$$S\_f = \mathbf{2} \cdot n\_{p,new} \cdot w\_{new} \cdot l\_{new} \tag{17}$$

This also impacts the surface area available for the exhaust gas to transmit its heat to the working fluid through wall or plates, which is given by:

$$\mathcal{S}\_{\mathcal{S}} = \mathcal{S}\_{\mathcal{f}} + \mathcal{S}\_{\mathcal{g},fins} \tag{18}$$

where Sg,fins is the surface area of fins at exhaust gas side. The surface area of the wall is linear dependent on evaporator length and width:

$$S\_w = l\_{new} \cdot w\_{new} \tag{19}$$

Finally, the flow cross-sectional area, Ai is given by,

$$A\_{i,new} = w\_{new} \cdot h\_{new} \qquad \qquad \{\text{i} = \text{fluid}, \text{ gas}\} \tag{20}$$

Accordingly, the Reynolds number for the working fluid and gas side is affected:

$$Re\_i = \frac{\dot{m}\_i \cdot dh\_i}{A\_{i,new} \cdot \eta\_i} \tag{21}$$

The component sizes are optimized based on fuel consumption and investment cost criteria. In the next section, the alternating optimization method is described in detail. The optimal sizes λopt that are finally determined are input for the overall performance analysis with switching

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Optimizing the controller and plant iteratively to converge the coupled variables can be computationally too expensive. Therefore, an alternating architecture is followed for only one complete loop, see Figure 7. The controller designed for a specific WHR system will give different performance for a resized WHR system. Consequently, the feed forward controller from Section 3.3 is applied, which calculates the pumps speeds, such that χf ≥ 1 at the outlet of both the evaporators for given engine exhaust heat flows. Although with lower performance

Model Predictive Control (MPC) strategy in Section 6.

Figure 6. Approach for optimal sizing and control of WHR systems.

5.1. Alternating system optimization

Figure 7. Optimization architecture.

where ηi is the viscosity, dhi is the hydraulic diameter, that is, outer gap height of one plate and m\_ i is the mass flow rate of the working fluid and gas. The heat transfer coefficient αi for the working fluid and exhaust gas also depends on Ai,new:

$$\alpha\_{i} = \frac{\mathcal{N}u\_{i} \cdot \Lambda\_{i}}{d\hbar\_{i}} = \frac{\mathcal{N}u\_{i}}{\mathcal{Re}\_{i}} \cdot \frac{\dot{m}\_{i}\Lambda\_{i}}{A\_{i,new} \cdot \eta\_{i}} \tag{22}$$

where Λi is the thermal conductivity of the working fluid and exhaust gas.

For varying evaporator length, there will be no change in the flow cross sectional area as well as in the exhaust gas side cross sectional area. As a result, there will be no effect on Reynolds number, Re, and the Nusselt number, Nu, which is directly proportional to Re. The surface areas available for exhaust gas and working fluid increase with increasing l and vice versa (see Eqs. (17)–(19)). These areas directly affect the working fluid temperature at the evaporator's outlet.

The cross-sectional areas Ai,new varies with width as well as with height and is inversely proportional to the heat transfer coefficients αfluid and αgas. The surface areas Sf and Sg increase with w and h and, hence, the working fluid temperature at the evaporator's outlet will behave in the same direction through equations for conservation of energy. However, Sw will stay the same with change in height, because the number of plates will change with this dimension.

With the introduced scaling factors, the evaporator size can be changed by varying its length, width or height depending on the requirements from the system, input heat flows, and type of working fluid. These three parameters have different impact on the evaporator's performance. Therefore, a sensitivity analysis has to be done to select the parameter that has the most positive impact on WHR system power output.

#### 5. WHR system size optimization

This section presents a methodology to optimize component size for WHR systems under transient driving conditions. Figure 6 gives an outline of the approach that is followed in this study. The scalable WHR system model developed in the previous section is crucial input for this approach. From a sensitivity analysis for the exhaust evaporator, scaling of the evaporator length is identified as the most promising route to maximize WHR power output. Details can be found in [16]. As a result, evaporator width and height will be set to their original system values in the sequel of this study. In summary, the following parameters are considered for optimal component sizing in order to maximize WHR power output:

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Figure 6. Approach for optimal sizing and control of WHR systems.

The component sizes are optimized based on fuel consumption and investment cost criteria. In the next section, the alternating optimization method is described in detail. The optimal sizes λopt that are finally determined are input for the overall performance analysis with switching Model Predictive Control (MPC) strategy in Section 6.

#### 5.1. Alternating system optimization

Rei ¼ m\_ i � dhi Ai,new � ηi

where ηi is the viscosity, dhi is the hydraulic diameter, that is, outer gap height of one plate and m\_ i is the mass flow rate of the working fluid and gas. The heat transfer coefficient αi for the

> ¼ Nui Rei

For varying evaporator length, there will be no change in the flow cross sectional area as well as in the exhaust gas side cross sectional area. As a result, there will be no effect on Reynolds number, Re, and the Nusselt number, Nu, which is directly proportional to Re. The surface areas available for exhaust gas and working fluid increase with increasing l and vice versa (see Eqs. (17)–(19)).

The cross-sectional areas Ai,new varies with width as well as with height and is inversely proportional to the heat transfer coefficients αfluid and αgas. The surface areas Sf and Sg increase with w and h and, hence, the working fluid temperature at the evaporator's outlet will behave in the same direction through equations for conservation of energy. However, Sw will stay the same with change in height, because the number of plates will change with this dimension.

With the introduced scaling factors, the evaporator size can be changed by varying its length, width or height depending on the requirements from the system, input heat flows, and type of working fluid. These three parameters have different impact on the evaporator's performance. Therefore, a sensitivity analysis has to be done to select the parameter that has the most

This section presents a methodology to optimize component size for WHR systems under transient driving conditions. Figure 6 gives an outline of the approach that is followed in this study. The scalable WHR system model developed in the previous section is crucial input for this approach. From a sensitivity analysis for the exhaust evaporator, scaling of the evaporator length is identified as the most promising route to maximize WHR power output. Details can be found in [16]. As a result, evaporator width and height will be set to their original system values in the sequel of this study. In summary, the following parameters are considered for

optimal component sizing in order to maximize WHR power output:

� m\_ iΛi Ai,new � ηi

αi ¼ Nui � Λi dhi

where Λi is the thermal conductivity of the working fluid and exhaust gas.

These areas directly affect the working fluid temperature at the evaporator's outlet.

working fluid and exhaust gas also depends on Ai,new:

90 Organic Rankine Cycle Technology for Heat Recovery

positive impact on WHR system power output.

• Exhaust gas evaporator length scaling λexh;

• EGR evaporator length scaling λEGR.

5. WHR system size optimization

• Expander scaling λexp ;

(21)

(22)

Optimizing the controller and plant iteratively to converge the coupled variables can be computationally too expensive. Therefore, an alternating architecture is followed for only one complete loop, see Figure 7. The controller designed for a specific WHR system will give different performance for a resized WHR system. Consequently, the feed forward controller from Section 3.3 is applied, which calculates the pumps speeds, such that χf ≥ 1 at the outlet of both the evaporators for given engine exhaust heat flows. Although with lower performance

Figure 7. Optimization architecture.

compared to PI control or MPC, it is seen to maintain the same trend for fuel consumption with different components sizes, without affecting the optimality of WHR system components sizes.

The standalone WHR system with feed forward controller is simulated on a 3D design grid of different sizes of EGR evaporator, exhaust evaporator and expander for a hot-start WHTC. WHR system performance is strongly affected by operating conditions. Therefore, besides overall (complete cycle) performance, also optimization is performed on urban, rural and highway driving parts, which are illustrated in Figure 8. The design grid is chosen such that: (1) it captures the main trend in outputs due to component sizing and (2) costs and total system mass remain acceptable. For the scaling factors, the following grid is chosen: λEGR ¼ λexh ¼ ½ � 0:4 : 0:1 : 1:5 and λexp ¼ ½ � 0:4 : 0:1 : 2:5 .

#### 5.1.1. Objective functions

Using exhaustive search, also referred to as brute force search, the WHR system performance is determined for each point on the grid. To obtain the optimal size of the plant, the following objective functions are defined:

• Fuel consumption (FC), which is determined from Eqs. (2)–(3). For the specified design space, WHTC results are summarized in Figure 9. Note that the net fuel consumption is normalized by using engine-only (without WHR system) results. Minimal fuel consumption is found at maximum evaporator size, although the reduction in fuel consumption decreases with increasing size. For highway conditions, where engine exhaust heat flows are relatively high, fuel economy increases for increasing expander sizes. The exhaust evaporator's size has a significant impact on fuel consumption, especially in the urban

region. Due to low exhaust gas heat flows in this region, the time for the working fluid to

• Specific investment cost (SIC, in €/kJ): in this study, we focus on installation (Costlabor) and material and production cost of the components (Costcomp) corresponding a specific

Figure 9. Normalized fuel consumption for different sizes of WHR system components on different driving conditions

SIC ¼ Costlabor þ Costcomp Ðtv

vapor. For the evaporators and expander, cost correlations are taken from [17]:

Costevap ¼ 190 þ 310 � Aevap � λevap

where Pwhrð Þt is the instantaneous net WHR power output and tv is cumulative time in

These equations clearly show that the component costs are proportional to the scaling factors to be applied. The cost of other components, such as pumps, piping, condenser and valves, are not included in the SIC. Their sizes are assumed to be fixed in this study, which will not affect the objective function. For SIC, similar graphs are generated as for FC. From these results, it is concluded that λEGR has negligible effect on SIC, whereas λexp has the biggest impact, because of its dominant share in the total system cost. Details can

0 Pwhrð Þt dt (23)

Cost exp ¼ 1:5 � 225 þ 170 � Vexp � λexp � � (24)

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extract heat increases with increase in length (or surface area) of evaporator.

WHR energy output:

from hot-start WHTC.

be found in [16].

Figure 8. Engine torque, engine speed and heat flows for hot start WHTC.

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compared to PI control or MPC, it is seen to maintain the same trend for fuel consumption with different components sizes, without affecting the optimality of WHR system components sizes. The standalone WHR system with feed forward controller is simulated on a 3D design grid of different sizes of EGR evaporator, exhaust evaporator and expander for a hot-start WHTC. WHR system performance is strongly affected by operating conditions. Therefore, besides overall (complete cycle) performance, also optimization is performed on urban, rural and highway driving parts, which are illustrated in Figure 8. The design grid is chosen such that: (1) it captures the main trend in outputs due to component sizing and (2) costs and total system mass remain acceptable. For the scaling factors, the following grid is chosen: λEGR ¼

Using exhaustive search, also referred to as brute force search, the WHR system performance is determined for each point on the grid. To obtain the optimal size of the plant, the following

• Fuel consumption (FC), which is determined from Eqs. (2)–(3). For the specified design space, WHTC results are summarized in Figure 9. Note that the net fuel consumption is normalized by using engine-only (without WHR system) results. Minimal fuel consumption is found at maximum evaporator size, although the reduction in fuel consumption decreases with increasing size. For highway conditions, where engine exhaust heat flows are relatively high, fuel economy increases for increasing expander sizes. The exhaust evaporator's size has a significant impact on fuel consumption, especially in the urban

λexh ¼ ½ � 0:4 : 0:1 : 1:5 and λexp ¼ ½ � 0:4 : 0:1 : 2:5 .

92 Organic Rankine Cycle Technology for Heat Recovery

Figure 8. Engine torque, engine speed and heat flows for hot start WHTC.

5.1.1. Objective functions

objective functions are defined:

Figure 9. Normalized fuel consumption for different sizes of WHR system components on different driving conditions from hot-start WHTC.

region. Due to low exhaust gas heat flows in this region, the time for the working fluid to extract heat increases with increase in length (or surface area) of evaporator.

• Specific investment cost (SIC, in €/kJ): in this study, we focus on installation (Costlabor) and material and production cost of the components (Costcomp) corresponding a specific WHR energy output:

$$SIC = \frac{\text{Cost}\_{\text{labor}} + \text{Cost}\_{\text{comp}}}{\int\_0^{t\_v} P\_{\text{ubir}}(t)dt} \tag{23}$$

where Pwhrð Þt is the instantaneous net WHR power output and tv is cumulative time in vapor. For the evaporators and expander, cost correlations are taken from [17]:

$$\begin{aligned} \text{Cost}\_{\text{evap}} &= 190 + 310 \cdot \text{A}\_{\text{evap}} \cdot \lambda\_{\text{evap}} \\ \text{Cost}\_{\text{exp}} &= 1.5 \cdot \left( 225 + 170 \cdot \text{V}\_{\text{exp}} \cdot \lambda\_{\text{exp}} \right) \end{aligned} \tag{24}$$

These equations clearly show that the component costs are proportional to the scaling factors to be applied. The cost of other components, such as pumps, piping, condenser and valves, are not included in the SIC. Their sizes are assumed to be fixed in this study, which will not affect the objective function. For SIC, similar graphs are generated as for FC. From these results, it is concluded that λEGR has negligible effect on SIC, whereas λexp has the biggest impact, because of its dominant share in the total system cost. Details can be found in [16].

