Minimum Losses Point Tracking and Minimum Current Point Tracking in Interior Pablo Moreno-Torres, Jorge Torres, Marcos Lafoz CIEMAT c/ Julián Camarillo, 30 Madrid, SPAIN Tel.: +34 / 91 335 7194. E-Mail: pablo.moreno-torres@ciemat.es URL: http://www.ciemat.es/portal.do Miguel Yeguas, Jaime R. Arribas Universidad Politécnica de Madrid c/ José Gutiérrez Abascal, 2 Madrid, SPAIN Tel.: +34 / 91 336 3129. E-Mail: jaime.rodriguez@upm.es URL: http://www.upm.es/ Acknowledgements This work was partially supported by the Comunidad de Madrid, which contributed to it through the SEGVAUTO-TRIES-CM Program (S2013/MIT-2713). Keywords «Variable speed drive», «Permanent magnet motor», «Motion control», «Efficiency». Abstract Advanced control strategies for efficiency optimization in interior are usually model-based, potentially providing very accurate results and good performance at the cost of parameter dependency and the associated drawbacks. Search-based methods, on the contrary, perform more modestly but depend neither on models nor on parameters. This paper compares both approaches in terms of steadystate efficiency. 1. Introduction. Permanent Magnet Synchronous Machines () are becoming the standard in high performance electrical drives due to their power density and their high energy efficiency. Interior (I) provide even higher performance, since they add a reluctance torque component to the main synchronous torque component that further increases power density and efficiency. The conventional control strategy for this type of machine is based on its Maximum Torque Per Ampere (MTPA) trajectory, which minimizes copper losses but neglects iron losses [1, 2]. As copper losses are predominant for many drives, and given that the optimum operating point from the copper losses point of view is usually close in the id-iq plane to the optimum operating point from the total losses point of view, MTPA control strategies are sufficient in most cases. Recently, advanced control strategies have been proposed to account for iron losses as well. These advanced strategies, which are based in models of the machine, have received different names, such as Maximum Efficiency Control [3], Maximum Efficiency Per Ampere [4], Optimal Efficiency [5] or Loss Minimization [6, 7], to give a few examples. All these proposals attempt to optimize the efficiency of the whole drive by including iron losses in one way or another. The common characteristic among all these methods is their dependence on motor parameters and specific power loss equations. Before MTPA control strategies were developed for I, some researchers had proposed empirical search methods to optimize the efficiency of these machines [8]. All these search methods (also known as physics-based methods, in contrast to model-based methods [7]) search for the operating point corresponding to the minimum input power in steady state. This is done by iterating a control variable such as the d-axis current. The main advantage of search methods is that they are independent of motor models or parameters, but they suffer from slow real-time convergence and may not be suitable for drives with fast dynamic torque demands [7]. Torque ripple and motor stress can also be an issue. EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.1
In the last two decades, model-based methods have relegated search methods to the background, to the point that it is difficult to find updated comparisons. The aim of this paper is precisely to help fill this gap. In this work, four different control strategies are considered: a conventional MTPA control, an upgraded Maximum Efficiency (ME) control, and two search-based controls, one that uses the drive input power and another that uses the machine input current. All four strategies have been implemented in a 3 kw 1500 rpm IPMSM and laboratory tests have been performed to confirm whether search algorithms are definitely inferior or not in terms of steady-state energy efficiency. 2. Power Losses in Interior-. Consider a conventional electrical drive comprising a DC-link, an inverter and an IPMSM, such as that in Figure 1. Power losses within such a system will include: copper losses in the stator winding of the machine, iron losses in both the stator and rotor magnetic laminations, eddy current losses in the permanent magnets, mechanical losses (bearings and windage), static losses in the power semiconductors (both conduction losses and blocking losses) and switching losses in the power semiconductors. Besides, other power consumptions such as those corresponding to the control system or the cooling system could arguably be included as losses, since they affect the overall energy transformation (from electrical energy to mechanical energy and vice versa). Figure 1. Electrical drive considered in this work. Of the aforementioned losses, only a few are controllable (i.e., they vary with the current vector components and ), and thus only a few can be optimized. These include copper, iron and magnet losses in the machine, and indirectly power electronics losses as well. Depending on machine size and its characteristics, some losses will be predominant over the rest. For small machines and for low speed machines, copper losses are majority, while magnets losses are always the lowest and hence they are usually neglected [9, 10]. From this point forward, this paper will focus on copper and iron losses only. 2.1. Stator winding losses. Copper losses are usually calculated in a simple and optimistic way: = (1) with =3 the number of phases, the DC resistance of the winding (which increases with temperature) and the fundamental RMS current. However, copper losses are affected by three complex phenomena: skin effect, proximity effect and current harmonics. The first two increase the AC resistance of the winding, especially at high frequencies, while the latter implies that not only the fundamental current is responsible for losses. Thus, equation (1) can be generalized as follows: EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.2
=, (2) where, is the AC resistance corresponding to the nth current harmonic, and is the RMS of that harmonic. Copper losses can be optimized because, for a given operating point (torque-speed), there is one current vector that can provide the required torque with minimum current, and therefore with minimum copper losses. 2.2. Iron losses. Iron losses include all those power losses that take place in the magnetic circuit of the machine: hysteresis losses, eddy current losses and excess losses. Many iron losses models can be found in the literature, which can be confusing as sometimes they are not easy to compare. Basically, there are two approaches to estimate iron losses in electrical machines: Steinmetz equation models (including loss separation models), and mathematical hysteresis models [11]. The former are simpler and require less parameters and knowledge of the material, while the latter are more accurate. One model belonging to the first approach is the following [12]: = + + = + +.. (3) where is the frequency and is the maximum amplitude of the magnetic flux density. The loss coefficients, and are usually calculated from the loss curves provided by the manufacturer, such as those in Figure 2. Figure 2. Iron loss as a function of flux density and frequency for material M600-50A. As shown by equation (3), iron losses strongly depend on the frequency and therefore on the speed of the machine. They also depend on the flux amplitude, which is the reason why they can be optimized: for a given operating point (torque-speed), there is one current vector that can provide the required torque with minimum iron losses. Notice that field harmonics generate iron losses as well. Consequently, iron losses also depend on the modulation technique (current hysteresis band, PWM, SVM, DTC ) and their corresponding parameters (band width, DC-link voltage, switching frequency ), since these factors define the harmonic content of the current and hence they affect field harmonics. 3. MTPA Trajectory and Maximum Efficiency (ME) Trajectory in I. For a given operating point (torque and speed), there is a current vector that minimizes copper losses (the one given by the MTPA trajectory, as described next), another current vector that minimizes EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.3
iron losses, and also a current vector that minimizes the sum of copper and iron losses [6]. Those current vectors that minimize copper losses (that minimize current) belong to the MTPA trajectory, which is depicted in Figure 3(a) for the 3 kw 1500 rpm IPMSM used in this work. Analogously, those current vectors that minimize copper and iron losses at the same time belong to the so-called maximum efficiency (ME) trajectories, as shown in Figure 3(b) for the same machine. Notice that the ME curve for zero speed is the MTPA when field harmonics are not considered, since no iron losses take place. (a) Figure 3. MTPA and ME trajectories for a 3 kw 1500 rpm IPMSM. (b) Figure 3(b) suggests that the difference between the MTPA curve and the ME curves is noticeable in terms of current space vector, especially at higher speeds. However, in terms of energy efficiency, those differences are negligible for many machines, included the one studied in this work. To illustrate this fact, two set of laboratory tests were performed at constant speed of 500 and 1400 rpm, respectively. During these tests, the load was kept constant at 50%, and different current space vectors were used to provide the required torque. By measuring the current demanded by the IPMSM and the power consumed by the whole drive, the curves depicted in Figure 4 were derived. P [W] P [W] I q [p.u.] I q [p.u.] (a) Figure 4. Power consumption at 50% load as a function of ( -vs-power curve). Figure 4(a) shows the power consumed by the drive at 500 rpm and 50% load as a function of. As can be seen, the operating point that minimizes power consumption is located at the left of the MTPA operating point (it benefits from further flux weakening). However, in absolute terms, the difference in power consumption is negligible. Actually, the range that optimizes energy efficiency is quite wide in practice, from -1.3 to -1.7 A for this specific operating point. Figure 4(b) contains the same information but in relative terms (0 power is assigned to the ME point), both for 500 and 1400 rpm. Notice that the ME point at higher speed is placed at the left of the one at lower speed, probably (b) EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.4
due to higher iron losses. Again, even at 1400 rpm the power difference between the MTPA and the ME operating points is negligible for this particular machine. 4. Minimum Losses Point Tracking (MLPT): concept, implementation and experimental results. Empiric and online tracking of the optimum steady-state operating point is not a new concept in electrical engineering. Maximum Power Point Tracking is a well-known control strategy in photovoltaic applications to maximize power output. In electrical machines, Minimum Power Point Tracking techniques were developed for induction machines first [13], and later for as well [8]. However, since MTPA-based control strategies were developed for I, it seems that search methods such as the Minimum Losses Point Tracking (MLPT) described in this section have lost interest. The core concept behind loss minimization search for I is to perturb one of the two available control variables (d-axis or q-axis current references, id* or iq*), wait for enough time for the drive to pass the subsequent transient, and see whether the perturbation increases or decreases the total power input of the drive, which must be measured. After this, the last two steady state operating points are compared to decide the direction of the next perturbation. The logic is very simple: if the previous perturbation has reduced the power, then the next perturbation is taken in the same direction; otherwise, the direction is reversed. Figure 5 illustrates this concept by showing different alternatives for the same working point (torque-speed), one of them being the conventional MTPA and another one the ME, which consumes less power. Of course, further considerations are needed to account for flux weakening above rated speed. Figure 5. MLPT operating principle. Practical implementation becomes trickiest due to the following reasons. Firstly and more importantly, the difference in term of power between the MTPA point and the ME point is usually negligible, as shown in Figure 4. Secondly, if the perturbation is large, then it is easier to distinguish between operating points, but the average power consumed by the drive is higher. However, if the perturbation is small, distinguishing becomes harder and the algorithm takes much more time to converge or to evolve between steady states. A compromise must be reached, and a satisfactory one is not always possible. Thirdly, the quality of the power measure can greatly influence the decision making of the algorithm, thus affecting its performance. Special care has to be put in the power measurement filtering and signal conditioning to avoid worsening this issue. Finally, stepwise current changes are not recommended in practice due to its consequences: torque steps and motor stress. Some solutions have been proposed in this sense, such as the use of continuous ramps to make the system work smoothly [8]. Next, the laboratory test bench will be briefly described. For a more detailed description, the reader is referred to [14, 15]. Figure 1 shows a schematic of the system (load not included). To provide constant resistive torque, a 5 kva Synchronous Machine (SM) and a resistive load were used. Modulation technique for the IPMSM was hysteresis band current control with constant DC-link voltage EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.5
(530 V DC ) and with average switching frequency ranging from 1 to 4 khz. PI-based back-emf compensation was implemented, as shown in the control scheme depicted in Figure 6. Figure 6. Control scheme corresponding to the MTPA strategy. Regarding current references, was chosen by the search algorithm (MLPT/MCPT) while was calculated by means of a PID controller whose purpose was to keep speed constant. All tests were performed in a narrow temperature range (ambient at 21 C±1 C) and in thermal steady-state. Conventional Hall-effect voltage and current sensors were used to measure the power/current used by the MLPT/MCPT algorithms, respectively. However, a high precision digital power meter (Yokogawa WT1600) was used to measure the power consumed by each control strategy for comparison purposes. Figure 7(a) contains the control scheme implemented in the DSP, while Figure 7(b) shows a picture of the test bench during one of the tests. (a) Figure 7. (a) MLPT control scheme. (b) Laboratory test bench. (b) Figure 8 shows experimental results of the MLPT algorithm. The starting point for the test is steady-state at 1400 rpm and 50% load under MTPA operation (, = -1.40 A). At t=0 the search algorithm is enabled. Decisions are made every 4 seconds and current ramps of = ±0.2A are used, as shown in Figure 8(c). The graph on the left shows the speed of the drive. As expected, the search method causes an increase in speed ripple, even when ramps are used instead of steps. Figure 8(b) contains the evolution of during 200 seconds. In average, the MLPT algorithm operates the drive with higher flux weakening than the MTPA strategy (, = -1.48 A). Speed [rpm] I d [A] I d [A] Figure 8. MLPT in steady state at 1400 rpm and 50% load: (a) speed, (b), (c) (detail). EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.6
