Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles

Applied Energy 88 (2011) 2183–2190

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles Sylvain Quoilin a,⇑, Richard Aumann b, Andreas Grill b, Andreas Schuster b, Vincent Lemort a, Hartmut Spliethoff b a b

Thermodynamics Laboratory, University of Liège, Campus du Sart Tilman, B49, B-4000 Liège, Belgium Technische Universität München, Institute for Energy Systems, Boltzmannstr. 15, 85748 Garching, Germany

a r t i c l e

i n f o

Article history: Received 24 May 2010 Received in revised form 2 August 2010 Accepted 5 January 2011

Keywords: Organic Rankine Cycle Waste heat recovery ORC Volumetric expander Dynamic modeling Control strategy

a b s t r a c t Organic Rankine Cycles (ORCs) are particularly suitable for recovering energy from low-grade heat sources. This paper describes the behavior of a small-scale ORC used to recover energy from a variable flow rate and temperature waste heat source. A traditional static model is unable to predict transient behavior in a cycle with a varying thermal source, whereas this capability is essential for simulating an appropriate cycle control strategy during part-load operation and start and stop procedures. A dynamic model of the ORC is therefore proposed focusing specifically on the time-varying performance of the heat exchangers, the dynamics of the other components being of minor importance. Three different control strategies are proposed and compared. The simulation results show that a model predictive control strategy based on the steady-state optimization of the cycle under various conditions is the one showing the best results. Ó 2011 Elsevier Ltd All rights reserved.

1. Introduction Interest in low-grade heat recovery has grown dramatically in the past decades. An important number of new solutions have been proposed to generate electricity from low temperature heat sources and are now applied to such diversified fields as solar thermal power, biological waste heat, engine exhaust gases, and domestic boilers. The potential for exploiting waste heat sources from engine exhaust gases or industrial processes is particularly promising [1], but these can vary in terms of flow rate and temperature over time, which complicates the regulation of waste heat recovery (WHR) devices. Among the proposed solutions, the Organic Rankine Cycle (ORC) system is the most widely used. Its two main advantages are the simplicity and the availability of its components. In such a system, the working fluid is an organic substance, better adapted than water to lower heat source temperatures. Unlike the traditional Rankine power cycles, local and small scale power generation is made possible by ORC technology. WHR ORCs have been studied in a number of previous works: Badr et al. [2], Gu et al. [3], Dai et al. [4], used simple thermodynamic models with constant pump and expander efficiencies to

⇑ Corresponding author. Tel.: +32 4 366 48 22; fax: +32 4 366 48 12. E-mail address: [email protected] (S. Quoilin). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd All rights reserved. doi:10.1016/j.apenergy.2011.01.015

compare different candidate working fluids. They showed that the cycle efficiency is very sensitive to the evaporating pressure, and that the optimal working fluid depends strongly on the considered application. Larjola [5] studied the use of an integrated high speed, oil-free turbogenerator-feed pump for a 100 kWe WHR ORC. Advanced cycle configurations have also been studied: Gnutek et al. [6]. proposed an ORC cycle with multiple pressure levels and sliding vane expansion machines using R123 in order to maximize the use of the heat source; Chen et al. [7] studied the transcritical CO2 power cycle as an alternative to the ORC cycle using R123 and showed that the generated output power is slightly higher with the transcritical cycle. Experimental studies of small-scale ORC units demonstrated that volumetric expanders are good candidates for small scale power generation, because of their reduced number of moving parts, reliability, wide output power range, broad availability, and good isentropic effectiveness [8]. In particular, experimental studies on scroll expanders showed very promising results, with reported isentropic effectiveness’s ranging from 48% to 68% [9–13]. The screw expander is another very promising solution. It operates at a slightly higher output power and shows the advantage of accepting a high liquid fraction at the inlet, allowing the design of ‘‘wet’’ cycles [14]. Although an abundant literature is available on the working fluid selection for ORCs, few papers propose a detailed modeling of the cycle: static models have been proposed by Quoilin et al.

