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Application of multi-model control with fuzzy switching to a micro hydro-electrical power plant
Renewable Energy 35 (2010) 2071e2079
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Application of multi-model control with fuzzy switching to a micro hydro-electrical power plant Issam Salhi a, *, Saïd Doubabi a, Najib Essounbouli b, Abdelaziz Hamzaoui b a
Laboratory of Electric Systems and Telecommunications (LEST), Faculty of Sciences and Technologies of Marrakesh, Cadi Ayyad University, BP 549, Av Abdelkarim Elkhattabi, Gueliz, Marrakesh, Morocco b CReSTIC, Reims University, 9, rue de Québec B.P. 396, F-10026 Troyes cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 June 2009 Accepted 9 February 2010 Available online 12 March 2010
Modelling hydraulic turbine generating systems is not an easy task because they are non-linear and uncertain where the operating points are time varying. One way to overcome this problem is to use TakagieSugeno (TS) models, which offer the possibility to apply some tools from linear control theory, whereas those models are composed of linear models connected by a fuzzy activation function. This paper presents an approach to model and control a micro hydro power plant considered as a non-linear system using TS fuzzy systems. A TS fuzzy system with local models is used to obtain a global model of the studied plant. Then, to combine efficiency and simplicity of design, PI controllers are synthesised for each considered operating point to be used as conclusion of an electrical load TS Fuzzy controller. The latter ensures the global stability and desired performance despite the change of operating point. The proposed approach (model and controller) is tested on a laboratory prototype, where the obtained results show their efficiency and their capability to ensure good performance despite the non-linear nature of the plant. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy Micro hydro power plant TakagieSugeno fuzzy inference system modelling Multi-model control
1. Introduction The global demand for clean energy continues to grow as indicated by the increase in distributed generation technologies and adoption of renewable energy resources. The extensive use of such energy sources is necessary to minimise the threat of global warming and climate change [1]. For example, micro hydro-electrical energy is considered as one of the most powerful renewable energy. It is produced by converting the potential energy of river water to kinetic energy via a turbine, and then to an electrical energy via a generator. It represents a good solution for remote communities that are far from grid networks, where the use of long transmission lines is prohibitively expensive because of the low population density (less than a few hundreds persons). This renewable energy source is considered as the earliest small scale renewable energy technology to be developed and has the potential to produce an important portion of power and is more reliable than solar or wind power, particularly if used in the right type of site.
* Corresponding author. Tel.: þ212 660 642 116; fax: þ212 524 433 170. E-mail addresses: [email protected] (I. Salhi), [email protected] (S. Doubabi), [email protected] (N. Essounbouli), abdelaziz. [email protected] (A. Hamzaoui). 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.02.008
Good electrical energy quality must be upheld through maintaining an uninterrupted power at a particular rated frequency and voltage for directly powering loads. Hence, voltage is regulated by controlling the generator excitation and the frequency by eliminating the difference between generation and load demand. In the latter case, controlling water flow through the action of a water regulating device on the turbine can be achieved using a classical servomotor [2e4]. However, this solution cannot ensure good performances when the load variation is large, which can lead to instability. These problems can be overcome using an “Electrical load Controller” (ELC), as mentioned by Henderson in [5]. The main idea of this approach is to keep the produced energy constant. According to the user consumption, a ballast load is adjusted to stabilise the frequency as presented in Fig. 1 [6,7]. Also, the hydro turbine features vary significantly with water flow and the unpredictable variation of the user load. Therefore, the ELC should be designed to work at any operating point, according to the quantity of water available and the users load variation. The design of an adequate controller that allows obtaining the desired performance requires a good analysis of the dynamic behaviour of micro hydro power plants (MHPP). To achieve this, it is necessary to develop an accurate model for describing the process. Analytical models are attractive since they provide a fundamental understanding of the relationships between the various input and output parameters.
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Because of its complexity and high degree of non-linearity, it is very difficult to obtain an accurate model for MHPP. To resolve this problem, the system could be identified around given operating points using classical methods [8,9]. However the constructed model would be closed depending on the considered operating point. An alternative method, the so-called TakagieSugeno (TS) type fuzzy models has been widely used to represent or approximate complex and non-linear systems. This fuzzy model is described by a family of fuzzy IF-THEN rules where each one represents a local linear inputeoutput relation of the system. The overall fuzzy model is achieved by smoothly blending these local linear models together through the fuzzy membership functions as presented in Fig. 2. Consequently, conventional linear system theories can be applied for the synthesis of the global controller. Based on the linear TS fuzzy model, the fruitful linear system theory can be applied to the analysis and controller synthesis of the non-linear system [10]. Recently, the stability issue of fuzzy control systems has been extensively investigated using linear matrix inequality techniques [11e13]. The main idea is to use feedback control law for each local model and the feedback gains are determined using the linear matrix inequality theory. However, these approaches suffer from long computation time, the complexity of the design procedure and non-optimal calculated gains. Another idea is to synthesise a local controller for each operating point and use a TS fuzzy system to switch between the local controllers according to the position of the system in the state space. Hence Essounbouli et al. have proposed [14] a hybrid control scheme based on a fuzzy supervisor which manages the combination of controllers of two types: with sliding mode control (SMC) and HN control. A
convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good tracking performance in both the transient state (SMC) and the steady state (HN), to provide a fast dynamic response to enlarge the stability limits of the system, and to efficiently reduce the chattering phenomena induced by the SMC. Based on the fact that proportional integral (PI) controllers give good trade-off between implementation cost and good tracking performance, this paper proposes to use them as local controllers. In this paper, the problem of maintaining the frequency of MHPP constant is analysed. The paper presents a control system that is suitable for turbine systems with both manual flow control and synchronous generators, especially permanent magnet machines which have no automatic voltage regulator. This work was motivated by problems encountered during the development of an ELC for a MHPP without a water flow governor. A simple manual gate allows adjusting the water flow by following the quantity existing in the river. The hydro turbine characteristics vary significantly with the unpredictable load on it, as well as the water flow which was explained previously. This presents a difficulty to designing an efficient and reliable controller knowing that, large load variation in the power system will be taken into account in this paper. From the perspective of the control, the micro hydro generating unit can be modelled as a system with two inputs and one output (2 1). The two inputs are wicket gate position and the electrical power consumed by users load and the output is the frequency of the voltage waveform. In this work, a TS fuzzy model is proposed to represent a MHPP prototype for all operating conditions. Some simple linear models for several operating points based on prototype characteristics were identified and were used to build the TS fuzzy model. The developed TS fuzzy model was experimentally validated, taking into consideration various working conditions (different water flow and user load variations). The application of fuzzy modelling provides good estimation of the prototype behaviour for all operating points including large variation of users load. Inspired by the work presented in [14], a TS fuzzy controller is proposed, in order to regulate the output of the MHPP prototype for all operating conditions, where the final part is composed by local PI controllers. Being suitable for non-linear and time varying systems, this technique is used to adjust the gains of the PI controller for each operating point through a multi-model control fuzzy switching. Gain values of the PI controller for each operating point were obtained using the root locus method prior to optimisation. The rest of this paper is structured as follows: a description of the experimental setup component is given in Section 2. In Section
Fig. 2. Structure of TS fuzzy model.
