A research on parabolic trough solar collector system control based on hedge algebra

A RESEARCH ON PARABOLIC TROUGH SOLAR COLLECTOR SYSTEM CONTROL BASED ON HEDGE ALGEBRA Cong Nguyen Huu

Trung Ngo Kien

Faculty of Electronics Engineering Thainguyen University of Technology – TNUT Thai Nguyen, Viet Nam [email protected]

Faculty of Electrical Engineering Thainguyen University of Technology – TNUT Thai Nguyen, Viet Nam [email protected]

Duy Nguyen Tien

Ha Le Thi Thu

Faculty of Electronics Engineering Thainguyen University of Technology – TNUT Thai Nguyen, Viet Nam [email protected]

Faculty of Electrical Engineering Thainguyen University of Technology – TNUT Thai Nguyen, Viet Nam [email protected]

Abstract—This paper presents a new method in controlling a parabolic trough solar collector system to improve the efficiency of the solar-to-thermal energy. It is designing an intelligent preprocessor using Hedge Algebra algorithm to calculate the setpoint for the control loop, in which besides the information about the trajectory calculated by a software, wind speed and fluid temperature of the collector are included. Moreover, this paper introduces a new simple flexible calculation tool which enables to calculate with a higher accuracy. Keywords—parabolic trough solar collector system, Hedge Algebra

I.

This paper represents a solar energy collecting system using PTSC and control system models. A solar energy collecting system using PTSC focuses energy into a tube across the trough. Due to the parabolic shape, trough can focus sunlight at 30-60 times its normal intensity on the receiver tube. Heat-exchange fluid (normally oil or water) which flows across the tube is heated by centralized energy. Collector is aligned in the East-West direction on the trough which is rotated to follow the sun to maximize solar energy to the receiver tube.

INTRODUCTION OF PTSC

Solar energy is one of energy resourses which were utilized early. However, applying this energy source into industrial technology in large-scale is a really topical issue and is considered widely. Therefore, researching in order to improve the performance of solar energy-used equipments and developing them to reality are essiential. Equipments using solar energy is high-cost, low-efficiency. Despite of the fact that PTSCs absorb high-temprature, the problem of positioning of following-sun collector is complicated. This leads to dificulties in operation. Figure 2. Fixed rate control

The optical efficiency of the collector is a function of five factors namely mirror surface reflectance, glass envelope transmittance, heat collection element absorptions, incidenceangle modifier and intercept factor [1]: ηo = ƒ(ρ, τ, α, K, γ)

(1)

for normal incidence conditions (K=1): ηo = [τ α ρ] γ

Figure 1. A PTSC system

(2)

These factors, namely, τ, α, ρ are physical properties of specific materials which is used to contruct the collector, and therefore, are constants. The intercept factor γ, which is ICARCV2010

constant for changes in beam irradiance and working fluid temperature, is a function of collector geometric parameters as well as error parameters. These errors arise during the construction and operation of a parabolic trough and include among others: •

Misalignment of the receiver.

•

Misalignment of the reflector.

•

Tracking errors.

•

Parabolic profile errors.

•

Sun image width error.

Since the optical efficiency is a function of γ, which is a function of tracking error, the tracking error directly affects thermal efficiency. In order to maximise the thermal efficiency of the collector, it is therefore necessary to reduce the tracking error by as much as possible which means ensuring that the collector tracking and control system keeps the parabolic surface pointing accurately towards the sun at all times. II.

APPLICATION OF HEDGE ALGEBRAS (HA) FOR CONTROL PROBLEMS

A. Almeria algorithm (PSA) This control model calculates the position of the sun from Almeria algorithm (Plataforma Solar de Almeria) [1]. Longtitude and latitude are parameters based on the geographical location of the trough. Variable is the instantaneous time extracted from sofware. Feedback signal is gained from the encremantal encoder for position detection. This signal, then, is compared to the real position of the trough.

