Multivariable loop-shaping control design for stability augmentation and oscillation rejection in wide-area damping using HVDC


Various studies of the western North American Power System (wNAPS) models have shown that particular inter-area oscillatory modes of the system are impacted by the modulation of real power in corresponding locations. Over time, these observations have been verified and validation has been further enhanced with the deployment of phasor measurement units. Conversely, in an expansive and coupled system with multiple lightly-damped modes, each of which correspond geographically to different groups of generators, a single-input, single-output (SISO) control system has been seen to lack the capability to damp all potentially harmful oscillations. In an attempt to resolve this drawback, damping of natural oscillations and stability augmentation has been provided to the system by a multi-input, multi-output (MIMO) wide-area damping control (WADC). To this note, the WADC impact on the forced response of an oscillating generator at frequency in the control bandwidth has become a popular research area.

Dr. Dakota Roberson (currently an assistant professor at the University of Idaho) and Dr. John F. O’Brien, an associate professor at the University of Wyoming conducted a study where they provided novel sensitivity weighting for a MIMO WADC in order to achieve specific feedback goals, assessed the effect of forced oscillation on WADCs, undertook a coupling analysis of the system, and carried out a contingency analysis on the large, highly resonant system. Their work is currently published in the research journal, Electric Power Systems Research.

Briefly, the research method employed commenced with the implementation investigation of the multivariable design and comparison to two SISO controllers implemented simultaneously using the same actuators. Next, the control synthesis was executed using a robust multivariable auto-synthesis method with modifications based on closed-loop behavior. The researchers then applied unique sensitivity weighting functions which resulted in MIMO controllers that emphasized feedback at troublesome frequencies while meeting prescribed bandwidth restrictions. Lastly, a forced oscillation was used to perturb the system at an eigen-frequency of interest so as to determine the effectiveness of each controller in rejecting oscillatory disturbances system-wide.

The authors observed that from the coupling analysis of the diagonal loop shaped controllers, the individually designed SISO loop shaped systems was a valid control approach to the multi-channel wide-area damping control problem. Additionally, they noted that improved performance was obtained with the addition of the high-order, multivariable compensator design using multivariable auto-synthesis methods whereby sensitivity was penalized so that feedback was applied strategically to achieve maximum performance available from each actuator.

In a nutshell, the study by Dakota Roberson and John O’Brien successfully presented a multivariable loop-shaping control design for stability augmentation and oscillation rejection in wide-area damping using high-voltage DC (HVDC) transmission. In general, the researchers observed that the multivariable controller approach showed substantial improvement over diagonal loop shaped compensation and required negligible additional intricacy to implement. Moreover, the multivariable controller system was seen to provide an improvement on disturbance rejection system-wide. Altogether, their work is a stepping stone for future work which will incorporate additional actuators, including distributed energy storage devices and other HVDC lines which may eventually be constructed.

About the author

Dakota Roberson received the B.S.E.E. degree with a minor in mathematics with Honors in 2013 and the Ph.D. in 2017 from the University of Wyoming,. He is currently an assistant professor in Electrical and Computer Engineering at the University of Idaho. His research interests are power systems control, renewable energy integration, detection theory, and statistics.

About the author

John F. O’Brien received the Ph.D. degree from Rensselaer Polytechnic Institute in 2001. He is an Associate Professor of Electrical and Computer Engineering at the University of Wyoming. He was a Member of Technical Staff at NASA’s Jet Propulsion Laboratory in the 1990s where he researched control applied to active space structures. His current research interest is high performance control with nonlinear compensation.


Dakota Roberson, John F. O’Brien. Multivariable loop-shaping control design for stability augmentation and oscillation rejection in wide-area damping using HVDC. Electric Power Systems Research, volume 157 (2018) page 238–250.

Go To Electric Power Systems Research

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