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Model-based Adaptation of Intelligent Controllers of Solar Collector Fields
Model-based Adaptation of Intelligent Controllers of Solar Collector Fields Esko K. Juuso ∗ ∗
Control Engineering Laboratory, Department of Process and Environmental Engineering, P.O. Box 4300, FI-90014 University of Oulu, Finland (e-mail: esko.juuso@ oulu.fi). Abstract: Solar power plants should collect the available thermal energy in a usable form within a desired temperature range. The collection is controlled by the flow of oil pumped through the pipes during the plant operation. The control system consists of a nonlinear linguistic equation (LE) controller with predefined adaptation models, some smart features for avoiding difficult operating conditions, and a working point controller to adapt the setpoint to the operating conditions. The intelligent LE control activates special features when needed. Fast start-up, smooth operation and efficient energy collection is achieved even in variable operating condition. In this paper new state indicators are introduced to analyse fluctuations of irradiation, temperature and oil flow: the fluctuations are obtained as moving differences of the high and the low values, which are calculated by generalised norms of high positive and high negative orders, respectively. The smart indicators react well to the changing operating conditions and can be used in smart working point control to further improve the operation for cloudy conditions and load disturbances. Keywords: Solar energy, intelligent control, nonlinear systems, adaptation, efficiency, linguistic equations, modelling, simulation 1. INTRODUCTION Solar power plants should collect any available thermal energy is in a usable form at the desired temperature range, which improves the overall system efficiency and reduces the demands placed on auxiliary equipments. In addition to seasonal and daily cyclic variations, the intensity depends also on atmospheric conditions such as cloud cover, humidity, and air transparency. In cloudy conditions, the collector field is maintained in a state of readiness for the resumption of full-scale operation. Solar collector field is a good test platform for various control methodologies (Camacho et al., 1997; Juuso, 1999). An overview of possible control strategies presented in (Camacho et al., 1997) include basic feedforward and PID schemes, adaptive control, model-based predictive control, frequency domain and robust optimal control and fuzzy logic control. A comparison of several intelligent controllers was presented in (Juuso, 1999). Feedforward approaches based directly on the steady state energy balance relationships can use measurements of solar irradiation and inlet temperature (Camacho et al., 1992). Lumped parameter models taking into account the sun position, the field geometry, the mirror reflectivity, the solar irradiation and the inlet oil temperature have been developed for a solar collector field (Camacho et al., 1997). A feedforward controller has been combined with different feedback controllers, even PID controllers operate for this purpose (Valenzuela and Balsa, 1998). The classical internal model control (IMC) can operate efficiently in varying time delay conditions (Farkas and Vajk, 2002).
Linguistic equations (LE) have been used in various industrial applications (Juuso, 1999, 2004). Modelling and control activities with the LE methodology started by the first controllers implemented in 1996 (Juuso et al., 1997) and the first dynamic models developed in 1999 (Juuso et al., 2000). The robust dynamic simulator based on linguistic equations is an essential tool in fine–tuning of these controllers (Juuso, 2005). The LE controllers also use model-based adaptation and feedforward features, which are aimed for preventing overheating, and the controller takes also care of the actual setpoints of the temperature (Juuso and Valenzuela, 2003). Manual adjustment of the working point limit has improved the operation considerably. Parameters of the LE controllers were first defined manually, and later tuned with neural networks and genetic algorithms. Genetic algorithms combined with simulation and model-based predictive control have further reduced temperature differences between collector loops (Juuso, 2006). Data analysis methods based on generalised norms, which were recently developed for condition monitoring (Juuso and Lahdelma, 2010), provide new data-driven tools for modelling (Juuso, 2010). A recursive version of the scaling approach was introduced in (Juuso, 2011). This paper analyses changes of operating conditions and introduces intelligent indicators to be used in adapting the LE controllers for start-up and operation in cloudy conditions and load disturbances. The analysis is based on experiments carried out in the Acurex Solar Collectors Field of the Plataforma Solar de Almeria in Spain.
all values xj > 0, i.e. ||τ Mjp ||p ∈ R. This norm combines two trends: a strong increase caused by the power p and a decrease with the power 1/p. The norm (1), which is a H¨older mean, also known as a power mean, was introduced for signal analysis in (Lahdelma and Juuso, 2008, 2011).