#### 5.1.2. Sizing optimization problem

Having defined the objective functions for FC and SIC, the optimization problem boils down to:

$$\min\_{\lambda\_{\text{exh}\_{\theta}}, \lambda\_{\text{EGR}\_{\theta}}, \lambda\_{\text{exp}}} J \tag{25}$$

subject to,

$$m\_{\rm erg}(\lambda\_{EGR}) + m\_{\rm exh}(\lambda\_{\rm exh}) + m\_{\rm exp}\left(\lambda\_{\rm exp}\right) \le M\_{\rm tot}^{\rm max} \tag{26}$$

where the multi-objective function J is given by:

$$J = \begin{cases} \int\_0^{t\_f} \dot{m}\_{fuel} dt \\\\ \text{SIC} \end{cases} \tag{27}$$

increasing λexh. Hence, Mmax

Figure 11. Optimal components sizes for Mmax

components is much more beneficial in terms of energy recovery.

tot plays a bigger role in sizing because increasing the size of other

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Apart from highway driving conditions, the optimal scaling of EGR evaporator is found to be bigger than the original one. During highway driving, the amount of heat that needs to be extracted from the exhaust gases is high, which leads to higher ethanol flows. The results

tot ¼ 210kg and for different objective functions.

Figure 10. Optimal component sizes to realize minimal fuel consumption for different mass constraints.

Note that mass of the WHR system is directly proportional to the components sizes and directly affects the overall load carrying capacity of a truck. Therefore, a limit, Mmax tot , is defined on the component mass associated with sizing.

#### 5.1.3. Sizing optimization for different system mass

As a next step to solve Eqs. (25)–(27), optimal λ setting is determined for different mass constraints Mmax tot . This is done using the lambda sweep plots for FC as well as SIC, similar to Figure 9. For each objective function, the best λEGR, λexh and λexp combination is determined, which gives lowest FC or SIC while meeting a varying Mmax tot . Figure 10 shows an example of results for using the FC objective function. The resulting scaling parameters are given for four different operating conditions associated with the hot WHTC. For the overall WHTC, the corresponding fuel consumption is shown in the lower plot. Similar plots are made for SIC.

#### 5.1.4. Best WHR sizing per objective function

Final step in the optimization approach is to select Mmax tot . For the purpose of benchmarking, the optimal component sizes associates with the two different optimization criteria are compared for a mass constraint equal to the original mass of the system: Mmax tot = 210 kg, which is indicated in the plots of Figure 10 by the blue vertical lines. The results of this final step are summarized in Figure 11.

The results clearly indicate that different operating conditions and different optimization criteria lead to different component sizing. However, optimal exhaust evaporator size is smaller (i.e., λexh < 1) than its original size for all the driving conditions and both FC and SIC optimization. The exhaust evaporator has the biggest mass of the three scaled components. Although longer exhaust evaporator have better performance, the increment reduces with Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions http://dx.doi.org/10.5772/intechopen.78590 95

Figure 10. Optimal component sizes to realize minimal fuel consumption for different mass constraints.

5.1.2. Sizing optimization problem

94 Organic Rankine Cycle Technology for Heat Recovery

where the multi-objective function J is given by:

on the component mass associated with sizing.

5.1.3. Sizing optimization for different system mass

5.1.4. Best WHR sizing per objective function

which gives lowest FC or SIC while meeting a varying Mmax

Final step in the optimization approach is to select Mmax

a mass constraint equal to the original mass of the system: Mmax

to:

subject to,

constraints Mmax

Figure 11.

Having defined the objective functions for FC and SIC, the optimization problem boils down

min λexh, λEGR, λexp

> Ðtf 0 m\_ fueldt

8 >><

>>:

SIC

Note that mass of the WHR system is directly proportional to the components sizes and

As a next step to solve Eqs. (25)–(27), optimal λ setting is determined for different mass

Figure 9. For each objective function, the best λEGR, λexh and λexp combination is determined,

results for using the FC objective function. The resulting scaling parameters are given for four different operating conditions associated with the hot WHTC. For the overall WHTC, the corresponding fuel consumption is shown in the lower plot. Similar plots are made for SIC.

optimal component sizes associates with the two different optimization criteria are compared for

the plots of Figure 10 by the blue vertical lines. The results of this final step are summarized in

The results clearly indicate that different operating conditions and different optimization criteria lead to different component sizing. However, optimal exhaust evaporator size is smaller (i.e., λexh < 1) than its original size for all the driving conditions and both FC and SIC optimization. The exhaust evaporator has the biggest mass of the three scaled components. Although longer exhaust evaporator have better performance, the increment reduces with

tot . This is done using the lambda sweep plots for FC as well as SIC, similar to

megrð Þþ λEGR mexhð Þþ λexh mexp λexp

J ¼

directly affects the overall load carrying capacity of a truck. Therefore, a limit, Mmax

J (25)

tot (26)

tot . Figure 10 shows an example of

tot . For the purpose of benchmarking, the

tot = 210 kg, which is indicated in

(27)

tot , is defined

� � ≤ Mmax

increasing λexh. Hence, Mmax tot plays a bigger role in sizing because increasing the size of other components is much more beneficial in terms of energy recovery.

Apart from highway driving conditions, the optimal scaling of EGR evaporator is found to be bigger than the original one. During highway driving, the amount of heat that needs to be extracted from the exhaust gases is high, which leads to higher ethanol flows. The results

Figure 11. Optimal components sizes for Mmax tot ¼ 210kg and for different objective functions.

indicate that the original evaporator is over dimensioned for this condition. For urban and rural conditions, where exhaust heat flows are low, the ethanol flow needs to be low to extract the maximum amount of heat. However, when mass flows reach the lower boundary condition and no vapor is generated, increased evaporator length would provide more surface area and hence more time for the working fluid to extract heat. This effect is confirmed for the EGR evaporator with bigger optimal sizes for urban and rural regions. As these regions play an important role in the overall cycle result, it is expected that similar λEGR is found for the overall cycle.

Considering the real time system dynamics of WHR system, the controller sampling time is chosen to be Ts ¼ 0:4 seconds. The prediction and control horizon are Ny ¼ 50 and Nu ¼ 4 time

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The proposed switching MPC strategy is validated on the highly dynamic, hot start WHTC. Disturbances from the engine, that is, engine speed and EGR and exhaust gas heat flows, are inputs for the simulation. The objective of the controller is to maintain vapor state. However, due to the highly dynamic disturbances and limitations of the control input, it is challenging to achieve this target for all the time. To avoid damage, the expander is bypassed using the

Figure 12 shows the vapor fraction after EGR and EXH evaporators, and the mixing junction for the original and optimized system. Vapor fraction is not meeting the reference (indicated by dashed line) between 200 and 400 s, due to the low heat flows in the urban region. However, the controller shows improved overall performance in terms of disturbance rejection, where the controller specifications, χf ,mix ≥ 1, are met with short periods of time reaching at 0.9

Figure 12. Comparison of vapor fraction after the EGR and EXH evaporators, mixing junction for MPC strategy between

original and optimally sized system (with vapor fraction according to Eq. (6)).

steps, respectively, for all the three linear models.

bypass valve, such that net power output: Pwhr ¼ 0.

6.1. Controller performance validation

(around 800 and 1200 s).

The optimal expander scaling is found to be bigger than the original one for all driving conditions. This especially holds for FC optimization. For highway conditions, λexp is twice the original one due, in order to exploit the high heat flows. The expander has the biggest impact on WHR system performance. With mass comparable to other components, this leaves room for increasing λexp .

Finally, these results also indicate that optimal sizing of a single component strongly depends on the performance of all components. Interaction between evaporators and expander as well as the total mass constraint play an important role.

#### 5.2. Selected optimal scaling of WHR components

In order to make a final decision on optimal component scaling, a trade off has to be made between the optimization criteria. Therefore, the impact on FC and SIC are analyzed for both criteria. Focus is on the overall cycle result, since this is assumed to be representative for realworld performance. As expected, fuel consumption can be reduced by 0.85% compared to the originally sized system (and 2.78% compared to engine-only mode) in case of FC minimization. In case of SIC minimization, compared to the original system, there is no FC reduction, but system costs are reduced by 25%. The SIC of the FC optimal system is 60 €/kJ higher than that for the SIC minimal case.

Comparison of both cases learns that the additional system costs associated with the FC minimum case, requires an additional 1 month truck operation for return on investment. Therefore, the final optimal components scaling for the WHR system are based on the values for FC minimization:

$$
\lambda\_{\text{exh},opt} = 0.63 \qquad \lambda\_{\text{EGR},opt} = 1.47 \qquad \lambda\_{\text{exp}},opt = 1.50 \tag{28}
$$

These values will be used in the sequel of this study.

## 6. Simulation results

In this section, the switching MPC strategy from [18] is applied to the standalone WHR system with optimal component sizes. A comparison is made with the original WHR system. The MPC strategy is first evaluated on a simple stepwise cycle data from a real Euro VI heavy-duty diesel engine and then on a hot-start World Harmonized Transient Cycle (WHTC) [16]. Considering the real time system dynamics of WHR system, the controller sampling time is chosen to be Ts ¼ 0:4 seconds. The prediction and control horizon are Ny ¼ 50 and Nu ¼ 4 time steps, respectively, for all the three linear models.

#### 6.1. Controller performance validation

indicate that the original evaporator is over dimensioned for this condition. For urban and rural conditions, where exhaust heat flows are low, the ethanol flow needs to be low to extract the maximum amount of heat. However, when mass flows reach the lower boundary condition and no vapor is generated, increased evaporator length would provide more surface area and hence more time for the working fluid to extract heat. This effect is confirmed for the EGR evaporator with bigger optimal sizes for urban and rural regions. As these regions play an important role in

The optimal expander scaling is found to be bigger than the original one for all driving conditions. This especially holds for FC optimization. For highway conditions, λexp is twice the original one due, in order to exploit the high heat flows. The expander has the biggest impact on WHR system performance. With mass comparable to other components, this leaves

Finally, these results also indicate that optimal sizing of a single component strongly depends on the performance of all components. Interaction between evaporators and expander as well

In order to make a final decision on optimal component scaling, a trade off has to be made between the optimization criteria. Therefore, the impact on FC and SIC are analyzed for both criteria. Focus is on the overall cycle result, since this is assumed to be representative for realworld performance. As expected, fuel consumption can be reduced by 0.85% compared to the originally sized system (and 2.78% compared to engine-only mode) in case of FC minimization. In case of SIC minimization, compared to the original system, there is no FC reduction, but system costs are reduced by 25%. The SIC of the FC optimal system is 60 €/kJ higher than

Comparison of both cases learns that the additional system costs associated with the FC minimum case, requires an additional 1 month truck operation for return on investment. Therefore, the final optimal components scaling for the WHR system are based on the values

In this section, the switching MPC strategy from [18] is applied to the standalone WHR system with optimal component sizes. A comparison is made with the original WHR system. The MPC strategy is first evaluated on a simple stepwise cycle data from a real Euro VI heavy-duty diesel engine and then on a hot-start World Harmonized Transient Cycle (WHTC) [16].

λexh, opt ¼ 0:63 λEGR, opt ¼ 1:47 λexp , opt ¼ 1:50 (28)

the overall cycle result, it is expected that similar λEGR is found for the overall cycle.

room for increasing λexp .

96 Organic Rankine Cycle Technology for Heat Recovery

that for the SIC minimal case.

for FC minimization:

6. Simulation results

as the total mass constraint play an important role.

5.2. Selected optimal scaling of WHR components

These values will be used in the sequel of this study.

The proposed switching MPC strategy is validated on the highly dynamic, hot start WHTC. Disturbances from the engine, that is, engine speed and EGR and exhaust gas heat flows, are inputs for the simulation. The objective of the controller is to maintain vapor state. However, due to the highly dynamic disturbances and limitations of the control input, it is challenging to achieve this target for all the time. To avoid damage, the expander is bypassed using the bypass valve, such that net power output: Pwhr ¼ 0.