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Nomenclature A c CS FF h h H Kp M _ M N Nrot p Q_ q_ r rv,in s T t U v V V_ w W X x x

area, m2 specific heat, J/(kg K) control signal filling factor, – heat transfer coefficient, W/(m2 K) specific enthalpy, J/(kg K) transfer function, – proportional gain, – mass, kg mass flow rate, kg/s number of nodes rotating speed, rpm pressure, Pa heat power, W heat flux, W/m2 ratio, – internal built-in volume ratio, – complex Laplace variable, – temperature, °C time, s heat transfer coefficient, W/(m2 K) specific volume, m3/kg volume, m3 volume flow rate, m3/s specific work, J/kg amount of work, J capacity fraction, – vapor quality, – axial distance, m

[15] and Kane [13], and a dynamic model of a WHR ORC using a turbine was proposed by Wei et al. [16]. However, to the authors’ knowledge, the dynamic modeling of a small-scale ORC using volumetric expander has never been proposed. In addition, the behavior and the regulation of such a cycle under variable heat source conditions has never been studied. This paper aims at proposing a dynamic model of a small-scale ORC using a volumetric expander. This model is then used to optimize the working conditions and to address the issue of the control strategy for variable waste heat sources.

Greek symbols e effectiveness g efficiency u level fraction q density, kg/m3 s time constant, s Subscripts and superscripts corr correlated cd condenser cf cold fluid em eletromechanical ev evaporator ex exhaust exp expander i relative to cell i in internal f working fluid hf hot fluid hr heat recovery l liquid optim optimum pp pump ref reference s swept su supply tp two-phase v vapor v volumetric w wall

The present work focuses on ORCs operating with variable heat sources. A generic variable heat source is thus defined and will be used to validate and to compare different control strategies. This heat source is considered to be hot water under pressure with variable temperature and flow rate, and is described in Fig. 2. This heat source could typically correspond to the profile internal combustion engine exhaust gases, via an intermediary heat transfer fluid loop.

2. System description and methodology Fig. 1 shows the conceptual scheme of the considered system. Even though the goal of this paper is not to describe a system in particular, but to propose a methodology for optimizing and controlling waste heat recovery ORCs, the parameters selected for the models proposed in Section 3 correspond to realistic components, typical of small-scale ORCs: The expander is an oil-free scroll expander, described in [11], the heat exchanger parameters are typical of coaxial evaporators and condensers. The pump is a volumetric pump (e.g. a diaphragm pump), whose speed is controlled by means of an inverter. The expander speed is also controlled with an inverter and varies within a reasonable range specified by the manufacturer. The selected working fluid is R245fa. It should be noted that fluid selection is an important and preliminary issue in ORC design. However, this selection is out of the scope of this paper, and it is therefore assumed that the study of the optimal working fluid was previously carried out.

Fig. 1. Conceptual scheme of the modeled ORC system.

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3.1. Evaporator model While large scale ORCs usually use different heat exchangers for the pre-heating (liquid) zone and for the vaporization (two-phase) zone, small-scale ORCs preferably use one single heat exchanger for the whole process. The evaporator model is inspired by the single-phase heat exchanger model proposed in the Thermopower Modelica library [19]. The heat exchanger is discretized into (N  1) cells, where the energy and mass conservation equations are applied (see Fig. 3). The momentum balance is neglected and the pressure is assumed to be constant in the whole heat exchanger. For each cell, a heat exchange area, a wall mass, a fluid volume and a heat transfer coefficient are defined: Fig. 2. Temperature and mass flow rate of the defined heat source.

In order to maximize the amount of energy recovered from this heat source, the working conditions of the ORC should constantly be adapted to the heat source temperature and flow rate. A proper control strategy must therefore be developed. The following methodology is proposed: 1. Static and dynamic models of the cycle are developed. The static model differs from the dynamic model in that all the time derivatives are set to zero. 2. The static model is used to optimize the working conditions of the cycle for a wide range of heat source and heat sink conditions. 3. The optimized working points are used to define a model-based control strategy. 4. The control strategy is implemented in the dynamic model and simulated with the random variable heat source. Its performance is finally compared to alternative control strategies. In addition to the objective of maximizing the recovered energy, the formation of droplets at the evaporator outlet must be avoided, since it can damage certain types of expanders. A positive superheating must therefore always be maintained by the control strategy.