Fig. 3. Experimental setup.
Fig. 1. Electrical load controller principle.
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Fig. 4. The functional plan of the installation.
3, the plant model is described. Linearised dynamics for both a micro hydroelectric power plant prototype and an electrical actuator are given in Sections 3.1 and 3.3 respectively. The frequency control synthesis is described in Section 4. Examples of TS fuzzy controller implementation are given in Section 5. Finally, a conclusion is given in Section 6.
2. Description of the experimental setup used In this paper, the MHPP prototype shown in Fig. 3 is used to carry out the experimental studies. This prototype (producing
a
200 W) consists of a Pelton turbine, a synchronous machine generator (single phase, Permanent Magnet, two poles) that feeds a load formed by six lamps, and a frequency sensor with no water governor but only a manual gate opening. The latter allows water flow to be varied and hence to simulate the change of the river flow. The DSPACEÓ control development using a DSPACEÓ 1104 board connected to a personal computer is used in order to validate our simulation results. The installation allows variable water flow (between 0 and 20 l/s). The nominal values of the system parameters are: Electric power: 200 W. Frequency: 50 Hz. Voltage: 220 V. Flow: 6.5 l/s Overspeed: 1400 rpm. Runner diameter: 21 cm. To simulate the real situation where a MHPP operates with random and unpredictable steps on the users load, six lamps with different powers are used (one lamp that consumes 60 W, one that consumes 40 W and 4 others that consume 25 W). The functional plan of the experimental setup is given by Fig. 4. 3. System modelling
b
3.1. The linear MHPP model The power system's dynamic response can be represented by different types of models, which are required for several purposes such as the study of low frequency oscillations, islanding and isolated operation, system restoration following a break-up, load acceptance and water-hammer dynamics in
Fig. 5. Generating set response to load rejections, for different operating points (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
Fig. 6. Simplified representation of the power plant at each operating point.
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Table 1 First order model parameters for ten operating points based on gate position and load variation. Wicket gate opening
Coefficients
Load variation 12.5%
26%
43%
T1: 1 pu
Ks Ts
0.22 0.46
0.244 0.48
0.252 0.46
T2: 0.75 pu
Coefficients Ks Ts
T3: 0.5 pu
37% 0.285 0.55
Load variation 28% 44% 0.4 0.44 0.8 0.8
56% 0.47 0.8
Coefficients Ks Ts
T4: 0.25 pu
Coefficients Ks Ts
Fig. 9. TS Fuzzy model of MHPP.
Load variation 16% 30% 0.26 0.266 0.5 0.5
Load variation 50% 0.57 0.9
penstock. The approximation of a high order system by one of a lower order is highly advantageous as it reduces the computation time of the transient response and thus useful for the controller design and control system analysis. The cost and complexity of the controller increase in direct proportion to the system's order. Using the prototype described previously, some tests were needed to give a general idea about the influence of the different inputs (user load consumption, position of gate opening) on the behaviour of the plant output, also to evaluate the simplest representation that should be associated to the plant. Each gate position (water flow) produces a nominal power Pn. For some positions of the wicket gate opening, some discharges and/or overload on the electrical consumption (noted Pe) were made. Fig. 5 shows the measured data for two gate positions. Discharges were applied at the instant t ¼ 4 s, followed by their associated overload after 10 s. As can be seen, in each case, the obtained response is similar to that of a first order system response
where the gain and time constant change according to both load consumption variation (DPe ¼ Pn Pe) and gate position (X). The hydroelectric generating system is a complex non-linear system. However, for each operating point (“X” and “DPe”) the plant can be represented by a first order system as shown in Fig. 6, where Pn is the power level, based on the gate position as mentioned previously. The model presented here is based on a relatively simple linear model, which is sufficient to represent the significant dynamics of the prototype response around each operating point. The transfer function coefficients Ks and Ts are recalculated based on the prototype response for some operating points. The measured input and output data were loaded into the System Identification Toolbox of MatlabÓ environment (using ident) in order to identify the transfer function coefficients. The system identification provided using MatlabÓ allows the building of mathematical models of a dynamic system based on measured data. The coefficients Ks and Ts were computed using the measured data obtained for different gate positions and different load variations. Table 1 gives the identified coefficients of the first order transfer function for four gate positions (T1eT4 of Table 1) and different load variations. With the combination of the four power levels based on gate position and different disturbances based on variation of the network load, ten different operating points were considered. From Table 1, the non-linear evolution of the coefficients Ks and Ts can be remarked, which confirms that it is impossible to represent the MHPP by the same first order model for all the operating point range. To overcome this problem, a TakagieSugeno fuzzy system is proposed to be used in order to obtain a global model of the MHPP.