Figure 12 shows the vapor fraction after EGR and EXH evaporators, and the mixing junction for the original and optimized system. Vapor fraction is not meeting the reference (indicated by dashed line) between 200 and 400 s, due to the low heat flows in the urban region. However, the controller shows improved overall performance in terms of disturbance rejection, where the controller specifications, χf ,mix ≥ 1, are met with short periods of time reaching at 0.9 (around 800 and 1200 s).

Figure 12. Comparison of vapor fraction after the EGR and EXH evaporators, mixing junction for MPC strategy between original and optimally sized system (with vapor fraction according to Eq. (6)).

case a switching MPC strategy (λi ¼ 1 MPC ð Þ) is applied. The optimally sized WHR system with feed forward control strategy (λi ¼ optimal FF ð Þ) reduces fuel consumption by 2.78%. Using a switching MPC strategy (λi ¼ optimal MPC ð Þ) gives a fuel consumption reduction of 3.82% as compared to the engine only mode. In summary, by optimizing the size of WHR system components, an additional 1.08% reduction in fuel consumption can be achieved

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A methodology for optimal components sizing is presented for waste heat recovery systems operated during dynamic engine conditions. Optimality was defined in terms of minimizing the fuel consumption of the overall powertrain system. The main challenge in developing this methodology is the coupling between system design and control parameters. Focus is on Euro-VI heavy-duty engines with a mechanically coupled WHR system. Based on this work, the

• An existing WHR system model [13] is extended with a detailed expander model and is made scalable for component size. Expander volume as well as evaporator length, width

• Sensitivity analysis shows that length is the most promising route to optimize power

• An alternating optimization architecture is presented, which uses the standalone, scalable WHR system model. This methodology combines an constrained optimization problem based on fuel consumption, system costs and system mass considerations with a feed

• This methodology is successfully followed for optimal design and control of WHR system for transient driving conditions while satisfying safe operation. The components scaled in this study are EGR and exhaust gas evaporator, and expander. Different optimal component sizes are found for city, urban, rural and overall hot-start WHTC

• By implementing a switching model predictive control (MPC) strategy on the optimally sized WHR system, time in vapor state is identical, while the net fuel consumption, as

compared to the originally sized WHR system, is reduced by:

forward pump controller in order to isolate system design from control design;

compared to the original WHR system using the methodology given in this study.

7. Conclusions

following conclusions are drawn:

and height can be varied;

output for evaporators;

driving conditions;

• Urban: 0.30%. • Rural: 1.46%.

• Highway: 1.61%.

• Overall hot-start WHTC: 1.08%.

Figure 13. Performance indices in terms of recovered thermal energy (left) and time in vapor (right) compared with original system.

The main objective of MPC tuning is to keep the vapor fraction of working fluid after both the evaporators' outlets close to reference data with good disturbance rejection properties. Due to different system dynamics, the values of the weighting matrices WΔu and Wy vary from the original to the optimally sized system. Hence, the performance of the two controllers, that is, MPC for original system and optimally sized system, is quantified in terms of net thermal energy recovered and total time in vapor state, tv for different parts of the WHTC. Figure 13 illustrates that the optimally sized system outperforms the original system in terms of recovered thermal energy for all the driving conditions. Note that the recovered energy is almost doubled when complete cycle is considered. This is due to the increased expander size leading to more power output. In terms of time in vapor, both systems behave similarly, with slightly increased tv for the optimal system over the full WHTC.

#### 6.2. Powertrain performance validation

The net fuel consumption results for the studied cases are compared with the engine only mode in Figure 14. The original sized WHR system gives a 1.94% reduction in fuel consumption using the feed forward controller (λi ¼ 1 FF ð Þ). An additional 0.8% reduction is found in

Figure 14. Fuel consumption for different driving conditions from hot-start WHTC.

case a switching MPC strategy (λi ¼ 1 MPC ð Þ) is applied. The optimally sized WHR system with feed forward control strategy (λi ¼ optimal FF ð Þ) reduces fuel consumption by 2.78%. Using a switching MPC strategy (λi ¼ optimal MPC ð Þ) gives a fuel consumption reduction of 3.82% as compared to the engine only mode. In summary, by optimizing the size of WHR system components, an additional 1.08% reduction in fuel consumption can be achieved compared to the original WHR system using the methodology given in this study.

## 7. Conclusions

The main objective of MPC tuning is to keep the vapor fraction of working fluid after both the evaporators' outlets close to reference data with good disturbance rejection properties. Due to different system dynamics, the values of the weighting matrices WΔu and Wy vary from the original to the optimally sized system. Hence, the performance of the two controllers, that is, MPC for original system and optimally sized system, is quantified in terms of net thermal energy recovered and total time in vapor state, tv for different parts of the WHTC. Figure 13 illustrates that the optimally sized system outperforms the original system in terms of recovered thermal energy for all the driving conditions. Note that the recovered energy is almost doubled when complete cycle is considered. This is due to the increased expander size leading to more power output. In terms of time in vapor, both systems behave similarly, with slightly

Figure 13. Performance indices in terms of recovered thermal energy (left) and time in vapor (right) compared with

The net fuel consumption results for the studied cases are compared with the engine only mode in Figure 14. The original sized WHR system gives a 1.94% reduction in fuel consumption using the feed forward controller (λi ¼ 1 FF ð Þ). An additional 0.8% reduction is found in

increased tv for the optimal system over the full WHTC.

Figure 14. Fuel consumption for different driving conditions from hot-start WHTC.

6.2. Powertrain performance validation

98 Organic Rankine Cycle Technology for Heat Recovery

original system.

A methodology for optimal components sizing is presented for waste heat recovery systems operated during dynamic engine conditions. Optimality was defined in terms of minimizing the fuel consumption of the overall powertrain system. The main challenge in developing this methodology is the coupling between system design and control parameters. Focus is on Euro-VI heavy-duty engines with a mechanically coupled WHR system. Based on this work, the following conclusions are drawn:

	- Overall hot-start WHTC: 1.08%.
	- Urban: 0.30%.
	- Rural: 1.46%.
	- Highway: 1.61%.

## Author details

Emanuel Feru1,2, Srajan Goyal2,3 and Frank Willems1,2\*

\*Address all correspondence to<EMAIL_ADDRESS>

## References

[1] Park T, Teng H, Hunter GL, van der Velde B, Klaver J. A rankine cycle system for recovering waste heat from hd diesel engines-experimental results, Technical report. SAE Technical Paper. 2011-01-1337. 2011

[10] Feru EE. Auto-calibration for efficient diesel engines with a waste heat recovery system.

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions

http://dx.doi.org/10.5772/intechopen.78590

101

[11] Feru E, Willems F, de Jager B, Steinxbuch M. Modeling and control of a parallel waste heat recovery system for Euro-VI heavy-duty diesel engines. Energies. 2014;7(10):6571-6592

[12] Silvas E, Hofman T, Murgovski N, Etman LFP., Steinbuch M. Review of optimization strategies for system-level design in hybrid electric vehicles. In: IEEE Transactions on

[13] Feru E, Kupper F, Rojer C, Seykens X, Scappin F, Willems F, Smits J, De Jager B, Steinbuch M. Experimental validation of a dynamic waste heat recovery system model for control

[14] Oom M. Identification and validation of an expander model for automotive waste heat recovery systems, Technical report. Eindhoven University of Technology; 2014

[15] Feru E, de Jager B, Willems F, Steinbuch M. Two-phase plate-fin heat exchanger modeling for waste heat recovery systems in diesel engines. Applied Energy. 2014;133:183-196 [16] Goyal S. Optimal sizing of waste heat recovery system for dynamic engine conditions,

[17] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic rankine cycles. Applied Thermal Engineering. 2011;31(14):2885-2893 [18] Feru E, Willems F, de Jager B, Steinbuch M. Model predictive control of a waste heat recovery system for automotive diesel engines. In: System Theory, Control and Comput-

Vehicular Technology. Jan 2017;66(1):57-70. DOI: 10.1109/TVT.2016.2547897

purposes, Technical report. SAE Technical Paper; 2013-01-1647. 2013

Master thesis CST 2016.137. Eindhoven University of Technology; 2016

ing (ICSTCC), 2014 18th International Conference. IEEE; 2014. pp. 658-663

Ph.D. thesis, Eindhoven University of Technology; 2015

[10] Feru EE. Auto-calibration for efficient diesel engines with a waste heat recovery system. Ph.D. thesis, Eindhoven University of Technology; 2015

Author details

References

Emanuel Feru1,2, Srajan Goyal2,3 and Frank Willems1,2\*

\*Address all correspondence to<EMAIL_ADDRESS>
2 Eindhoven University of Technology, Eindhoven, The Netherlands

tomorrow. MTZ Worldwide eMagazine. 2011;72(4):52-56

Technical report. Eindhoven University of Technology; 2016

systems. Applied Energy. 2013;105:293-303

[1] Park T, Teng H, Hunter GL, van der Velde B, Klaver J. A rankine cycle system for recovering waste heat from hd diesel engines-experimental results, Technical report. SAE

[2] Bredel DE, Nickl IJ, Bartosch D-IS. Waste heat recovery in drive systems of today and

[3] Grelet V. Rankine cycle based waste heat recovery system applied to heavy duty vehicles: Topological optimization and model based control. Ph.D. thesis, Université de Liège,

[4] Goyal S. Optimal sizing of waste heat recovery system for HD truck: Steady state analysis,

[5] Horst TA, Rottengruber H-S, Seifert M, Ringler J. Dynamic heat exchanger model for performance prediction and control system design of automotive waste heat recovery

[6] Horst TA, Tegethoff W, Eilts P, Koehler J. Prediction of dynamic rankine cycle waste heat recovery performance and fuel saving potential in passenger car applications considering interactions with vehicles energy management. Energy Conversion and Management.

[7] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M. Part load based thermo-economic optimization of the organic rankine cycle (orc) applied to a com-

[8] Seher D, Lengenfelder T, Gerhardt J, Eisenmenger N, Hackner M, Krinn I. Waste heat recovery for commercial vehicles with a rankine process. In: 21st Aachen Colloquium on

[9] Quoilin S, Aumann R, Grill A, Schuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery organic rankine cycles. Applied Energy.

bined heat and power (chp) system. Applied Energy. 2013;111:871-881

Automobile and Engine Technology, Aachen, Germany. Oct, 2012. pp. 7-9

1 TNO Automotive, Helmond, The Netherlands

Technical Paper. 2011-01-1337. 2011

3 FlandersMake, Lommel, Belgium

100 Organic Rankine Cycle Technology for Heat Recovery

Liège, Belgique; 2016

2014;78:438-451

2011;88(6):2183-2190

**Chapter 6**

**Provisional chapter**

**Dynamic Modeling of ORC Power Plants**

**Dynamic Modeling of ORC Power Plants**

DOI: 10.5772/intechopen.78390

This chapter presents dynamic modeling approaches suitable for organic Rankine cycle (ORC) power plants. Dynamic models are necessary for the better understanding of the plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating range. One example is the proportion of liquid and vapor phase in the condenser and evaporator that must be kept within acceptable ranges to avoid stalling or temperature shocks during transient conditions. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand accordingly. The aim of the chapter is to investigate and review the methodologies applicable for dynamic

**Keywords:** dynamic modeling, transient conditions, simulation, time constants, ORC,

The mathematical modeling of the dynamic systems and analysis of their dynamic characteristics is essential for developing the control and monitoring systems. A dynamic model is able to trace the variation of the system operating parameters in all operating conditions and consequently detect the critical points and outranges. Generally, the dynamic behavior of a system including mechanical, electrical, fluid, thermal, and so on can be described by a set of

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Mohsen Assadi and Yaser Mollaei Barzi

Mohsen Assadi and Yaser Mollaei Barzi

http://dx.doi.org/10.5772/intechopen.78390

simulation of ORC power plants.

thermal power plant

**1.1. Basics of dynamic modeling**

**1. Introduction**

**Abstract**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Dynamic Modeling of ORC Power Plants Dynamic Modeling of ORC Power Plants**

#### Mohsen Assadi and Yaser Mollaei Barzi Mohsen Assadi and Yaser Mollaei Barzi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78390

#### **Abstract**

This chapter presents dynamic modeling approaches suitable for organic Rankine cycle (ORC) power plants. Dynamic models are necessary for the better understanding of the plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating range. One example is the proportion of liquid and vapor phase in the condenser and evaporator that must be kept within acceptable ranges to avoid stalling or temperature shocks during transient conditions. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand accordingly. The aim of the chapter is to investigate and review the methodologies applicable for dynamic simulation of ORC power plants.

