Algorithms

Load frequency control (LFC) is essential for maintaining frequency stability and regulating tie-line power in interconnected power systems. Conventional fixed-order PI and PID controllers offer limited tuning flexibility for complex multi-area systems, whereas fractional-order controllers provide additional tuning parameters at the cost of increased optimization complexity. Furthermore, the performance of optimization-based LFC schemes depends strongly on the selected objective function, as conventional integral criteria, such as the integral of time-weighted absolute error (ITAE), may not adequately distinguish between candidate responses with different error magnitudes and persistence. To address this research gap, this study investigates an exponential time-weighted cost function, termed the integral exponential time-weighted error saturation (IEMTES) criterion. Its principal contribution is the exponential transformation of the time-weighted error before integration. This preserves an ITAE-related first-order contribution while introducing higher-order nonlinear error terms; a saturation mechanism limits the exponential argument. The objective is to evaluate the effectiveness of IEMTES, in combination with the Glider Snake Optimizer (GSO), for tuning four controller structures: PI, PID, FOPID, and FOIID. Two benchmark systems are considered: a two-area non-reheat thermal system and a three-area thermal–thermal–hydro system incorporating generation rate constraints (GRCs). For the investigated GSO–FOIID configuration in the three-area system, the ITAE decreases from 76.20 with ITAE-based optimization to 69.69 with IEMTES-based optimization, corresponding to an improvement of approximately 8.5%. Additional evaluations consider random step-load patterns, larger load perturbations, and parameter variations. The findings are limited to the investigated systems, controller structures, disturbances, parameter ranges, and optimization settings.

In motor current signature analysis, bearing-related components are weak and their spectral location varies with operating conditions and fault morphology. This paper proposes KESK, the kurtosis of the Hilbert-envelope spectrum of the most impulsive wavelet-packet subband in each current window, and evaluates it as one additional feature to a 38-feature baseline using one phase current from 20 Paderborn bearings (11,173 windows). With supervised energy selection inside training folds, new recordings, unseen operating conditions and unseen bearings were evaluated separately. On the primary recording-level partition, XGBoost macro-F1 increased by 0.002 with KESK, 0.003 with a training-selected fixed node and 0.003 with a DC-free KESK variant; over ten additional partitions, the mean increments were 0.002, 0.003 and 0.007, respectively. With an operating condition held out, the fixed node reduced macro-F1 ($-0.014$; 95% CI $-0.024$ to $-0.005$) and the DC-free variant increased it ($+0.016$; $0.008$ to $0.023$). With bearings held out, macro-F1 was 0.48–0.49 for every representation. On nine bearings excluded from all design decisions, a pre-specified test did not confirm the DC-free advantage ($-0.003$; $-0.012$ to $0.005$). Envelope-spectrum kurtosis therefore provides a small but reproducible amount of complementary information at negligible additional computational cost, although baseline composition and validation level have a substantially greater influence on estimated performance.

A buffer requirement inferred from one optimized schedule can depend on the solver’s choice among equally good schedules. This study develops a mixed-integer model of batching and picking-packing scheduling with effective order deadlines and instantaneous whole-batch admission and a target-constrained model that minimizes waiting space over all schedules attaining the certified relaxed lexicographic optimum; equivalent event states reduce repeated matrix coefficients. Generated experiments used eight exact demand families, 24 search families, and a scalability extension with 8 to 192 orders. Minimum-buffer boundaries were verified for 30 of 32 exact configurations, requiring 0–3 positions, and the selected relaxed schedule exceeded this minimum in 16 cases. One position below the minimum, the component lost was the late-order count in 3, tardiness in 7, and picking effort in 10 of 20 configurations; raising a positive buffer from one to two positions never reduced late orders. Certification extended to 10 orders within 180 s per call. The sparse formulation reduced nonzeros by 70.19–82.31%. Guided search won 56 and lost 148 comparisons against ILS/VND, the compact-repair package won 66 and lost 132 against guided search, and at 96 and 192 orders with 30 s budgets, guided search won 17 and lost 16. Under one-tick duration deviations, the certified minimum was exceeded in 38.8% of re-timed samples, and one additional position reduced this to 4.9%. The conclusions are limited to the tested generated configurations.