Fig. 7. Generated membership functions for wicket gate position.
Fig. 8. Generated membership functions for variation in the electrical power consumption.
I. Salhi et al. / Renewable Energy 35 (2010) 2071e2079
a
b
Fig. 10. Validation of the constructed model for different steps in load consumption at two gate positions (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
3.2. TakagieSugeno fuzzy model In the last decade, the application of artificial intelligence in modelling to other scientific and engineering disciplines has been successfully explored. In the case of hydro power plants there is
a
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still an opportunity to develop such models reliably [15]. Fuzzy modelling is supposed adequate for situations where there is a large uncertainty or unknown variation in plant parameters. The TakagieSugeno (TS) fuzzy model is a notable way to describe a non-linear dynamic system using local linear models. It has been employed successfully for solving modelling problems in practice such as in [16e19]. Further details are available in [20,21]. In this paper, the TS fuzzy systems approach is introduced to develop explicit models to capture the fuzzy and the non-linear relationships between the plant's two inputs (variation of the electrical consumption, gate position) and the output (frequency of the voltage waveform). A TS fuzzy model using fuzzy ifethen rules is built from obtained parameters of a linear model for some operating points. Fig. 7 shows the four generated membership functions corresponding to the process parameter (x1) characterising gate positions. The generated membership functions corresponding to the fuzzy sets of the process parameter (x2) for the quality characterising variation of the electrical consumption are shown in Fig. 8. The positive values of the process parameter x2 (which represent the case of overload) and the negative values (representing the case of discharge) are taken into consideration. Using the fuzzy rules, the appropriate TS fuzzy model's output (frequency) is estimated according to the associated linear model. Fig. 9 shows the used simulinkÓ block to represent the studied MHPP. The application of fuzzy modelling provides a good estimation of the prototype behaviour for all combinations of turbine characteristics and consumption variations. This implies that for any gate level and any applied load variation, the TS fuzzy model approximates the appropriate linear model of the system. The TS fuzzy inference engine combines the local linear models according to input vectors in order to find a proper model of the system capable of generating the appropriate output.
b
Fig. 11. The error absolute value for validation of the proposed model at each gate position a and b.
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Fig. 12. Block diagram used to identify the actuator.
Fig. 14. Block diagram of the hydroelectric unit closed-loop.
An on-line test was performed on the studied prototype in order to validate the proposed TS fuzzy model. The DSPACEÓ control development with a DSPACEÓ 1104 board connected to a personal computer is used. Fig. 10 shows the prototype responses (solid lines) for different discharges and overloads of the load consumption for two different operating points. The discharges were applied at the instant t ¼ 4 s and their appropriate overloads at the instant t ¼ 14 s. Dashed lines represent the TS fuzzy model responses. It can be seen that the simulation results and the experimental ones are in close accord, confirming the good approximation of the identified TS fuzzy model. This result is also verified by Fig. 11, which shows the absolute value of the calculated error between experimental and simulation results. It can be seen from the figure that the error is small, remaining under 3 102 (pu) and thus confirming the pertinence of the identified TS fuzzy model.
3.3. Identification of the used actuator The actuator in the proposed control scheme must compensate the disconnected consumption of the electrical power. An Analogue Power Controller (APC) connected to a ballast load was chosen as an actuator. When the APC is excited by the control signal (U), it dissipates some electrical power (Pd) in the ballast load according to the control's value. To identify its transfer function (G(p)), the scheme in Fig. 12 was used, where S(p) represents the detailed model of the hydroelectric plant. The APC was excited by changing control output value and this was done for several operating points. The responses obtained led to identification of the transfer function G(p) as the following second-degree transfer function:
GðpÞ ¼
83:03 p2 þ 7:9p þ 62:41
(1)
Fig. 13 shows the curves obtained from both the simulated and experimentally measured results. 4. Electrical load PI controller and local stability analysis As mentioned in Section 2, micro hydro power is emerging as a major contributor of electrical energy. Therefore, its control process is becoming very important. Moreover equipment tear as well as generation and operation costs can be reduced by using a sufficient control strategy. In addition, optimum adjustment of PI controller is vital to ensure the stability and satisfactory transient behaviour of the MHPP. The controller gain Kc must be chosen such that a good shape of the transient response is obtained. It cannot be too high, otherwise instability may result. Although various techniques, mostly based on trial-and-error approaches, have been addressed to choose the integration time Ti, there is no guarantee to achieve the most desirable response, especially when the parameters of the system change. A frequency domain method to determine the optimum values for the parameters of PID controller is presented in [22]. Another method based on gain scheduling is proposed in [23]. In this paper, coefficients (Kc and Ti) of PI controller for disturbance attenuation were first obtained according to Routh table conditions and then optimised using MatlabÓ 7.1-SimulinkÓ software. The control law for a PI controller is given by the following expression:
Z ui ¼ Kc ei þ
Kp e dt Ti i
(2)
where ei is the tracking error. The controller transfer function is given as:
CðpÞ ¼
Kc ð1 þ Ti pÞ Ti p
Fig. 13. Output frequency of the power system using the APC.
