Hydro-turbine governor control: theory, techniques and limitations

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1 University of Wollongong Research Online Faculty of Engineering and Information Sciences - Paers: Part A Faculty of Engineering and Information Sciences 006 Hydro-turbine governor control: theory, techniques and limitations J Culberg University of Tasmania Michael Negnevitsy University of Tasmania, michael.negnevitsy@utas.edu.au Kashem M. Muttaqi University of Tasmania, ashem@uow.edu.au Publication Details J. Culberg, M. Negnevitsy & K. A. Kashem, "Hydro-turbine governor control: theory, techniques and limitations," in Australasian Universities Power Engineering Conference (AUPEC 006), 006, Research Online is the oen access institutional reository for the University of Wollongong. For further information contact the UOW Library: research-ubs@uow.edu.au

2 Hydro-turbine governor control: theory, techniques and limitations Abstract With the entry of Tasmania into the national electricity maret, equiment ugrades are required in many arts of the existing ower system. This resents an oortunity to embrace new technology, in order to enhance the current efficiency and roductivity of the system. One area is that of hydro-turbine seed governors, an integral art of maintaining the frequency of the outut. This aer analyses the current standard control algorithm for turbine governors, the PID controller. It illustrates the rocesses involved, tuning and their limitations. Finally, alternative control systems are discussed. Keywords limitations, turbine, theory, hydro, control, techniques, governor Discilines Engineering Science and Technology Studies Publication Details J. Culberg, M. Negnevitsy & K. A. Kashem, "Hydro-turbine governor control: theory, techniques and limitations," in Australasian Universities Power Engineering Conference (AUPEC 006), 006, This conference aer is available at Research Online: htt://ro.uow.edu.au/eisaers/4405

3 See discussions, stats, and author rofiles for this ublication at: htt:// HydroTurbine Governor Control: Theory, Techniques and Limitations ARTICLE CITATIONS DOWNLOADS 36 VIEWS 93 3 AUTHORS, INCLUDING: Michael Negnevitsy University of Tasmania Kashem M. Muttaqi University of Wollongong 195 PUBLICATIONS,03 CITATIONS 110 PUBLICATIONS 1,031 CITATIONS SEE PROFILE SEE PROFILE Available from: Kashem M. Muttaqi Retrieved on: 3 Setember 015

4 Hydro-Turbine Governor Control: Theory, Techniques and Limitations J. Culberg, M. Negnevitsy and M. A. Kashem School of Engineering University of Tasmania Hobart, TAS ABSTRACT With the entry of Tasmania into the national electricity maret, equiment ugrades are required in many arts of the existing ower system. This resents an oortunity to embrace new technology, in order to enhance the current efficiency and roductivity of the system. One area is that of hydro-turbine seed governors, an integral art of maintaining the frequency of the outut. This aer analyses the current standard control algorithm for turbine governors, the PID controller. It illustrates the rocesses involved, tuning and their limitations. Finally, alternative control systems are discussed. 1. INTRODUCTION Hydro Tasmania is currently ugrading much of its lant and equiment, mostly due to the wear and tear of existing systems. This is art of an overall ugrade rogram intended to bring Tasmania s ower industry into line with the National Electricity Maret Management Comany (NEMMCO) standards. One imortant tye of equiment to be ugraded in many ower generation facilities is the turbine governor. The turbine governor is a system that regulates the inlet of water into a turbine, which in turn rotates the generator to roduce electricity. In order to maintain a required generated frequency of 50Hz the seed of rotation must be et constant. The turbine governor receives information on the current rotational seed of the turbine and adjusts the water flow to maintain the seed at the correct level. Many of the governors currently in use by Hydro Tasmania are of older, urely mechanical design. While effective, these suffer from mechanical wear due to aging. As these units reach the end of their woring life, relacement is essential. At the resent moment in time, the relacement of choice within Hydro Tasmania is a Proortional-Integral-Derivative (PID) controller adated to function as the governor for a turbine. The use of PID controllers is widesread and oular in many modern industries. The oularity of PID controllers stems in art to their wide alicability to a variety of single