Fig. 1. Layout of the Acurex solar collector field. 2. SOLAR COLLECTOR FIELD The aim of solar thermal power plants is to provide thermal energy for use in an industrial process such as seawater desalination or electricity generation. In addition to seasonal and daily cyclic variations, the intensity depends also on atmospheric conditions such as cloud cover, humidity, and air transparency. Unnecessary shutdowns and start-ups of the collector field are both wasteful and time consuming. With fast and well damped controllers the plant can be operated close to the design limits thereby improving the productivity of the plant (Juuso et al., 1998). The Acurex field supplies thermal energy (1 M Wt ) in form of hot oil to an electricity generation system or a Multi–Effect Desalination Plant. The solar field consists of parabolic–trough collectors, see (Juuso et al., 1997). Control is achieved by means of varying the flow pumped through the pipes in the collector field (Fig. 1) during the plant operation. In addition to this, the collector field status must be monitored to prevent potentially hazards situations, e.g. oil temperatures greater than 300 o C. The temperature increase in the field may rise up to 110 degrees. In the beginning of the daily operation, the oil is circulated in the field, and the flow is turned to the storage system (Fig. 1) when an appropriate outlet temperature is achieved. The valves are used only for openclose operation, and the overall flow F to the collector field is controlled by the pump. 3. DATA ANALYSIS Data analysis is based on generalised norms and moments. 3.1 Generalised norms
||τ Mjp ||p = (Mjp )1/p = [
1 N
i=1
3.2 Scaling functions Membership definitions provide nonlinear mappings from the operation area of the (sub)system to the linguistic values represented inside a real-valued interval [−2, 2], denoted as the linguistic range, see (Juuso, 2004). In current systems, the membership definitions consist of two second order polynomials: one for negative values, X ∈ [−2, 0), and one for positive values, X ∈ [0, 2]. The polynomials are configured with five parameters. The nonlinear scaling methodology based on generalised norms (1) and skewness, (γkp )j =
N 1 [(xj )i − ||τ Mjp ||p ]k , N σjk i=1
(2)
provides good results for the automatic generation of scaling functions when all values (xj )i are positive. The standard deviation σj is the norm (1) with the order p = 2. The parameters of the scaling functions can be recursively updated with by including new samples into calculations. The number of samples Ks can be increasing or fixed with some forgetting or weighting (Juuso, 2011). 4. INTELLIGENT LE CONTROL The intelligent control system consists of a nonlinear LE controller with predefined adaptation models. For the solar collector field, the goal is to reach the nominal operating temperature 180 − 295 o C and keep it in changing operating conditions (Fig. 2). 4.1 Feedback LE controller
The generalised norm is defined by N
The norm values increase with increasing order, and the increase is monotonous if all the signals are not equal. The mean, the harmonic mean and the root mean square (rms) are special cases of (1), which represents the norms between the minimum and the maximum corresponding the orders p = −∞ and p = ∞, respectively. When p < 0, all the signal values should be non-zero, i.e. x = 0. When the order p → 0, we obtain from (1) the geometric mean. The computation of the generalised norms can be divided into the computation of equal sized sub-blocks, i.e. the norm for several samples can be obtained as the norm for the norms of individual samples. (Lahdelma and Juuso, 2008, 2011) The norm can be extended to variables including negative values (Juuso, 2011).
(xj )pi ]1/p ,
(1)
where the order of the moment p ∈ R is non-zero, and N is the number of data values obtained in each sample time τ . The norm (1) calculated for variables xj , j = 1, . . . , n, have same dimensions as the corresponding variables. The norm ||τ Mjp ||p can be used as a central tendency value if
General feedback linguistic equation (LE) controllers use error ej (k), derivative of the error Δej (k), and sum of errors δej (k), where k is the discrete time index. These can be obtained for any variable xj , j = 1, . . . , m, and mapped to the linguistic range [−2, 2] by nonlinear scaling with variable specific membership definitions (fe )j , (fΔe )j and (fδe )j , respectively. As all these functions consist of two second order polynomials, the corresponding inverse
280
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ref wp
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Fig. 2. Test results of the Linguistic Equation Controller: temperatures, oil flow and irradiation (Juuso, 2005): setpoint wp Tref is limited by Tref , Tcont is delay corrected Tin , and [Tlow , Thigh ] represent the fluctuations of Tout . functions include square root functions. The linguistic values of the inputs, e j (k), Δej (k), and δej (k), are limited to the range [−2, 2] by using the functions only in the operating range: outside the scaled values are -2 and 2 for low and high values, respectively. A PI-type LE controller is represented by Δu ij (k) = KP (i, j) Δej (k) + KI (i, j) ej (k),
(3)
which contains coefficients KP (i, j) and KI (i, j), and varij Δu ij ]T . The linguistic value of the change ables [ ej Δe ij , is obtained by (3) and limited of control, denoted as Δu to the range [−2, 2], and the scaled to the real values Δuij (k) by the membership definitions of the change of error denoted as (fΔu )i : Δuij (k) = (fΔu )i (Δu ij (k)).
(4)
The output i of a single input single output (SISO) controller is calculated by adding the effect of the controlled variable j to the manipulated variable i: ui (k) = ui (k − 1) + Δuij (k).
(5)
In the solar collector field, the feedback controller is a PItype LE controller with one manipulating variable and one controlled variable. The error ej (k) is the deviation of the outlet temperature, Tout , from the setpoint, and the manipulated variable i is the oil flow, F . High irradiation allows higher temperatures. The inlet temperature and the
solar irradiation are taken into account in the adaptation part. (Juuso, 2006). The scaling function for the error ej (k) and the change of control Δuij can be generated for different operating conditions by using the scaling function of the corresponding variable. The derivative of the error Δej (k) and the sum of errors δej (k) are defined in the controller tuning. (Juuso, 2011) 4.2 Predefined adaptation Oscillations are considerably reduced by modifying the operation of the controller by adaptive scaling of the manipulating variable i based on the working point m wp wpi (k) = xj (k) + bW wij (6) i , j=1
wp where x j (k) and wij are the linguistic values of the variable j, j = 1, . . . , m, and the corresponding weight factors. The bias term bW i is specific to the manipulating variable. The working point, wpi (k) ∈ [−2, 2], is a deviation from the normal operation. The change of control is multiplied by a scaling factor sci (k), which is obtained from the wpi (k) by membership definitions of sci (k).