Ai ¼

A ; N1

V ; N1

Mw;i ¼

Mw N1

ð1Þ

For both sides, the mass balance is written: N1 X 1

dM i _ N1 _ 1M ¼M dt

ð2Þ

Mi being the mass of fluid in each cell, given by:

i  Vi Mi ¼ q

ð3Þ

with

q i ¼

qi þ qiþ1 2

ð4Þ

Neglecting the diffusion term, the energy conservation principle gives:

Aq

_ dh _ dh ¼ A dp þ dQ þM dt dx dt dx

ð5Þ

The heat exchanger is spatially discretized according to the finite volumes method, in the form of:

i  Vi  q

dhi _ i  ðhiþ1  hi Þ ¼ Q_ i þ Ai  dp þM dt dt

ð6Þ

_ i is the mean flow rate between nodes i and i + 1. where M The heat balance over the metal wall is expressed by:

cw  M w  3. Dynamic modeling

Vi ¼

dT w;i ¼ A  ðq_ f ;i þ q_ hf ;i Þ dt

ð7Þ

The heat fluxes q_ are calculated by: This section describes the modeling of each component of the waste heat recovery ORC. The models are implemented under Modelica and the fluid properties are computed using the ‘‘ExternalMedia’’ library [17] coupled to Fluidprop [18].

q_ f ;i ¼ U f ;i  ðT f ;i  T w;i Þ

ð8Þ

q_ hf ;i ¼ U hf ;i  ðT hf ;i  T w;i Þ

ð9Þ

Fig. 3. Modeling paradigm of the evaporator.

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The heat transfer coefficient on the hot fluid side is set to a constant value. The heat transfer coefficient on the working fluid side is set to three different values depending on the fluid state in the cell. In order to avoid any inconsistency, the transition between two different heat exchange coefficients is performed on a non null quality width by interpolating between the two coefficients. The transition between the liquid and the two-phase coefficient, for example, is interpolated for 0.05 < x < 0.05, x being defined by:

x¼

h  hl hv  hl

ð10Þ

The average heat flow for each cell is finally computed on both sides by:

q_ i þ q_ iþ1 Q_ ¼ Ai 2

ð11Þ

The number of nodes selected for the present simulations is set to 10, since it turns out to be a good tradeoff between accuracy and computation time: the errors in the prediction of the steady-state heat flow for N = 5, N = 10, N = 20 are respectively 7.6%, 2.16% and 1.2% compared to the case with N = 100 (Calculation performed in the typical working conditions of the ORC with an evaporating temperature of 85 °C). The parameters of the evaporator model are summarized in Table 1. 3.2. Expander model The expander angular momentum is assumed negligible compared to the dynamics of the evaporator. A steady-state model is therefore used. Volumetric expanders, such as the scroll, screw or reciprocating technologies present an internal built-in volume ratio (rv,in) corresponding to the ratio between the inlet pocket volume and the outlet pocket volume. Under-expansion occurs when the internal pressure ratio imposed by the expander is lower than the system pressure ratio. In that case, the pressure in the expansion chambers at the end of the expansion process (pin) is higher than the pressure in the discharge line. Over-expansion occurs when the internal pressure ratio imposed by the expander is higher than the system pressure ratio.

Table 2 Expander model parameters. Parameter

Value

Parameter

Value

rv,in FF Nrot,max

4.05 0.6 5500 rpm

Vs Nrot,min

108 cm3 550 rpm

Under and over-expansion losses can be modeled by splitting the expansion into two consecutive steps [11]:  Isentropic expansion:

w1 ¼ hsu  hin

ð12Þ

hi being the isentropic enthalpy at pressure pin.  Constant volume expansion:

w2 ¼ v in  ðpin  pex Þ

ð13Þ

w2 is positive in case of under-expansion, and negative in case of over-expansion (Fig. 4). The total expansion work is then obtained by summing w1 and w2. Other losses such as internal leakage, supply pressure drop, heat transfers and friction are lumped into one single mechanical efficiency gmech:

_ exp ¼ M _  ðw1 þ w2 Þ  g W mech

ð14Þ

And, since the expansion is assumed adiabatic:

hex ¼ hsu 

_ exp W _ M

ð15Þ

For given rotational speed and fluid flow rate, the expander imposes the evaporating pressure [15]. This is computed by:

_ ¼ FF  qsu  V s  Nrot M 60

ð16Þ

FF being the filling factor (equivalent to the volumetric efficiency in compressor mode), set to a typical value provided by Lemort et al. [11]. The expander model parameters are summarized in Table 2. 3.3. Condenser model

Table 1 Evaporator model parameters. Parameter

Value

Parameter

Value (W/m2 K)

A Vhf Vf Mw N

3 m2 9.8 l 5.8 l 20 kg 10

Uhf Uf,l Uf,tp Uf,v

1000 260 900 360

Dynamic behavior of the cycle with variable heat source temperature and flow rate being the main focus of this paper, the temperature and flow rate of the heat sink are assumed to be constant _ cf ¼ cst; T cf ;su ¼ cst). This assumption entails only limin time (i.e. M ited variations of the working conditions on the condenser, compared to the evaporator. It allows avoiding a dynamic model of the condenser, and has the beneficial effect of reducing the computational effort. The condenser scheme is shown in Fig. 5. It is modeled by a constant pinch point value, defined by:

pinchcd ¼ minðT f ;ex;cd  T cf ;su ; T f ;su;tp;cd  T cf ;ex;tp Þ

Fig. 4. Under and over-expansion losses.