DOI: 10.5772/intechopen.78390

**Keywords:** dynamic modeling, transient conditions, simulation, time constants, ORC, thermal power plant

## **1. Introduction**

#### **1.1. Basics of dynamic modeling**

The mathematical modeling of the dynamic systems and analysis of their dynamic characteristics is essential for developing the control and monitoring systems. A dynamic model is able to trace the variation of the system operating parameters in all operating conditions and consequently detect the critical points and outranges. Generally, the dynamic behavior of a system including mechanical, electrical, fluid, thermal, and so on can be described by a set of

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

transient differential equations (ODE or PDE) which originates from the governing physical principals and inherent physical characteristics.

performance is also the foundation for developing control systems during the early design stage of an ORC power plant. In an ORC dynamic operation analysis, the following factors

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 105

• the time response of the ORC components (including turbine, pump, heat exchangers, etc.) and identification of the slowest responding component to an input parameter change; • the total system response time, overshoots, and identification of limitations and outranges;

• an unexpected slow or sharp transient in response to change in one or multiple physical

Much of the recent research on ORC systems focused on finding the ideal working fluids and developing turbines and heat exchangers that can provide the highest efficiency for the given power plant layout and the nominal steady-state operational conditions. A wide range of literature is available dealing with the steady-state operation of ORC systems for geothermal

A thorough exposition on the dynamic modeling of ORCs is given in a two-part series by Paliano and Putten [7] and [8]. They give insight into the requirements for dynamic model development and validation of Rankine cycle systems and present a simulation of a 600 kWe biomass-fired steam power plant. They use a self-developed dynamic cycle analysis library using an object-oriented, general simulation software (http://www.mathworks.com). The developed models are designed for observing transients around the steady state and do not cope well with unusual circumstances, such as sudden large drops in the temperature of the

The dynamic modeling of the organic Rankine cycle (ORC) was also carried out by Wei et al. [9] targeting ORC system control and diagnostic. They tested two different modeling approaches for this purpose, focusing on computational time, simulation accuracy, and complexity. The first approach was based on the moving boundary numerical method and the second one was performed using the general discretization technique. The code was developed in Modelica and simulated by the Dymola module. After comparison and evaluation of the two approaches, they suggested the moving boundary approach as the most suitable ones

Sohel et al. [6] published their study on the dynamic modeling of a 5.4 MW binary cycle unit of a geothermal power plant. Pentane was used as the ORC motive fluid and it is powered by separated brine from the geothermal fluid. The results of simulation were compared to the plant performance data and the prediction capability of the model at steady and transient

operational conditions was proved with reasonably good accuracy.

are of interest to be investigated and identified [5].

• recognition of the start-up and shut-down operation mode;

variables like thermal input, power output, and so on;

power plants, while dynamic models and studies are not so common [6].

• the part-load capability of the system.

**1.3. State of the art (literature review)**

heating fluid or start-up and shutdown.

for control design applications.

The basic concepts that have to be known in dynamic modeling include system inertia, initial condition, input stimulus variable, and time constant.

The *inertia of a system* is defined by its tendency to remain unchanged or its resistivity against the variation. Obviously, the system's dynamic response depends on its inherent inertia and also the input stimulus which causes the system to break through its initial steady-state condition. To simulate and predict a system's dynamic response, all parameters and properties of the system which affect system inertia have to be known and considered. In mathematics and particularly in dynamic systems, an *initial condition* is the value of an evolving variable at some specific point in time (typically denoted as t = 0). Generally, initial conditions are needed in order to be able to trace the changes in the system's variables in time. Initial conditions affect the value of dynamic variables (state variables) at any time in the future [1].

In dynamic modeling, it is assumed that the system's initial state is disturbed due to an external excitation or load change which forces the system to respond dynamically. This input excitation pulse is called *input stimulus variable*. The input stimulus can be an impulse function, a step function, a linear function, a sinusoidal function or any other type of timedependent function.

Moreover, *time constant* is defined as a time which represents the speed with which a particular system can respond to change, typically equal to the time taken for a specified parameter to vary conventionally by a factor of 1–1/*e* (approximately 0.6321). Actually, it is a criterion that enables us to evaluate the response speed and inertia of the system and also to compare the response time of different systems to each other. Physically, a smaller time constant means a quicker system response. For example, time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or heating [2]. This concept is also used in other dynamic systems including mechanical vibration and damping, electrical circuits, electronic systems, fluid and hydraulic systems, thermodynamic systems, chemical and electrochemical processes, and so on [3].

In this chapter, we are going to focus on thermal power plants' dynamic behavior modeling and specialize it for ORC power plants.

### **1.2. Theory of thermal power systems and organic Rankine cycles' dynamic operation**

In the development of thermal power plants, a good estimation/prediction of the plant behavior under design and/or during operation is highly desired [4]. Thermal power systems and especially organic Rankine cycles (ORCs) have complex starting and shut-down mechanisms and normally undergo fluctuations in operating conditions during their service period. Therefore, their dynamic behavior has to be identified to ensure the secure and continuous operation of the system when facing fluctuations and perturbations. The dynamic plant performance is also the foundation for developing control systems during the early design stage of an ORC power plant. In an ORC dynamic operation analysis, the following factors are of interest to be investigated and identified [5].

transient differential equations (ODE or PDE) which originates from the governing physical

The basic concepts that have to be known in dynamic modeling include system inertia, initial

The *inertia of a system* is defined by its tendency to remain unchanged or its resistivity against the variation. Obviously, the system's dynamic response depends on its inherent inertia and also the input stimulus which causes the system to break through its initial steady-state condition. To simulate and predict a system's dynamic response, all parameters and properties of the system which affect system inertia have to be known and considered. In mathematics and particularly in dynamic systems, an *initial condition* is the value of an evolving variable at some specific point in time (typically denoted as t = 0). Generally, initial conditions are needed in order to be able to trace the changes in the system's variables in time. Initial conditions

In dynamic modeling, it is assumed that the system's initial state is disturbed due to an external excitation or load change which forces the system to respond dynamically. This input excitation pulse is called *input stimulus variable*. The input stimulus can be an impulse function, a step function, a linear function, a sinusoidal function or any other type of time-

Moreover, *time constant* is defined as a time which represents the speed with which a particular system can respond to change, typically equal to the time taken for a specified parameter to vary conventionally by a factor of 1–1/*e* (approximately 0.6321). Actually, it is a criterion that enables us to evaluate the response speed and inertia of the system and also to compare the response time of different systems to each other. Physically, a smaller time constant means a quicker system response. For example, time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or heating [2]. This concept is also used in other dynamic systems including mechanical vibration and damping, electrical circuits, electronic systems, fluid and hydraulic systems, thermodynamic systems, chemical and

In this chapter, we are going to focus on thermal power plants' dynamic behavior modeling

In the development of thermal power plants, a good estimation/prediction of the plant behavior under design and/or during operation is highly desired [4]. Thermal power systems and especially organic Rankine cycles (ORCs) have complex starting and shut-down mechanisms and normally undergo fluctuations in operating conditions during their service period. Therefore, their dynamic behavior has to be identified to ensure the secure and continuous operation of the system when facing fluctuations and perturbations. The dynamic plant

**1.2. Theory of thermal power systems and organic Rankine cycles' dynamic**

affect the value of dynamic variables (state variables) at any time in the future [1].

principals and inherent physical characteristics.

104 Organic Rankine Cycle Technology for Heat Recovery

dependent function.

**operation**

electrochemical processes, and so on [3].

and specialize it for ORC power plants.

condition, input stimulus variable, and time constant.

#### **1.3. State of the art (literature review)**

Much of the recent research on ORC systems focused on finding the ideal working fluids and developing turbines and heat exchangers that can provide the highest efficiency for the given power plant layout and the nominal steady-state operational conditions. A wide range of literature is available dealing with the steady-state operation of ORC systems for geothermal power plants, while dynamic models and studies are not so common [6].

A thorough exposition on the dynamic modeling of ORCs is given in a two-part series by Paliano and Putten [7] and [8]. They give insight into the requirements for dynamic model development and validation of Rankine cycle systems and present a simulation of a 600 kWe biomass-fired steam power plant. They use a self-developed dynamic cycle analysis library using an object-oriented, general simulation software (http://www.mathworks.com). The developed models are designed for observing transients around the steady state and do not cope well with unusual circumstances, such as sudden large drops in the temperature of the heating fluid or start-up and shutdown.

The dynamic modeling of the organic Rankine cycle (ORC) was also carried out by Wei et al. [9] targeting ORC system control and diagnostic. They tested two different modeling approaches for this purpose, focusing on computational time, simulation accuracy, and complexity. The first approach was based on the moving boundary numerical method and the second one was performed using the general discretization technique. The code was developed in Modelica and simulated by the Dymola module. After comparison and evaluation of the two approaches, they suggested the moving boundary approach as the most suitable ones for control design applications.

Sohel et al. [6] published their study on the dynamic modeling of a 5.4 MW binary cycle unit of a geothermal power plant. Pentane was used as the ORC motive fluid and it is powered by separated brine from the geothermal fluid. The results of simulation were compared to the plant performance data and the prediction capability of the model at steady and transient operational conditions was proved with reasonably good accuracy.

An ORC dynamic modeling package was presented by Casella et al. [10] for the system design and prediction of the off-design conditions. They validated their results with Triogen ORC system data [11]. The system standard module included Triogen turbo-generator, turbo pump, condenser, and recuperator, while the evaporator could be designed and customized for available energy sources. For evaporator heat exchanger modeling purpose, they used one-dimensional heat transfer equations and considered a standard geometry with some simplifying correlations.

input heat load, were assessed using the dynamic model with reference to a sample heat load

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 107

Furthermore, Xu et al. [17] developed a dynamic organic Rankine cycle waste heat recovery model (ORC-WHR) using Simulink and an engine model for heavy-duty diesel applications. Their physics-based ORC-WHR system model, constructed in GT-POWER software platform, included parallel evaporators, flow control valves, a turbine expander, a reservoir, pumps, compressible volumes, and junctions. Experimental data for the ORC-WHR component models were identified and collected over a wide range of steady-state and transient operational conditions. The data were collected from an ORC-WHR system on a 13 L heavy-duty diesel engine. The model was supposed to serve as a virtual plant for offline simulations to explore the potential of fuel savings and emission reduction for different driving cycles of the heavy-

The reviewed papers presented here illuminate different modeling methodologies and strategies with various levels of accuracy and computational time/cost (based on the system application and modeling purpose). In addition, it is expected that a comprehensive dynamic model enables a full-range analysis of a system's transient response to variation of input parameters, that is, minimum (near-zero) to maximum possible input thermal load. The function, representing the input variations, should be flexible enough to enable the users to study

It is also advantageous to be able to switch these inputs and outputs around for improved flexibility. In addition, adaptation of the model to closed loop control systems should be con-

In this chapter, a general framework is devised to provide a flexible dynamic modeling approach adaptable to different ORC system applications and different dynamic modeling purposes based on the reviewed modeling attempts and reported results. The modeling framework incorporates step-by-step dynamic modeling methodology for both component and system levels. Technical aspects as well as assumptions and required considerations for ORC dynamic modeling are described. Besides, component assembling approaches to build dynamic models of the whole ORC system are discussed and key aspects and related noticeable remarks are highlighted. Moreover, the potential applicable software tools as well as developed computer codes and data libraries customized for transient modeling of ORC power plants are reviewed,

To build a comprehensive and meanwhile enough fast dynamic model of an ORC power system, the intelligent selection of component models with proper input/output parameters as well as appropriate simplifying assumptions is crucial. The ORC systems are generally utilized for the very vast range of heat recovery applications for each of which the specific type of components might be used with different operating characteristics and conditions. For example, various types and sizes of heat exchangers, expanders, pumps, valves, and so on are used for the ORCs depending on the scale of thermal power input, working fluid, secondary

profile of the hot water source and at different timescales.

duty trucks and provide guidelines for the experimental studies.

**2. Dynamic modeling of ORC at the component level**

the effects on the power output as the function of time.

sidered too.

evaluated, and described.

Desideri et al. [12] developed a dynamic model of the ORC system, validated both in steadystate and transient conditions via experimental data using a 10 kWe waste heat recovery (WHR) ORC system with a screw expander. They used an open-source Modelica library, ThermoCycle, developed by the Energy Systems Research Unit at the University of Liege. The commercial program Dymola (Dynamic Modeling Laboratory) was used to perform all the simulations. They implemented a liquid receiver model after the condenser to incorporate the accumulated liquid in the tank based on the phase equilibrium assumption. Moreover, effects of the noncondensable gases were incorporated in their model using the gas mixture theory.

Eventually, they demonstrated that the ThermoCycle library can reliably be used for the modeling of such thermodynamic systems, allowing, for instance, the implementation and simulation of various control strategies.