(3)
I. Salhi et al. / Renewable Energy 35 (2010) 2071e2079
5. Electrical load TS fuzzy controller and global stability analysis
Table 2 PI controller parameters for T1 gate position. Gate position
T1: 1 pu
Coefficients
Load variation
Kcmax Timin
12.5%
30%
42.5%
1.06 0.286
0.98 0.291
0.93 0.286
The method used readily handles a detailed model of the hydroelectric plant S(p) and of the APC. The plant component transfer functions GðpÞ ¼ Kg $u2 =ðu2 þ 2$x$up þ p2 Þ and S(p) are known, and the controller transfer function C(p) is to be determined. The power plant unit in closed-loop is represented by the block diagram in Fig. 14 and the closed-loop transfer function representing the dynamics of users load variation dependent frequency is given by:
The hydroelectric generating system is complex and nonlinear, therefore fixed control structure and preset controller parameters are not suitable for it [15]. To overcome this problem, this paper proposes an electrical load based TS fuzzy controller to regulate the output of the MHPP prototype for all operating conditions. This technique is suitable for non-linear and time varying systems, and is used to adjust the gains of the PI controller according to each operating point through a multimodel control fuzzy switching. The global stability of the system governed by the Electrical load TS Fuzzy controller is proven based on Wong et al.'s theorem [14,24,25]. Fig. 15 shows the used MatlabÓ/SimulinkÓ diagram representing the MHPP model and the electrical load TS fuzzy controller, where Pd is the dissipated power on the Ballast load.
2x 1 Ks Ti p 1 þ p þ 2 p2 u u HðpÞ ¼ 2$T $x Ti $Ts 4 1 2$Ti $x s 3 p þ Ti þ 2 p þ Ti þ Ts p2 þ Ti Kc $Kg $Ks þ 1 p þ Kc $Kg $Ks 2
u
u
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u
(4)
u
The following conditions that must be satisfied to guarantee the stability of the system, were obtained using the Routh table:
8 Ti _0 ; Kc _0 2 > 2x þ 4x Ts u þ 2xTs2 u2 > > < Kc 3 ¼ Kcmax Ts uKg Ks 2 > > Kg Ks Kc ð1 þ 2xTs uÞ > : ¼ Timin Ti _ u 1 þ Kg Ks Kc 2x þ 4x2 Ts u þ 2xTs2 u2 Ts uKg Ks Kc (5) For given gate positions (T1), Table 2 provides the critical coefficients of the PI controllers. In this work, it is assumed that the user load variations are not measured, which means that the controller parameters would not vary according to these variations. For the position (T1), the optimised PI gain and integral time were taken as Kc ¼ 0.6 and Ti ¼ 0.4. The evolution of frequency versus time is shown in Fig. 16-b. Experimental results are represented by a solid line and simulation results by a dashed line.
The electrical load TS fuzzy controller obtained was tested experimentally on the studied prototype in order to assess its ability to keep the frequency on its steady state value, as well as to prove the capability of the controller to keep good system behaviour for both, small and large load rejections. The resulting frequency versus time plots for different load variations and two different gate positions are given in Fig. 16. This figure shows the results for four different variations on electrical consumption (20% and 50%; discharge and overload for each). Solid lines represent experimental responses and dashed lines, the simulation results. As can be seen, the stabilising time is less than 2 s, and the desired frequency of 50 Hz is attained. Hence, the controller is able to maintain the frequency at the desired value. Furthermore, it is clearly seen from the figure that the simulation results are close to those obtained experimentally. The frequency can be seen to rise above 55.65 Hz (1.113 pu) at its peak. The time to return within the dead band (the return time) is in the order of 1.32 s and the time to return to its steady state value is in the order of 1.63 s.
Fig. 15. Power plant control using a TS fuzzy controller.
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a
b
Fig. 16. Unit frequency response to step load disturbance using TS Fuzzy controller for two different gate position. (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
a
6. Conclusion and scope for future work This paper presents an application of multi-model control with TS fuzzy switching to a micro hydroelectric power plant under random user load variation. The studied system was a laboratory prototype, which was identified on some local operating points. Thereby, a TS fuzzy model was built based on the identified local linear models, in order to represent the studied system. A comparison of the behaviour of both the TS fuzzy model and experimental setup, demonstrates the pertinence of the proposed model. The insignificant discrepancy between the simulated and experimental results for both the cases of open and close loop, presents a successfully solution using a TS fuzzy model. Additionally, this paper illustrates that the proposed electrical load TS fuzzy controller based on several PI controllers can efficiently control the hydroelectric power plant system studied. The key features of the proposed controller are its strong adaptability and robustness. It shows good performance under different working conditions. Even for random and large load variations, the controller maintains satisfactory dynamics and guarantees closed-loop stability for all operating conditions. The presented control system ensures a high quality of electrical power and a cost-effective solution for rural electrification. It can be easily synthesised and installed to control either micro hydro power plants with manual flow control or guide vane governors. Furthermore, its cost represents less than one percent of that of the electro-mechanical equipment (turbineealternator), hence a smaller percentage of the total budget of the plant is spent. Our priority for further work is the proposition of a fuzzy controller that will guarantee a good quality of the generated power and manage the available water in order to save it depending on the load demand, since the ELC wastes precious energy that could be used gainfully. References
b
Fig. 17. Square error between the measurement and simulation results at each operating point.
Fig. 17 shows the calculated absolute value of the discrepancy between experimental and simulation results. It is observed that the discrepancy is small, and for the transient dynamic it does not exceed 5 102 (pu). Thus, the pertinence of the electrical load multi-model control with TS fuzzy switching is confirmed.