ð17Þ

The subcooling at the condenser exhaust is also an input of the model, and can be imposed in practice by making use of the static pressure head between the pump and the liquid receiver, or by the addition of a subcooler. Given the subcooling and the pinch point, the condenser model predicts the condensing temperature. A liquid receiver model is added at the condenser exhaust, in order to absorb the liquid level fluctuations of the evaporator. The total volume of the tank is a model parameter, and the liquid relative level u is computed by:

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The cycle efficiency gcycle:

W net ¼ gcycle 

Z

t2

Q_ eV dt

ð24Þ

t1

The heat recovery efficiency ehr:

Z

t2

Q_ eV dt ¼ ehr 

Z

t1

Fig. 5. Condenser model.

t2

_ hf  ðhsu;hf  hhf ;ref Þdt M

hhf,ref being the hot fluid reference enthalpy at 25 °C. The overall energy conversion efficiency is finally defined by:

Table 3 Condenser model parameters and inputs.

gov erall ¼ gcycle  ehr

Parameter

Value

Parameter

Value

Pinchcd _ cd M

10 K 0.5 kg/s

Vtank Tcf,su

20 l 25 °C

Table 4 Pump model parameters. Parameter

Value

Parameter

V_ su;pp;max a0 a2

0.25 l/s

gem,pp

0.93 0.2

a1 a3

d/ 1 _ ex;cd  M _ su;pp Þ ¼  ðM dt qf ;l  V tank

ð25Þ

t1

Value

ð26Þ

4. Control strategy The goal of this work is to define a control strategy for a smallscale ORC working with a heat source that varies in terms of temperature and mass flow. The first step is to optimize the working conditions of the cycle for a given static heat source. As a general rule, the following statements should be taken into account:

0.9 0.11 0.06

ð18Þ

The condenser model parameters are summarized in Table 3.

 The condensing pressure should be maintained as low as possible.  The superheating at the evaporator exhaust should be as low as possible when using high molecular weight organic fluids [21].  The optimal evaporation temperature results of an optimization of the overall heat recovery efficiency (see below). Increasing the evaporation temperature implies several antagonist effects:

3.4. Pump model The pump internal isentropic efficiency is defined by:

ein;pp ¼

v su;pp  ðpex;pp  psu;pp Þ hex;pp  hsu;pp

ð19Þ

An empirical law provided by Vetter [20] is fitted by a thirdorder polynomial in the form of:

ein;pp ¼ a0 þ a1  logðX pp Þ þ a2  logðX pp Þ2 þ a3  logðX pp Þ3

ð20Þ

Xpp being the pump capacity fraction defined by:

X pp ¼

v su;pp M_ pp V_ su;pp;max

ð21Þ

Xpp is limited by the following boundary conditions: 0:1 6 X pp 6 1 An additional electromechanical efficiency is added to obtain to pump overall efficiency:

eov erall;pp ¼ gem;pp  ein;pp

 The under-expansion losses in the expander are increased, and its efficiency is decreased.  The heat recovery efficiency is decreased since the heat source is cooled down to a higher temperature.  The expander specific work is increased since the pressure ratio is increased. These influences are illustrated in Fig. 6. For this particular steady-state working point, an optimum evaporation temperature of 117 °C is obtained. In order to best match these conditions, two degrees of freedom are available: the pump speed and the expander speed. These two degrees of freedom are used to control the two main working conditions, i.e. the evaporating temperature and the superheating.

ð22Þ

The different pump model parameters are summarized in Table 4. 3.5. Cycle model The global model of the cycle is obtained by interconnecting each subcomponent model according to the causality scheme described in [15]. Several performance indicators can be defined. The net work output:

W net ¼

Z

t2

t1

_ exp  W _ pp dt W

ð23Þ Fig. 6. WHR effectiveness, cycle efficiency and overall efficiency.

