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Dynamics of power systems with numerous power converters
1 The dynamics of AC/DC power grids with numerous converters
The dominant dynamic phenomena in conventional power systems (centralised generation with large rotating machines) are at low frequencies (below 2Hz) and do not exceed 5Hz. The control engineering did not
play significant role in traditional power systems, comparing for example with aerospace or chemical engineering. These slow dynamic phenomena can be adequately studied using many phasor based power system
simulation tools (like PSS/E, ERACS). The recent, public-domain modelling platform PSAT deserves lot of
praise for enabling open access to all files on a platform that in some aspects exceeds performance of commercial software. These software possess steady-state power flow algorithms and time-domain simulation.
They are ideally suitable for analysis of complex networks with numerous electromechanical machines and
their stability in very low frequency domain. The eigenvalue studies on these software have enabled development of PSS (Power Systems Stabiliser) which has become common control for damping machinemachine dynamic interactions.
With the introduction of first High Voltage Direct Current (HVDC) systems in the 1950s and the
development of Flexible AC Transmission Systems (FACTS) in the 1990s it has become evident that
converter systems have much faster dynamics and new modeling and control techniques are needed. The
development of EMTP-type simulation platforms, like PSCAD/EMTDC, has brought significant benefits,
since they enabled detailed studies of power electronics in power networks. These software have been
mostly beneficial for converter control design, for high-speed switching transients and for harmonic studies
at high frequencies (even over 10kHz). PSCAD and other simulation tools are a high-power version of
simulation platforms used with variable speed drives. While they facilitate accurate converter studies, the
EMTP-type tools operate only in time domain and they are typically used to study a single converter with an
equivalent power grid. The following are two serious limitations with EMTP-type simulation platforms:
 The simulation time-step must be very small (around 1s-50s) because of detailed switching modeling.
If the number of converters is increased, or the power system/controller is complex, the simulation
becomes unacceptably slow. A 4-converter system of modest complexity simulated with PSCAD on a
typical modern PC requires over 1min simulation time for each second of real time.
 They support only time domain studies. The design is always performed using repetitive trial-and-error
runs by observing time domain traces. Frequently, it is most challenging to reach a stable steady-state.
They do not have capability of steady-state power flow solution primarily because of diffciulties with
converter equivalent modeling in power flow algorithms. There is no capability to use any of the
dynamic analysis/design techniques, which are based on transfer function or state-space representation
(like eigenvalue of frequency domain analysis).
The dynamic studies of converter systems have traditionally been much more challenging than with AC
machines. Some of the reported dynamic difficulties include: second harmonic resonance with cable-based
HVDC, interactions between SVC and HVDC, and torsional interactions between TCSC and thermal generators. It is safe to say that we have very little understanding of converter to converter interactions from
control and dynamic point of view. There are no coordinating controllers that would consider dynamics of
several converters. Indeed very few publications have been reported on multiple converters in power networks. The standard converter (SVC, HVDC, STATCOM) controllers are typically designed assuming that
the converter is connected to a passive power system, i.e. a constant source behind impedance. They are always “local” in nature and neglect interactions in the power grid or regard grid dynamics as uncertainty or
disturbances. Such approach is overly simplified in power networks which are already equipped with converter systems since these typically already use wide bandwidth controllers that significantly impact the new
installation. The control aspects will play more important role in modern power systems. The future converters in power networks will have same coordinating control with the dominant power system components, similar to PSS with machine to machine interactions at low frequencies.
The design of controllers for DC transmission networks, perhaps involving numerous VSC AC/DC converters, will be extremely difficult with time-domain EMTP platforms or the phasor-based software. However the dynamic stability and control design with DC networks will play much more important role than
with AC grids.
A converter connected to transmission system will typically have dominant dynamics in the frequency
range 2Hz<f<50Hz for thyristor based topologies (like SVC or conventional HVDC), and dynamics in the
range 20Hz<f<150Hz for converters using turn-off switches (like STATCOM or HVDC light). There are no
power system software tools that could perform eigenvalue analysis in frequency range above 5Hz. An eigenvalue study of converter integration requires manual coding of basic dynamic equations in C or
MATLAB, the development of equivalent continuous converter models and linearisation. Such study typically necessitates a PhD research project for each new case. The small-signal linearised models enable efficient study of dynamics and good example is second harmonic instability with HVDC.
2 The analytical modelling of converter systems
In recent years there has been notable research effort towards understanding wide-bandwidth dynamics
of converter systems used with high-power networks. The accurate linearised continuous (averaged) models
on MATLAB platform have been developed for line-commutated converters (as with HVDC), for shunt
connected (Static Var Compensator), and series connected (Thyristor Controlled Series Compensator) ACAC converters and for Voltage Source Converters. Also, the Phase Locked Loops and their impact on converter dynamics have been studied. These models use standard state-space representation (non-linear or linearised) based on DQ frame detailed power system modelling and they have satisfactory accuracy in the
bandwidth of typical controllers, i.e. up to 150Hz. More importantly, the models have all physically meaningful states, parameters and subsystems. It has been shown that these models show good accuracy when
compared with detailed PSCSAD simulation. Yet, the analytical model produces step responses two orders
of magnitude faster than the PSCAD simulation.
These analytical models are suitable for the use with advanced HVDC controller design, as an example
for operation with extremely weak inverter AC grids. The inability to operate with weak inverter AC grid is
one of the most serious limitations of the thyristor-based HVDC. The root locus study compares can compare the candidate control strategies at inverter converter with low short circuit ratios. The feedback control
method that shows best properties and provides stable HVDC operation can be selected. Also the control
strategies that have very long locus branches indicate high sensitivity to parameter variations and may not be
suitable. Such dynamic study can not be done with “power flow” platforms (like PSS/E) since they can not
represent high frequencies of interest. On the other hand, similar multidimensional controller design would
take considerable effort on detailed simulators like PSCAD, since they do not have capability of eigenvalue
analysis.
The analytical models reported in literature are developed “manually”, by writing individual dynamic
equations for the considered system. They are complex, being typically of 20th–40th order, and they are
coded only for the specific test system (typically a converter system with controllers and the AC grid). In
order to model a new system, or change topology in the existing model, they require equation-level manual
programming, which is tedious and demands high skills. An eigenvalue study is typically a “second” research project, after one PhD is completed on modelling a new converter topology. There have also been
attempts to develop small-signal linearised models of multiterminal HVDC and DC grids but the time demanded for manual code writing is excessive. Considering as an example a DC grid consisting of 9 converters. They are assumed to be in relative proximity since DC cable impedances are very low. Each converter
has two control inputs and typically 4 control loops because of cascade control structure. There will be multivariable control interactions between these 36 control loops which will require systematic and simultaneous control design.
The IEEE industry applications society has introduced a working group on analytical converter modelling (at lower power levels) recently, because of the importance of converter controls in industry applications.
There are no known algorithms for systematic analytical modelling of converters. Our studies will attempt to teach machines to autonomously develop analytical converter models and to routinely perform the
dynamic studies.
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