inut single outut (SISO) alications. They are also common, maing them easy to obtain. PID controllers are not without their limitations, however. They are unsuitable for comlex systems and lac the ability to adjust to change over time. Intelligent systems offer an alternative aroach to control hydroturbines, avoiding the roblems associated with PID controllers. Systems such as Fuzzy Logic controllers, Artificial Neural Networs and Adative Neuro Fuzzy Inference Systems offer effective control for comlex systems, while remaining relatively simle and easy to imlement.. THEORY OF PID CONTROL A PID controller uses an algorithm that rovides the control signal in a feedbac control loo. The name derives from the three functions involved in calculating the corrections.[1] The Proortional function deals with resent values, multilying the current error by a set value P and subtracting the resultant value from the rocess s inut. This is only alicable in the erformance band where P is roortional to the error of the system. The main roblem with a urely Proortional controller is that it will over-react to small errors, causing the system to oscillate. While these oscillations will eventually be reduced and eliminated, it is better to avoid them. Also, while a Proortional controller can achieve a steady state, it is almost imossible to avoid a constant error at this state. Ideally, the controller should have no error at the steady state. This is where the Integral stage comes into lay. The Integral stage handles ast values, integrating the error over a eriod of time. This is then multilied by a constant and subtracted from the rocess s inut. The integral term subtracts art of the average error, hence the average difference between the outut and the setoint is always being reduced. This hels reduce the oscillations of a Proortional controller, in that the amlitude of the resonse is adjusted to match the scale of the error (that is, a small error will not generate a large resonse). The Integral stage also ensures that the stable state error is reduced to zero.

5 A system that uses P and I terms only will react slowly to changes in the control variable. As the changes will not manifest themselves in the rocess outut, the controller s reaction will be delayed. The Derivative term attemts to overcome this by redicting the future erformance of the system. It does this by taing the first derivative over time of the error. This is multilied by a constant and subtracted from the rocess s inut. This allows the controller to resond to a change in the system much faster than it would otherwise. The larger the derivative term is, the faster the resonse to a change is. When all three functions are combined, the controller can reduce error to zero in a stable state and react raidly to changes in the overall system. To find the values of the constants used in the PID system, the controller must be tuned..1 TUNING METHODS The basic equation for a PID controller is given as follows []: 1 () G c s = K c 1+ + Tds Tis (1) Where G c (s) is the controller, K c is the roortional gain, T i is the integral constant and T d is the derivative constant. The rocesses used to find the values of these constants are nown as tuning methods. When designing a controller (of any tye) the rimary urose of the controller must be foremost in all considerations. This can include attenuation of load disturbances, sensitivity to measurement noise, robustness to model uncertainty and the ability to follow the set-oint. Issues to be considered include the system dynamics, any ossible non-linearities, otential disturbances and the rocess uncertainty [1]. Consequently the first ste in any tuning rocess is to decide the exact requirements in advance of determining any control arameters. The system to be controlled must be understood, the desired oerating condition nown and any contributing factors taen into account. Once this has been achieved the controller can be designed to meet the required erformance criteria and manage the rocess effectively. Manual tuning methods tyically deend on being able to test the resonse of a system manually, and then adjust the values of the PID until a satisfactory resonse has been found. Some methods of calculating aroximate values are also used. These values would then be adjusted manually to achieve the required erformance. Most modern industrial facilities use PID tuning software to ensure consistent results. These utilise the same methods in the manual methods, automating the rocess to reduce the time required and to hel imrove