of intake pressure and exhaust pressure as a function of BMEP for a turbocharged engine depends on the design of the turbocharger. We have taken here an example provided by a previous simulation [1] conducted on a Diesel engine.

Figure 24 illustrates the intake pressure and the injection advance at every operating point simulated. We can see that for higher loads the allowable intake pressure lowers; we can also see that a lower intake temperature will reduce the allowable intake pressure.

Fig. 24. Intake maximum pressure for different charging modes, function of engine load

These intake pressures make the maximum gas pressure during Diesel cycle reach 180 bars, as shown in Figure 25, while in turbocharged mode, maximal pressure is significantly lower.

In this section, we will compare different charging modes on different criteria, for different

All CAES charged modes are operating at maximum allowable intake pressure, that is intake pressure for witch maximum gas pressure during thermodynamic cycle reaches 180 bars and at an exhaust pressure of 1 bar, while turbocharged mode operates at an intake pressure and exhaust pressure both dependant on BMEP but almost equal. All operating points are set with an optimal injection advance, the one that maximizes the cycle efficiency, even if the intake allowed pressure has to be decreased. As mentioned before, the variation of intake pressure and exhaust pressure as a function of BMEP for a turbocharged engine depends on the design of the turbocharger. We have taken here an example provided by a

Figure 24 illustrates the intake pressure and the injection advance at every operating point simulated. We can see that for higher loads the allowable intake pressure lowers; we can

2 4 6 8 10 12 14 16 18 20 22

CAES charged +50°C CAES charged +25°C CAES charged +0°C CAES charged -50°C Turbo charged +25°C

BMEP [bars]

Fig. 24. Intake maximum pressure for different charging modes, function of engine load

These intake pressures make the maximum gas pressure during Diesel cycle reach 180 bars, as shown in Figure 25, while in turbocharged mode, maximal pressure is

also see that a lower intake temperature will reduce the allowable intake pressure.

operating points, after optimization. The charging modes considered are:

**Optimization result at different loads** 

 CAES Charged mode at 50°C; CAES charged mode at 25°C; CAES charged mode at 0°C; CAES Charged mode at -50°C; Turbo charged mode at 25°C.

previous simulation [1] conducted on a Diesel engine.

1

significantly lower.

1.5

2

2.5

Intake pressure [bars]

3

3.5

4

4.5

Fig. 25. Maximum cylinder pressure for different charging modes, function of engine load

When comparing fuel consumption of CAES charged mode with turbocharged mode, we observe in Figure 26 that at lower loads, the reduction is higher. That is due to the more important absolute pneumatic power as intake pressure is higher, relatively to the total power of the engine. We notice also that better fuel economy for lower intake temperature for the same reasons as described in the previous paragraph.

Fig. 26. Fuel specific consumption for different charging modes, function of engine load

Optimal Design of an Hybrid Wind-Diesel System with

5.5

**4. General conclusion and auto-critique** 

function of engine load

polynomial model).

6 6.5 7 7.5 8

8.5 9 9.5 10 10.5

Fuel economy per kg of air [g/kg]

Compressed Air Energy Storage for Canadian Remote Areas 293

CAES charged +50°C CAES charged +25°C CAES charged +0°C CAES charged -50°C

2 4 6 8 10 12 14 16 18 20 22

BMEP [bars]

Fig. 28. Fuel economy per kilogram of air consumed, for different CAES charging modes,

This document is a milestone study to demonstrate the interest around the WDCAS in portraying its potential to reduce fuel consumption and increase the efficiency of the diesel engine. We demonstrated that we can expect savings which can reach 50%. However, physical limits can jeopardise the achievement to this level of economy. Among these limits, we quote mainly those due to the permeability limit of the intake valves if a sound blocking takes place. Most, if the supercharging pressure is important Furthermore, some models used, were the object of validation in previous publications. In the case of our present study, we extrapolate the use of these models in zones beyond those in which they were validated. Among these models, the most important one being the engine performance (efficiency) according to the Air-to-Fuel ratio and which proposes appropriate sizing and representation of the gain in consumption that we forecasted. It is therefore necessary to either verify their validation in these conditions, or substitute more physical models (example: simulation of the thermodynamic cycle instead of using a

Finally, the air consumption is one important criterion as the storage tank volume depends on it. Figure 27 shows that air consumption increases at low loads and also at low temperature because filling is better. In order to optimize the use of stored air, another criterion is necessary. We have calculated and illustrated in Figure 28, the fuel economy per kilogram of air consumed. This criterion has to be maximized in order to get the maximum advantage of stored air. As we can notice at Figure 28, it is more interesting to use CAES charged mode at low and very low loads. We can also see that even if it has positive effect on fuel consumption, very low intake air temperature is less suitable when considering consumed air quantity.

In case the storage pressure is higher than the intake temperature, it is needed therefore to expand it before introducing it into the engine intake. A temperature drop will probably accompany this expansion. In that case, we recommend heating the air after its expansion, using a free of charge source as the engine cooling system or an exhaust gas exchanger.

Fig. 27. Air specific consumption for different charging modes, function of engine load

Finally, the air consumption is one important criterion as the storage tank volume depends on it. Figure 27 shows that air consumption increases at low loads and also at low temperature because filling is better. In order to optimize the use of stored air, another criterion is necessary. We have calculated and illustrated in Figure 28, the fuel economy per kilogram of air consumed. This criterion has to be maximized in order to get the maximum advantage of stored air. As we can notice at Figure 28, it is more interesting to use CAES charged mode at low and very low loads. We can also see that even if it has positive effect on fuel consumption, very low intake air temperature is less suitable when considering

In case the storage pressure is higher than the intake temperature, it is needed therefore to expand it before introducing it into the engine intake. A temperature drop will probably accompany this expansion. In that case, we recommend heating the air after its expansion, using a free of charge source as the engine cooling system or an exhaust gas

2 4 6 8 10 12 14 16 18 20 22

CAES charged +50°C CAES charged +25°C CAES charged +0°C CAES charged -50°C Turbo charged +25°C

BMEP [bars]

Fig. 27. Air specific consumption for different charging modes, function of engine load

consumed air quantity.