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Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Application of multi-model control with fuzzy switching to a micro hydro-electrical power plant Issam Salhi a, *, Saïd Doubabi a, Najib Essounbouli b, Abdelaziz Hamzaoui b a
Laboratory of Electric Systems and Telecommunications (LEST), Faculty of Sciences and Technologies of Marrakesh, Cadi Ayyad University, BP 549, Av Abdelkarim Elkhattabi, Gueliz, Marrakesh, Morocco b CReSTIC, Reims University, 9, rue de Québec B.P. 396, F-10026 Troyes cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 June 2009 Accepted 9 February 2010 Available online 12 March 2010
Modelling hydraulic turbine generating systems is not an easy task because they are non-linear and uncertain where the operating points are time varying. One way to overcome this problem is to use TakagieSugeno (TS) models, which offer the possibility to apply some tools from linear control theory, whereas those models are composed of linear models connected by a fuzzy activation function. This paper presents an approach to model and control a micro hydro power plant considered as a non-linear system using TS fuzzy systems. A TS fuzzy system with local models is used to obtain a global model of the studied plant. Then, to combine efficiency and simplicity of design, PI controllers are synthesised for each considered operating point to be used as conclusion of an electrical load TS Fuzzy controller. The latter ensures the global stability and desired performance despite the change of operating point. The proposed approach (model and controller) is tested on a laboratory prototype, where the obtained results show their efficiency and their capability to ensure good performance despite the non-linear nature of the plant. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy Micro hydro power plant TakagieSugeno fuzzy inference system modelling Multi-model control
1. Introduction The global demand for clean energy continues to grow as indicated by the increase in distributed generation technologies and adoption of renewable energy resources. The extensive use of such energy sources is necessary to minimise the threat of global warming and climate change [1]. For example, micro hydro-electrical energy is considered as one of the most powerful renewable energy. It is produced by converting the potential energy of river water to kinetic energy via a turbine, and then to an electrical energy via a generator. It represents a good solution for remote communities that are far from grid networks, where the use of long transmission lines is prohibitively expensive because of the low population density (less than a few hundreds persons). This renewable energy source is considered as the earliest small scale renewable energy technology to be developed and has the potential to produce an important portion of power and is more reliable than solar or wind power, particularly if used in the right type of site.
* Corresponding author. Tel.: þ212 660 642 116; fax: þ212 524 433 170. E-mail addresses: [email protected] (I. Salhi), [email protected] (S. Doubabi), [email protected] (N. Essounbouli), abdelaziz. [email protected] (A. Hamzaoui). 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.02.008
Good electrical energy quality must be upheld through maintaining an uninterrupted power at a particular rated frequency and voltage for directly powering loads. Hence, voltage is regulated by controlling the generator excitation and the frequency by eliminating the difference between generation and load demand. In the latter case, controlling water flow through the action of a water regulating device on the turbine can be achieved using a classical servomotor [2e4]. However, this solution cannot ensure good performances when the load variation is large, which can lead to instability. These problems can be overcome using an “Electrical load Controller” (ELC), as mentioned by Henderson in [5]. The main idea of this approach is to keep the produced energy constant. According to the user consumption, a ballast load is adjusted to stabilise the frequency as presented in Fig. 1 [6,7]. Also, the hydro turbine features vary significantly with water flow and the unpredictable variation of the user load. Therefore, the ELC should be designed to work at any operating point, according to the quantity of water available and the users load variation. The design of an adequate controller that allows obtaining the desired performance requires a good analysis of the dynamic behaviour of micro hydro power plants (MHPP). To achieve this, it is necessary to develop an accurate model for describing the process. Analytical models are attractive since they provide a fundamental understanding of the relationships between the various input and output parameters.
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Because of its complexity and high degree of non-linearity, it is very difficult to obtain an accurate model for MHPP. To resolve this problem, the system could be identified around given operating points using classical methods [8,9]. However the constructed model would be closed depending on the considered operating point. An alternative method, the so-called TakagieSugeno (TS) type fuzzy models has been widely used to represent or approximate complex and non-linear systems. This fuzzy model is described by a family of fuzzy IF-THEN rules where each one represents a local linear inputeoutput relation of the system. The overall fuzzy model is achieved by smoothly blending these local linear models together through the fuzzy membership functions as presented in Fig. 2. Consequently, conventional linear system theories can be applied for the synthesis of the global controller. Based on the linear TS fuzzy model, the fruitful linear system theory can be applied to the analysis and controller synthesis of the non-linear system [10]. Recently, the stability issue of fuzzy control systems has been extensively investigated using linear matrix inequality techniques [11e13]. The main idea is to use feedback control law for each local model and the feedback gains are determined using the linear matrix inequality theory. However, these approaches suffer from long computation time, the complexity of the design procedure and non-optimal calculated gains. Another idea is to synthesise a local controller for each operating point and use a TS fuzzy system to switch between the local controllers according to the position of the system in the state space. Hence Essounbouli et al. have proposed [14] a hybrid control scheme based on a fuzzy supervisor which manages the combination of controllers of two types: with sliding mode control (SMC) and HN control. A
convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good tracking performance in both the transient state (SMC) and the steady state (HN), to provide a fast dynamic response to enlarge the stability limits of the system, and to efficiently reduce the chattering phenomena induced by the SMC. Based on the fact that proportional integral (PI) controllers give good trade-off between implementation cost and good tracking performance, this paper proposes to use them as local controllers. In this paper, the problem of maintaining the frequency of MHPP constant is analysed. The paper presents a control system that is suitable for turbine systems with both manual flow control and synchronous generators, especially permanent magnet machines which have no automatic voltage regulator. This work was motivated by problems encountered during the development of an ELC for a MHPP without a water flow governor. A simple manual gate allows adjusting the water flow by following the quantity existing in the river. The hydro turbine characteristics vary significantly with the unpredictable load on it, as well as the water flow which was explained previously. This presents a difficulty to designing an efficient and reliable controller knowing that, large load variation in the power system will be taken into account in this paper. From the perspective of the control, the micro hydro generating unit can be modelled as a system with two inputs and one output (2 1). The two inputs are wicket gate position and the electrical power consumed by users load and the output is the frequency of the voltage waveform. In this work, a TS fuzzy model is proposed to represent a MHPP prototype for all operating conditions. Some simple linear models for several operating points based on prototype characteristics were identified and were used to build the TS fuzzy model. The developed TS fuzzy model was experimentally validated, taking into consideration various working conditions (different water flow and user load variations). The application of fuzzy modelling provides good estimation of the prototype behaviour for all operating points including large variation of users load. Inspired by the work presented in [14], a TS fuzzy controller is proposed, in order to regulate the output of the MHPP prototype for all operating conditions, where the final part is composed by local PI controllers. Being suitable for non-linear and time varying systems, this technique is used to adjust the gains of the PI controller for each operating point through a multi-model control fuzzy switching. Gain values of the PI controller for each operating point were obtained using the root locus method prior to optimisation. The rest of this paper is structured as follows: a description of the experimental setup component is given in Section 2. In Section
Fig. 2. Structure of TS fuzzy model.