standardisation.. FREQUENCY DOMAIN METHOD This tuning rocess was ut forward by C.K. Sanathanan [3] in His aer discussed the tuning of PID controllers to act as a governor for a hydroelectric generator, but the rinciles can be alied to systems that have a similar arrangement. The bloc diagram for the system is shown in Figure 1 below [3]: Figure 1: Bloc Diagram for Control Loo The first bloc reresents the PID controller. V(s) and T(s) describe individual comonents of a hydrogenerator system (the gate and turbine-enstoc resectively) but could just as easily be a single lant. P(s) reresents the turbo-generator itself. N R is the reference seed inut (the required seed of the generator in revolutions er minute), M L is the load laced on the system. N S is the actual seed of the generator, which is used to determine the error of the system (E). The first stes in the rocess [3] involves obtaining detailed transfer functions that describe the oeration of the lant (V, T and P). Once these are nown a reference model is constructed to reresent the system in a theoretical sense. This is shown in Figure [3]: Figure : Generalised Model In this system, G C (s) reresents the controller, G 1 (s) combines V(s) and T(s) into a single bloc and G (s) is equal to P(s). The reference model is reresented in Figure 3 [3]: Figure 3: Reference Model To find G C (s), the following equation is used [3]: G C () s A( s) [ 1 A() s ] G () s G () s = () 1 The reference model A(s) is constructed from the nown transfer functions for the lant comonents (G 1 (s) and G (s)), with the oles chosen arbitrarily to fix the erformance at a user-secified level. Once A(s) is nown, a modified reference model is simulated:

6 Resonse to 10% load rejection Reference Model Detailed Model Figure 4: Modified Reference Model The transfer function of B(s) is found using the following equation [3]: A () () s B s = (3) [ 1 A() s ] G () s Once an accetable erformance has been achieved using the reference model, the values for the PID controller are obtained using the frequency resonse of the following [3]: K () s = sg () s C (4) Once this has been found, the values for the PID controller can be found using the following [3]: () s Kˆ = K I + K Ps + K Ds Kˆ () s K() s Otimisation between Kˆ () s (5) and K(s) is carried out using a means square error reduction rocess. At this oint the PID arameters are nown, and can be used to simulate the erformance of the lant for verification. A simulation of a controller tuned using the above method was carried out in Matlab. Models identical to those resented in [3] were created in Simulin and the erformance recorded. A set-oint of 1500 was used, with a 10% load rejection introduced. For this examle, the oles of the reference model were chosen such that each had a daming factor of (for a 5% overshoot margin). This led to the PID arameters being chosen as K I = 0.37, K P =.7 and K D =.916. The reference model was calculated to have the following transfer function [3]: () ( s s )( s ( ) ) s s B s = (8) s The erformance of the reference model against that of the final controller is comared in Figure 5 below: Outut (setoint at 1500) Time (s) Figure 5: Simulation results for Frequency Domain tuned PID controller.3 ROBUST METHOD This method was ut forward in a 005 aer by Krishnamoorthy Natarajan [4]. The aer roosed a method of tuning PID controllers for hydroturbine seed control that would offer a robust control system. The aim was to develo an effective control system using PID algorithms that would have similar erformance to more comlicated control systems using high-level functions. The model used was that of a hydroelectric turbine and generator air connected to an equivalent networ to reresent the load. The rocess itself is described in fairly general terms. The maximum frequency-domain resonse of the system to a ste load disturbance is minimised over all oerating oints, subject to nominal stability at each oerating oint. Robust stability at each oerating oint is enforced by a gain margin of 10dB and a hase margin enalty of 45. For a given PID gain, the nominal stability at each oerating oint is gauged by calculating the closed-loo oles at that oint. If any are found in the right-half lane (RHP) of the Lalace domain a enalty function () for nominal stability (ns) at an oerating oint () is created, as defined by [4]: ns ns = = L, if closed - loo oles in RHP 0, if no closed - loo oles in RHP L is chosen to be larger than any other ossible enalty function values to stress the imortance of nominal stability at an oerating oint. The author of the aer chose a value of 1000 for this urose. As hase and gain margins are usually inequality constraints, the enalty function for robust stability should be zero (or close to zero) whenever the inequality constraints are satisfied. Conversely, the enalty function should be large when the inequality constraints are not met. The enalty functions for hase margin (m) and gain margin (gm) at a given oerating oint are given as [4]: m ( φ ) [ 1+ tanh( ( φ φ ))] = (9) 1 d

7 gm 3[ 4 d ( m ) 1+ tanh( ( m m ) = )] (10) where φ is the estimated hase margin (in radians) at the oerating oint, m is the estimated gain margin (in db) at the oerating oint, φ d is the desired hase margin (in radians) and m d is the desired gain (in db). 1 through to 4 are ositive constants chosen at the designer s discretion. It was stated that the desired hase and gain margins were set at 45 and 10dB resectively for the uroses of the study [4]. The sharness of the transition region between when the constraints are satisfied and when they are not in the enalty function can be increased by increasing and 4, while 1 and 3 control the magnitude of the enalty. For the uroses of the study, values of 1 = = 3 = 4 =50 were used. The closed-loo frequency resonse of the unit frequency deviation (n) to a ste load disturbance (d) should be minimised for closed-loo erformance. This is denoted as G (jω) for oerating oint. From this, the erformance index at the oerating oint suitable for minimisation to obtain controller gains can be exressed as [4]: ωe [ ω,ω ] 1 ( jω) + ns + m gm F = max G + (11) Where ω 1 and ω are the minimum and maximum frequencies (in radians er second) of the range over which erformance is demanded. This is further modified to suit the uroses of a single PID controller to the following [4]: F = max G ωe [ ω1,ω ] = 1,...N N ( jω) + [ + + ] (1) ns m gm = 1 Here, N is the number of oerating oints over which F should be minimised. For the uroses of the aer, the author chose N = 9. The author further notes that the minimisation of both F and F is a non-linear oeration. The author used the Nelder-Mead simlex search model (cited but not given) to find solutions for his research. The range of frequencies over which erformance is demanded for (1) is given as 0.01 to 100 rad/s. Frequencies below 0.01 rad/s have slow settling times while frequencies above 100 rad/s do not contribute to the erformance index as the resonse is already well attenuated at this oint. Frequencies as high as 100 rad/s are included as the enalty functions shown earlier are estimated by numerical interolation from the relevant transfer functions (obtained from the lant model). As the frequencies at which gain and hase margin occur during the otimisation are not nown in advance, a large frequency range is used to avoid any need for extraolation. case to roceed to convergence using the search model mentioned earlier. The final results of these trials agreed to the first two decimal laces, giving the values in (13). When simulating the erformance of the PID controllers tuned using this method, three equivalent networs were considered. These were named N1, N and N3. N1 reresented a nominal networ, with normal loads. The N networ corresonded to a heavily loaded networ with a large caacity, while the N3 networ reresented a lightly loaded networ with low caacity. The nature of each networ was secified by the values of the base changer (B) and the mechanical start time of the equivalent system (T S ). For each networ, three oerating oints were secified. These were T1, T and T3. T1 simulated an oerating oint of.5mw. T denoted an oerating oint of 84.3MW and T3 reresented an oerating oint of 113.0MW. These oerating oints were set using the turbine coefficients. These are shown in Table 1[4]. Oerating dm/dz dm/dh dm/db dm/dw db/dz dq/dz dq/dh dq/db dq/dw Point T Point T Point T Table 1: Turbine Coefficients The model rovided in [4] was recreated in Matlab, and simulations carried out using the values shown in Table 1. The simulation results are shown in Figures 6, 7 and 8 Frequency deviation (.u.) N1 Networ Unit frequency deviation resonse to 0MW disturbance Time (seconds) Figure 6: N1 Networ Simulation Results T1 Oerating Point T Oerating Point T3 Oerating Point With the values outlined earlier, the author determined the transfer function of the PID controller to be as follows [4]: 0.49 C () s = s + (13) s This was obtained by maing a number of initial estimates of the actual arameters and allowing each