0

5

10

15

20

Air Consumption [kg/kWh]

25

30

35

40

exchanger.

Fig. 28. Fuel economy per kilogram of air consumed, for different CAES charging modes, function of engine load

#### **4. General conclusion and auto-critique**

This document is a milestone study to demonstrate the interest around the WDCAS in portraying its potential to reduce fuel consumption and increase the efficiency of the diesel engine. We demonstrated that we can expect savings which can reach 50%. However, physical limits can jeopardise the achievement to this level of economy. Among these limits, we quote mainly those due to the permeability limit of the intake valves if a sound blocking takes place. Most, if the supercharging pressure is important Furthermore, some models used, were the object of validation in previous publications. In the case of our present study, we extrapolate the use of these models in zones beyond those in which they were validated. Among these models, the most important one being the engine performance (efficiency) according to the Air-to-Fuel ratio and which proposes appropriate sizing and representation of the gain in consumption that we forecasted. It is therefore necessary to either verify their validation in these conditions, or substitute more physical models (example: simulation of the thermodynamic cycle instead of using a polynomial model).

Optimal Design of an Hybrid Wind-Diesel System with

2004.

NREL. www.nrel.org.

Yukon; 2001. [10] www.nunavutpower.com.

94-169-C; 1994.

1997. [16] www.danvest.com.

Compressed Air Energy Storage for Canadian Remote Areas 295

[3] La stratégie énergétique du Québec 2006e2015. L'énergie pour construire le Québec de

[4] Hunter R, Elliot G. WindeDiesel systems e a guide to the technology and its implementation. Cambridge (UK): Cambridge University Press; 1994. [5] Forcione A. Système jumelé éolien-Diesel aux Îles-de-la-Madeleine (Cap-aux-Meules) e

[7] Ibrahim H, Ilinca A, Perron J. Solutions actuelles pour une meilleure gestion et

[9] Maisson JF. Wind power development in sub-arctic conditions with severe rime icing. In:

[11] Reeves B. Kotzebue electric association wind projects. In: Proceedingsof NREL/AWEA

[12] Singh V. Blending wind and solar into the Diesel generator market. Renewable Energy Policy Project (REPP) research report, Winter 2001, No. 12, Washington, C. [13] Reid R. Application de l'éolien en réseaux non reliés. Liaison Énergie-

[14] Jean Y, Nouaili A, Viarouge P, Saulnier B, Reid R. Développement d'un système

[15] Gagnon R, Nouaili A, Jean Y, Viarouge P. Mise à jour des outils de modélisation et de

[17] Ilinca A, Chaumel JL. Implantation d'une centrale éolienne comme source d'énergie

[18] Ibrahim H, Ilinca A, Perron J. Energy storage systems e characteristics and comparisons.

[19] Ibrahim H, Ilinca A, Perron J. Comparison and analysis of different energy storage

[20] Belhamed M, Moussa S, Kaabeche A. Production d'électricité au moyen d'un système

l'énergie éolienne et les sites isolées, Îles de la Madeleine; 2005.

Renewable & Sustainable Energy Reviews 2008;12(5):1221-50.

JEDHPSS représentatif d'un village typique des réseaux non relies. Rapport IREQ-

simulation du Jumelage Éolien-Diesel à Haute Pénétration Sans Stockage et rédaction du devis de fabrication de la charge de lissage. Rapport IREQ-97- 124-C;

d'appoint pour des stations de télécommunications. Colloque international sur

techniques based on their performance index. IEEE Canada, Electrical Power Conference 2007, "Renewable and alternative energy resources", EPC2007,

hybride éolien-photovoltaïque-Diesel. Revue Énergies Renouvelables: Zones

Canadian Society for Mechanical Engineering, 5e8 June 2008. [8] ACÉÉ. Association canadienne de l'énergie éolienne. http://www.canwea.com.

2002 windeDiesel workshop, Anchorage, Alaska, USA, 2002.

Francophonie,N\_35/2e Trimestre; 1997.

Montreal, Canada, October 25-26, 2007.

Arides; 2002:49-54.

Établissement de la VAN optimale. Institut de Recherche, Hydro-Québec, Février;

intégration de la ressource éolienne. CSME/SCGM Forum 2008 at Ottawa. The

Presented at the circumpolar climate change summit and exposition, Whitehorse,

demain. http://www.mrnf.gouv.qc.ca/energie/eolien.

[6] HOMER v2.0 e the optimisation model for distributed power.

However, it has been demonstrated that when the intake pressure increases of 1 bar, maximal cylinder gas pressure increases about 40 bars. Considering that this maximal cylinder gas pressure needs to stay below a certain threshold for reliability reasons, the intake pressure is limited to 4 bars for the low loads and 3 bars for the high loads, as shown in Figure 14. This is a very big problem because that means that we have two options:

	- If the expansion happens through an orifice, a very high temperature drop occurs; the gas looses its entropy, and the global efficiency (energy discharged/energy stored) would be very low.
	- If the expansion happens through an air motor or air turbine, then it would be more efficient to expand the air until atmospheric pressure without any pneumatic Hybridization of the Diesel engine.

Other concepts of pneumatic hybrid Diesel engine are being studied to solve this problem.