In this application, the main working point variables are the effective solar irradiation, Ief f , and the temperature difference between inlet and outlet temperatures, Tdif f = Tout − Tin . The ambient temperature Tamb has a minor wp effect. For the other variables wij = 0. Usually, the
working point wpmin = 0 (Fig. 3): the irradiation I˜ef f and the temperature difference, T˜dif f , are on the same level. High working point (wpi > 0) means low T˜dif f compared to the irradiation level I˜ef f . Correspondingly, low working point (wpi < 0) means high T˜dif f compared to the irradiation level I˜ef f . The normal limit (wpmin = 0) reduces oscillations by using slightly lower setpoints during cloudy periods (Fig. 3). This is not sufficient when the irradiation is high between cloudy periods. Higher limits (wpmin = 1) shorten the oscillation periods after clouds more efficiently (Fig. 4).
where KP (i, j) is the coefficient used in (3). The scaling functions of the initial error eIj by using the scaling function of the corresponding variable. The asymmetrical action (ASA) is aimed for fine-control in cases where a precise setpoint tracking is required.
Measured Limit Corrected Limit 11
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ΔI
eff
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o
(7)
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KP (i, j) = (1 + BCj (k)) KP (i, j),
1
Δ F ( l/s)
The adaptive part contains additional braking and asymmetrical actions (Juuso, 1999). The predictive braking action (PBA) is used to ensure smooth recovery after severe disturbances or smooth change to a considerably different setpoint. For each controlled variable j, the PBA uses a braking rate coefficient BC j which is based on the initial error eIj and the current change of error Δej :
2
0 10 10 0 10 1 0.5 0 10
2
Fig. 4. Working point and state indicators in a case with heavy cloudy periods.
Working Point
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5. SMART LE CONTROL −1
diff
ΔT
Δ F ( l/s)
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13 Local Time
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Measured Limit Corrected Limit
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Fig. 3. Working point and state indicators in a case with short cloudy periods.
The solar collector field operates well also in less favourable conditions if predefined adaption and smart features for avoiding difficult operating conditions and a cascade controller for obtaining smooth operation (Juuso, 2011). Too high temperatures are usually results of following cases: • The inlet temperature changes considerably from the average level corresponding to case known to the controller; • Temperature is rising so fast that the controller cannot handle efficiently the evolving situation; • The temperature difference between the inlet and the outlet is too high, i.e. the working point wp is too low. These additional control actions were introduced to avoid oscillatory conditions as delays make it difficult to damp oscillations with feedback control. Alternatively these situations are tackled by changing the setpoint as well: the setpoint is reduced if the irradiation or the inlet temperature is staying on a lower level long time (Juuso and Valenzuela, 2003). Cascade control is activated in the start-up to facilitate fast temperature increase without oscillatory behaviour and for load disturbances. In cloudy conditions the cascade control also reduces considerably the overshoot after clouds. (Juuso, 2005)
5.1 State indicators
Same orders and time periods are used for the norms in cases of the temperature difference and the oil flow. Fast
Working Point
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Measured Limit Corrected Limit 11
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The cloudy conditions are detected by calculating the difference of the high and the low values of the corrected irradiation. These values are calculated as moving norm values from the latest minute, which includes five measurement values, τ = 15 s. Then an average of 25 latest values is used as the indicator, i.e. latest five minutes will have an effect on the indicator value. The norms (1) with high positive and high negative order are more robust than the maximum and minimum. The orders are 30 and -30, respectively. The difference, denoted by ΔIef f , indicates variable irradiation well (Figs. 3, 4 and 5). Severity of cloudy periods is detected efficiently: difficult periods shown in Fig. 4 result much higher indicator values than weaker cloud periods shown in Fig. 3 and very short periods of clouds shown in Fig. 5. Just a small sign of clouds is seen in Fig. 6.
2
Δ F ( l/s)
The setpoint is limited by the working point limit wpmin , which was given manually in previous test runs. Indicators are needed to make the working point changes automatic for cloudy conditions and load disturbances, which introduce fast increase and oscillation of temperature and oil flow. Manual actions are easily late and kept active too long time.
0 10 10 0 10 1 0.5 0 10
2
Fig. 6. Working point and state indicators on a clear day with load disturbances. increase and oscillation of are detected with ΔTdif f and F . Fast temperature increase is detected in the start-up phase in all cases shown in Figs. 3, 4 and 6. Also irradiation disturbances introduce fast temperature increase (Figs. 3 and 4). If this increase is not taken into account in control, also the oil flow starts to oscillate.
Working Point
1
0
−1
diff
ΔT
Δ F ( l/s)
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13 Local Time
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( oC)
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Δ Ieff ( W/m )
−2 10
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Fig. 5. Working point and state indicators in a case of setpoint tracking.