8 Frequency deviation (.u.) 0 x N Networ Unit frequency deviation resonse to 0MW disturbance T1 Oerating Point T Oerating Point T3 Oerating Point at an accetable rate. If the actuator saturates at a resonse level that does not actually decrease the error, the system may become unstable [1, 5]. Another roblem associated with actuators is one of mechanical wear of the device. Such a device may develo a dead-band, esecially in a system that reeatedly maes small adjustments in a limited range. This will mean that the control signal will have to include the dead-band, at which oint a new dead-band will be established over time due to additional wear [1, 5]. Frequency deviation (.u.) Time (seconds) Figure 7: N Networ Simulation Results N3 Networ Unit frequency deviation resonse to 0MW disturbance T1 Oerating Point T Oerating Point T3 Oerating Point Time (seconds) Figure 8: N3 Networ Simulation Results These results match the overall shae of those rovided in the original aer. As can be seen, the PID controller achieves a steady state within minutes of a load disturbance. It should be noted that the nature of the model is such that the load disturbance is introduced to the equivalent networ, rather to the generator directly..4 LIMITATIONS OF PID CONTROLLERS While versatile, the PID controller is not without its limitations and roblems. In higher order systems, for examle, the erformance of PID controllers is distinctly lacing when comared to more sohisticated controllers. Normally PID controllers are best suited to no greater than nd order systems [1]. A more general roblem that can aly to any PID controller is one of integrator wind-u. This occurs when the actuator that realises the control signal has a resonse range that is less than that of the controller. In such a case the actuator saturates it is woring at its maximum level which is actually less than what was required of it by the controller. The system will effectively be running in an oen loo as the resonse of the controller is no longer directly affected by the outut. The error will therefore will continue to be integrated, resulting in a very large integral term (hence the hrase integrator wind-u ). In such a case the system may oscillate until the error finally reduces to a oint where the control signal no longer exceeds the caacity of the actuator, at which oint the error will finally be reduced This raises an additional roblem associated with PID controllers, which is that they cannot adjust to changes over time. Once a PID controller has been tuned it will remain fixed at that oint indefinitely. The system it controls, however, will be constantly (albeit gradually) changing due to age and mechanical wear. If the system as a whole changes then the PID arameters may no longer be as alicable as they had been on the day of installation. Thus any PID controller will see a steady decrease in its effectiveness over time (without maintenance or human intervention), which will eventually reach a stage where it can no longer control the system [1, 5]. Finally, there is a roblem with the tuning rocess itself. Most tuning methods for PID controllers are not 100% accurate for all cases; it is standard ractice to use the calculated values as a starting oint and adjust the PID controller to better suit the overall system once it has been installed. Even software based auto-tuning PID controllers do this to a degree, albeit in an automated rocess. This maes the rocess of installing PID controllers a otential roblem for a site that requires standardisation across several searate but dulicate systems [1, 5]. 3. INTELLIGENT SYSTEMS Intelligent systems emulate an asect (or asects) of human intelligence [6]. This can include the ability to learn and human decision maing rocesses. By using human aroaches to roblems, intelligent systems can be used in a wide variety of roles. This includes being used as a controller, a tas at which intelligent systems have roven themselves able. Three tyes of intelligent system are articularly suitable for control systems, namely Fuzzy Logic, Artificial Neural Networs (ANN) and Adative Neuro Fuzzy Inference Systems (ANFIS). 3.1 FUZZY LOGIC Fuzzy Logic is a system that reresents human decision maing rocesses in a mathematical form. Humans are inherently imrecise by nature, using descritors such as fast or slow for turbine seed. Fuzzy logic reresents such terms in a numerical fashion, using fuzzy sets. This aroach avoids the cris nature of conventional Boolean logic, which can cause ste imulses when transitioning between states. The use of human descritors also allows for the easy imlementation of exert rules [6].