T=dom(TEMPERATURE) = {Large, Small, very Large, very Small, more Large, more Small, approximately Large, approximately Small, little Large, little Small, less Large, less Small, very more Large, very more Small, very possible Large, very possible Small, …}. Then the linguistic domain T=dom(TEMPERATURE) can be considered as an abstract algebra AT=(T, G, H, ≤), where: T is the set terms domain AT; G is the set of free generators (set of free generators: Large, Small; H is the set of one-argument operators which are called linguistic hedges; ≤ is an semantically ordering relation, these algebras can be axiomatized based on certain suitably chosen properties of linguistic terms and hedges that can be formulated in term of the semantic odering relation ≤ and are called hedge algebras. Example: based on semantics, these semantically ordering relations are true: Small≤Large, more Large≤very Large, very Small ≤ more Small, possible Small ≤ Large, Small ≤ possible Small, … Definition 1: Given a HA AT = (T, G, H, ≤), f: T→[0, 1] is the set of semantic quantifying mapping (SQM) of AT if ∀h,k∈H+ or ∀h,k∈H- and ∀x,y∈T, then we have: f (hx)-f (x) f (hy )-f ( y ) = f (kx)-f (x) f (ky )-f ( y )

(3)

Considering these intervals : Large, Very Small, … Based on viewpoint of HA, fuzziness can be defined quite clearly based on size of the set H(x) shown in Figure 4:

Sun Zenith angle (ξ ξZ) Altitude angle α = 900 - ξZ

North West

Azimuth angle (γγ)

Figure 4. Fuzziness of linguistic intervals

Given a semantic quantifying mapping f of X. Considering ∀x∈X, fuzziness of x then can be measured by the diameter of f(H(x)) ⊆ [0,1].

South

East Figure 3. The position of the sun from PSA

Position of the sun can be calculated as follows [1]. B. Hedge Algebras-based control 1) Introduction of Hedge Algebras Hedge Algebras (HA) is the development based on the logic perception of linguistics [2]. The input/output relationship in fuzzy logic must define membership functions discontinuously whereas then HA creates an algebraic structure in terms of functions of linguistic input-output variables. Example: Consider a set of linguistic intervals which is a linguistic domain of TEMPERATURE truth variabe including:

Definition 2: Fuzziness measures A function fm: T→[0,1] is said to be a fuzziness measure if: fm(c-)=θ>0 and fm(c+)=1-θ>0, in which c- and c+ are negative and positive base terms. Assume set of hedges H=H+∪H-, H- = {h1, h2, …, hp} with h1>h2> … >hp, H+ = {hp+1, hp+2, …, hp+q} with hp+1 p 2 i= p+1 

(9)

It is explicit that an if-then clause can determine a point, so that n clauses of (8) can make a curve in linguistic space X×Y and is called the fuzzy curve C. Then an approximate reasoning problem can be transformed to an interpolative problem with respect to the fuzzy curve C. Assume f X and f Y are SQMs corresponding to X and Y. These functions will transform the fuzzy curve C to a real curve C’ in space of [0, 1]×[0, 1]. Therefore, a fuzzy logic problem can be turned into an ordinary interpolation one by using SQMs. approximate reasoning method: Interpolative reasoning based on SQMs.

Therefore, an idea of designing a controller is expressed as Figure 5: •

Value of rotation angle Pc (calculated value) is calculated by a software using data which are longtitude and latitude parameters of geographical location as well as the realtime.

•

A HA-based pre-processor is set up to determine: Ps = Pc± ∆P

with Ps is the setpoint for the control loop of PID controller to control trough-motion motor. The model of control system is shown as follows:

Figure 6. Simulation diagram of the system

Assuming that the direction of wind is always oppsite to the rotation direction of the trough. This means that, the higher the wind speed is, the higher the position of the trough is, compared to the position of the trajectory. The higher the fluid temperature in the tube gets, the closer the direction of the trough reaches to controlled position. Then the higher the temperature is, the lower the position error between the trough and trajectory is.

