Data-driven methods for real-time voltage stability assessment
Licentiatavhandling, 2020

Voltage instability is a phenomenon that limits the operation and the transmission capacity of a power system. An operation state close to the security limits enables a cost-effective utilization of the system but it could also make the system more vulnerable to disturbances. The transition towards a more sustainable energy system, with a growing share of renewable generation, will increase the complexity in voltage stability assessment and cause significant planning and operational challenges for transmission system operators.

The overall aim of this thesis is to develop a real-time voltage stability assessment tool which can be used to assist transmission system operators in monitoring voltage security limits and to provide early warnings of possible voltage instability. The thesis first analyzes the difference between static and dynamic voltage security margins, both theoretically and numerically. The results of the analysis show that power systems with a high share of loads with fast restoration dynamics, such as induction motors or power electronic controlled loads, may cause conventional static methods to assess the voltage security margins to become unreliable. Methods relying on a dynamic assessment of the security margin are in these circumstances more reliable.

However, dynamic assessment of voltage security margins is computationally challenging and can in most cases not be estimated in the time frame required by system operators in critical situations. To overcome this challenge, a machine learning-based method for fast and robust computing of the dynamic voltage security margin is proposed and tested in this thesis. The method, based on artificial neural networks, can provide real-time estimations of voltage security margins, which are then validated using a search algorithm and actual time-domain simulations. The two-step approach is proposed to mitigate any inconsistency issues associated with neural networks under new or unseen operating conditions.

Finally, a new method for voltage instability prediction is developed. The method is proposed to be used as an online tool for system operators to predict the system’s near-future stability condition given the current operating state. The method uses a more advanced neural network based on long-short term memory. The results from case studies using the Nordic 32 test system show good performance and the network can accurately, within only a few seconds, predict voltage instability events in almost all test cases.

security assessment

neural networks

Dynamic voltage security margin

machine learning

voltage instability prediction

voltage stability

Opponent: Hjörtur Jóhannsson, Technical University of Denmark, Denmark


Hannes Hagmar

Chalmers, Elektroteknik, Elkraftteknik

Fast Dynamic Voltage Security Margin Estimation: Concept and Development

IET Smart Grid,; Vol. 3(2020)p. 470-478


On-line Voltage Instability Prediction using an Artificial Neural Network

2019 IEEE Milan PowerTech, PowerTech 2019,; (2019)

Paper i proceeding

A Survey of Voltage Stability Indicators Based on Local Synchronized Phasor Measurements

2018 North American Power Symposium (NAPS),; (2019)

Paper i proceeding

H. Hagmar, L. Tong, R. Eriksson, L. A. Tuan, "Voltage Instability Prediction Using a Deep Recurrent Neural Network," submitted to Transactions on Power Systems, 2020.

Avancerad visualisering av spänningsstabilitetsgränser och systemskydd baserat på realtidsmätningar

Svenska kraftnät, 2016-06-01 -- 2020-12-31.

Energimyndigheten (44358-1), 2016-06-01 -- 2020-12-31.


Hållbar utveckling




Datavetenskap (datalogi)


Annan elektroteknik och elektronik




Opponent: Hjörtur Jóhannsson, Technical University of Denmark, Denmark

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