9 3. ARTIFICIAL NEURAL NETWORKS An ANN emulates the ability of the human brain to learn. ANNs imitate the human brain to a limited extent by using artificial neurons, which behave aroximately lie organic neurons do. Signals assed between neurons are subject to a multilier nown as a weight. Neurons will fire, that is generate a signal, when the inuts it receives satisfy a reset condition. By adjusting the weights within a networ of neurons according to the current error, an ANN can learn, as the weights will be adjusted to a oint where the error is zero. In this way an ANN can be trained to comlete a tas without the need for external human tuning. Additionally, an ANN can self-adjust over time by retraining with oerational data. Hence an ANN can change over time as the system it is involved in changes [6] EXAMPLE OF ANN CONTROL In the following examle, a hydro-governor was simulated in Matlab. The model for this system was obtained from a aer by Woznia [7]. This reresented the turbine with a simle negative feedbac loo, the system being reresented with the following transfer function [7]: ( + I )( s 1) P ( s + )( s + ) P s G = (14) s intelligent system can tune the controller raidly without the need for human intervention. Ideal results arise when the tuning system is used continuously, so that the controller s arameters are constantly adjusted to comensate for changes within lant arameters. This aroach, unfortunately, maybe incomatible with NEMMCO standards, which require a controller s resonses to a set of re-determined inuts be constant over time. Another aroach to using intelligent systems in control systems is to use the intelligent system to form the controller itself. This avoids a level of comlexity instead of tuning an existing controller, the intelligent system is the controller itself. An ANN used in this way would be caable of self-tuning itself to suit the lant it is to control. A fuzzy logic system would have the advantage of smoother resonses than can be derived from a more conventional aroach. The ANFIS system mentioned earlier combines the best of both worlds, imlementing a Fuzzy Logic system with an ANN. This rovides a system that can use fuzzy logic and learn. To develo a controller utilising intelligent systems, data from existing hydroelectric turbines is required. This includes, but is not limited to, Penstoc Pressure, Guide Vane Position, Machine Power Outut, Seed, System Frequency, Circuit Breaer osition, Sto command, Start command, system setoint and the revious error. A redictive controller was used, in which an ANN is used to relicate the behaviour of the system. This ANN is then used to redict the resonse of the lant to a given inut, and an aroriate control signal for a given system inut is determined. The chart in Figure 9 illustrates the erformance of the controller. 60 Outut of ANN-controlled Hydrogenerator Frequency (Hz) Time (s) Figure 9: Outut Frequency of ANN-controlled Hydro-Generator 3.3 POTENTIAL APPLICATIONS OF INTELLIGENT SYSTEMS IN GENERATOR CONTROL The use of intelligent systems in control systems has great otential. One alication that has seen some develoment is to use an intelligent system to tune the arameters of a conventional control system such as a PI controller [8, 9]. This has many advantages, as the

10 4. CONCLUSION The fundamental basics of PID controllers have been illustrated, with two tuning methods outlined to demonstrate the rocess of adating these devices to a system. As can be seen, such methods are time consuming when erformed manually, and at best give an aroximate set of arameters for the PID system that should be fine tuned in the field. It has also been high-lighted that PID controllers are not without their limitations. They are inadequate for controlling comlex systems, they lac the ability to adat to changes within the controlled system over time, they can be rendered unstable by inadequate equiment and they are difficult to standardise. Intelligent systems offer a way of either automatically tuning PID controllers without the need for manual finetuning, or to act as the control system itself. ACKNOWLEDGEMENTS This research has been funded by the Australian Research Council under ARC Discovery Grant K , "Australian Research Council - Hydro-Turbine Governor Control Utilising Intelligent Systems. REFERENCES [1] K. Ǻstrőm and T. Hägglund, PID Controllers: Theory, Design, and Tuning, nd ed. USA: Instrumentation, Systems, and Automation Society, [] A. O'Dwyer, Handboo of PI and PID Controller Tuning Rules. London: Imerial College Press, 003. [3] C. K. Sanathanan, "A Frequency Domain Method For Tuning Hydro Governors," IEEE Transactions on Energy Conversion, vol. 3, , March [4] K. Natarajan, "Robust PID Controller Design for Hydroturbines," IEEE Transactions on Energy Conversion, vol. 0, , Setember 005. [5] D. P. Atherton and S. Majhi, "Limitations of PID Controllers," resented at American Control Conference, San Diego, California, [6] M. Negnevitsy, Artificial Intelligence, nd ed. Harlow: Pearson Education Limited, 005. [7] L. Woznia, "A Grahical Aroach to Hydrogenerator Governor Tuning," IEEE Transactions on Energy Conversion, vol. 5, , Setember [8] Q. P. Ha and M. Negnevitsy, "Cascade PI- Controllers With Fuzzy Tuning," resented at Sixth IEEE International Conference on Fuzzy Systems, Barcelona, Sain, [9] Q. P. Ha and M. Negnevitsy, "Fuzzy Tuning in Electric Power Generation Control," resented at Fourth International Conference on Advances in Power System Control, Oeration & Management, Hong Kong, 1997.