Figure 8. Position

HA-based control model uses an intelligent algorithm to define the position (trajectory) of trough including effect factors mentioned above inorder to receive the maximum volume of heat. The intelligent calculating model is built by three inputs: calculated position of the trough, fluid temperature and wind speed. The output will be the controlled position of the trough. Linguistic variables are constructed from variables of plant. Inputs:

Position = {rev-fas, rev-med, rev-slo, stop, fwd-slo, fwdmed, fwd-fas} Rules of fuzzy model can be determined as follows:

•

Wind speed: WIND_SPEED = [0 to 100].

•

Position of trough: POSITION = [-100 to 100].

•

Temperature of fluid: FLUITD_TEMP = [0 to 100].

Outputs: •

Figure 9. Fluid_Temp

Controlled position: POSITION_1 = [-100 to 100].

Control rules are constructed based on: •

Data WIND_SPEED is extracted from Anemometer.

•

Data FLUITD_TEMP is taken from temperature sensor.

•

Data POSITION is determined by the software based on geographical location and realtime.

Fuzzy set are built as follows:

Figure 7. Wind_Speed

TABLE I. Rule No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

WIND_ SPEED win-zer win-zer win-zer win-med win-med win-med win-max win-max win-max win-zer win-zer win-zer win-med win-med win-med win-max win-max win-max win-zer win-zer win-zer win-med win-med win-med win-max win-max win-max

CONTROL RULE TABLE

FLUITD _TEMP cold med hot cold med hot cold med hot cold med hot cold med hot cold med hot cold med hot cold med hot cold med hot

POSITION (Pc) enc-neg enc-neg enc-neg enc-neg enc-neg enc-neg enc-neg enc-neg enc-neg enc-zer enc-zer enc-zer enc-zer enc-zer enc-zer enc-zer enc-zer enc-zer enc-pos enc-pos enc-pos enc-pos enc-pos enc-pos enc-pos enc-pos enc-pos

POSITION_1 (Ps) rev-med rev-med rev-fas rev-slo rev-med rev-fas rev-slo rev-slo rev-med stop rev-slo rev-med fwd-slo stop rev-slo fwd-med fwd-slo stop fwd-med fwd-med fwd-slo fwd-fas fwd-med fwd-slo fwd-fas fwd-fas fwd-med

Using linear HA, and selecting the group of calculating parameters for semantical quantification of variables as follows: •

WIND_SPEED

= { 0, Less, θ, Great, 1}

•

FLUITD_TEMP = { 0, Cold, θ, Hot, 1}

•

POSITION

= { 0, Neg, θ, Pos, 1}

•

POSITION_1

= { 0, Slow, θ, Fast, 1}

H- = { Little} = {h-1} ; q = 1 H+ = {Very} = { h1} ; p = 1 θ = 0.5 µ(Very) = 0.5 = µ(h1) ; (β = 0.5) µ(Little) = 0.5 = µ(h-1) ; (α = 0.5) Therefore: fm(Less) = θ = 0.5 fm(Great) = 1-fm(Less) = 1-0.5 = 0.5 fm(Cold) = θ = 0.5 fm(Hot) = 1-fm(Cold) = 1-0.5 = 0.5 fm(Neg) = θ = 0.5 fm(Pos) = 1-fm(Neg) = 1-0.5 = 0.5 fm(Slow) = θ = 0.5 fm(Fast) = 1-fm(Slow) = 1-0.5 = 0.5 From (9), semantically quantifying intervals of variables can be calculated: v(Less)=v(Cold)=v(Neg)=v(Slow)=0.25

23 24 25 26 27

0.5 0.75 0.25 0.5 0.75

0.5 0.5 0.75 0.75 0.75

0.75 0.75 0.75 0.75 0.75

0.8333 0.8333 0.6667 0.6667 0.8333

After replacing “and” operation by “product” operation and simplifying the table above, then we have: TABLE III.

