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A method to investigate dc-network instabilities in multi-terminal HVDC systems is presented. The method consists of defining subsystems, called in this paper Z and Y, which can be interpreted as a dc-network impedance matrix and as set of converter admittances, respectively. Through the analysis of the Z and Y-terms, it is shown that resonances originated from the system’s dc network can be amplified if the converters show a negative dc-side susceptance. Moreover, it is also shown that converters located at different terminals can contribute to instability if the resonances to which they are exposed are of the same frequency. The analysis method is applied to a four-terminal HVDC system as an example and, using the theory developed in this paper, mitigation measures are applied. The results are verified through time-domain simulations.

This study proposes a comprehensive set of performance indicators that should be used when evaluating the hosting capacity (HC) of a system. Descriptions are given for the most relevant phenomena a ...

This paper attempts to provide another view of the application of sequence domain analysis to study the stability of ac-grid connected converters. The approach is based on the definition of positive and negative sequence electrical quantities and on the use of the generalized Nyquist stability criterion in its basic form. Thus, a simple expression to perform the stability analysis is obtained, which allows to identify the contribution of each subsystem on the overall system stability.

Instabilities related to dc-side resonances can occur in voltage-source-converter-based high voltage dc (VSC-HVDC) when resonances originated in dc-transmission links coincide with a nonpassive behavior of one of the VSCs within the VSC-HVDC system. Through Nyquist stability criterion, it is shown in this paper that when the VSC that controls the direct voltage has a nonpassive behavior, the size of dc-side resonance peak also has a negative impact on the instability, i.e., the higher the resonance peak, the greater the risk of instability. Then, the impact of transmission link configurations on the dc-side resonance characteristic is investigated, including overhead transmission lines and dc-side filters. Based on the analysis presented in this paper, it is proposed that, around the dc-side resonance frequency, the magnitude of the VSC subsystem transfer function should be limited to the inverse of the resonance peak at highest. Finally, time-domain simulations show the effectiveness of the proposed countermeasure in stabilizing the system.

A modeling approach is presented in this paper in order to investigate instabilities originating from dc-network resonances in voltage-source converter HVDC (VSC-HVDC) systems. Through frequency-domain modeling, it is shown that the VSC-HVDC system can be represented as a feedback interconnection of two subsystems. These subsystems are defined in this paper as a dc network impedance connected to a VSC dc-side power-dependent admittance. The conditions in which this admittance has a negative conductance are investigated since they can amplify dc network resonances. It is found that when the VSC that controls the direct voltage injects power into the dc network, the mentioned conductance becomes negative above certain frequencies. In addition, the impact of weak ac grids, control system delays, and other direct voltage controllers on the studied conductance is investigated. The theoretical findings are verified through time-domain simulations.

The independent channel design approach proposes that the stability of a multiple-input multiple output system can be studied through the analysis of single-input single-output (SISO) systems. In the case of the grid-connected converters (GCCs) studied in this paper, two SISO systems are defined as positive and negative sequence channels, PSC and NSC, respectively. Further simplifications for the SISO systems are proposed so that the simplified PSC and NSC are decoupled. The advantage of studying decoupled SISO systems is that the identified instabilities can be given a physical interpretation. For example, it is found that instabilities related to ac-grid resonances are due to the fact that the GCC acts as a negative conductance in the PSC. Instability is less likely to occur in the NSC since resonances take place at a higher resonance frequency where the GCC acts as a positive conductance. It is also argued that the proposed simplification is able to reproduce fairly close instabilities related to ac-grid resonances, while for instabilities of other nature, complete expressions need to be used.

A simplified method is proposed to investigate potential instabilities originated from dc-side resonances in multi-terminal HVDC systems. The method consists of identifying the resonances from the points to where the converters are connected. The method is applied to a four-terminal HVDC system, and the analysis indicates there are two resonance phenomena and a group of converters have the most significant impact on the first resonance, while the others on the second resonance. The four-terminal HVDC system is implemented in a Real-Time Digital Simulator and three dc-network configurations are investigated through the proposed method. The test results show the validity of the theoretical findings.

