Induction motors (IMs) consume most of the electricity used in industry, and the efficiency of their drives is classified through the IE and IES classes of IEC 60034-30-1 and IEC 61800-9-2. This PRISMA 2020 systematic review examines energy-efficient model predictive control (MPC) for IM drives using a three-axis taxonomy: efficiency objective (electrical loss, thermal/economic, degradation), solution paradigm (model-based, data-driven, learning-augmented), and uncertainty handling (nominal, observer-based, adaptive/robust). Of the 65 included studies, 43 concern induction-machine drives, but only three of these report an industrial, process, or marine load, and 20 of the 65 address traction or transport. The largest reported effects, 49–65% reductions in drive-cycle loss or energy and light-load efficiency gains of up to about 30 percentage points on a 0.75 kW machine, were obtained in simulation. Hardware-validated IM results mostly amount to about 0.7–4% in efficiency at fixed operating points and 8–18% in drive-cycle energy relative to other MPC variants. These figures are not directly comparable because loss boundaries, operating points, baselines, and validation methods differ. No included study combines a thermal/economic or degradation objective with a data-driven or learning paradigm and adaptive/robust uncertainty handling. Open problems and a research agenda on thermally adaptive economic MPC are outlined.

Economic model predictive control (MPC) of induction motor drives minimizes a loss model that usually omits saturation, additional load loss, the core-loss increment under pulse-width modulation, and the junction-temperature dependence of switching energy. A published thermally adaptive economic MPC is extended in three ways. First, it is proven that the DC-link power residual is structurally blind to losses supplied through the air gap when torque is reconstructed from measured currents; therefore, only stator-terminal and converter losses can be learned without a torque sensor, and a physics-informed residual model is identified and fed to the thermal observer. Second, the magnetizing curve is learned from the reactive-power balance by a set-membership estimator contracted by monotonicity and concavity. Third, the guaranteed flux band tightens the current, torque-reserve, and voltage constraints of the economic target problem, whose feasible set grows monotonically during learning. In simulations of 2.2, 7.5, and 37 kW drives with pump and conveyor cycles and a structurally mismatched plant, the winding-temperature estimation error decreased from 5.5–10.7 K to 1.3–1.6 K, torque error from 0.74–1.45% to 0.24–0.40% of rated torque, cycle energy came within 0.06–0.23% of an oracle, and voltage-headroom violations were eliminated at an energy cost of 0.03–0.18 percentage points.

In loss-minimizing model predictive control of induction motor drives, the torque reference is often enforced by a quadratic penalty. Since every newton-meter costs loss, it leaves a steady torque error, and its weight has no physical basis. The error is shown to equal \( λ_M/(2q_M M^* ) \), where \( λ_M \) is the marginal loss per unit torque of the loss-optimal steady state, and a penalty on the absolute torque error removes it once its weight, in W/(N·m), exceeds the largest \( λ_M \)below the reference. The closed form of \( λ_M \) is derived from a temperature-dependent machine and inverter loss model. For a 7.5 kW drive at 36 simulated operating points, the closed-loop threshold equaled the marginal loss at fixed flux, which coincides with \( λ_M \) except on the voltage-limit boundary (up to 15% lower). The nominal quadratic weight left errors of 0.46–3.88%; with exact measurements the absolute-value penalty kept them below 10^-4%, also on pump and conveyor cycles, while the loss per unit of work changed by at most 0.6%. Without flux reservation it lowers and delays the torque during a current-limited flux rebuild, unlike a combined absolute-value and quadratic term. Field-orientation mismatch, measurement noise and dead time cause errors that the penalty does not remove.

Off-grid pumping stations with photovoltaic (PV) generation, a battery and an elevated tank are usually dispatched by level and state-of-charge rules, and the induction motor drive is treated as a load of constant efficiency. This study formulates a supervisory thermally aware economic model predictive controller (TA-EMPC-S) that schedules battery power, PV curtailment and pump duty together with pump speed, rotor flux and a two-node motor thermal state, and that prices pump starts. A simulated 7.5 kW station was operated over four one-week scenarios by TA-EMPC-S, simpler EMPC variants, a level-control rule and a tuned PV-following variable-speed rule (RB-VFD). Against RB-VFD, TA-EMPC-S reduced unserved demand by 39.3% in a heat wave with an overcast spell and by 48.9% on average over 20 realizations with forecast errors, and it was the only strategy without thermal derating when motor cooling was degraded, even with an erroneous cooling model. In a sunny week it cut battery throughput by 14.2% but started the pump more often. Variable speed and anticipation produced most of the benefit, whereas flux optimization changed the specific energy by less than 1%.

Economic model predictive control (MPC) of induction motor drives selects the flux from a loss model that usually omits saturation, additional load loss, the core-loss increment under pulse-width modulation, and the junction-temperature dependence of switching loss. A thermally adaptive economic MPC is extended with learned components, and each effect is isolated. The exact DC-link power balance shows that losses supplied through the air gap are unobservable without a torque sensor, whereas the additional load loss is observable; its estimate is passed to the stator node of the thermal observer. The magnetizing curve is learned from the reactive-power balance by a set-membership estimator contracted by monotonicity and concavity, and the resulting flux band tightens the current, reserve, and voltage constraints of the economic layer. Fifteen controller variants were simulated on 2.2, 7.5, and 37 kW drives on pump and conveyor cycles, including 600 Monte-Carlo samples. In nominal runs, the winding-temperature error fell from 5.5–10.2 K to 1.1–1.6 K and the torque error from 0.7–1.6% to 0.2–0.4% of rated torque. Across the samples, the stator voltage exceeded its planning limit in one case, against 13–36 per 100 without learning, and conveyor-cycle energy fell by 0.26–0.42 percentage points; pump-cycle differences were not resolved.