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Table 5 Parameters of the PI controllers. Parameter

Pump PI controller

Expander PI controller

Kp b ti

0.7 1 2s

2 1 3s

It should be noted that the action of these two parameters have very different time constants. A modification of the pump flow rate alters the working conditions of the evaporator and therefore induces a change in the evaporating temperature and/or in the amount of superheating, but with a delay due to the thermal and fluid dynamics of the heat exchanger. In contrast, a modification of the expander speed induces an almost immediate change in the evaporating pressure: the volumetric flow rate absorbed by the device is modified, while the mass flow rate is kept constant; the two flow rates are reconciled through a change in fluid density, mediated via a shift in vapor pressure. The evaporating temperature being a more critical working condition than the superheating, it is decided to control the evaporating temperature with the expander speed and the superheating with the pump flow rate. PI controllers are used to maintain the desired working conditions. The choice of PI controllers over PID controllers is justified by their satisfactory behavior in the simulations performed in Section 4 and by the higher sensitivity of PID controllers to measurement noise. The control signal is described by the equation:

  Z 1 CS ¼ K p  b  e þ  e þ track  dt ti

ð27Þ

where e is the error between the present value and the set point, both scaled between 0 and 1, b is the set point weight on the proportional action, Kp is the proportional gain, and ti is the integral time constant. The control signal saturates at 0 and at 1. The variable ‘‘track’’ is defined as the difference between CS and its saturated value, in order to avoid integral windup. Kp, b and ti are parameters to be tuned. This is done manually, with the aim of minimizing the stabilization time towards a steady-state of the system. The following parameters (Table 5) are obtained. Three different control strategies are defined and are described hereunder. 4.1. Constant evaporating temperature The most common control strategy is to define a constant evaporating temperature and superheating. In this case, it is not possible to know a priori which constant evaporating temperature will be optimal for the process. This regulation strategy requires two measurements: Tev and DTex,ev. It is presented in Fig. 7. 4.2. Optimum evaporating temperature As shown in Fig. 6, an optimum evaporating temperature can be obtained for given working conditions. Three inputs are sufficient

Fig. 7. First regulation strategy: constant evaporating temperature.

to determine this evaporating temperature: the condensation temperature, the heat source temperature and the heat source flow rate. However, it is important to base the control system on variables that are easily measurable. In the systems under consideration here, the mass flow rate of the heat source is difficult to measure in a cost-effective way. On the other hand, the working fluid flow rate is easily accessible, either by direct measurement, or by rela_ hf can tion to the pump speed. Since the superheating is fixed, M _ f , provided that the evaporating temperbe directly correlated to M ature and the heat source temperature are known. The optimal evaporating temperature can therefore be correlated to the heat source temperature, to the condensing temperature and to the working fluid mass flow rate. In order to determine this optimum over a broad range of working conditions the model described in Section 3 is implemented in steady-state in Engineering Equation Solver [22]. The optimum evaporating temperature is determined using the Golden Section Search method [23] for 31 working points and for working conditions varying in the following range:

20 6 T cd ð CÞ 6 40 _ hf ðkg=sÞ 6 0:15 0:05 6 M 120 6 T hf ;su ð CÞ 6 300 This range of working conditions is typical of a kW-scaled waste heat recovery ORC working with a heat source varying from 120 to 300 °C. A linear regression is then performed in order to predict Tev. A first order polynomial is preferred to higher order expressions in order to avoid the Runge phenomenon [24]. Due to the quadratic character of the relationship between Tev and Thf,su, log(Thf,su) is used instead. The following relationship is obtained, predicting the optimal evaporating temperature with R2 = 98.4%:

_ f þ 0:93  T cd þ 90  logðT hf ;su Þ T eV;optim ¼ 132  45  M

ð28Þ

The principle of this regulation is presented in Fig. 8. 4.3. Correlated pump speed A third regulation strategy is tested to obtain a faster reaction of the pump to varying working conditions. The 31 optimized working points described in Section 4.2 are used to derive a relationship between the optimized working fluid flow rate, the heat source temperature, the condensing temperature and the expander speed. The expander speed is selected because it constitutes an indirect measurement of the flow rate for a given evaporating temperature. The correlated, optimized working fluid flow rate is therefore the flow rate that leads to the optimum evaporating temperature in steady-state. It is defined as follows:

_ corr ¼ a0 þ a1  T hf þ a2  Nrot þ a3  T cd M

ð29Þ 2

The coefficients ai are identified with R = 97.7%.

