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Stability of power electronic converters connected to power grids is commonly assessed by using the impedance criterion. On the contrary, stability of power grids is typically analysed by using network state-space representation and system eigenvalues. It has been already reported in the literature that the impedance criterion may lead to erroneous results if the dynamics of the grid frequency is not taken into consideration. Meanwhile, the eigenvalue analysis is still considered as a reliable method for finding instabilities. However, the equivalence between these two methods (impedance criterion with frequency dynamics included and eigenvalue analysis) has not been thoroughly studied before. In this paper, the impedance method with frequency dynamics included is compared with the conventional eigenvalue analysis for a system fully based on electronic interfaces. Analytical expressions that link both methods are provided, showing that they are identical under certain conditions. Then, both methods are applied to a system based on a grid-forming and a grid-following converter. The results obtained from real-time simulations performed in OPAL-RT are used to validate the theoretical developments and main contributions of this work.

In recent years, transmission system operators have started requesting converter-interfaced generators (CIGs) to participate in grid services such as power oscillation damping (POD). As power systems are prone to topology changes because of connection and disconnection of generators and electrical lines, one of the most important requirements in the POD controller design is to account for these changes and to deal with them by using either adaptive or robust approaches. The robust approach is usually preferred by system operators because of the fixed structure of the controller. In this paper, a procedure to design POD controllers for CIG-based power plants that takes into consideration all possible network configurations is presented. This procedure is based on frequency-response techniques, so it is suitable for the commissioning in newly installed power plants, even in those cases when a detailed small-signal model of the system is not available. This procedure can be used to damp critical system modes by using active power, reactive power, or both power components simultaneously. The proposed procedure is applied to the design of the POD controller for a CIG-based power plant connected to the IEEE 39 Bus system. Simulations performed in Matlab and SimPowerSystems are used to validate the proposed design procedure.

Low-frequency oscillations are an inherent phenomena in transmission networks and renewable energy plants should be configured to damp them. Commonly, a centralised controller is used in PV plants to coordinate PV generators via communication channels. However, the communication systems of PV plants introduce delays of a stochastic nature that degrade the performance of centralised control algorithms. Therefore, controllers for oscillation damping may not operate correctly unless the communication channel characteristics are not considered and compensated. In this paper, a centralised controller is proposed for the oscillation damping that uses a PV plant with all the realistic effects of communication channels taken into consideration. The communication channels are modelled based on measurements taken in a laboratory environment. The controller is designed to damp several modes of oscillation by using the open-loop phase shift compensation. Theoretical developments were validated in a laboratory using four converters acting as two PV inverters, a battery and a STATCOM. A real-time processing platform was used to implement the centralised controller and to deploy the communication infrastructure. Experimental results show the communication channels impose severe restrictions on the performance of centralised POD controllers, highlighting the importance of their accurate modelling and consideration during the controller design stage.

This paper proposes a recursive, virtual admittance based, secondary controller for DG units that improves the voltage profile in distribution networks. First, the adaptation of the virtual admittance concept for the goal of voltage regulation is explained. Then, a recursive secondary controller is developed to periodically update the virtual admittance gains. The controller is formulated as an optimization problem with current and stability limitations as constraints. Measurements across the grid, transmitted through low-bandwidth communications, are used to simplify the calculations, resulting in a recursive algorithm. Weight vectors are included in the objective function to allow participation flexibility of each converter. Results show that the primary virtual admittance controller is able to mitigate over- and under-voltages in steady state and under transient conditions. Subsequently, the secondary controller is shown to further improve the voltage profiles across the grid. Experimental results obtained from a laboratory environment, comprising three DG units and a grid emulator, validate the functionality of the complete control structure., Comment: in IEEE Transactions on Smart Grid

This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of complex frequency. This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased., Comment: 10 pages, 22 figures

Traditional power theories and one of their most important concepts --apparent power-- are still a source of debate and, as shown in the literature, they present several flaws that misinterpret the power-transfer phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been applied to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, power theories based on GA are revisited. Several drawbacks and inconsistencies of previous works are identified and modifications to the so-called geometric algebra power theory (GAPoT) are presented. This theory takes into account power components generated by cross-products between current and voltage harmonics in the frequency domain. Compared to other theories based on GA, it is compatible with the traditional definition of apparent power calculated as the product of RMS voltage and current. Also, mathematical developments are done in a multi-dimensional Euclidean space where the energy conservation principle is satisfied. The paper includes a basic example and experimental results in which measurements from a utility supply are analysed. Finally, suggestions for the extension to three-phase systems are drawn.