Date of Award


Degree Type


Degree Name

Master of Science (MS)


Electrical Engineering and Computer Science


Eftekharnejad, Sara

Subject Categories

Electrical and Computer Engineering | Engineering


The thesis investigates methods for estimating inertia in systems at different levels of renewable energy penetrations. Estimating renewable generators' inertia is challenging because their structures differ from traditional generators. Moreover, the power generated from renewable energy resources is not stable, depending on weather conditions. When a power grid has a disturbance, photovoltaic inverter control influences a power grid inertia by different controllers, such as power factor and reactive power control, to bring a power grid back to a steady state. The changing reactive power impacts the frequency, which strongly relates to inertia and increases the inertia estimation problem.

Several papers proposed different approaches to estimating renewable generators' inertia. The two main categories of estimating inertia are model-based and measurement-based methods. The model-based methods mimic an actual renewable generator behavior to calculate inertia. It is a complicated model specialized for specific renewable devices, but unlike the measurement-based methods, it can estimate the inertia in the steady state. The measurement-based methods find the patterns in measured data and use classification or regression functions to calculate inertia. A measurement model can monitor a power grid in real time. However, the method needs parameter oscillation, representing power imbalance in a power grid. This thesis proposes three measurement-based models to estimate inertia for systems under levels of photovoltaic systems: Symbolic Aggregate Approximation, Back Propagation Neural Network, and Minimum Volume Enclosing with a Gradient Descent Machine Model.

The measurement-based inertia estimation models need large-scale system measurement data. PowerWorld Simulator has a function to analyze the transient stability, which is utilized in this thesis to generate simulated data for this. Reducing photovoltaic output power can mimic the impact of weather changes. Different types of photovoltaic controllers have various behavior.

The Symbolic Aggregate Approximation transfers continuous data into discrete data. The advantage of this method over other techniques is its ability to compress large-scale data and the reduced data storage requirements. Hence, the model demonstrates the best performance for estimating the inertia.

The Minimum Volume Enclosing Ellipsoid visualizes measurement data, including frequency, generator output power, and bus voltage, on a 3-dimensional space. The volume of the enclosed ellipsoid is the output that yields label inertia. During a fault in a power system, the volume of the ellipsoid increases. The Gradient Descent Model estimates an optimal regression curve to match volume with label inertia as the estimated inertia.

The Back Propagation Neural Network is a nonlinear classification method. With multiple layers and neurons, this method can efficiently cluster complex input features, such as the frequency of all buses and generator output power. The error between the estimated inertia and the label inertia is used to modify the branches' weight to reduce error. The disadvantage of the second and third models is that they do not have a better performance than the first one.


Open Access



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