Fig. 3. Experimental setup.
Fig. 1. Electrical load controller principle.
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Fig. 4. The functional plan of the installation.
3, the plant model is described. Linearised dynamics for both a micro hydroelectric power plant prototype and an electrical actuator are given in Sections 3.1 and 3.3 respectively. The frequency control synthesis is described in Section 4. Examples of TS fuzzy controller implementation are given in Section 5. Finally, a conclusion is given in Section 6.
2. Description of the experimental setup used In this paper, the MHPP prototype shown in Fig. 3 is used to carry out the experimental studies. This prototype (producing
a
200 W) consists of a Pelton turbine, a synchronous machine generator (single phase, Permanent Magnet, two poles) that feeds a load formed by six lamps, and a frequency sensor with no water governor but only a manual gate opening. The latter allows water flow to be varied and hence to simulate the change of the river flow. The DSPACEÓ control development using a DSPACEÓ 1104 board connected to a personal computer is used in order to validate our simulation results. The installation allows variable water flow (between 0 and 20 l/s). The nominal values of the system parameters are: Electric power: 200 W. Frequency: 50 Hz. Voltage: 220 V. Flow: 6.5 l/s Overspeed: 1400 rpm. Runner diameter: 21 cm. To simulate the real situation where a MHPP operates with random and unpredictable steps on the users load, six lamps with different powers are used (one lamp that consumes 60 W, one that consumes 40 W and 4 others that consume 25 W). The functional plan of the experimental setup is given by Fig. 4. 3. System modelling
b
3.1. The linear MHPP model The power system's dynamic response can be represented by different types of models, which are required for several purposes such as the study of low frequency oscillations, islanding and isolated operation, system restoration following a break-up, load acceptance and water-hammer dynamics in
Fig. 5. Generating set response to load rejections, for different operating points (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
Fig. 6. Simplified representation of the power plant at each operating point.
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Table 1 First order model parameters for ten operating points based on gate position and load variation. Wicket gate opening
Coefficients
Load variation 12.5%
26%
43%
T1: 1 pu
Ks Ts
0.22 0.46
0.244 0.48
0.252 0.46
T2: 0.75 pu
Coefficients Ks Ts
T3: 0.5 pu
37% 0.285 0.55
Load variation 28% 44% 0.4 0.44 0.8 0.8
56% 0.47 0.8
Coefficients Ks Ts
T4: 0.25 pu
Coefficients Ks Ts
Fig. 9. TS Fuzzy model of MHPP.
Load variation 16% 30% 0.26 0.266 0.5 0.5
Load variation 50% 0.57 0.9
penstock. The approximation of a high order system by one of a lower order is highly advantageous as it reduces the computation time of the transient response and thus useful for the controller design and control system analysis. The cost and complexity of the controller increase in direct proportion to the system's order. Using the prototype described previously, some tests were needed to give a general idea about the influence of the different inputs (user load consumption, position of gate opening) on the behaviour of the plant output, also to evaluate the simplest representation that should be associated to the plant. Each gate position (water flow) produces a nominal power Pn. For some positions of the wicket gate opening, some discharges and/or overload on the electrical consumption (noted Pe) were made. Fig. 5 shows the measured data for two gate positions. Discharges were applied at the instant t ¼ 4 s, followed by their associated overload after 10 s. As can be seen, in each case, the obtained response is similar to that of a first order system response
where the gain and time constant change according to both load consumption variation (DPe ¼ Pn Pe) and gate position (X). The hydroelectric generating system is a complex non-linear system. However, for each operating point (“X” and “DPe”) the plant can be represented by a first order system as shown in Fig. 6, where Pn is the power level, based on the gate position as mentioned previously. The model presented here is based on a relatively simple linear model, which is sufficient to represent the significant dynamics of the prototype response around each operating point. The transfer function coefficients Ks and Ts are recalculated based on the prototype response for some operating points. The measured input and output data were loaded into the System Identification Toolbox of MatlabÓ environment (using ident) in order to identify the transfer function coefficients. The system identification provided using MatlabÓ allows the building of mathematical models of a dynamic system based on measured data. The coefficients Ks and Ts were computed using the measured data obtained for different gate positions and different load variations. Table 1 gives the identified coefficients of the first order transfer function for four gate positions (T1eT4 of Table 1) and different load variations. With the combination of the four power levels based on gate position and different disturbances based on variation of the network load, ten different operating points were considered. From Table 1, the non-linear evolution of the coefficients Ks and Ts can be remarked, which confirms that it is impossible to represent the MHPP by the same first order model for all the operating point range. To overcome this problem, a TakagieSugeno fuzzy system is proposed to be used in order to obtain a global model of the MHPP.
