A generic approach to modern electrical drives (Tutorial at PEMC 2024)
Abstract
Electrical drives consume more than 50% of the globally generated electricity. Hence, advances in research on modelling, control and operation of electrical drives (machine+inverter) have been made.
This tutorial covers all aspects of modern electrical drives such as:
- nonlinear modelling and dynamic simulation of the electro-mechanical system considering e.g. (i) magnetic saturation & cross-coupling, (ii) back-emf harmonics, (iii) skin & proximity effects, and (iv) copper and iron losses;
- high-performance control compensating for (i) voltage-source inverter nonlinearities and dead-times, (ii) machine nonlinearities, (iii) current cross-coupling and (iv) voltage constraints; and
- optimal operation management by optimal feedforward torque control (OFTC) to guarantee an operation of the electrical drive at its physical current and voltage limits while efficiency is maximized for all operation strategies such as Maximum Torque per Losses (MTPL), Field Weakening (FW), Maximum Current (MC) and Maximum Torque per Voltage (MTPV)
All aspects are covered without imposing simplifying assumptions on the system. The generic approach allows to apply the presented methods for modelling, simulation, control and operation to all kind of electrical drives. Numerical, analytical and/or look-up tables (LUTs) approaches are discussed and compared. The proposed approach is suitable for any electrical machine (e.g. synchronous machines with/without electrical excitation or doubly fed induction machines). Simulation and measurement results illustrate effectiveness and applicability of the generic approach.
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The paper proposes a nonlinear current control system of reluctance synchronous machines (RSMs) in combination with analytical flux linkage prototype functions. For highly nonlinear machines, such as RSMs, the magnetic characteristics change significantly throughout the whole operation range due to saturation and cross-coupling effects. Therefore, the current controller tuning must be adapted online to achieve a fast and accurate tracking performance. The proposed current controllers are derived based on the system theoretic concept of the exact input/output (I/O) linearization of the current dynamics. Thus, the nonlinear control system is simplified to an integrator which, in combination of proportional-integral (PI) controllers, can be tuned by means of pole placement similar to a phase-locked loop (PLL). For I/O linearization and control, the magnetic saturation and cross-coupling effects in the flux linkages and the differential inductances must be considered which is done by the utilization of analytical flux linkage prototype functions instead of lookup tables (LUTs). The performance of the developed nonlinear current control system is validated by both, simulation and experimental results, for a highly nonlinear 1.5 kW RSM. The results underpin (i) the very high approximation accuracy and the continuity and differentiability of the flux linkage prototype functions over the whole operation range and (ii) the very fast and accurate tracking performance of the nonlinear I/O control system.
This article presents a real-time realization of a continuous-control-set model predictive current controller for the two types of permanent magnet synchronous machines: 1) surface-mounted permanent magnet synchronous machine (SMPMSM) and 2) interior permanent magnet synchronous machine (IPMSM). The constrained optimization problem is solved online using a slack formulation of the primal-dual interior-point method. The proposed controller is tested on a 14.5 kW SMPMSM based on the linear time-invariant (LTI) model of the machine and on a 0.5 kW IPMSM. For the latter, we present in detail how the nonlinear first-principles modeling yields the fastest possible transient as well as an offset-free steady-state performance. The experimental results were obtained at sampling times typically used in the electrical drive applications (125 and 100
s for the two machines, respectively).
Physically motivated and analytical prototype functions are proposed to approximate the nonlinear flux linkages of nonlinear synchronous machines (SMs) in general; and reluctance synchronous machines (RSMs) and interior permanent magnet synchronous machines (IPMSMs) in particular. Such analytical functions obviate the need of huge lookup tables (LUTs) and are beneficial for optimal operation management and nonlinear control of such machines. The proposed flux linkage prototype functions are capable of mimicking the nonlinear self-axis and cross-coupling saturation effects of SMs. Moreover, the differentiable prototype functions allow to easily derive analytical expressions for the differential inductances by simple differentiation of the analytical flux linkage prototype functions. In total, two types of flux linkage prototype functions are developed. The first flux linkage approximation is rather simple and obeys the energy conservation rule for “symmetric” flux linkages of RSMs. With the gained knowledge, the second type of prototype functions is derived in order to achieve approximation flexibility necessary for SMs with permanent (or electrical) excitation with “unsymmetric” flux linkages due to the excitation offset. All proposed flux linkage prototype functions are continuously differentiable, obey the energy conservation rule and, as fitting results show, achieve a (very) high approximation accuracy over the whole operation range.