5.2 Working point control In the beginning of the start-up, the oil temperature decreases in the field, i.e. Tdif f < 0, leading to negative power and efficiency values for a while (Juuso, 2011). Working point wpi = 2 during the circulation on the field. The temperature rises first to the level of the inlet temperature, i.e. Tdif f = 0, and then to sufficiently high temperature to be taken to the storage system. Start-up is very fast in good weather conditions: effective energy collection starts in less than 30 minutes (Fig. 2), and the increase of irradiation is utilised efficiently, Tdif f goes to normal level, i.e. wpi also goes to zero if the irradiation is normal (Fig. 3). Limiting the setpoint of the outlet temperature improved operation considerably in the start-up stage and also when the inlet temperature changes (Fig. 2). During the tests the working point (wpmin ) was changed manually: wpmin = 0 was used in the morning, and before 13:00 hours wpmin was raised for a while to two and then level one was kept for the rest of the afternoon. The start-up was very smooth
when the setpoint was defined by wpmin = 0. After the load disturbance, there was hardly any overshoot and the oscillations were damped fast although the temperature change was drastic. (Juuso, 2005) The new indicators increase the limit wpmin in the beginning of the startup, and a short period of additional limits is enough on a clear day (Figs. 5 and 6). In these cases the limit Tdif f = 0 operates well, but in cloudy conditions the correction continues longer time (Figs. 3 and 4). Setpoints, which are under the limit defined by the working point limit, can be reached smoothly on a clear day (Figs. 5 and 6). There is some improvement potential for short cloudy periods (Fig. 5). The whole working point range is not necessarily available. The irradiation level was too high for the setpoint after 14 o’clock in the case shown in Fig. 6: the oil flow reached the maximum but the temperature was still increasing. On the other hand, the limits wpmin < 0 can be acceptable if the oscillations can be handle sufficiently well (Fig. 5). Variable inlet oil conditions were handled well by using the limit wpmin = 1 in the case shown in Fig. 2. The new indicators propose slightly smaller changes for the setpoint (Fig. 6). Oscillation of the oil flow seen in Fig. 2 supports smaller setpoint changes. The new indicators are promising to be used to improve the operation. Smooth setpoint changes reduce the need of predictive braking. Manual actions are taken if the working points wpmin < 0 are needed. Additionally, faster temperature increase is accepted in the start-up phase if the oil flow goes too high (Fig. 6). 6. CONCLUSION The intelligent LE control system is based on predefined model-based adaptation techniques. The system activates special features when needed. Fast start-up, smooth operation and efficient energy collection is achieved even in variable operating condition. The new state indicators react well to the changing operating conditions and can be used in smart working point control to further improve the operation. REFERENCES Camacho, E., Berenguel, M., and Rubio, F.R. (1997). Adaptive Control of Solar Plants. Springer, London. Camacho, E., Rubio, F., and Hughes, F. (1992). Selftuning control of a solar power plant with a distributed collector field. IEEE System Control Magazine, (April), 72–78. Farkas, I. and Vajk, I. (2002). Internal model-based controller for a solar plant. In CD-ROM Preprints of the 15th Triennial World Congress, 6 pp. IFAC. Juuso, E. and Lahdelma, S. (2010). Intelligent scaling of features in fault diagnosis. In Proceedings of the 7th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, 22-24 June, 2010, Stratford-upon-Avon, UK, 15 pp. BINDT. Juuso, E.K. (1999). Fuzzy control in process industry: The linguistic equation approach. In H.B. Verbruggen, H.J. Zimmermann, and R. Babuska (eds.), Fuzzy Algorithms for Control, International Series in Intelligent Technologies, 243–300. Kluwer, Boston.
Juuso, E.K. (2004). Integration of intelligent systems in development of smart adaptive systems. International Journal of Approximate Reasoning, 35, 307–337. Juuso, E.K. (2005). Modelling and control of a solar thermal power plant. In P.Horacek, M. Simandl, and P. Zitek (eds.), Proceedings of 16th Triennial World Congress, Prague, July 3-8, 2005, 368–373. IFAC. Juuso, E.K. (2006). Modelling and simulation in development and tuning of intelligent controllers. In I. Troch and F. Breitenecker (eds.), Proceedings of 5th Vienna Symposium on Mathematical Modelling, February 8-10, 2006, Vienna, Austria, Argesim Report 30, 6–1 – 10. Argesin Verlag, Vienna. ISBN 3-901608-30-3. Juuso, E.K. (2010). Data-based development of hybrid models for biological wastewater treatment in pulp and paper industry. In Proceedings of the 7th EUROSIM Congress on Modelling and Simulation, Prague, September 6-10, 2010, 10 pp. Juuso, E.K. (2011). Recursive tuning of intelligent controllers of solar collector fields in changing operating conditions. In S. Bittani, A. Cenedese, and S. Zampieri (eds.), Proceedings of the 18th World Congress The International Federation of Automatic Control, Milano (Italy) August 28 - September 2, 2011, 12282–12288. IFAC. Juuso, E.K., Balsa, P., and Leivisk¨a, K. (1997). Linguistic Equation Controller Applied to a Solar Collectors Field. In Proceedings of the European Control Conference ECC’97, Brussels, July 1 - 4, 1997, volume Volume 5, TH-E I4, paper 267 (CD-ROM), 6 pp. Juuso, E.K., Balsa, P., and Valenzuela, L. (1998). Multilevel linguistic equation controller applied to a 1 mw solar power plant. In Proceedings of the ACC’98, Philadelphia, PA, June 24–26, 1998, volume 6, 3891–3895. ACC. Juuso, E.K., Schauten, D., Slawinski, T., and Kiendl, H. (2000). Combination of linguistic equations and the fuzzy-rosa method in dynamic simulation of a solar collector field. In L. Yliniemi and E. Juuso (eds.), Proceedings of TOOLMET 2000 Symposium Tool Environments and Development Methods for Intelligent Systems, Oulu, April 13-14, 2000, 63–77. Oulun yliopistopaino, Oulu. Juuso, E.K. and Valenzuela, L. (2003). Adaptive intelligent control of a solar collector field. In Proceedings of Eunite 2003 - European Symposium on Intelligent Technologies, Hybrid Systems and their implementation on Smart Adaptive Systems, July 10-11, 2003, Oulu, Finland, 26–35. Wissenschaftsverlag Mainz, Aachen. Lahdelma, S. and Juuso, E. (2008). Signal processing in vibration analysis. In Proceedings of the Fifth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, 15-18 July 2008, Edinburgh, UK, 867–878. BINDT. Lahdelma, S. and Juuso, E. (2011). Signal processing and feature extraction in vibration analysis. Part 1: Methodology. The International Journal of Condition Monitoring, 1(2), 46–53. Valenzuela, L. and Balsa, P. (1998). Series and parallel feedforward control schemes to regulate the operation of a solar collector field. In Proceedings of the 2nd User Workshop Training and Mobility of Researchers Programme at Plataforma Solar de Almeria, November 10-11, 1998, 19–24. Ciemat.