Ziviani et al. [13] discussed the challenges involved in ORC modeling for low-grade thermal energy recovery. They studied and reviewed various software packages, to identify the most applicable and suitable ones for ORC system modeling. Their recommended package list included Matlab/Simulink, EES, Phyton, Modelica, AMESim, and Cycle-Tempo.

In another relevant study, Grelet et al. [14] presented a method to model heat exchangers used in waste heat recovery Rankine-based systems in heavy-duty trucks using the water ethanol mixture and recovering heat from the exhaust gas recirculation (EGR) system. The model predicted both the heat transfer and physical properties of the working fluid such as temperature and density after the heat exchange process. The authors claim that the model presents an advantage of being low in terms of computational needs and is suitable for control software integration. Grelet et al. [15] published also another paper investigating the transient performance of a waste heat recovery Rankine cycle-based system for a heavy-duty truck and compared it to the steady-state study. Simple thermodynamic simulations are carried out assuming certain conditions for the comparison of several working fluids. Fluid choice and concept optimization are conducted, taking into account integration constraints (heat rejection, packaging, etc.). The study exposes the importance of the modeling phase when designing Rankine cycle-based heat recovery systems (HRSs) and yields a better understanding when it comes to the integration of a Rankine cycle in a truck.

Marchionni et al. [16] presented a modeling approach to analyze and design waste heat to power conversion units based on an ORC. They implemented the model in the commercial software platform GT-SUITE. Sub-models were developed and calibrated for the components like plate heat exchangers and multistage centrifugal pumps using performance data of industrial map data at design and off-design conditions. The pump and turbine speed were optimized at different operating conditions of the evaporator to maximize the net power output. Furthermore, the effects of thermal inertial of the evaporator, in response to transient input heat load, were assessed using the dynamic model with reference to a sample heat load profile of the hot water source and at different timescales.

An ORC dynamic modeling package was presented by Casella et al. [10] for the system design and prediction of the off-design conditions. They validated their results with Triogen ORC system data [11]. The system standard module included Triogen turbo-generator, turbo pump, condenser, and recuperator, while the evaporator could be designed and customized for available energy sources. For evaporator heat exchanger modeling purpose, they used one-dimensional heat transfer equations and considered a standard geometry with some sim-

Desideri et al. [12] developed a dynamic model of the ORC system, validated both in steadystate and transient conditions via experimental data using a 10 kWe waste heat recovery (WHR) ORC system with a screw expander. They used an open-source Modelica library, ThermoCycle, developed by the Energy Systems Research Unit at the University of Liege. The commercial program Dymola (Dynamic Modeling Laboratory) was used to perform all the simulations. They implemented a liquid receiver model after the condenser to incorporate the accumulated liquid in the tank based on the phase equilibrium assumption. Moreover, effects of the non-

Eventually, they demonstrated that the ThermoCycle library can reliably be used for the modeling of such thermodynamic systems, allowing, for instance, the implementation and

Ziviani et al. [13] discussed the challenges involved in ORC modeling for low-grade thermal energy recovery. They studied and reviewed various software packages, to identify the most applicable and suitable ones for ORC system modeling. Their recommended package list

In another relevant study, Grelet et al. [14] presented a method to model heat exchangers used in waste heat recovery Rankine-based systems in heavy-duty trucks using the water ethanol mixture and recovering heat from the exhaust gas recirculation (EGR) system. The model predicted both the heat transfer and physical properties of the working fluid such as temperature and density after the heat exchange process. The authors claim that the model presents an advantage of being low in terms of computational needs and is suitable for control software integration. Grelet et al. [15] published also another paper investigating the transient performance of a waste heat recovery Rankine cycle-based system for a heavy-duty truck and compared it to the steady-state study. Simple thermodynamic simulations are carried out assuming certain conditions for the comparison of several working fluids. Fluid choice and concept optimization are conducted, taking into account integration constraints (heat rejection, packaging, etc.). The study exposes the importance of the modeling phase when designing Rankine cycle-based heat recovery systems (HRSs) and yields a better understand-

Marchionni et al. [16] presented a modeling approach to analyze and design waste heat to power conversion units based on an ORC. They implemented the model in the commercial software platform GT-SUITE. Sub-models were developed and calibrated for the components like plate heat exchangers and multistage centrifugal pumps using performance data of industrial map data at design and off-design conditions. The pump and turbine speed were optimized at different operating conditions of the evaporator to maximize the net power output. Furthermore, the effects of thermal inertial of the evaporator, in response to transient

condensable gases were incorporated in their model using the gas mixture theory.

included Matlab/Simulink, EES, Phyton, Modelica, AMESim, and Cycle-Tempo.

ing when it comes to the integration of a Rankine cycle in a truck.

plifying correlations.

106 Organic Rankine Cycle Technology for Heat Recovery

simulation of various control strategies.

Furthermore, Xu et al. [17] developed a dynamic organic Rankine cycle waste heat recovery model (ORC-WHR) using Simulink and an engine model for heavy-duty diesel applications. Their physics-based ORC-WHR system model, constructed in GT-POWER software platform, included parallel evaporators, flow control valves, a turbine expander, a reservoir, pumps, compressible volumes, and junctions. Experimental data for the ORC-WHR component models were identified and collected over a wide range of steady-state and transient operational conditions. The data were collected from an ORC-WHR system on a 13 L heavy-duty diesel engine. The model was supposed to serve as a virtual plant for offline simulations to explore the potential of fuel savings and emission reduction for different driving cycles of the heavyduty trucks and provide guidelines for the experimental studies.

The reviewed papers presented here illuminate different modeling methodologies and strategies with various levels of accuracy and computational time/cost (based on the system application and modeling purpose). In addition, it is expected that a comprehensive dynamic model enables a full-range analysis of a system's transient response to variation of input parameters, that is, minimum (near-zero) to maximum possible input thermal load. The function, representing the input variations, should be flexible enough to enable the users to study the effects on the power output as the function of time.

It is also advantageous to be able to switch these inputs and outputs around for improved flexibility. In addition, adaptation of the model to closed loop control systems should be considered too.

In this chapter, a general framework is devised to provide a flexible dynamic modeling approach adaptable to different ORC system applications and different dynamic modeling purposes based on the reviewed modeling attempts and reported results. The modeling framework incorporates step-by-step dynamic modeling methodology for both component and system levels. Technical aspects as well as assumptions and required considerations for ORC dynamic modeling are described. Besides, component assembling approaches to build dynamic models of the whole ORC system are discussed and key aspects and related noticeable remarks are highlighted. Moreover, the potential applicable software tools as well as developed computer codes and data libraries customized for transient modeling of ORC power plants are reviewed, evaluated, and described.

## **2. Dynamic modeling of ORC at the component level**

To build a comprehensive and meanwhile enough fast dynamic model of an ORC power system, the intelligent selection of component models with proper input/output parameters as well as appropriate simplifying assumptions is crucial. The ORC systems are generally utilized for the very vast range of heat recovery applications for each of which the specific type of components might be used with different operating characteristics and conditions. For example, various types and sizes of heat exchangers, expanders, pumps, valves, and so on are used for the ORCs depending on the scale of thermal power input, working fluid, secondary transfer fluid, and the specific operating conditions. Based on the ORC system application and its specific operating conditions, a proper model with reasonable simplifying assumptions has to be considered for component modeling. In this section, we will discuss modeling methodology and analogy of the ORC components, trying to clarify general aspects of the mathematic formulation and simulation details. In some cases, we need to specialize the models for a particular component or specific assumptions requiring further modeling details.

Generally, the heat exchanger as a power plant component is simulated using one-dimensional heat and mass transfer equations because of the acceptable accuracy of one-dimensional models and limitation in computational time especially for the dynamic models and control applications. One-dimensional consideration leads to the following assumptions which nor-

• The pressure drop is considered in some models but omitted in others. It depends on the

• Mass accumulation is considered for the fluids (even though it is neglected in some devel-

• The heat exchanger could be assumed either with or without phase change depending on

• One-dimensional mass and energy equations are considered and the equations are solved numerically along the heat exchanger. For more simple modeling, lumped thermal capacitance can also be assumed for both the metal pipe and the fluids; hence, just one thermal

• The external pipe is assumed to be ideally insulated from the environment; hence, heat

• Axial heat conduction in working fluid, wall, and exhaust gas is not considered (even

Heat exchanger modeling tools are generally based on the finite difference method, applying the energy conservation and mass conservation equations in a differential form. The

each of length ∆x, that are the places where the conservation equations are applied. For each discrete volume three nodes can be defined in the radial direction: one referring to the state of the transfer fluid in the annulus (indexed by tf), one to the state of the metal constituting the metal pipe (indexed by p), and one referring to the organic fluid within the internal pipe

The system inputs are characterized by the parameters representing the two fluids at the heat exchanger inlet. Particularly their temperature, pressure, and mass flow rate must be known, and the fluid pressures are introduced since many properties depend also upon pressure. The output generated by the system can be any of the state variables but of particular interest; in the view of linking the heat exchanger to other components in a complex network, the state of the fluids leaving the exchanger must be provided, as the temperature of the two fluids. Due to the counter-flow design this temperature will be the one calculated at the node with index

longitudinal lumped volumes,

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 109

• The wall and fluid temperature in the radial direction is internally uniform.

though in some modeling attempts, it is taken into account).

straight pipe in a typical heat exchanger design is split into nx

1 for the fluid flowing in the annulus, as shown in **Figure 3** [18].

(indexed by f), according to the scheme of **Figure 2**.

• Energy accumulation is considered in both metal pipe and the two working fluids.

importance of the pressure loss in a specific modeling strategy.

mally are applied:

oped models for simplicity).

the actual case under study.

losses are neglected.

node needs to be defined with such assumptions.

#### **2.1. Heat exchanger (evaporator, condenser, etc.)**

In the ORC waste heat recovery systems, the heat exchangers are generally used either as evaporators or as condensers. Evaporators absorb heat from the heat source and release it to the working fluid while the condensers reject heat from the working fluid to cooling water. Since the evaporators and condensers are crucial components when determining the overall dynamic behavior of the ORCs, the heat exchanger model should be characterized by sufficient flexibility to allow simple generalization of the design.

Different types of heat exchangers might be used in the ORC systems including plate/compact heat exchangers, tubular co-flow/counter-flow heat exchangers, shell and tube heat exchangers, and so on. The detailed heat and mass transfer equations are slightly different for different types of heat exchangers due to their configuration and geometry, but the principles are the same for all these heat exchanger types. Here, we will present the modeling methodology and general equations used.

For the modeling purpose, the heat exchangers are normally represented as a straight pipe, despite the fact that different and more complex designs are usually adopted in order to enhance the heat exchanged and to reduce the overall dimensions of the system (see a schematic sample configuration in **Figure 1**) [18]. The assumption of a straight pipe, however, simplifies the resulting dynamic problem to a great extent and is commonly adopted when the heat exchanger dynamic modeling is considered [9, 19].

**Figure 1.** An example of a compact heat exchanger development into a unidirectional pipe [18].

Generally, the heat exchanger as a power plant component is simulated using one-dimensional heat and mass transfer equations because of the acceptable accuracy of one-dimensional models and limitation in computational time especially for the dynamic models and control applications. One-dimensional consideration leads to the following assumptions which normally are applied:

transfer fluid, and the specific operating conditions. Based on the ORC system application and its specific operating conditions, a proper model with reasonable simplifying assumptions has to be considered for component modeling. In this section, we will discuss modeling methodology and analogy of the ORC components, trying to clarify general aspects of the mathematic formulation and simulation details. In some cases, we need to specialize the models for a particular component or specific assumptions requiring further modeling details.

In the ORC waste heat recovery systems, the heat exchangers are generally used either as evaporators or as condensers. Evaporators absorb heat from the heat source and release it to the working fluid while the condensers reject heat from the working fluid to cooling water. Since the evaporators and condensers are crucial components when determining the overall dynamic behavior of the ORCs, the heat exchanger model should be characterized by suf-

Different types of heat exchangers might be used in the ORC systems including plate/compact heat exchangers, tubular co-flow/counter-flow heat exchangers, shell and tube heat exchangers, and so on. The detailed heat and mass transfer equations are slightly different for different types of heat exchangers due to their configuration and geometry, but the principles are the same for all these heat exchanger types. Here, we will present the modeling methodology

For the modeling purpose, the heat exchangers are normally represented as a straight pipe, despite the fact that different and more complex designs are usually adopted in order to enhance the heat exchanged and to reduce the overall dimensions of the system (see a schematic sample configuration in **Figure 1**) [18]. The assumption of a straight pipe, however, simplifies the resulting dynamic problem to a great extent and is commonly adopted when

**2.1. Heat exchanger (evaporator, condenser, etc.)**

108 Organic Rankine Cycle Technology for Heat Recovery

and general equations used.

ficient flexibility to allow simple generalization of the design.

the heat exchanger dynamic modeling is considered [9, 19].

