Induction Motor Optimum Flux Search Algorithms with ... - CiteSeerX

Induction Motor Optimum Flux Search Algorithms with Transient State Loss Minimization using a Fuzzy Logic based Supervisor J. Moreno-Eguílaz, Miguel Cipolla, Juan Peracaula Paulo J. da Costa Branco Department of Electronic Engineering Departamento de Engenharia Electrotècnica Polytechnic University of Catalonia. Instituto Superior Técnico Diagonal 647, P9, 08028 Barcelona, SPAIN Av. Rovisco Pais 1096 Lisboa Codex, PORTUGAL Abstract—A review of different optimum flux search algorithms for loss minimization in a vector-controlled induction motor drive is presented. A fuzzy logic controller, actuating as a supervisor, is proposed to work, with reduced flux levels during transients, to optimize efficiency also in dynamic mode. Experimental results demonstrate the validity of the proposed methods.

I. INTRODUCTION It is estimated that more than 50% of the world electric energy generated is consumed by electric machines [1]. Improving efficiency in electric drives is important, mainly, for two reasons: economic saving and reduction of environmental pollution [2]. Induction motors have a high efficiency at rated speed and torque. However, at light loads, iron losses increase dramatically, reducing considerably the efficiency [3], [4]. To improve the motor efficiency, the flux must be reduced, obtaining a balance between copper and iron losses [5]. Basically, there exist two different approaches to improve the efficiency: A. Loss Model based Approach If a motor loss model is available [4], [5], the loss minimization optimum flux is computed analytically. The main advantage is the simplicity of this method, not requiring extra hardware. However, it is mandatory an accurate knowledge of motor parameters, which change considerably with temperature, saturation, skin effect, etc. In theory, the Optimum Control Theory [6] let us solve the problem of efficiency optimization with tools (like dynamic programming) to calculate the optimum flux trajectories. However, this approach presents difficulty to be implemented [7] and it is also very sensitive to parameter changes.

knowledge of motor parameters. However, it is only efficient at steady-state condition and with high powers, the method has convergence problems. In this work, different optimum flux search algorithms are proposed and compared, taking into consideration the complexity of the method, the convergence speed and the presence of torque oscillations. For transients, a fuzzy logic based controller [11], actuating as a supervisor, is proposed to optimize efficiency with reduced flux levels. Experimental results with an indirect field oriented control are obtained using a standard induction motor at our laboratory. II. OPTIMUM FLUX SEARCH ALGORITHMS At steady state, the input power for an induction motor drive is a flux dependent convex function. The philosophy of search algorithms is to decrease the motor flux as a function of the power consumption until the minimum loss point is found, obtaining a balance between copper and iron losses. The proposed search algorithms in this work are: A. Rosenbrock Method The flux φ is changed gradually (1) in one direction while we are approaching ( ∆Pn < 0 ) to the optimum flux. When the algorithm detects we are moving away ( ∆Pn > 0 ), the flux is changed in the other direction, until the required accuracy is achieved.  k = 1; if ∆Pn < 0 1 φ n +1 = φ n + k∆φ n ;  (1) k = − ; if ∆Pn > 0 2  where ∆Pn = Pn − Pn −1 , and ∆φ n = φ n − φ n −1 . This method is very simple and always converges. However, the convergence speed may be slow, depending on the initial flux perturbation and the acceleration constant k.

B. Power Measure based Approach B. Proportional Method In this approach, an optimum flux search algorithm is used, and the drive power consumption is measured [2], [8]-[10]. Obviously, this approach does not require the

To accelerate the optimum flux search process is possible to use not only the sign of the consumed power (1), but also

the module of the input power. The algorithm can be expressed by: (2) φ n+1 = φ n − k ∆Pn sign(∆φ n ) where k is a positive number. This algorithm presents convergence problems and oscillations if k is a constant value. Better results are obtained if k is a nonlinear function varying with system conditions. C. Gradient Method This algorithm is based on the classic gradient direction search methods, using the gradient of the input power (3). The gradient is computed using a 1st order lineal approximation. (3) φ n +1 = φ n − k∇Pn This method has problems around the optimum flux due to the difficulty to obtain a good numerical approximation of the gradient. D. Fibonacci Method This method consist of sampling the input power of the motor working at different fluxes which distances are function of Fibonacci’s series (Fk: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...). E. Search Method using Fuzzy Logic This algorithm [2] is based on a fuzzy logic controller which uses heuristic rules to improve the converge speed and avoid oscillations around the optimum flux. The

antecedents are the power change ( ∆Pn ) and the flux change ( ∆φ n−1 ) and the consequent is the new flux change ( ∆φ n ) (Table I). TABLE I FUZZY RULES TO FIND THE OPTIMUM FLUX (OUTPUT ∆φ n ).