Control Engineering Laboratory, Department of Process and Environmental Engineering, P.O. Box 4300, FI-90014 University of Oulu, Finland (e-mail: esko.juuso@ oulu.fi). Abstract: Solar power plants should collect the available thermal energy in a usable form within a desired temperature range. The collection is controlled by the flow of oil pumped through the pipes during the plant operation. The control system consists of a nonlinear linguistic equation (LE) controller with predefined adaptation models, some smart features for avoiding difficult operating conditions, and a working point controller to adapt the setpoint to the operating conditions. The intelligent LE control activates special features when needed. Fast start-up, smooth operation and efficient energy collection is achieved even in variable operating condition. In this paper new state indicators are introduced to analyse fluctuations of irradiation, temperature and oil flow: the fluctuations are obtained as moving differences of the high and the low values, which are calculated by generalised norms of high positive and high negative orders, respectively. The smart indicators react well to the changing operating conditions and can be used in smart working point control to further improve the operation for cloudy conditions and load disturbances. Keywords: Solar energy, intelligent control, nonlinear systems, adaptation, efficiency, linguistic equations, modelling, simulation 1. INTRODUCTION Solar power plants should collect any available thermal energy is in a usable form at the desired temperature range, which improves the overall system efficiency and reduces the demands placed on auxiliary equipments. In addition to seasonal and daily cyclic variations, the intensity depends also on atmospheric conditions such as cloud cover, humidity, and air transparency. In cloudy conditions, the collector field is maintained in a state of readiness for the resumption of full-scale operation. Solar collector field is a good test platform for various control methodologies (Camacho et al., 1997; Juuso, 1999). An overview of possible control strategies presented in (Camacho et al., 1997) include basic feedforward and PID schemes, adaptive control, model-based predictive control, frequency domain and robust optimal control and fuzzy logic control. A comparison of several intelligent controllers was presented in (Juuso, 1999). Feedforward approaches based directly on the steady state energy balance relationships can use measurements of solar irradiation and inlet temperature (Camacho et al., 1992). Lumped parameter models taking into account the sun position, the field geometry, the mirror reflectivity, the solar irradiation and the inlet oil temperature have been developed for a solar collector field (Camacho et al., 1997). A feedforward controller has been combined with different feedback controllers, even PID controllers operate for this purpose (Valenzuela and Balsa, 1998). The classical internal model control (IMC) can operate efficiently in varying time delay conditions (Farkas and Vajk, 2002).
Linguistic equations (LE) have been used in various industrial applications (Juuso, 1999, 2004). Modelling and control activities with the LE methodology started by the first controllers implemented in 1996 (Juuso et al., 1997) and the first dynamic models developed in 1999 (Juuso et al., 2000). The robust dynamic simulator based on linguistic equations is an essential tool in fine–tuning of these controllers (Juuso, 2005). The LE controllers also use model-based adaptation and feedforward features, which are aimed for preventing overheating, and the controller takes also care of the actual setpoints of the temperature (Juuso and Valenzuela, 2003). Manual adjustment of the working point limit has improved the operation considerably. Parameters of the LE controllers were first defined manually, and later tuned with neural networks and genetic algorithms. Genetic algorithms combined with simulation and model-based predictive control have further reduced temperature differences between collector loops (Juuso, 2006). Data analysis methods based on generalised norms, which were recently developed for condition monitoring (Juuso and Lahdelma, 2010), provide new data-driven tools for modelling (Juuso, 2010). A recursive version of the scaling approach was introduced in (Juuso, 2011). This paper analyses changes of operating conditions and introduces intelligent indicators to be used in adapting the LE controllers for start-up and operation in cloudy conditions and load disturbances. The analysis is based on experiments carried out in the Acurex Solar Collectors Field of the Plataforma Solar de Almeria in Spain.
all values xj > 0, i.e. ||τ Mjp ||p ∈ R. This norm combines two trends: a strong increase caused by the power p and a decrease with the power 1/p. The norm (1), which is a H¨older mean, also known as a power mean, was introduced for signal analysis in (Lahdelma and Juuso, 2008, 2011).