**Figure 1.** An example of a compact heat exchanger development into a unidirectional pipe [18].

Heat exchanger modeling tools are generally based on the finite difference method, applying the energy conservation and mass conservation equations in a differential form. The straight pipe in a typical heat exchanger design is split into nx longitudinal lumped volumes, each of length ∆x, that are the places where the conservation equations are applied. For each discrete volume three nodes can be defined in the radial direction: one referring to the state of the transfer fluid in the annulus (indexed by tf), one to the state of the metal constituting the metal pipe (indexed by p), and one referring to the organic fluid within the internal pipe (indexed by f), according to the scheme of **Figure 2**.

The system inputs are characterized by the parameters representing the two fluids at the heat exchanger inlet. Particularly their temperature, pressure, and mass flow rate must be known, and the fluid pressures are introduced since many properties depend also upon pressure. The output generated by the system can be any of the state variables but of particular interest; in the view of linking the heat exchanger to other components in a complex network, the state of the fluids leaving the exchanger must be provided, as the temperature of the two fluids. Due to the counter-flow design this temperature will be the one calculated at the node with index 1 for the fluid flowing in the annulus, as shown in **Figure 3** [18].

Here, the rotational speed and the pressure ratio are input variables, while mass flow rate and efficiency (from which power and torque can be derived) are outputs; however, the input/output variables could be changed or replaced depending on specific application requirements or design/optimization strategies [17]. The turbine can be integrated with an electric generator or it can also be mechanically connected to an engine crank shaft through a transmission, as in [21]. Due to the choked flow status at high expansion ratios 10–30, turbine expander mass flow rate can be written as a linear function of turbine inlet pressure as shown in Eq. (1) [17].

*hout*,*turb* = *hin*,*turb* − *ηis*,*turb*(*hin*,*turb* − *hout*,*is*,*turb*) (2)

*ηis*,*turb* = *map*( *Nturb*, *pin*,*turb* /*pout*,*turb*, *Tin*,*turb*) (3)

*hout*,*is*,*turb* = *map*( *Sout*,*turb*, *pout*,*turb*) (4)

*Sout*,*turb* = *Sin*,*turb* (5)

*Sis*,*turb* = *map*( *hin*,*turb*, *pin*,*turb*) (6)

The turbine efficiency map has to be provided by the turbine manufacturer. Outlet temperature, Tout,tur, is calculated from outlet enthalpy and outlet pressure using a thermodynamic table

*Tout*,*turb* = *map*( *hout*,*turb*, *pout*,*turb*) (7)

*turb* = *aturb pin*,*turb* + *bturb* (1)

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 111

*m*̇

of the working fluid.

**Figure 4.** Block diagram of the turbine/expander model.

The outlet enthalpy is calculated by isentropic efficiency as follows:

**Figure 2.** Discretization assumed for typical tubular counter-flow heat exchanger with phase change and main heat fluxes involved [18].

**Figure 3.** The heat exchanger block.

Subscribes f1 and f2 refer to fluid 1 (in the inner pipe) and fluid 2 (in the annulus), respectively, and subscribe p relates to the pipe body. Once the system has been fully defined, the heat and mass transfer coefficients and correlations must be introduced to calculate the actual thermal fluxes.

An interesting study conducted on this topic is by García-Vallardes et al. [20], in which the thermal and fluid dynamic behavior of a tubular heat exchanger (could be applied as evaporator or condenser) are simulated numerically. Continuity, momentum and energy conservation equations were applied for the internal and annulus tubes to accurately predict the heat and mass transfer inside the heat exchanger. Energy conservation equations have in fact been applied to the external tube and insulation, hence dropping the hypothesis of the ideally insulated system. However, such detailed simulation of the heat exchanger is not useful for the modeling of dynamic ORC systems, since one needs to compromise between expected accuracy and computational time and cost.

#### **2.2. Expander**

The expander turbine is simulated generally as a component based upon steady-state characteristic curves. Inputs/outputs of the system are shown in **Figure 4**.

Here, the rotational speed and the pressure ratio are input variables, while mass flow rate and efficiency (from which power and torque can be derived) are outputs; however, the input/output variables could be changed or replaced depending on specific application requirements or design/optimization strategies [17]. The turbine can be integrated with an electric generator or it can also be mechanically connected to an engine crank shaft through a transmission, as in [21]. Due to the choked flow status at high expansion ratios 10–30, turbine expander mass flow rate can be written as a linear function of turbine inlet pressure as shown in Eq. (1) [17].

$$
\dot{m}\_{\text{turb}} = a\_{\text{turb}} p\_{\text{in,turb}} + b\_{\text{turb}} \tag{1}
$$

The outlet enthalpy is calculated by isentropic efficiency as follows:

$$h\_{out,tuvb} = h\_{in,tuvb} - \eta\_{is,tuvb} (h\_{in,tuvb} - h\_{out,is,tuvb}) \tag{2}$$

$$\eta\_{is, turb} = \max\{ \left( \mathbf{N}\_{uub'}, p\_{iu, nub'} / p\_{out, nub'}, T\_{in, nub} \right) \tag{3}$$

$$h\_{out,is,turb} = \text{map}\left(\mathbb{S}\_{out,turb'}, p\_{out,ub}\right) \tag{4}$$

$$\mathcal{S}\_{out,turb} = \mathcal{S}\_{in,turb} \tag{5}$$

$$S\_{is,taub} = \text{map}\left(h\_{i\text{u},taub'}, p\_{i\text{u},taub}\right) \tag{6}$$

The turbine efficiency map has to be provided by the turbine manufacturer. Outlet temperature, Tout,tur, is calculated from outlet enthalpy and outlet pressure using a thermodynamic table of the working fluid.

$$T\_{out, turb} = \text{map}\left(h\_{out, turb'}, p\_{out, turb}\right) \tag{7}$$

**Figure 4.** Block diagram of the turbine/expander model.

Subscribes f1

fluxes involved [18].

110 Organic Rankine Cycle Technology for Heat Recovery

**2.2. Expander**

and f2

**Figure 3.** The heat exchanger block.

accuracy and computational time and cost.

refer to fluid 1 (in the inner pipe) and fluid 2 (in the annulus), respectively, and

subscribe p relates to the pipe body. Once the system has been fully defined, the heat and mass transfer coefficients and correlations must be introduced to calculate the actual thermal fluxes.

**Figure 2.** Discretization assumed for typical tubular counter-flow heat exchanger with phase change and main heat

An interesting study conducted on this topic is by García-Vallardes et al. [20], in which the thermal and fluid dynamic behavior of a tubular heat exchanger (could be applied as evaporator or condenser) are simulated numerically. Continuity, momentum and energy conservation equations were applied for the internal and annulus tubes to accurately predict the heat and mass transfer inside the heat exchanger. Energy conservation equations have in fact been applied to the external tube and insulation, hence dropping the hypothesis of the ideally insulated system. However, such detailed simulation of the heat exchanger is not useful for the modeling of dynamic ORC systems, since one needs to compromise between expected

The expander turbine is simulated generally as a component based upon steady-state charac-

teristic curves. Inputs/outputs of the system are shown in **Figure 4**.

Turbine boundary conditions are pressure and enthalpy at the inlet and pressure at outlet. In addition, the inlet and outlet are adiabatic. The heat transfer between turbine outer surface and ambient is considered based on the turbine isentropic efficiency map.

#### **2.3. Pump**

The pumps of the ORC system have to maintain both pressure and working fluid mass flow. The HP pump is considered here to be a positive displacement type, whereas the feed pump is an inline roller cell pump. Due to the dominance of the HP pump, only the HP pump model is formulated here. The pump mass flow rate is interpolated using the map (Eq. (8)) provided by the ORC system manufacturer [22]. Pump power consumption and outlet temperature are calculated by Eq. (9) and (10).

$$
\dot{m}\_{pump} = \text{map}\left(\text{N}\_{pump}\right) \tag{8}
$$

*Hres* = \_\_*V*

different based on the thermodynamic state of the fluid.

Here, *V*0

environment.

pressure ratio [23]:

Here, γ =

*m*̇ = *O Cd A*0 √

Cp \_\_\_ Cv *m*̇ = *O Cd A*0 (

**2.5. Valve**

*V*0

is the entire reservoir volume and V is instant volume of the working fluid.

Then, *Hres* represents the ratio of the reservoir's fluid level to the reservoir's total height. Reservoir boundary conditions are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. The reservoir is assumed to be adiabatic, that is, no heat loss to the

The proportional valves or distribution/control valves are commonly used in ORC heat recovery units to enhance the flexibility and controllability of the system. Depending on the fluid state when flowing over the valve, the flow might be either incompressible or compressible. The valve located after the pump operates normally with incompressible fluid flow, while the working fluid passes through a valve before the expander, is usually super-heated vapor and shows compressible behavior. Hence, the mathematical model defined for the valves is

When the working fluid is in liquid state and thus incompressible, the outlet temperature is assumed to be equal to the inlet temperature due to the small temperature change across the incompressible valves. The necessary boundary condition for the incompressible flow valve is mass flow rate from the pump at the inlet. The valves are assumed adiabatic, that is, no heat loss to the environment. Therefore, a simple mass conservation equation, describing the relation between the valve opening ratio and the mass flow passing through the valve, can be used. Then the valve opening ratio has to be given as an input parameter. Besides, the valve's pressure loss (if found to be considerable) can be calculated by the formulation provided by the manufacturer as a function of mass flow rate. The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They can be modeled based on the compressible flow status: subsonic flow or supersonic flow depending on inlet/outlet

> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 2*γ* \_\_\_

> > \_\_\_\_\_\_ *γ pin ρin if* 0 ≤ *p*

valve and no heat loss consideration (hin = hout), the outlet temperature is calculated as [8]:

*Tout* = *f*(*pout*, *hout*) (15)

] *if* (

\_\_\_*out pin* ≤ ( \_\_\_2 *γ* + 1)

is heat capacity ratio. With the isentropic assumption of the process across the

\_\_\_2 *γ* + 1) *γ* \_\_\_\_\_ (*γ*−1) ≤ *p* \_\_\_*out pin*

*γ* \_\_\_\_\_ (*γ*−1) ≤ 1 (*Subsonic*)

(*Supersonic*) (14)

*p* \_\_\_*out pin* ) \_\_2 *γ* − ( *p* \_\_\_*out pin* ) *γ*+1 \_\_\_ *γ*

*γ* − 1 *pin ρin*[(

*γ*+1 \_\_\_\_\_ 2(*γ*−1) √

\_\_\_2 *γ* + 1) (13)

113

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390

$$P\_{pump} = \frac{\dot{m}\_{pump}}{\rho} \frac{(p\_{out,pump} - p\_{in,pump})}{\eta\_{is,pump}} \tag{9}$$

$$T\_{out,pump} = \left. T\_{in,pump} + \frac{\left(1 - \eta\_{i,pump}\right)P\_{pump}}{\dot{m}\_{pump}C\_{p,pump}} \right. \tag{10}$$

where ρ is the working fluid density upstream of the pump, pin,pump, pout,pump are upstream and downstream pressures, respectively, Cp,pump is the upstream specific heat capacity of the working fluid, and ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow rate and the rotational speed, which can be drawn from the pump map data [22].

#### **2.4. Reservoir**

The reservoir in an ORC system works as a buffer storage for the working fluid in order to supply fluid or accumulate it as the ORC system experiences transients. When the ORC system starts, the working fluid level is low in the reservoir because the entire circuit is full of liquid. When the system warms up, part of the ORC system is occupied by vaporized working fluid and the working fluid level in the reservoir increases compared to the cold condition. To calculate the working fluid level as well as the mean temperature, both mass balance and energy balance are applied in the reservoir. The mass balance can be described by Eq. (11) and the energy balance is given typically by Eq. (12). The reservoir working fluid level can be obtained by Eq. (13) [17].

$$\frac{d\,m\_f}{dt} = \dot{m}\_{f,in} - \dot{m}\_{f,out} \tag{11}$$

$$\frac{d(mh)}{dt} = \dot{m}\_{ln}h\_{in} - \dot{m}\_{out}h\_{out} \tag{12}$$

$$H\_{\rm res} = \frac{V}{V\_o} \tag{13}$$

Here, *V*0 is the entire reservoir volume and V is instant volume of the working fluid. Then, *Hres* represents the ratio of the reservoir's fluid level to the reservoir's total height. Reservoir boundary conditions are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. The reservoir is assumed to be adiabatic, that is, no heat loss to the environment.