∆Pn \ ∆φ n −1 N

PB PM PS ZE NS NM NB

PM PS PS ZE NS NM NB

P NM NS NS ZE PS PM PB

PB: Positive Big PM: Positive Medium PS: Positive Small ZE: Zero NB: Negative Big NM: Negative Medium NS: Negative Small

III. EXPERIMENTAL RESULTS The search algorithms have been implemented and tested at our laboratory with an indirect vector-controlled induction motor drive (Fig. 1). The experimental equipment consists of a MOSFET current-controlled voltage inverter and a 1.5 kW induction motor. The induction machine is coupled to a brake system consisting of a DC generator with an electronically controlled load. The power measurement is done at the drive input, sampling ac voltage and current with a transformer and a Hall-effect current sensor, respectively. A software routine computes the consumed power with a digital average. An 80486 microprocessor, running at 66 MHz, is the control computer. All the software was programmed in C language for simplicity.

Fig. 1. Indirect vector-controlled induction motor drive with efficiency optimization and a fuzzy logic supervisor.

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Fig. 3. Experimental results using the Proportional method.

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Fig. 5. Experimental results using the Fuzzy Logic based Optimization Method. Left column. Rotor speed and reference torque current isq* evolution (Experimental Results).

Right column. Consumed input power and reference flux current isd* (Experimental Results).

IV. DISCUSSION OF SEARCH METHODS Figs. 2 to 5 show experimental results using the indirect vector control with speed 0.25 p.u. and torque 0.1 p.u. As can be observed, all methods reach the optimum flux to loss minimization after about 8 seconds. However, some remarks must be pointed out. Rosenbrock method is the simplest of all. It produces some perturbations on the electromagnetic torque (and then on the speed: Fig. 2) when very reduced flux levels are imposed. For these tests, the initial flux perturbation has been considered at 10% of the rated flux. With the proportional method, excellent results can been obtained if the optimization gain k is adjusted correctly. When the algorithm is near the optimum flux, the reference flux current step must be reduced drastically to avoid oscillations because the power remains approximately constant (Fig. 3). The gradient based search algorithm was tested only by simulations because it causes instability in the drive when the flux level is close to the optimum flux. With Fibonacci search method, some important oscillations can be observed on the speed (Fig. 4) due to the big flux changes imposed to the machine. This can be compensated with different methods as stated in [2]. The fuzzy logic based search method provides excellent results (Fig. 5), although it is necessary to include two gains [2], speed and torque dependent, to let the controller optimize at different powers. This method is the fastest one, because it is the most complex and uses heuristic rules. It can be demonstrated that the fuzzy logic based search method consists of a gradient based search

[12] with adaptive flux steps and infinitum search with non-null flux step around the minimum loss point. V. OPTIMIZATION IN DYNAMIC MODE So far, we have been only considering optimization at steady-state condition. The above fuzzy logic based search controller is only effective with constant speed and torque. When a torque perturbation or command speed change is produced, the search process stops. All the works in recent literature [2], [8]-[10], propose to establish the rated flux during a dynamic transition. This permits to have the maximum torque capability in order to get the optimum transient response. However, the transient torque and speed response may not be so important for some practical applications (it is the case of an elevator or a crane). For example, if the process has many small load torque perturbations. In these cases, efficiency optimization can take priority. In this paper, we propose to work with reduced flux levels during dynamic transitions, minimizing power losses in dynamic mode and accelerating the search process at steady state. For this, a fuzzy logic controller, actuating as a supervisor, is designed (Fig. 6). During transients, the controller increases the flux, depending on the speed error and its derivative. If the transient is very large or the speed error is very large, the flux is established at rated level, in order to let the drive track the reference command. Although there exist very complex solutions to improve efficiency during transients, the proposed one provides good results in a very simple and cheap way.

Fig. 6. Diagram of the proposed fuzzy logic supervisor to increment the flux current.

The proposed controller is very simple, containing two tables of heuristic rules, distinguishing a torque transition and a reference speed change. The controller only

provides positive flux increments, actuating as a supervisor, since it supervises the search algorithm right command tracking, incrementing the flux if necessary.

The antecedents are the speed error eω and its derivative eω and the consequent is the flux current * increment ∆isd (Fig. 6). eω = ω *m − ω m (4) where ω *m is the rotor speed reference and ω m is the actual speed. (5) eω = deω / dt For convenience, the inputs and the output were scaled with three different coefficients N e , N d , N u to make the tuning easier. Tables II and III show the rules for a positive torque transition and for a positive reference speed change, respectively. TABLE II RULES FOR A POSITIVE TORQUE TRANSITION

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During the transient due to a change in speed command (Figs. 13, 14), energy can also be optimized (Figs. 15, 16) by using the fuzzy logic supervisor, demonstrating the validity of the proposed method for transients. The main drawback of this controller is how to tune its gains, N e , N d , N u . The most simple method is by trial and error. Present research is focused on how to design an autonomous efficiency controller, using the energy consumed in a mechanical cycle to adjust the controller gains, in order to get the optimum response from the point of view of efficiency. And important open question is how to quantify the benefits of the proposed solution for all operation points of the machine. A more detailed description of the proposed solution using the fuzzy logic based supervisor can be found in [12].