Fig. 1. Layout of the Acurex solar collector field. 2. SOLAR COLLECTOR FIELD The aim of solar thermal power plants is to provide thermal energy for use in an industrial process such as seawater desalination or electricity generation. In addition to seasonal and daily cyclic variations, the intensity depends also on atmospheric conditions such as cloud cover, humidity, and air transparency. Unnecessary shutdowns and start-ups of the collector field are both wasteful and time consuming. With fast and well damped controllers the plant can be operated close to the design limits thereby improving the productivity of the plant (Juuso et al., 1998). The Acurex field supplies thermal energy (1 M Wt ) in form of hot oil to an electricity generation system or a Multi–Effect Desalination Plant. The solar field consists of parabolic–trough collectors, see (Juuso et al., 1997). Control is achieved by means of varying the flow pumped through the pipes in the collector field (Fig. 1) during the plant operation. In addition to this, the collector field status must be monitored to prevent potentially hazards situations, e.g. oil temperatures greater than 300 o C. The temperature increase in the field may rise up to 110 degrees. In the beginning of the daily operation, the oil is circulated in the field, and the flow is turned to the storage system (Fig. 1) when an appropriate outlet temperature is achieved. The valves are used only for openclose operation, and the overall flow F to the collector field is controlled by the pump. 3. DATA ANALYSIS Data analysis is based on generalised norms and moments. 3.1 Generalised norms
||τ Mjp ||p = (Mjp )1/p = [
1 N
i=1
3.2 Scaling functions Membership definitions provide nonlinear mappings from the operation area of the (sub)system to the linguistic values represented inside a real-valued interval [−2, 2], denoted as the linguistic range, see (Juuso, 2004). In current systems, the membership definitions consist of two second order polynomials: one for negative values, X ∈ [−2, 0), and one for positive values, X ∈ [0, 2]. The polynomials are configured with five parameters. The nonlinear scaling methodology based on generalised norms (1) and skewness, (γkp )j =
N 1 [(xj )i − ||τ Mjp ||p ]k , N σjk i=1
(2)
provides good results for the automatic generation of scaling functions when all values (xj )i are positive. The standard deviation σj is the norm (1) with the order p = 2. The parameters of the scaling functions can be recursively updated with by including new samples into calculations. The number of samples Ks can be increasing or fixed with some forgetting or weighting (Juuso, 2011). 4. INTELLIGENT LE CONTROL The intelligent control system consists of a nonlinear LE controller with predefined adaptation models. For the solar collector field, the goal is to reach the nominal operating temperature 180 − 295 o C and keep it in changing operating conditions (Fig. 2). 4.1 Feedback LE controller
The generalised norm is defined by N
The norm values increase with increasing order, and the increase is monotonous if all the signals are not equal. The mean, the harmonic mean and the root mean square (rms) are special cases of (1), which represents the norms between the minimum and the maximum corresponding the orders p = −∞ and p = ∞, respectively. When p < 0, all the signal values should be non-zero, i.e. x = 0. When the order p → 0, we obtain from (1) the geometric mean. The computation of the generalised norms can be divided into the computation of equal sized sub-blocks, i.e. the norm for several samples can be obtained as the norm for the norms of individual samples. (Lahdelma and Juuso, 2008, 2011) The norm can be extended to variables including negative values (Juuso, 2011).
(xj )pi ]1/p ,
(1)
where the order of the moment p ∈ R is non-zero, and N is the number of data values obtained in each sample time τ . The norm (1) calculated for variables xj , j = 1, . . . , n, have same dimensions as the corresponding variables. The norm ||τ Mjp ||p can be used as a central tendency value if
General feedback linguistic equation (LE) controllers use error ej (k), derivative of the error Δej (k), and sum of errors δej (k), where k is the discrete time index. These can be obtained for any variable xj , j = 1, . . . , m, and mapped to the linguistic range [−2, 2] by nonlinear scaling with variable specific membership definitions (fe )j , (fΔe )j and (fδe )j , respectively. As all these functions consist of two second order polynomials, the corresponding inverse
280
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Temperature (oC)
Temperature (oC)
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ref wp
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Fig. 2. Test results of the Linguistic Equation Controller: temperatures, oil flow and irradiation (Juuso, 2005): setpoint wp Tref is limited by Tref , Tcont is delay corrected Tin , and [Tlow , Thigh ] represent the fluctuations of Tout . functions include square root functions. The linguistic values of the inputs, e j (k), Δej (k), and δej (k), are limited to the range [−2, 2] by using the functions only in the operating range: outside the scaled values are -2 and 2 for low and high values, respectively. A PI-type LE controller is represented by Δu ij (k) = KP (i, j) Δej (k) + KI (i, j) ej (k),
(3)
which contains coefficients KP (i, j) and KI (i, j), and varij Δu ij ]T . The linguistic value of the change ables [ ej Δe ij , is obtained by (3) and limited of control, denoted as Δu to the range [−2, 2], and the scaled to the real values Δuij (k) by the membership definitions of the change of error denoted as (fΔu )i : Δuij (k) = (fΔu )i (Δu ij (k)).
(4)
The output i of a single input single output (SISO) controller is calculated by adding the effect of the controlled variable j to the manipulated variable i: ui (k) = ui (k − 1) + Δuij (k).
(5)
In the solar collector field, the feedback controller is a PItype LE controller with one manipulating variable and one controlled variable. The error ej (k) is the deviation of the outlet temperature, Tout , from the setpoint, and the manipulated variable i is the oil flow, F . High irradiation allows higher temperatures. The inlet temperature and the
solar irradiation are taken into account in the adaptation part. (Juuso, 2006). The scaling function for the error ej (k) and the change of control Δuij can be generated for different operating conditions by using the scaling function of the corresponding variable. The derivative of the error Δej (k) and the sum of errors δej (k) are defined in the controller tuning. (Juuso, 2011) 4.2 Predefined adaptation Oscillations are considerably reduced by modifying the operation of the controller by adaptive scaling of the manipulating variable i based on the working point m wp wpi (k) = xj (k) + bW wij (6) i , j=1
wp where x j (k) and wij are the linguistic values of the variable j, j = 1, . . . , m, and the corresponding weight factors. The bias term bW i is specific to the manipulating variable. The working point, wpi (k) ∈ [−2, 2], is a deviation from the normal operation. The change of control is multiplied by a scaling factor sci (k), which is obtained from the wpi (k) by membership definitions of sci (k).
In this application, the main working point variables are the effective solar irradiation, Ief f , and the temperature difference between inlet and outlet temperatures, Tdif f = Tout − Tin . The ambient temperature Tamb has a minor wp effect. For the other variables wij = 0. Usually, the
working point wpmin = 0 (Fig. 3): the irradiation I˜ef f and the temperature difference, T˜dif f , are on the same level. High working point (wpi > 0) means low T˜dif f compared to the irradiation level I˜ef f . Correspondingly, low working point (wpi < 0) means high T˜dif f compared to the irradiation level I˜ef f . The normal limit (wpmin = 0) reduces oscillations by using slightly lower setpoints during cloudy periods (Fig. 3). This is not sufficient when the irradiation is high between cloudy periods. Higher limits (wpmin = 1) shorten the oscillation periods after clouds more efficiently (Fig. 4).
where KP (i, j) is the coefficient used in (3). The scaling functions of the initial error eIj by using the scaling function of the corresponding variable. The asymmetrical action (ASA) is aimed for fine-control in cases where a precise setpoint tracking is required.
Measured Limit Corrected Limit 11
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o
(7)
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KP (i, j) = (1 + BCj (k)) KP (i, j),
1
Δ F ( l/s)
The adaptive part contains additional braking and asymmetrical actions (Juuso, 1999). The predictive braking action (PBA) is used to ensure smooth recovery after severe disturbances or smooth change to a considerably different setpoint. For each controlled variable j, the PBA uses a braking rate coefficient BC j which is based on the initial error eIj and the current change of error Δej :
2
0 10 10 0 10 1 0.5 0 10
2
Fig. 4. Working point and state indicators in a case with heavy cloudy periods.
Working Point
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5. SMART LE CONTROL −1
diff
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Measured Limit Corrected Limit
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Fig. 3. Working point and state indicators in a case with short cloudy periods.
The solar collector field operates well also in less favourable conditions if predefined adaption and smart features for avoiding difficult operating conditions and a cascade controller for obtaining smooth operation (Juuso, 2011). Too high temperatures are usually results of following cases: • The inlet temperature changes considerably from the average level corresponding to case known to the controller; • Temperature is rising so fast that the controller cannot handle efficiently the evolving situation; • The temperature difference between the inlet and the outlet is too high, i.e. the working point wp is too low. These additional control actions were introduced to avoid oscillatory conditions as delays make it difficult to damp oscillations with feedback control. Alternatively these situations are tackled by changing the setpoint as well: the setpoint is reduced if the irradiation or the inlet temperature is staying on a lower level long time (Juuso and Valenzuela, 2003). Cascade control is activated in the start-up to facilitate fast temperature increase without oscillatory behaviour and for load disturbances. In cloudy conditions the cascade control also reduces considerably the overshoot after clouds. (Juuso, 2005)
5.1 State indicators
Same orders and time periods are used for the norms in cases of the temperature difference and the oil flow. Fast
Working Point
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Measured Limit Corrected Limit 11
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The cloudy conditions are detected by calculating the difference of the high and the low values of the corrected irradiation. These values are calculated as moving norm values from the latest minute, which includes five measurement values, τ = 15 s. Then an average of 25 latest values is used as the indicator, i.e. latest five minutes will have an effect on the indicator value. The norms (1) with high positive and high negative order are more robust than the maximum and minimum. The orders are 30 and -30, respectively. The difference, denoted by ΔIef f , indicates variable irradiation well (Figs. 3, 4 and 5). Severity of cloudy periods is detected efficiently: difficult periods shown in Fig. 4 result much higher indicator values than weaker cloud periods shown in Fig. 3 and very short periods of clouds shown in Fig. 5. Just a small sign of clouds is seen in Fig. 6.
2
Δ F ( l/s)
The setpoint is limited by the working point limit wpmin , which was given manually in previous test runs. Indicators are needed to make the working point changes automatic for cloudy conditions and load disturbances, which introduce fast increase and oscillation of temperature and oil flow. Manual actions are easily late and kept active too long time.
0 10 10 0 10 1 0.5 0 10
2
Fig. 6. Working point and state indicators on a clear day with load disturbances. increase and oscillation of are detected with ΔTdif f and F . Fast temperature increase is detected in the start-up phase in all cases shown in Figs. 3, 4 and 6. Also irradiation disturbances introduce fast temperature increase (Figs. 3 and 4). If this increase is not taken into account in control, also the oil flow starts to oscillate.
Working Point
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Δ F ( l/s)
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Measured Limit Corrected Limit
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Fig. 5. Working point and state indicators in a case of setpoint tracking.
5.2 Working point control In the beginning of the start-up, the oil temperature decreases in the field, i.e. Tdif f < 0, leading to negative power and efficiency values for a while (Juuso, 2011). Working point wpi = 2 during the circulation on the field. The temperature rises first to the level of the inlet temperature, i.e. Tdif f = 0, and then to sufficiently high temperature to be taken to the storage system. Start-up is very fast in good weather conditions: effective energy collection starts in less than 30 minutes (Fig. 2), and the increase of irradiation is utilised efficiently, Tdif f goes to normal level, i.e. wpi also goes to zero if the irradiation is normal (Fig. 3). Limiting the setpoint of the outlet temperature improved operation considerably in the start-up stage and also when the inlet temperature changes (Fig. 2). During the tests the working point (wpmin ) was changed manually: wpmin = 0 was used in the morning, and before 13:00 hours wpmin was raised for a while to two and then level one was kept for the rest of the afternoon. The start-up was very smooth
when the setpoint was defined by wpmin = 0. After the load disturbance, there was hardly any overshoot and the oscillations were damped fast although the temperature change was drastic. (Juuso, 2005) The new indicators increase the limit wpmin in the beginning of the startup, and a short period of additional limits is enough on a clear day (Figs. 5 and 6). In these cases the limit Tdif f = 0 operates well, but in cloudy conditions the correction continues longer time (Figs. 3 and 4). Setpoints, which are under the limit defined by the working point limit, can be reached smoothly on a clear day (Figs. 5 and 6). There is some improvement potential for short cloudy periods (Fig. 5). The whole working point range is not necessarily available. The irradiation level was too high for the setpoint after 14 o’clock in the case shown in Fig. 6: the oil flow reached the maximum but the temperature was still increasing. On the other hand, the limits wpmin < 0 can be acceptable if the oscillations can be handle sufficiently well (Fig. 5). Variable inlet oil conditions were handled well by using the limit wpmin = 1 in the case shown in Fig. 2. The new indicators propose slightly smaller changes for the setpoint (Fig. 6). Oscillation of the oil flow seen in Fig. 2 supports smaller setpoint changes. The new indicators are promising to be used to improve the operation. Smooth setpoint changes reduce the need of predictive braking. Manual actions are taken if the working points wpmin < 0 are needed. Additionally, faster temperature increase is accepted in the start-up phase if the oil flow goes too high (Fig. 6). 6. CONCLUSION The intelligent LE control system is based on predefined model-based adaptation techniques. The system activates special features when needed. Fast start-up, smooth operation and efficient energy collection is achieved even in variable operating condition. The new state indicators react well to the changing operating conditions and can be used in smart working point control to further improve the operation. REFERENCES Camacho, E., Berenguel, M., and Rubio, F.R. (1997). Adaptive Control of Solar Plants. Springer, London. Camacho, E., Rubio, F., and Hughes, F. (1992). Selftuning control of a solar power plant with a distributed collector field. IEEE System Control Magazine, (April), 72–78. Farkas, I. and Vajk, I. (2002). Internal model-based controller for a solar plant. In CD-ROM Preprints of the 15th Triennial World Congress, 6 pp. IFAC. Juuso, E. and Lahdelma, S. (2010). Intelligent scaling of features in fault diagnosis. In Proceedings of the 7th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, 22-24 June, 2010, Stratford-upon-Avon, UK, 15 pp. BINDT. Juuso, E.K. (1999). Fuzzy control in process industry: The linguistic equation approach. In H.B. Verbruggen, H.J. Zimmermann, and R. Babuska (eds.), Fuzzy Algorithms for Control, International Series in Intelligent Technologies, 243–300. Kluwer, Boston.
Juuso, E.K. (2004). Integration of intelligent systems in development of smart adaptive systems. International Journal of Approximate Reasoning, 35, 307–337. Juuso, E.K. (2005). Modelling and control of a solar thermal power plant. In P.Horacek, M. Simandl, and P. Zitek (eds.), Proceedings of 16th Triennial World Congress, Prague, July 3-8, 2005, 368–373. IFAC. Juuso, E.K. (2006). Modelling and simulation in development and tuning of intelligent controllers. In I. Troch and F. Breitenecker (eds.), Proceedings of 5th Vienna Symposium on Mathematical Modelling, February 8-10, 2006, Vienna, Austria, Argesim Report 30, 6–1 – 10. Argesin Verlag, Vienna. ISBN 3-901608-30-3. Juuso, E.K. (2010). Data-based development of hybrid models for biological wastewater treatment in pulp and paper industry. In Proceedings of the 7th EUROSIM Congress on Modelling and Simulation, Prague, September 6-10, 2010, 10 pp. Juuso, E.K. (2011). Recursive tuning of intelligent controllers of solar collector fields in changing operating conditions. In S. Bittani, A. Cenedese, and S. Zampieri (eds.), Proceedings of the 18th World Congress The International Federation of Automatic Control, Milano (Italy) August 28 - September 2, 2011, 12282–12288. IFAC. Juuso, E.K., Balsa, P., and Leivisk¨a, K. (1997). Linguistic Equation Controller Applied to a Solar Collectors Field. In Proceedings of the European Control Conference ECC’97, Brussels, July 1 - 4, 1997, volume Volume 5, TH-E I4, paper 267 (CD-ROM), 6 pp. Juuso, E.K., Balsa, P., and Valenzuela, L. (1998). Multilevel linguistic equation controller applied to a 1 mw solar power plant. In Proceedings of the ACC’98, Philadelphia, PA, June 24–26, 1998, volume 6, 3891–3895. ACC. Juuso, E.K., Schauten, D., Slawinski, T., and Kiendl, H. (2000). Combination of linguistic equations and the fuzzy-rosa method in dynamic simulation of a solar collector field. In L. Yliniemi and E. Juuso (eds.), Proceedings of TOOLMET 2000 Symposium Tool Environments and Development Methods for Intelligent Systems, Oulu, April 13-14, 2000, 63–77. Oulun yliopistopaino, Oulu. Juuso, E.K. and Valenzuela, L. (2003). Adaptive intelligent control of a solar collector field. In Proceedings of Eunite 2003 - European Symposium on Intelligent Technologies, Hybrid Systems and their implementation on Smart Adaptive Systems, July 10-11, 2003, Oulu, Finland, 26–35. Wissenschaftsverlag Mainz, Aachen. Lahdelma, S. and Juuso, E. (2008). Signal processing in vibration analysis. In Proceedings of the Fifth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, 15-18 July 2008, Edinburgh, UK, 867–878. BINDT. Lahdelma, S. and Juuso, E. (2011). Signal processing and feature extraction in vibration analysis. Part 1: Methodology. The International Journal of Condition Monitoring, 1(2), 46–53. Valenzuela, L. and Balsa, P. (1998). Series and parallel feedforward control schemes to regulate the operation of a solar collector field. In Proceedings of the 2nd User Workshop Training and Mobility of Researchers Programme at Plataforma Solar de Almeria, November 10-11, 1998, 19–24. Ciemat.