5. Minimum Current Point Tracking (MCPT): concept, implementation and experimental results. The operating principle of the MCPT algorithm is similar to that of the MLPT. The main difference is that phase current (RMS) is used as input for the search algorithm instead of power [16]. As this current measurement is usually cleaner and less noisy, the algorithm decision-making is much more regular, and follows a constant pattern, as shown in Figure 9(b). For comparison purposes, the same intervals and ramps were used in both MLPT and MCPT. Speed [rpm] I d [A] I d [A] Figure 9. MCPT in steady state at 1400 rpm and 50% load: (a) speed, (b), (c) (detail). The results show that the MCPT algorithm operates around the corresponding MTPA point (, = -1.40 A), which is what it is expected to do. When comparing MLPT and MCPT power consumption, the following values were measured: Table I: Power measurements corresponding to the tests from Figure 8 and Figure 9. MLPT (Fig. 7) MCPT (Fig. 8) As measured by the DSP (for making decisions) As measured by the digital power meter (for comparison) Power delivered to the load (for consistency) 1572 W 1574.7 W 1097 W 1575 W 1573.4 W 1097 W So according to the DSP measurement (conventional sensors), the MLPT algorithm consumes less power in average that the MCPT algorithm in this particular case. This makes sense, as the former is minimizing that specific power measurement while the latter is minimizing phase current. However, when comparing both tests with a high-precision high-quality measurement, we found that the MLPT algorithm was actually using an average of 1.3 W extra power compared to the MCPT algorithm. This result illustrates how the MLPT is not well suited to optimize energy efficiency in practice, when conventional voltage and current sensors are used to measure the power consumed by the drive. Due to the shape of the -vs-power curve (Figure 4), which implies that small variations of around the optimum value imply negligible power increases, power optimization for this machine only makes sense when a high-quality power measurement is available. And of course, providing such a measurement is absurd to reduce power losses in 2 W at most. 6. MTPA, ME, MLPT and MCPT comparison in steady-state. In this section, results of power consumed in steady-state are given for a 50% load and for two different speeds, both of them below rated speed (1500 rpm). EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.7
Table II: Control strategy comparison in terms of power consumption. Power [W] @ 500 rpm Power [W] @ 1400 rpm MTPA 652.8 1571.1 ME 652.7 1570.9 MLPT 656.4 1575.3 MCPT 656.3 1573.4 Note: Power values are calculated as the average of up to 5 equivalent tests. For the sake of clarity, the same results are shown in Figure 10 in relative terms (0 power is assigned to the ME point). As depicted in that figure, search methods perform worse than model-based methods in terms of energy efficiency, although it is also true that power differences are very low in general: less than 5 W of maximum difference at 1400 rpm, when total power is around 1570 W (0.3%). Hence, in this particular case control strategy should be chosen based on other criteria rather than energy efficiency. It is also worth noting that MCPT reaches better performance than MLPT in average, at least with the particular implementation used in this work. But again, power differences are very small both in absolute and relative terms. Consequently, drawing any conclusions regarding energy efficiency based only on these results seems hasty. What is clear is that MCPT does not necessarily imply worse energy efficiency than MLPT in this machine, and given its other advantages (higher repeatability, no need of extra sensors or hardware modifications) it should be considered at the preferred search-based method for this particular IPMSM. 