Fig. 8. Second regulation strategy: optimal evaporating temperature.

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Fig. 9. Third regulation strategy: correlated pump speed.

In addition, the signal sent to the pump is filtered by a first order low-pass filter in order to avoid fast oscillations and unsteadinesses. A time constant s of two seconds is selected. The following transfer function is therefore used:

H¼

1

ssþ1

¼

1 2sþ1

Fig. 11. Evolution of the superheating over time (2nd strategy).

ð30Þ

The correlated pump speed regulation strategy is presented in Fig. 9. 5. Dynamic simulation The simulation model described in Section 3 is tested with the generic heat source defined in Fig. 2. A simulation is run for each control strategy and for five constant evaporating temperatures (80, 90, 100, 110 and 120 °C) in order to compare their respective performance. 5.1. Simulation results Fig. 10 and Fig. 11 show the superheating and the evaporating temperature with their set point for the second regulation strategy. As expected, the evaporating temperature matches its set point temperature better than the superheating due to the delayed action of a pump flow rate modification. Fig. 11 shows however that the control system is able to maintain a positive superheating and therefore avoid the formation of liquid droplets that could damage the expander. Fig. 12 shows the expander speed for the different controls strategies. It can be noted than for low evaporating temperatures, the expander speed saturates to its maximum allowed value: the evaporating temperature can no longer be maintained at its set point value by the control system. For Tev = 120 °C, the expander speed reaches its minimum value between t = 20 s to t = 99 s.

Fig. 12. Expander speed for different control strategies.

Fig. 13. Superheating and quality at expander inlet (3rd strategy).

Table 6 Cycle performance.

Fig. 10. Optimal/actual evaporating temperatures (2nd strategy).

Control

gcycle (%)

ehr (%)

goverall (%)

Tev = 80 °C Tev = 100 °C Tev = 120 °C Tev,optim _ corr M

7.83 9.98 10.50 10.61 9.88

69.29 64.00 56.76 61.93 64.71

5.42 6.40 5.97 6.57 6.40

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control strategies, it cannot be used as a predictive model to accurately evaluate the energy recovery potential of a particular configuration. This is due to the various simplifying modeling hypothesis, such as constant heat transfer coefficients, neglected pressure drops, and constant pinch value. Future work will concentrate on the improvement, on the validation, and on the exploitation of the dynamic model. The model’s capabilities will be exploited in the context of start and stop procedures, fully automated heat source potential detection, and autonomous decision of starting the WHR system. References

Fig. 14. Overall efficiency vs. temperature (1st strategy).

Fig. 13 shows the fluid quality at the expander exhaust for the third regulation. Fluid superheating is almost never achieved (i.e. xex,ev < 1 and DTex,ev < 0), which is not acceptable. Important fluctuations are also noted. 5.2. Comparison between control strategies The performance indicators are presented in Table 6 for each control strategy. The optimized evaporating temperature strategy is the one yielding the highest overall efficiency (6.6%). The constant evaporating temperature strategy also shows a good efficiency for 100 < Tev < 110, but this efficiency falls sharply for different evaporating temperatures (Fig. 14). 6. Conclusion A dynamic model of a small-scale Organic Rankine Cycle has been developed under the Modelica environment. A discretized evaporator model has been used and the volumetric expander model accounts for under and over-expansion losses. The simulation results show that small-scale ORCs are well adapted to waste heat recovery with variable heat source flow rate and temperature. A proper control strategy must however be defined because cycle performance can drop rapidly. An overall waste heat recovery efficiency of 6.6% was obtained for the defined heat source. The control of both the expander and the working fluid pump is required in order to take the best profit of variable heat sources. Three different control strategies were tested: a constant evaporating temperature, an optimized evaporating temperature depending on the actual working conditions, and a pump speed based on the expander speed. The best results are obtained with the optimized evaporating temperature regulation. This regulation makes use of a steady-state optimization model of the system run with a wide range of parameters bracketing the possible working conditions. The drawback of a non-optimized constant evaporating temperature regulation strategy is the fact that the ideal evaporating temperature cannot be known a priori. The third regulation strategy was not able to consistently maintain superheating at the expander inlet, resulting in unsteady operation compared with the two first strategies. It should be noted that, although the dynamic model in its presents form is able to compare the relative performance of different

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