The aim of this paper is to provide a definition of a parameter that can be used for the study of the dc-network dynamics in VSC-HVDC systems. Through an appropriate selection of subsystem within a point-to-point VSC-HVDC system, a dc-side power dependent admittance is defined. The particularity of this admittance is that, if negative, there is a risk that a dc-side resonance becomes amplified. The dc-side power dependent admittance is measured in a EMT model and compared with a linearized mathematical model, showing good agreement between them. The usefulness of the defined admittance is shown through the assessment of various controller modifications on the dc-network stability enhancement. Finally, the conclusions from the analysis are verified through time domain simulations.

In this paper, an approach to evaluate the dynamic performance of the dc side of a voltage-source-converter-based HVDC (VSC-HVDC) system is proposed. The approach is based on the analysis of subsystems which compose the HVDC system. The VSC and the dc grid subsystems are defined in this paper and their frequency responses under different conditions are studied. An explicit expression for the transfer function of the VSC subsystem connected to a strong ac grid is derived, and through this, it is shown that the VSC subsystem frequency response has a 180° phase shift at high frequencies and when it injects power into the dc cable. The frequency response of the dc grid subsystem shows a resonant behaviour due to the RLC nature of the dc cable. In unstable cases, the resonance becomes undamped due to negative conductance characteristic of the VSC subsystem at the dc grid resonance frequency. The transfer function of a VSC subsystem connected to a weak ac grid is derived as well, and it is shown that the amplification of the resonance originated in the dc cable is more considerable.

In this paper, the dc dynamic performance of VSC-HVDC systems is investigated using the frequency domain approach. In a previous work, it has been found through the eigenvalue analysis that, in some situations, the VSC-HVDC system becomes unstable when the converter which controls the direct-voltage injects power exceeding a certain value. However, the cause of the instability was not addressed. This paper attempts to answer some of the remaining questions in the previous work through the frequency response of the elements that compose the system. In order to facilitate the analysis, appropriate assumptions have been made. The transfer function of both, dc grid and the converter which controls the direct-voltage, are derived. The results from the analysis show that, depending on the direction of the power, the frequency response of the converter has a negative resistance characteristic which amplifies resonances in the dc grid.

In this paper, an analysis of the dc dynamics of multiterminal VSC-HVDC systems using the small signal modeling method is presented. Usually, the VSC controllers are designed under the consideration that they operate independently of each other. However, the possible interactions among them and the dc grid should be studied, especially in multi-terminal topologies. In this paper, three VSC-HVDC systems are modeled and, after linearization, the eigenvalues of the system are calculated for different loading conditions. The results from this analysis are compared to those obtained from more detailed models using PSCAD. It is shown that the operating point, the gains of the direct-voltage controller and the cable dynamics have an impact on the system performance.

A typical power system voltage collapse scenarios is often ended with the undesirable operation of the Zone-3 distance relay of the transmission lines. This paper presents a protection scheme to avoid power system voltage collapse using a combined method of distance relay's Zone-3 blocking scheme and a sensitivity-based load shedding selection. The Zone-3 distance relay blocking is based on the proper differentiation between transmission line overloading and line faulted conditions, using a fast estimation of power flow based on Line Outage Distribution Factor (LODF) and Generation Shift Factor (GSF). The Zone-3 distance relay of the transmission line would be blocked if the power flow change over the line is determined to be due to an overload so that more time would be available for the system to take necessary control actions. One of the important control actions is the emergency load shedding. A method based on the calculated sensitivities GSF to identify the most effective load shedding positions and amounts is proposed. The proposed method has been implemented in the Advanced Real-Time Interactive Simulator for Training and Operation (ARISTO) software with the Nordic 32-bus test system. ARISTO offers the possibility to test the proposed scheme since it can be seen as the virtual power system with all live information. The analyses of power system voltage collapse scenarios with and without the proposed scheme implemented have shown the effectiveness of the scheme to prevent the voltage collapses.