Due to its merits of fast dynamic response, flexible inclusion of constraints and the ability to handle multiple control targets, model predictive control has been widely applied in the symmetry topologies, e.g., electrical drive systems. Predictive current control is penalized by the high current ripples at steady state because only one switching state is employed in every sampling period. Although the current quality can be improved at a low switching frequency by the extension of the prediction horizon, the number of searched switching states will grow exponentially. To tackle the aforementioned issue, a fast quadratic programming solver is proposed for multistep predictive current control in this article. First, the predictive current control is described as a quadratic programming problem, in which the objective function is rearranged based on the current derivatives. To avoid the exhaustive search, two vectors close to the reference derivative are preselected in every prediction horizon. Therefore, the number of searched switching states is significantly reduced. Experimental results validate that the predictive current control with a prediction horizon of 5 can achieve an excellent control performance at both steady state and transient state while the computational time is low.
A novel Artificial Neural Network (ANN) Based Optimal Feedforward Torque Control (OFTC) strategy is proposed which, after proper ANN design, training and validation, allows to analytically compute the optimal reference currents (minimizing copper and iron losses) for Interior Permanent Magnet Synchronous Machines (IPMSMs) with highly operating point dependent nonlinear electric and magnetic characteristics. In contrast to conventional OFTC, which either utilizes large look-up tables (LUTs; with more than three input parameters) or computes the optimal reference currents numerically or analytically but iteratively (due to the necessary online linearization), the proposed ANN-based OFTC strategy does not require iterations nor a decision tree to find the optimal operation strategy such as e.g., Maximum Torque per Losses (MTPL), Maximum Current (MC) or Field Weakening (FW). Therefore, it is (much) faster and easier to implement while (i) still machine nonlinearities and nonidealities such as e.g., magnetic cross-coupling and saturation and speed-dependent iron losses can be considered and (ii) very accurate optimal reference currents are obtained. Comprehensive simulation results for a real and highly nonlinear IPMSM clearly show these benefits of the proposed ANN-based OFTC approach compared to conventional OFTC strategies using LUT-based, numerical or analytical computation of the reference currents.
The proposed identification method allows for a simultaneous estimation of nonlinear output voltage deviations in voltage source inverters (VSIs) and nonlinear synchronous machine models. Based on the identified characteristics with the help of physically inspired structured artificial neural networks (ANNs), an efficient tuning of the current control system can be performed and the nonlinear voltage deviations caused by parasitic effects and dead-time distortions can be accurately compensated for. The identification is performed without position sensor while the rotor is mechanically locked by utilising measured phase currents and reference machine voltages only. Experiments for an interior permanent magnet synchronous machine (IPMSM) and a reluctance synchronous machine (RSM) show that the proposed method is capable of identifying the current dependent self-axis and cross-axis flux linkages, differential inductances and the nonlinear VSI voltage deviations as well as the phase resistance at the same time. The proposed method is fast and generic. Besides the rated machine current, voltage and frequency, no prior system knowledge is required making it applicable for the self-commissioning of any electrical synchronous machine drive.
For electrically excited synchronous machines (EESMs) used in automotive applications, the flux linkages are nonlinear and the magnetic saturation plays an important role. The coupling between
d
-axis and exciter axis in EESMs introduces a significant fluctuation of the flux linkages due to current changes. To cope with these problems, a novel observer incorporating flux linkage saturation and dynamics caused by the coupling is proposed. The flux is not regarded as linear, but the absolute and differential inductances are used in the observer. Moreover, the current dynamics induced flux variations are compensated for. As the system is nonlinear and time-varying, Lyapunov's method is used to prove the stability of the system and to derive a speed-adaptive algorithm. The experimental results on an EESM test bench confirm the effectiveness of the proposed method.