Fig. 7. Generated membership functions for wicket gate position.
Fig. 8. Generated membership functions for variation in the electrical power consumption.
I. Salhi et al. / Renewable Energy 35 (2010) 2071e2079
a
b
Fig. 10. Validation of the constructed model for different steps in load consumption at two gate positions (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
3.2. TakagieSugeno fuzzy model In the last decade, the application of artificial intelligence in modelling to other scientific and engineering disciplines has been successfully explored. In the case of hydro power plants there is
a
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still an opportunity to develop such models reliably [15]. Fuzzy modelling is supposed adequate for situations where there is a large uncertainty or unknown variation in plant parameters. The TakagieSugeno (TS) fuzzy model is a notable way to describe a non-linear dynamic system using local linear models. It has been employed successfully for solving modelling problems in practice such as in [16e19]. Further details are available in [20,21]. In this paper, the TS fuzzy systems approach is introduced to develop explicit models to capture the fuzzy and the non-linear relationships between the plant's two inputs (variation of the electrical consumption, gate position) and the output (frequency of the voltage waveform). A TS fuzzy model using fuzzy ifethen rules is built from obtained parameters of a linear model for some operating points. Fig. 7 shows the four generated membership functions corresponding to the process parameter (x1) characterising gate positions. The generated membership functions corresponding to the fuzzy sets of the process parameter (x2) for the quality characterising variation of the electrical consumption are shown in Fig. 8. The positive values of the process parameter x2 (which represent the case of overload) and the negative values (representing the case of discharge) are taken into consideration. Using the fuzzy rules, the appropriate TS fuzzy model's output (frequency) is estimated according to the associated linear model. Fig. 9 shows the used simulinkÓ block to represent the studied MHPP. The application of fuzzy modelling provides a good estimation of the prototype behaviour for all combinations of turbine characteristics and consumption variations. This implies that for any gate level and any applied load variation, the TS fuzzy model approximates the appropriate linear model of the system. The TS fuzzy inference engine combines the local linear models according to input vectors in order to find a proper model of the system capable of generating the appropriate output.
b
Fig. 11. The error absolute value for validation of the proposed model at each gate position a and b.
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Fig. 12. Block diagram used to identify the actuator.
Fig. 14. Block diagram of the hydroelectric unit closed-loop.
An on-line test was performed on the studied prototype in order to validate the proposed TS fuzzy model. The DSPACEÓ control development with a DSPACEÓ 1104 board connected to a personal computer is used. Fig. 10 shows the prototype responses (solid lines) for different discharges and overloads of the load consumption for two different operating points. The discharges were applied at the instant t ¼ 4 s and their appropriate overloads at the instant t ¼ 14 s. Dashed lines represent the TS fuzzy model responses. It can be seen that the simulation results and the experimental ones are in close accord, confirming the good approximation of the identified TS fuzzy model. This result is also verified by Fig. 11, which shows the absolute value of the calculated error between experimental and simulation results. It can be seen from the figure that the error is small, remaining under 3 102 (pu) and thus confirming the pertinence of the identified TS fuzzy model.
3.3. Identification of the used actuator The actuator in the proposed control scheme must compensate the disconnected consumption of the electrical power. An Analogue Power Controller (APC) connected to a ballast load was chosen as an actuator. When the APC is excited by the control signal (U), it dissipates some electrical power (Pd) in the ballast load according to the control's value. To identify its transfer function (G(p)), the scheme in Fig. 12 was used, where S(p) represents the detailed model of the hydroelectric plant. The APC was excited by changing control output value and this was done for several operating points. The responses obtained led to identification of the transfer function G(p) as the following second-degree transfer function:
GðpÞ ¼
83:03 p2 þ 7:9p þ 62:41
(1)
Fig. 13 shows the curves obtained from both the simulated and experimentally measured results. 4. Electrical load PI controller and local stability analysis As mentioned in Section 2, micro hydro power is emerging as a major contributor of electrical energy. Therefore, its control process is becoming very important. Moreover equipment tear as well as generation and operation costs can be reduced by using a sufficient control strategy. In addition, optimum adjustment of PI controller is vital to ensure the stability and satisfactory transient behaviour of the MHPP. The controller gain Kc must be chosen such that a good shape of the transient response is obtained. It cannot be too high, otherwise instability may result. Although various techniques, mostly based on trial-and-error approaches, have been addressed to choose the integration time Ti, there is no guarantee to achieve the most desirable response, especially when the parameters of the system change. A frequency domain method to determine the optimum values for the parameters of PID controller is presented in [22]. Another method based on gain scheduling is proposed in [23]. In this paper, coefficients (Kc and Ti) of PI controller for disturbance attenuation were first obtained according to Routh table conditions and then optimised using MatlabÓ 7.1-SimulinkÓ software. The control law for a PI controller is given by the following expression:
Z ui ¼ Kc ei þ
Kp e dt Ti i
(2)
where ei is the tracking error. The controller transfer function is given as:
CðpÞ ¼
Kc ð1 þ Ti pÞ Ti p
Fig. 13. Output frequency of the power system using the APC.