INPUT/OUTPUT RELATIONSHIP BASED ON SEMANTIC QUANTIFICATION (SIMPLIFIED)

Rule No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

WIND_SPEED & FLUITD_TEMP & ENCODER 0 0.015625 0.03125 0.046875 0.0625 0.0625 0.09375 0.09375 0.09375 0.125 0.140625 0.1875 0.28125 0.421875

POSITION_1 0 0 0.167 0.167 0.167 0.333 0.333 0.5 0.667 0.667 0.667 0.833 0.833 1

Figure 10 represents the graph of input/output relation. 1.2

1

v(Great)=v(Hot)=v(Pos)=v(Fast)=0.75 0.8

From the original table for fuzzy control model, a table of correspondingly semantically quantifying control rules is achieved: TABLE II. Rule No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

SIMPLIFYING TABLE OF SEMANTICAL QUANTIFICATION WIND_ SPEED 0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.25

FLUITD _TEMP 0.25 0.25 0.25 0.5 0.5 0.5 0.75 0.75 0.75 0.25 0.25 0.25 0.5 0.5 0.5 0.75 0.75 0.75 0.25 0.25 0.25 0.5

POSITION (Pc) 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75

POSITION_1 (Ps) 0.1667 0.1667 0.3333 0 0.1667 0.1667 0 0 0.1667 0.5 0.6667 0.8333 0.3333 0.5 0.6667 0.1667 0.3333 0.5 0.8333 0.8333 1 0.6667

0.6

0.4

0.2

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Figure 10. Input/output relation of the HA-based pre-processor

Simulation results by using Matlab:

This paper has described two new concepts to control a PTSC system: •

Designing an intelligent pre-processor to calculate the setpoint for the control loop, in which, besides the information about the trajectory calculated by a software, wind speed and fluid temperature of the collector are included.

•

Using HA as a new - flexible calculation tool which is constructed inherently on the background of fuzzy models. However, the quantity of linguistic varables in HA can be arbitrarily large. Compared to fuzzy logic, the usage of a processor based on HA is more simple. Moreover, this processor enables to calculate with a higher accuracy because there is a few effective factors affecting reasoning processes.

•

Through the simulation results on Matlab, it can be realized that whenever wind speed and fluid temperature change, the HA-based intelligent calculating model can offer a correspondingly setpoint which is suitable to real physical process. Hence, heating efficiency of the PTSC system can be improved. The correctness of the designing algorithm therefore is justified and it enlarges an applicable ability into reality.

•

However, the controlling accuracy may depend on backlash gear in the motion system which has not been mentioned yet in this research.

Pc

Ps

Figure 11. Software calculated trajectory (Pc) and Processed control trajectory (Ps)

REFERENCES [1]

Ps

Figure 12. Control value and output signal Conclusion

P. Naidoo, T.I. Van Niekerk and M. Brooks, “Intelligent control & tracking of a parabolic trough solar collector”, IFAC, 2002, available on: http://www.nt.ntnu.no/users/skoge/prost/proceedings/afcon03/Papers/01 1.pdf. [2] "Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts", Executive Summary (47 pages), Full Report (344 pages), Sargent and Lundy LLC, October 2003 [3] "Parabolic Trough Systems", EERE. [4] John A. Duffie, W. A. B., Solar Energy laboratory (1980). Solar Engineering of Thermal Processes. New York, John Wiley & Sons. [5] Vernon E. Dudley, G. J. K., Michael Sloan, David Kearney (1994). Test results SEGS LS-2 Solar Collector. [6] B. Koyuncu and K. Balasubramanian, “A microprocessor controlled automatic sun tracker,” IEEE Trans. Consumer Electron., vol. 37, no. 4, pp. 913-917, 1991. [7] J. D. Garrison, “A program for calculation of solar energy collection by fixed and tracking collectors,” Sol. Energy, vol. 72, no. 4, pp. 241-255, 2002. [8] Nguyen Cat Ho, W. Wechler, Hedge algebra: An algebraic approach to structures of sets of linguistic truth intervals , Fuzzy sets and systems 35(1990) 281-293. [9] Nguyen Cat Ho, W. Wechler, Extended algebra and their application to fuzzy logic, Fuzzy sets and systems 52 (1992) 259-281. [10] N.C.Ho, V.N.Lan and L.X.Viet, Optimal hedge-algebras-based controller: Design and application, Fuzzy Sets and Systems. Vol. 159 (2008), 968-989, 2008.