5 Power comparison MLPT 4 MLPT MCPT P [W] 3 2 MCPT 1 MTPA MTPA 0 500rpm 1400rpm Figure 10. Power consumed by each control strategy with respect to ME. 7. Conclusion Despite their potential advantages, search methods (MLPT, MCPT) have generally worse performance than model-based methods (MTPA, ME), at least in moderate-power low-speed I such as the one used in this work. In practice, the advantages of the former are negligible (parameter independency) or lost due to practical limitations (higher energy efficiency), while their drawbacks become very relevant and difficult to alleviate. Search methods only make sense in steady-state, and they will always produce more torque/speed ripple than model-based control strategies. Considering that they offer very little improvement in other aspects, they result unattractive in most applications. For the particular IPMSM used in this work, power optimization (ME, MLPT) yields negligible increased benefit with respect to current minimization (MTPA, MCPT) in terms of energy efficiency. This is due to the small size (3 kw) and the relatively low speed (1500 rpm) of the machine under study. Consequently, it is the authors opinion that MTPA should be the weapon of choice for this particular drive. Higher speeds would probably increase the benefits of a ME strategy, although the influence of field harmonics on iron losses would have to be considered before reaching any conclusion. EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.8
Finally, if a search method was preferred for any reason, the results included in this paper suggest that it is better to work with current minimization (MCPT) rather than power (MLPT), at least for this particular machine. MCPT does not require extra sensors and it has higher repeatability, which in practice means that it usually reaches higher energy efficiency than MLPT when both search algorithms are implemented in the way described in this paper. In this sense, additional research is needed, with different I and different implementations of both search methods, to further clarify this point. References [1] G. Gallegos-Lopez, F. S. Gunawan, and J. E. Walters, "Optimum torque control of permanent-magnet AC Machines in the field-weakened region," IEEE Transactions on Industry Applications, vol. 41, pp. 1020-1028, 2005. [2] J. Yu-Seok, S. Seung-Ki, S. Hiti, and K. M. Rahman, "Online Minimum-Copper-Loss Control of an Interior Permanent-Magnet Synchronous Machine for Automotive Applications," IEEE Transactions on Industry Applications, vol. 42, pp. 1222-1229, 2006. [3] J. B. Adawey, S. Yamamoto, T. Kano, and T. Ara, "Maximum efficiency drives of interior permanent magnet synchronous motor considering iron loss and cross-magnetic saturation," in International Conference on Electrical Machines and Systems (ICEMS) 2009, pp. 1-6. [4] N. Ronggang, X. Dianguo, W. Gaolin, D. Li, Z. Guoqiang, and Q. Lizhi, "Maximum Efficiency Per Ampere Control of Permanent-Magnet Synchronous Machines," IEEE Transactions on Industrial Electronics, vol. 62, pp. 2135-2143, 2015. [5] C. Mademlis, I. Kioskeridis, and N. Margaris, "Optimal efficiency control strategy for interior permanentmagnet synchronous motor drives," IEEE Transactions on Energy Conversion, vol. 19, pp. 715-723, 2004. [6] S. Morimoto, Y. Tong, Y. Takeda, and T. Hirasa, "Loss minimization control of permanent magnet synchronous motor drives," IEEE Transactions on Industrial Electronics, vol. 41, pp. 511-517, 1994. [7] X. Wei and R. D. Lorenz, "Dynamic Loss Minimization Using Improved Deadbeat-Direct Torque and Flux Control for Interior Permanent-Magnet Synchronous Machines," IEEE Transactions on Industry Applications, vol. 50, pp. 1053-1065, 2014. [8] S. Vaez, V. I. John, and M. A. Rahman, "An on-line loss minimization controller for interior permanent magnet motor drives," IEEE Transactions on Energy Conversion, vol. 14, pp. 1435-1440, 1999. [9] A. Fukuma, S. Kanazawa, D. Miyagi, and N. Takahashi, "Investigation of AC loss of permanent magnet of SPM motor considering hysteresis and eddy-current losses," IEEE Transactions on Magnetics, vol. 41, pp. 1964-1967, 2005. [10] R. Dutta, L. Chong, and F. M. Rahman, "Analysis and experimental verification of losses in a concentrated wound interior permanent magnet machine," Progress In Electromagnetics Research B, vol. 48, pp. 221-248, 2013. [11] A. Krings and J. Soulard, "Overview and Comparison of Iron Loss Models for Electrical Machines," KTH Royal Institute of Technology, 2010. [12] D. Lin, P. Zhou, W. N. Fu, Z. Badics, and Z. J. Cendes, "A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis," IEEE Transactions on Magnetics, vol. 40, pp. 1318-1321, 2004. [13] S. K. Sul and M. H. Park, "A novel technique for optimal efficiency control of a current-source inverter-fed induction motor," IEEE Transactions on Power Electronics, vol. 3, pp. 192-199, 1988. [14] P. Moreno-Torres, M. Blanco, M. Lafoz, and J. Arribas, "Educational Project for the Teaching of Control of Electric Traction Drives," Energies, vol. 8, p. 921, 2015. [15] P. Moreno-Torres, "Analysis and Design Considerations of an Electric Vehicle Powertrain regarding Energy Efficiency and Magnetic Field Exposure," PhD dissertation in Electrical Engineering, Universidad Politécnica de Madrid, 2016. [16] P. Moreno-Torres, J. R. Arribas, M. Lafoz, and M. Blanco, "Método y sistema para optimizar la corriente consumida por un accionamiento eléctrico con un motor síncrono," Spain Patent Application, application number P201630198, February 2016. EPE'16 ECCE Europe ISBN: 9789075815252 and CFP16850-USB P.9