#### **2.5. Valve**

Turbine boundary conditions are pressure and enthalpy at the inlet and pressure at outlet. In addition, the inlet and outlet are adiabatic. The heat transfer between turbine outer surface

The pumps of the ORC system have to maintain both pressure and working fluid mass flow. The HP pump is considered here to be a positive displacement type, whereas the feed pump is an inline roller cell pump. Due to the dominance of the HP pump, only the HP pump model is formulated here. The pump mass flow rate is interpolated using the map (Eq. (8)) provided by the ORC system manufacturer [22]. Pump power consumption and outlet temperature are

*ρ*

(*pout*,*pump* − *pin*,*pump*) \_\_\_\_\_\_\_\_\_\_\_\_\_ *ηis*,*pump*

> *m*̇ *pump Cp*,*pump*

where ρ is the working fluid density upstream of the pump, pin,pump, pout,pump are upstream and downstream pressures, respectively, Cp,pump is the upstream specific heat capacity of the working fluid, and ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow

The reservoir in an ORC system works as a buffer storage for the working fluid in order to supply fluid or accumulate it as the ORC system experiences transients. When the ORC system starts, the working fluid level is low in the reservoir because the entire circuit is full of liquid. When the system warms up, part of the ORC system is occupied by vaporized working fluid and the working fluid level in the reservoir increases compared to the cold condition. To calculate the working fluid level as well as the mean temperature, both mass balance and energy balance are applied in the reservoir. The mass balance can be described by Eq. (11) and the energy balance is given typically by Eq. (12). The reservoir working fluid level can be

*dt* = *m*̇

*dt* = *m*̇

*f*,*in* − *m*̇

*in hin* − *m*̇

*f*,*out* (11)

*out hout* (12)

rate and the rotational speed, which can be drawn from the pump map data [22].

\_\_\_\_\_\_\_\_\_\_\_\_

*pump* = *map*( *Npump*) (8)

(9)

(10)

and ambient is considered based on the turbine isentropic efficiency map.

**2.3. Pump**

**2.4. Reservoir**

obtained by Eq. (13) [17].

*d mf* \_\_\_\_

*d*(*mh*) \_\_\_\_\_

calculated by Eq. (9) and (10).

*m*̇

112 Organic Rankine Cycle Technology for Heat Recovery

*Ppump* = *m*̇ \_\_\_\_\_ *pump*

*Tout*,*pump* = *Tin*,*pump* + (1 − *ηis*,*pump*) *Ppump*

The proportional valves or distribution/control valves are commonly used in ORC heat recovery units to enhance the flexibility and controllability of the system. Depending on the fluid state when flowing over the valve, the flow might be either incompressible or compressible. The valve located after the pump operates normally with incompressible fluid flow, while the working fluid passes through a valve before the expander, is usually super-heated vapor and shows compressible behavior. Hence, the mathematical model defined for the valves is different based on the thermodynamic state of the fluid.

When the working fluid is in liquid state and thus incompressible, the outlet temperature is assumed to be equal to the inlet temperature due to the small temperature change across the incompressible valves. The necessary boundary condition for the incompressible flow valve is mass flow rate from the pump at the inlet. The valves are assumed adiabatic, that is, no heat loss to the environment. Therefore, a simple mass conservation equation, describing the relation between the valve opening ratio and the mass flow passing through the valve, can be used. Then the valve opening ratio has to be given as an input parameter. Besides, the valve's pressure loss (if found to be considerable) can be calculated by the formulation provided by the manufacturer as a function of mass flow rate. The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They can be modeled based on the compressible flow status: subsonic flow or supersonic flow depending on inlet/outlet pressure ratio [23]:

$$\dot{m} = O\,\mathcal{C}\_d A\_0 \sqrt{\frac{2\gamma}{\gamma - 1} p\_{in} \rho\_{in} \left[ \left( \frac{p\_{out}}{p\_{in}} \right)^{\frac{2}{\gamma}} - \left( \frac{p\_{out}}{p\_{in}} \right)^{\frac{\gamma + 1}{\gamma}} \right]} \quad \text{if } \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{(\gamma - 1)}} \le \frac{p\_{out}}{p\_{in}} \le 1 \text{ (Subosonic)}$$

$$\dot{m} = O\,\mathcal{C}\_d A\_0 \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \sqrt[4]{\gamma} \, p\_{in} \rho\_{in} \text{ if } 0 \le \frac{p\_{out}}{p\_{in}} \le \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{(\gamma - 1)}} \text{ (Supersonic)}\tag{14}$$

Here, γ = Cp \_\_\_ Cv is heat capacity ratio. With the isentropic assumption of the process across the valve and no heat loss consideration (hin = hout), the outlet temperature is calculated as [8]:

$$T\_{out} = f(p\_{out}, h\_{out}) \tag{15}$$

The boundary conditions necessary for these valves are pressure and enthalpy at the inlet and pressure at the outlet.

#### **2.6. Pipes and junctions**

#### *2.6.1. Pipes*

The pressure and heat loss through the pipes containing the liquid state are normally negligible compared with other components. If in a certain case their contribution is found to be considerable, they could be mathematically modeled using the general fluid mechanics principles using pipe-flow pressure loss and heat transfer equations. However, the pipe flow after the evaporators and upstream of the turbine valves are considered as compressible volumes, which has to be taken into account, especially for their dynamic inertia applied to the system [24]. Three equations are utilized in this volume: mass balance, energy balance, and the ideal gas law [25]. Three parameters can be calculated by solving these three equations: working fluid's mass inside the volume, working fluid's mean temperature, and mean pressure inside the volume [8].

$$
\mu \frac{dm}{dt} + m \gets\_v \frac{dT}{dt} = \dot{H}\_{in} - \dot{H}\_{out} \tag{16}
$$

**3. System-level dynamic modeling**

transient conditions;

inserted in the simulation models;

adding new fixed common state variables.

**3.2. Initialization of the system simulation model**

in the initial condition list definition [9].

**3.1. Integration of the component dynamic models**

Once dynamic models of every individual component are ready and evaluated with known input state variables and calculated outputs, the components are interconnected to build a thermodynamic model of the whole thermal power system. Before interconnecting the individual component models to each other, the following important issues have to be reviewed:

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 115

• ensuring the validity and accuracy of the component models for both steady-state and

• creating and fully parameterizing the ORC components, the boundary sources, and sinks. Besides, the operating range and limitations for all components have to specified and

• defining appropriate known and unknown variables for the system, based on the design or optimization requirements and strategy. More detailed aspects of the system variable

• omitting the unnecessary fixed common variables of the individual component models or

After above-listed considerations and the preparation of required data, the ORC components will be connected properly to establish the system model. Connecting the component models means uniting the common variables of a specific component to its neighboring components

Apparently, the initialization of closed-loop dynamic models is a difficult task which should be carefully approached and planned. To initialize the dynamic model, the initial conditions have to be defined appropriately. At some point during the initialization process, one must thoroughly plan the thermodynamic cycle as a steady-state problem to find appropriate states for the initialization of the problem [5]. Initial state points can be set as parameters calculated by a steady-state model in which the analysis is expected to begin in a time domain. Initialization problems require starting arrays for all components, which can also be stored as parameters in the test bench level. Diagnostic and summary variables should also be included

The ORC dynamic model developers must prepare an input/output variable list considering the aspects mentioned in Section 3.1, where all fixed model inputs based on the real-test

so that the set of components create a closed loop by linking them to each other.

**3.3. Input and output parameters and identification of the constraints**

definition that need to be considered are presented in Section 3.3.

$$\frac{RT}{V}\frac{dm}{dt} + \frac{p}{T}\frac{dT}{dt} - \frac{dp}{dt} = 0\tag{17}$$

where u represents specific internal energy, cv represents specific heat capacity, Ḣ in and Ḣ out represent inlet and outlet enthalpy flow rate, R represents ideal gas constant, and V represents vapor volume. Boundary conditions of the compressible vapor volume are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. Meanwhile, the inlet, outlet, and outer surfaces are all assumed to be adiabatic.

#### *2.6.2. Junctions*

Pressure loss in the pipe junctions is negligible. Besides, the junctions are assumed to be adiabatic with no heat loss to the environment. Similar to the reservoir, junctions are modeled by mass balance and energy balance via Eq. (18) and (19), respectively [8].

$$
\dot{m}\_{\text{mix}} = \dot{m}\_1 + \dot{m}\_2 \tag{18}
$$

$$
\dot{m}\_{\text{mix}} h\_{\text{mix}} = \dot{m}\_1 h\_1 + \dot{m}\_2 h\_2 \tag{19}
$$

The junction boundary conditions are mass flow rate and enthalpy at the inlet and the outlet which are considered to be adiabatic.

## **3. System-level dynamic modeling**

The boundary conditions necessary for these valves are pressure and enthalpy at the inlet and

The pressure and heat loss through the pipes containing the liquid state are normally negligible compared with other components. If in a certain case their contribution is found to be considerable, they could be mathematically modeled using the general fluid mechanics principles using pipe-flow pressure loss and heat transfer equations. However, the pipe flow after the evaporators and upstream of the turbine valves are considered as compressible volumes, which has to be taken into account, especially for their dynamic inertia applied to the system [24]. Three equations are utilized in this volume: mass balance, energy balance, and the ideal gas law [25]. Three parameters can be calculated by solving these three equations: working fluid's mass inside the volume, working fluid's mean temperature, and mean pressure inside the volume [8].

*dt* + *m Cv*

*V* \_\_\_ *dm dt* + *p*\_\_ *T* \_\_\_ *dT dt* − *dp*\_\_\_

mass balance and energy balance via Eq. (18) and (19), respectively [8].

\_\_\_ *dT dt* = *H*̇

represent inlet and outlet enthalpy flow rate, R represents ideal gas constant, and V represents vapor volume. Boundary conditions of the compressible vapor volume are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. Meanwhile, the inlet, outlet, and outer

Pressure loss in the pipe junctions is negligible. Besides, the junctions are assumed to be adiabatic with no heat loss to the environment. Similar to the reservoir, junctions are modeled by

*mix* = *m*̇

The junction boundary conditions are mass flow rate and enthalpy at the inlet and the outlet

*mix hmix* = *m*̇

1 + *m*̇

1 *h*1 + *m*̇

*in* − *H*̇

*out* (16)

in and Ḣ

out

*dt* = 0 (17)

2 (18)

2 *h*2 (19)

represents specific heat capacity, Ḣ

pressure at the outlet.

114 Organic Rankine Cycle Technology for Heat Recovery

**2.6. Pipes and junctions**

*u* \_\_\_ *dm*

*RT*\_\_\_

surfaces are all assumed to be adiabatic.

*m*̇

*m*̇

which are considered to be adiabatic.

*2.6.2. Junctions*

where u represents specific internal energy, cv

*2.6.1. Pipes*

## **3.1. Integration of the component dynamic models**

Once dynamic models of every individual component are ready and evaluated with known input state variables and calculated outputs, the components are interconnected to build a thermodynamic model of the whole thermal power system. Before interconnecting the individual component models to each other, the following important issues have to be reviewed:

After above-listed considerations and the preparation of required data, the ORC components will be connected properly to establish the system model. Connecting the component models means uniting the common variables of a specific component to its neighboring components so that the set of components create a closed loop by linking them to each other.

#### **3.2. Initialization of the system simulation model**

Apparently, the initialization of closed-loop dynamic models is a difficult task which should be carefully approached and planned. To initialize the dynamic model, the initial conditions have to be defined appropriately. At some point during the initialization process, one must thoroughly plan the thermodynamic cycle as a steady-state problem to find appropriate states for the initialization of the problem [5]. Initial state points can be set as parameters calculated by a steady-state model in which the analysis is expected to begin in a time domain. Initialization problems require starting arrays for all components, which can also be stored as parameters in the test bench level. Diagnostic and summary variables should also be included in the initial condition list definition [9].

#### **3.3. Input and output parameters and identification of the constraints**

The ORC dynamic model developers must prepare an input/output variable list considering the aspects mentioned in Section 3.1, where all fixed model inputs based on the real-test condition are presented. The model outputs which are to be calculated as a result of the simulation need to be fixed too. Then the variation of the outputs as a function of the time step can be studied and investigated. Besides, different post-processing activities can be considered, using the simulation results.

*3.4.4. Subsystem interaction*

*3.5.1. Matlab/Simulink*

has to be considered and incorporated in the simulation.