(3)
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5. Electrical load TS fuzzy controller and global stability analysis
Table 2 PI controller parameters for T1 gate position. Gate position
T1: 1 pu
Coefficients
Load variation
Kcmax Timin
12.5%
30%
42.5%
1.06 0.286
0.98 0.291
0.93 0.286
The method used readily handles a detailed model of the hydroelectric plant S(p) and of the APC. The plant component transfer functions GðpÞ ¼ Kg $u2 =ðu2 þ 2$x$up þ p2 Þ and S(p) are known, and the controller transfer function C(p) is to be determined. The power plant unit in closed-loop is represented by the block diagram in Fig. 14 and the closed-loop transfer function representing the dynamics of users load variation dependent frequency is given by:
The hydroelectric generating system is complex and nonlinear, therefore fixed control structure and preset controller parameters are not suitable for it [15]. To overcome this problem, this paper proposes an electrical load based TS fuzzy controller to regulate the output of the MHPP prototype for all operating conditions. This technique is suitable for non-linear and time varying systems, and is used to adjust the gains of the PI controller according to each operating point through a multimodel control fuzzy switching. The global stability of the system governed by the Electrical load TS Fuzzy controller is proven based on Wong et al.'s theorem [14,24,25]. Fig. 15 shows the used MatlabÓ/SimulinkÓ diagram representing the MHPP model and the electrical load TS fuzzy controller, where Pd is the dissipated power on the Ballast load.
2x 1 Ks Ti p 1 þ p þ 2 p2 u u HðpÞ ¼ 2$T $x Ti $Ts 4 1 2$Ti $x s 3 p þ Ti þ 2 p þ Ti þ Ts p2 þ Ti Kc $Kg $Ks þ 1 p þ Kc $Kg $Ks 2
u
u
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u
(4)
u
The following conditions that must be satisfied to guarantee the stability of the system, were obtained using the Routh table:
8 Ti _0 ; Kc _0 2 > 2x þ 4x Ts u þ 2xTs2 u2 > > < Kc 3 ¼ Kcmax Ts uKg Ks 2 > > Kg Ks Kc ð1 þ 2xTs uÞ > : ¼ Timin Ti _ u 1 þ Kg Ks Kc 2x þ 4x2 Ts u þ 2xTs2 u2 Ts uKg Ks Kc (5) For given gate positions (T1), Table 2 provides the critical coefficients of the PI controllers. In this work, it is assumed that the user load variations are not measured, which means that the controller parameters would not vary according to these variations. For the position (T1), the optimised PI gain and integral time were taken as Kc ¼ 0.6 and Ti ¼ 0.4. The evolution of frequency versus time is shown in Fig. 16-b. Experimental results are represented by a solid line and simulation results by a dashed line.
The electrical load TS fuzzy controller obtained was tested experimentally on the studied prototype in order to assess its ability to keep the frequency on its steady state value, as well as to prove the capability of the controller to keep good system behaviour for both, small and large load rejections. The resulting frequency versus time plots for different load variations and two different gate positions are given in Fig. 16. This figure shows the results for four different variations on electrical consumption (20% and 50%; discharge and overload for each). Solid lines represent experimental responses and dashed lines, the simulation results. As can be seen, the stabilising time is less than 2 s, and the desired frequency of 50 Hz is attained. Hence, the controller is able to maintain the frequency at the desired value. Furthermore, it is clearly seen from the figure that the simulation results are close to those obtained experimentally. The frequency can be seen to rise above 55.65 Hz (1.113 pu) at its peak. The time to return within the dead band (the return time) is in the order of 1.32 s and the time to return to its steady state value is in the order of 1.63 s.
Fig. 15. Power plant control using a TS fuzzy controller.
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a
b
Fig. 16. Unit frequency response to step load disturbance using TS Fuzzy controller for two different gate position. (a: 60% of the maximal wicket gate opening and b: 100% of the maximal wicket gate opening).
a
6. Conclusion and scope for future work This paper presents an application of multi-model control with TS fuzzy switching to a micro hydroelectric power plant under random user load variation. The studied system was a laboratory prototype, which was identified on some local operating points. Thereby, a TS fuzzy model was built based on the identified local linear models, in order to represent the studied system. A comparison of the behaviour of both the TS fuzzy model and experimental setup, demonstrates the pertinence of the proposed model. The insignificant discrepancy between the simulated and experimental results for both the cases of open and close loop, presents a successfully solution using a TS fuzzy model. Additionally, this paper illustrates that the proposed electrical load TS fuzzy controller based on several PI controllers can efficiently control the hydroelectric power plant system studied. The key features of the proposed controller are its strong adaptability and robustness. It shows good performance under different working conditions. Even for random and large load variations, the controller maintains satisfactory dynamics and guarantees closed-loop stability for all operating conditions. The presented control system ensures a high quality of electrical power and a cost-effective solution for rural electrification. It can be easily synthesised and installed to control either micro hydro power plants with manual flow control or guide vane governors. Furthermore, its cost represents less than one percent of that of the electro-mechanical equipment (turbineealternator), hence a smaller percentage of the total budget of the plant is spent. Our priority for further work is the proposition of a fuzzy controller that will guarantee a good quality of the generated power and manage the available water in order to save it depending on the load demand, since the ELC wastes precious energy that could be used gainfully. References
b
Fig. 17. Square error between the measurement and simulation results at each operating point.
Fig. 17 shows the calculated absolute value of the discrepancy between experimental and simulation results. It is observed that the discrepancy is small, and for the transient dynamic it does not exceed 5 102 (pu). Thus, the pertinence of the electrical load multi-model control with TS fuzzy switching is confirmed.
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