Reference : Stabilität wechselrichtergeführter Inselnetze
Dissertations and theses : Doctoral thesis
Engineering, computing & technology : Energy
Stabilität wechselrichtergeführter Inselnetze
[en] Stability of Inverter Driven Island Power Grids
Jostock, Markus mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
University of Luxembourg, ​Luxembourg, ​​Luxembourg
Docteur en Sciences de l'Ingénieur
Sachau, Jürgen mailto
Hadji-Minaglou, Jean-Régis mailto
Tuttas, Christian mailto
Schlichenmaier, Martin mailto
Engler, Alfred mailto
[en] inverters ; island grids ; stability ; control model ; distributed energy resources ; droop control
[en] The PhD thesis develops a control model for island grids, where voltage source inverters with droop control adapt frequency and voltage amplitude and no classic rotating generators are present. The presented linear, time invariant model is based on a state space control model of inverters and linearised power flow equations for the grid lines, the grid topology is captured in a node incidence matrix. Such a compound model for inverter driven island grids has not yet been developed to the author’s knowledge. Most existing models have been formulated for very small grids or inverter constellations.
The presented control model allows to investigate grids with a very high number of inverters and with arbitrary grid structures and facilitates the calculation of the compound state space model and the MIMO transfer function matrix. No explicit re-formulation of the differential equations is necessary for different grid topologies, as this information is captured in the node incidence matrix.
The thesis further investigates the stability of inverter driven island grids, i.e. power grids decoupled from the interconnected European power grid and in which most of the primary sources are renewable energy sources, injected via voltage source inverters. As inverters do not have rotating masses and thus no rotational inertia, they can be actuated much faster than classical synchronous generators. The effect of this property on the overall system stability is investigated in this work.
The grid frequency is considered as a distributed parameter, where during transient phases, each grid node has its own valid phase angle speed. During transient phases, the inverters adjust injection frequency according to their droop, due to a local active power change. Until all inverters have adapted their injection frequencies, in each grid node a separate phase speed is valid. This behaviour could be verified with laboratory experiments and is integrated into the formal model with a graph theory approach.
The power flow through grid lines due to voltage changes is a physical effect and practically immediate, while the adaptation of voltage amplitude and frequency through the inverters is a slower action depending on the inverter control algorithm. The separate modelling of inverters with their droop control on the one hand and the passive grid structure with the load flows on the other hand is justified by singular perturbation.
An inverter driven island grid in droop mode can become unstable. Different parameters of the model have an influence on the system stability.
A stability analysis is performed on simple grid structures as line, ring and lattice structure based on pole-zero plots. The influence of single parameters on the pole positions is investigated. Three pole regions appear for the compound model, their position and form is depending on the model parameters.
For the model of the inverter two time constants are assumed: the smaller time constant Tm models the physically minimal possible delay in a PT1 element, while the larger time constant TWR can be adjusted arbitrarily by programming in an inverter. Both time constants determine more or less the position and form of one pole region each. If both time constants approach each other, conjugate complex poles appear. For large values of TWR the system can become unstable as poles move into the right half pane.
This thesis reaches the following conclusions:
Small rated power values of the inverters lead to potential instability as small power perturbations may cause large frequency changes. Since this effect is related to the value of the time constants, a stabilising effect can be observed when the time constants of the inverters are minimised, which enables the inverters to react more quickly to the frequency changes.
An increasing number of inverters in the grid increases the system order and thus the number of poles. Under unfavourable conditions these poles may be badly damped and may develop into dominant complex conjugate poles.
Similar effects can be observed for short grid lines: in systems with short grid connections, the inverters have a stronger electric coupling, bringing forward dominant pole pairs.
The control of voltage and frequency by droops has been developed for in- ductive high voltage grids. In low voltage grids with ohmic line characteristics the droops lead to cross coupling between the voltage and frequency controller, causing an additional voltage reaction due to an active power change and an additional frequency reaction due to a reactive power change. This effect can be counteracted by the rotation of the measured P and Q coordinates in the droop control. The rotation angle is strongly related to the impedance angle at the point of connection of the inverter. Using P/Q rotation reduces the number of dominant pole pairs and fosters the integration of higher numbers of inverters without reaching the stability limits of the grid.
Based on the laboratory results, a method for detection of the optimal P/Q rotation angle has been filed for patent.
Fonds National de la Recherche - FnR
Researchers ; Professionals ; Students
Published through Books-on-Demand under ISBN 9783732263028

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