In ORC-based heat recovery systems, the operation of the plant that generates heat might be influenced by the integration of the ORC. For such systems, the impact on lateral subsystems

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 117

For example, in an ORC heat recovery system for a heavy-duty truck (experimented and simulated by Grelet et al. [15] and also Xu et al. [17]), the ORC system shares the cooling system of the vehicle and therefore the charge air cooling capacity can be lower, which has a negative impact on the engine performance. Another example is the use of exhaust gas recirculation (EGR) as the heat source in a heat recovery system designed for heavy-duty trucks. This leads to a trade-off between EGR cooling and ORC performance, which could impact negatively the engine emissions. Several other interactions such as the exhaust back pressure or the weight penalty could also be cited. In such heat recovery systems (HRSs), the performance, and thereby the fuel economy, will be dependent on all the aspects mentioned above. It is therefore critical to model the complete system and its surrounding environment in order to optimize the whole integrated setup. It helps to select the best design using simulation and

After reviewing the modeling methodologies of ORC systems, an analysis has been conducted in this section, in order to determine available commercial software that might have been employed as tools for implementing the modeling processes. Other computer-based models within the field of the energy conversion system, available in the open literature, have also been surveyed. The analysis has brought to identify some software that may appear to be proper for the scope. Software that have been used for power cycle modeling purposes are Matlab/Simulink, AMESim, Trnsys, Modelica (OpenModelica, Dymola, Wolfram System Modeler, and MapleSim are all based on Modelica), GateCycle, EES, Phyton, Cycle-Tempo, and GT-SUITE. It should be noted that the analysis of commercial software reported here is neither complete nor exhaustive but is limited to those packages that have been found by the authors to be applicable for dynamic, thermodynamic, and energy modeling purposes. These software have been utilized in order to provide a deeper understanding of their characteristics and a brief description is presented here. Some of these software like GateCycle and Trnsys, while appropriate for some applications, turned out to be improper for the scope of the ORC dynamic analysis, and therefore will not be discussed here. Matlab/Simulink, AMESim, and Modelica feature some common characteristics that make them more suitable for the development of customized dynamic component models of energy systems, for both control purposes

thereby reduce the number of experimental tests needed to be carried out [15].

and optimization. Therefore, they will be further discussed briefly here [18].

Matlab is a high-performance language for technical modeling and computation; the name Matlab stands for matrix laboratory. The Matlab language is a high-level matrix/array language with controls flow statements, functions, data structures, input/output, and objectoriented programming features. Matlab/Simulink is a general purpose software package

**3.5. Survey of available codes for modeling power plant systems**

It has to be kept in mind that the number of unknown variables of the whole system has to be equal to the number of equations so that the differential sets of equations are closed. Otherwise, the equations are not solved or won't have unique results. When the component models are integrated to build the thermal power system, the number of unknown variables for each component will be different from the case when the component models were simulated individually. It is usually helpful if components are connected one by one and simulated step by step to ensure the correct connectivity and the number of input/output variables.

Moreover, the output variable trends are strongly dependent on the constraints forced to the simulation model. Obviously, the output trends will follow the real plant's output when the system constraints imposed during simulation are the same as for the real plant [26].

#### **3.4. Key aspects of ORC power systems to be considered for the analysis**

#### *3.4.1. Working fluid*

There are several aspects to be taken into account when using a working fluid for a specific application. The aspects that have to be considered include fluid deterioration, environmental aspects, as well as boiling, condensation, and freezing temperatures that decide the operating ranges. The above limitations have to be incorporated in the simulation tool.

#### *3.4.2. Heat sources*

The heat sources have different grades of quality (temperature levels) and quantity (amount of thermal energy). The dynamic model has to take into account the possible range of operating temperatures and the amount of thermal energy of the heat sources. If the number of heat sources is larger than one, additional complexity and more challenges for the design of the system (fluid, expansion machine, control, etc.) will arise. Generally, variation in heat source parameters is a common input to the stimulation of the ORC systems, which leads to a dynamic response.

#### *3.4.3. Heat sink*

For a specific ORC application, the heat sink available is usually an independent or commonly used cooling package including radiators containing a coolant, which is cooled by means of cooling fans or an air-cooling module. The integration of a heat recovery system model into the cooling module results in more conclusive and realistic results, which eventually limit the amount of heat that can be converted into useful work. In addition, thermal and mass inertia of the heat sink (cooling module) may affect dynamic behavior and time response of the whole system. Therefore, a complete system analysis including the cooling package is necessary to find the optimal way of recovering the heat from a heat source and to design a reliable control and monitoring system.

#### *3.4.4. Subsystem interaction*

condition are presented. The model outputs which are to be calculated as a result of the simulation need to be fixed too. Then the variation of the outputs as a function of the time step can be studied and investigated. Besides, different post-processing activities can be considered,

It has to be kept in mind that the number of unknown variables of the whole system has to be equal to the number of equations so that the differential sets of equations are closed. Otherwise, the equations are not solved or won't have unique results. When the component models are integrated to build the thermal power system, the number of unknown variables for each component will be different from the case when the component models were simulated individually. It is usually helpful if components are connected one by one and simulated step by step to ensure the correct connectivity and the number of input/output variables.

Moreover, the output variable trends are strongly dependent on the constraints forced to the simulation model. Obviously, the output trends will follow the real plant's output when the

There are several aspects to be taken into account when using a working fluid for a specific application. The aspects that have to be considered include fluid deterioration, environmental aspects, as well as boiling, condensation, and freezing temperatures that decide the operating

The heat sources have different grades of quality (temperature levels) and quantity (amount of thermal energy). The dynamic model has to take into account the possible range of operating temperatures and the amount of thermal energy of the heat sources. If the number of heat sources is larger than one, additional complexity and more challenges for the design of the system (fluid, expansion machine, control, etc.) will arise. Generally, variation in heat source parameters is a common input to the stimulation of the ORC systems, which leads to

For a specific ORC application, the heat sink available is usually an independent or commonly used cooling package including radiators containing a coolant, which is cooled by means of cooling fans or an air-cooling module. The integration of a heat recovery system model into the cooling module results in more conclusive and realistic results, which eventually limit the amount of heat that can be converted into useful work. In addition, thermal and mass inertia of the heat sink (cooling module) may affect dynamic behavior and time response of the whole system. Therefore, a complete system analysis including the cooling package is necessary to find the optimal way of recovering the heat from a heat source and to design a

system constraints imposed during simulation are the same as for the real plant [26].

**3.4. Key aspects of ORC power systems to be considered for the analysis**

ranges. The above limitations have to be incorporated in the simulation tool.

using the simulation results.

116 Organic Rankine Cycle Technology for Heat Recovery

*3.4.1. Working fluid*

*3.4.2. Heat sources*

a dynamic response.

reliable control and monitoring system.

*3.4.3. Heat sink*

In ORC-based heat recovery systems, the operation of the plant that generates heat might be influenced by the integration of the ORC. For such systems, the impact on lateral subsystems has to be considered and incorporated in the simulation.

For example, in an ORC heat recovery system for a heavy-duty truck (experimented and simulated by Grelet et al. [15] and also Xu et al. [17]), the ORC system shares the cooling system of the vehicle and therefore the charge air cooling capacity can be lower, which has a negative impact on the engine performance. Another example is the use of exhaust gas recirculation (EGR) as the heat source in a heat recovery system designed for heavy-duty trucks. This leads to a trade-off between EGR cooling and ORC performance, which could impact negatively the engine emissions. Several other interactions such as the exhaust back pressure or the weight penalty could also be cited. In such heat recovery systems (HRSs), the performance, and thereby the fuel economy, will be dependent on all the aspects mentioned above. It is therefore critical to model the complete system and its surrounding environment in order to optimize the whole integrated setup. It helps to select the best design using simulation and thereby reduce the number of experimental tests needed to be carried out [15].

#### **3.5. Survey of available codes for modeling power plant systems**

After reviewing the modeling methodologies of ORC systems, an analysis has been conducted in this section, in order to determine available commercial software that might have been employed as tools for implementing the modeling processes. Other computer-based models within the field of the energy conversion system, available in the open literature, have also been surveyed. The analysis has brought to identify some software that may appear to be proper for the scope. Software that have been used for power cycle modeling purposes are Matlab/Simulink, AMESim, Trnsys, Modelica (OpenModelica, Dymola, Wolfram System Modeler, and MapleSim are all based on Modelica), GateCycle, EES, Phyton, Cycle-Tempo, and GT-SUITE. It should be noted that the analysis of commercial software reported here is neither complete nor exhaustive but is limited to those packages that have been found by the authors to be applicable for dynamic, thermodynamic, and energy modeling purposes. These software have been utilized in order to provide a deeper understanding of their characteristics and a brief description is presented here. Some of these software like GateCycle and Trnsys, while appropriate for some applications, turned out to be improper for the scope of the ORC dynamic analysis, and therefore will not be discussed here. Matlab/Simulink, AMESim, and Modelica feature some common characteristics that make them more suitable for the development of customized dynamic component models of energy systems, for both control purposes and optimization. Therefore, they will be further discussed briefly here [18].

#### *3.5.1. Matlab/Simulink*

Matlab is a high-performance language for technical modeling and computation; the name Matlab stands for matrix laboratory. The Matlab language is a high-level matrix/array language with controls flow statements, functions, data structures, input/output, and objectoriented programming features. Matlab/Simulink is a general purpose software package suitable for dynamic systems, which is well known among the control community as it offers excellent performance qualities for designing regulation algorithms. It makes the tool an ideal candidate for process and control engineers, working with the same software package. The environment provided by Matlab software facilitates a general overview of all computations step by step, that can be used for a wide range of applications including simulation, data acquisition, data analysis, and visualization as well as scientific and engineering graphics.

The system modeling is carried out in four steps [18]:

nent is chosen.

*3.5.3. Modelica*

control layout.

• Sketch mode: The stage in which different components are linked.

• Run mode: The stage in which the simulation is executed.

• Sub-model mode: The stage in which the physical sub-model associated with each compo-

Modelica language is designed basically for the modeling of multi-component systems to provide an environment in which a virtual system can be built, similar to what is implemented by engineers in real system development. As an example, standard components like compressor, turbine, and heat exchanger can be selected based on the manufacturers' catalogs with related technical interfaces and specifications [27]. For this purpose, some manufacturer's catalogs are proposed to be used with Modelica standard libraries. If a particular subsystem or component doesn't exist in

Mathematical component models are generally described by differential, algebraic, and discrete equations in Modelica. Hence, the solution method of the describing equations doesn't need to be specified by the users. The software decides the algorithm, the computational methodology,

on the free Modelica library ThermoFluid are presented. The library development is carried out in an Airbus Deutschland research project and is focused on obtaining a library for

lyzed (**Figure 5**). The developed model can be used for optimization of specific heat exchangers and evaluation of optimum system configuration as well as for optimization of system

The literature survey concerning non-commercial models of inter-connectable components of energy system networks resulted in very few examples, which has led to the conclusion that this field still lacks a complete and exhaustive review work. The models proposed are mainly developed for specific applications and often are limited concerning scalability, flexibility, or generality. Examples of custom libraries of components for dynamic modeling and analysis

In [29, 30] a modular code for dynamic simulation of a single-shaft gas turbine is presented. The code, called CAMEL, is a modular object-oriented process simulator, for energy

refrigeration systems based

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 119

refrigeration cycle has been ana-

) as the

• Parameter mode: The stage in which the parameters for each sub-model are chosen.

the software library, it can be built by the user based on software standardized interfaces.

or strategy to be used to solve the equations of a particular system and its components.

detailed numerical investigation of refrigeration systems with carbon dioxide (CO2

In [28], the results of development of a Modelica library for CO2

refrigerant. Using the developed component library a CO2

*3.5.4. Customized tools for simulation of energy systems*

of complex energy systems can be found in [29–31].

For the dynamic modeling purpose, Simulink provides a graphical user interface (GUI) for building models as block diagrams, using click-and-drag mouse operations. Because Matlab and Simulink are integrated, one can simulate, analyze, and revise models in either environment at any point. Application of Matlab language code and its integration with the Simulink environment, in order to create the desired models of components considered in the analysis of energy systems, depend on the equations used, the methodology applied, and the input/ output parameters, which will be discussed in the next sections [18].

#### *3.5.2. AMESim*

AMESim is an advanced modeling environment for performing simulations of engineering systems. The main features and applications of this tool are:

The software has the typical feature of an icon-based program and engineering systems can be built by adding symbols or icons to a drawing area. AMESim therefore enables the users to build complex multi-domain system models through an interactive graphical interface. The resulting sketch is easy to understand and offers a logical representation of the system model under investigation. When the sketch is complete, simulation of the system proceeds in the following stages:

The system modeling is carried out in four steps [18]:

#### *3.5.3. Modelica*