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The product-sum was used as inference method and the center of gravity was implemented as defuzzification method to get a fast algorithm in real time. Figures 7 and 8 show the membership functions for the antecedents and for the consequent, respectively. Figures 9, 10, 11, 12 show the advantages of using the fuzzy logic supervisor during a torque transition. As can be seen, efficiency during the transient is improved considerably, although the transient speed response is not so good and fast (Fig. 10).

Fig. 7. Membership functions for the antecedents.

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Fig. 10. Speed evolution with a torque perturbation using reduced flux in the transition. Transition with reduced flux 3.5

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VI. CONCLUSIONS In this work, a review of different search algorithms to improve efficiency at steady-state condition has been presented. Among others, the main conclusions are: - All the proposed algorithms must be initialized correctly, getting a compromise between convergence speed and oscillations around the optimum flux. - The search algorithm execution speed depends on the rotor time constant, which varies considerably with motors of different powers. - All the proposed search methods provide acceptable results, although the fuzzy logic based method has a good convergence speed and avoids oscillations in the electromagnetic torque. - The power can be measured at the drive input or at the DC bus. However, the former is better because the system optimum point is obtained. - With reduced flux, the maximum torque decreases, and then special care must be taken with overloads. - The torque oscillations due to flux changes must be compensated. For transients, a new fuzzy logic based controller, actuating as a supervisor has been proposed to optimize efficiency during transients. Two different rule tables have been designed for torque transitions and for reference speed changes. Experimental results of the proposed controllers with a 1.5 kW induction motor drive demonstrate the validity of the described methods. Present research is focused on how to design an autonomous efficiency controller, using the energy consumed in a mechanical cycle to adjust the controller gains, in order to get the optimum response from the point of view of efficiency. And important open question is how to quantify the benefits of the proposed solution for all operation points of the machine. And obviously, the compromise between efficiency optimization and a good dynamic response always depends on the kind of application. ACKNOWLEDGMENT

The research leading to this work was sponsored by grant no. TIC94-0562 of the Ministerio de Educación y Ciencia Comisión Interministerial de la Ciencia y la Tecnología (CICYT) - Spain and by grant no. FI94/3.002 of the Direcció General de Recerca - Comissionat per a Universitats i Recerca (CIRIT) - Generalitat de Catalunya, Spain. REFERENCES [1]

W. Leonhard, “Controlled AC drives, a successful transfer from ideas to industrial practice,” CETTI 95, Brazil, pp. 1-12, September 11-12, 1995. [2] G.C.D. Sousa, B.K. Bose, and J.G. Cleland, “Fuzzy logic based online efficiency optimization control of an indirect vector-controlled induction motor drive,” IEEE Transactions on Industrial Electronics, vol. 42, no. 2, pp. 192-198, April 1995. [3] A. Kusko, and D. Galler, “Control means for minimization of losses in ac and dc motor drives,” IEEE Transactions on Industry Applications, vol. 19, no. 4, pp. 561-570, July/August 1983. [4] G.O.Garcia, J.C. Mendes Luís, R.M. Stephan, and E.H. Watanabe, “An efficient controller for an adjustable speed induction motor drive,” IEEE Transactions on Industrial Electronics, vol. 41, no. 5, pp. 533-539, October 1994. [5] I. Kioskeridis, and N. Margaris, “Loss minimization in induction motor adjustable-speed drives,” IEEE Transactions on Industrial Electronics, vol. 43, no. 1, pp. 226-231, February 1996. [6] S.S. Rao, Optimization, Theory and Applications, Wiley Eastern Limited: Bombay, 1984. [7] R.D. Lorenz, and S. Yang, “Efficiency-optimized flux trajectories for closed-cycle operation of field-orientation induction machine drives,” IEEE Transactions on Industry Applications, vol. 28, no. 3, pp. 574580, May/June 1992. [8] J.C. Moreira, T.A. Lipo, and V. Blasko, “Simple efficiency maximizer for an adjustable frequency induction motor drive,” IEEE Transactions on Industry Applications, vol. 27, no. 5, pp. 940-945, Sep/October 1991. [9] I. Kioskeridis, and N. Margaris, “Loss minimization in scalarcontrolled induction motor drives with search controllers,” IEEE Transactions on Power Electronics, vol. 11, no. 2, pp. 213-220, March 1996. [10] G. Kim, I. Ha, and M. Ko, “Control of induction motors for both high dynamic performance and high power efficiency,” IEEE Transactions on Industrial Electronics, vol. 39, no. 4, pp. 323-333, August 1992. [11] M. Cipolla, J. M. Moreno-Eguilaz, and J. Peracaula “Fuzzy control of an induction motor with compensation of system dead-time,” IEEE Power Electronics Specialist Conference, PESC'96, Baveno, Italy, June 24-27, 1996. [12] J. M. Moreno-Eguilaz, M. Cipolla, P. Branco, and J. Peracaula, “Fuzzy logic based improvements in efficiency optimization of induction motor drives,” IEEE International Conference on Fuzzy Systems 1997, FUZZ-IEEE’97, Barcelona, Spain, July 1-5, 1997, in press.