Probabilistic intraday PV power forecast using ensembles of deep Gaussian mixture density networks

There is a growing interest of estimating the inherent uncertainty of photovoltaic (PV) power forecasts with probability forecasting methods to mitigate accompanying risks for system operators. This study aims to advance the field of probabilistic PV power forecast by introducing and extending deep Gaussian mixture density networks (MDNs). Using the sum of the weighted negative log likelihood of multiple Gaussian distributions as a minimizing objective, MDNs can estimate flexible uncertainty distributions with nearly all neural network structures. Thus, the advantages of advances in machine learning, in this case deep neural networks, can be exploited. To account for the epistemic (e.g., model) uncertainty as well, this study applies two ensemble approaches to MDNs. This is particularly relevant for industrial applications, as there is often no extensive (manual) adjustment of the forecast model structure for each site, and only a limited amount of training data are available during commissioning. The results of this study suggest that already seven days of training data are sufficient to generate significant improvements of 23.9% in forecasting quality measured by normalized continuous ranked probability score (NCRPS) compared to the reference case. Furthermore, the use of multiple Gaussian distributions and ensembles increases the forecast quality relatively by up to 20.5% and 19.5%, respectively

Modeling and control design of a contact-based, electrostatically actuated rotating sphere

The performance of micromirrors in terms of their maximum deflection is often limited due to mechanical constraints in the design. To increase the range of achievable deflection angles, we present a novel concept in which a free-lying sphere with a flat side as reflector can be rotated. Due to the large forces needed to move the sphere, multiple electrostatic actuators are used to cooperatively rotate the sphere in iterative steps by impacts and friction. A parameterized system-level model of the configuration is derived, which considers arbitrary multi-contact scenarios and can be used for simulation, analysis, and control design purposes. Due to the complex, indirect relation between the actuator voltages and the sphere motion, model-based numerical optimization is applied to obtain suitable system inputs. This results in rotation sequences, which can be understood as a sequence of motion primitives, thus transforming the continuous time model into an abstract discrete time model. Based on this, we propose a feedback control strategy for trajectory following, considering model uncertainties by a learning scheme. High precision is achieved by an extension controlling the angular change of each rotation step. The suitability of the overall approach is demonstrated in simulation for maximum angles of 40°, achieving angular velocities of approximately 10°/s

Design and optimal control of a multistable, cooperative microactuator

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty