General conclusions

The research work reported in this thesis advances current knowledge in the modelling of the STATCOM, back-to-back and point-to-point VSC-HVDC links and multi-terminal VSC-HVDC sys- tems aimed at power flows and time-domain, dynamic simulations of electrical power systems. The starting point is the development of a comprehensive model of the VSC, this being the basic build- ing block with which the STATCOM, two-terminal and multi-terminal VSC-HVDC links are assem- bled. These models are useful to carry out steady-state and dynamic simulations of AC/DC net- works, with the AC networks represented by their positive-sequence equivalents, using phasorial information.

From the outset, the emphasis of the research work was placed on the realisation of a VSC model which would capture the essential steady-state and dynamic characteristics of the actual equipment. This required a fundamentally different modelling approach to the classical VSC repre- sentation which uses an idealised controllable voltage source (or current source) and quite clearly, do not possess an explicit DC node. To circumvent this problem, the VSC model put forward in this research uses a compound phase-shifting transformer and an equivalent shunt admittance with which key control properties of PWM-based converters may be linked. The phase-shifting trans- former decouples, angle-wise, the circuits connected at both ends of the ideal complex transformer in such a way that a notional DC side and AC side of the converter model are created. The equiva- lent shunt admittance is responsible for the VAR absorption/generation process of the converter to provide, for instance, voltage control during steady-state operation. This two-port circuit of the VSC, with its DC and AC sides explicitly available, results in a flexible building block which underpins, in quite a natural manner, the back-to-back, point-to-point and multi-terminal VSC-HVDC systems for cases of both, steady-state and dynamic operating regimes. This has resulted in a number o f key improvements in the VSC’s representation: (i) the switching and conduction losses are included in

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the model in quite a natural manner; (ii) the tap magnitude of the phase-shifting transformer is di- rectly associated to the amplitude modulation index of the converter; (iii) the DC bus of the con- verter may be directly connected to, say, another VSC, back-to-back, or by using the model of a DC cable giving rise to a point-to-point VSC-HVDC configuration; (iv) in fact, any number of these converter models may be interlinked with ease at their DC buses, to constitute a multi-terminal VSC-HVDC scheme. Moreover, the VSC model was made more realistic by a dding an AC phase reactor, an AC filter capacitor and an interfacing OLTC transformer on its AC side and, on its DC side, a shunt capacitor and a series smoothing inductor with its resistive part included. The full model of the VSC unit and, by extension, its derived formulations, yields a realistic representation of this equipment even though they are lumped-type models. Their steady-state and dynamic re- sponses compare well with the responses of the more-detailed, s witching-based models available in EMT-type simulation programs such as Simulink.

A great deal of research effort was paid to the modelling of the back-to-back and point-to-point VSC-HVDC links, to incorporate realistic control mechanisms. Each one of these two-terminal VSC-HVDC models was endowed with four degrees of freedom, a feature that conforms well with actual installations, i.e., simultaneous voltage control on the two AC terminals, DC bus voltage regulation and regulation of the transmitted power through the DC link. The VSC-HVDC link was modelled bearing in mind the standard HVDC application of transmitting a scheduled DC power transfer, the steady-state and dynamic operating regimes were considered. This was followed by adapting the model to encompass the particular application when the VSC-HVDC link feeds into passive, near-zero inertia AC networks; the aim was to provide frequency support to weak AC networks and, accordingly, power flows and dynamic simulations were considered. It should be brought to attention that its effective participation in frequency regulation was possible owing to the frequency control scheme in use, which is based on the regulation of the angular aperture that exists between the internal phase-shifting angle of the rectifier and the voltage angle at its AC ter- minal. This was amenable to power flow regulation in the DC link and, hence, to frequency control in the supported AC network, where it was shown that the inverter acts as a virtual synchronous generator, with its AC bus playing the role of the reference node for all the other nodes in the low- inertia AC network. The control scheme was comprehensively investigated using a wide range of gains of the frequency controller, demonstrating its great effectiveness owing to the fast speed of response of the rectifier station of the VSC-HVDC link, which is in the range of a few milliseconds.

These developments were taken as springboard to tackle the most challenging topic of multi- terminal VSC-HVDC systems, where a generalised frame-of-reference has emerged that greatly improves on existing multi-terminal VSC-HVDC models. The proposed frame-of-reference to carry out steady-state and dynamic solutions of multi-terminal VSC-HVDC systems uses a modular building block which represents the fundamental-frequency operation of a VSC unit. The dynamic frame-of-reference is fitted with three different VSC dynamic models (control strategies) applicable

123 to each pairing AC sub-network, namely, the slack converter whose aim is to control its DC voltage, the scheduled-power converter which injects a scheduled amount of power and the passive con- verter which is connected to an AC network with no frequency control equipment. The model of the multi-terminal VSC-HVDC system was tested using a three-terminal scheme and a six-terminal scheme. The former was used to carry out a comprehensive comparison against an EMT-type model exhibiting similar characteristics, to demonstrate that the RMS-type model resembles to switching-based models in terms of the accuracy of its internal variables’ responses for the steady- state and dynamic operating regimes. The larger multi-terminal VSC-HVDC system has demon- strated the principle that this new framework is suitable for solving AC/DC power systems where a single or multiple perturbations at any of the AC networks or at the DC network may occur.

Concerning the numerical solution of these models, the Newton-Raphson method was used as the computing engine with which the whole set of algebraic and discretised differential equations were solved, for efficient iterative solutions of the steady-state and operating regimes. The model- ling approach used to encompass the STATCOM, back-to-back and point-to-point HVDC links and multi-terminal HVDC systems was a unified framework; one that suitably accommodates and solves, in a simultaneous manner, all the equations resulting from the VSC-based devices together with the AC s ub-networks. The flow chart presented in Chapter 3, Fig. 3.8, summarizes the adopt- ed modelling approach for the RMS-type models of the STATCOM and VSC-HVDC models for both variants s teady-state and dynamic operating regimes. In general terms and using case stud- ies, it has been demonstrated that the new framework enables the comprehensive assessment of the main operational variables of the VSC-FACTS and VSC-HVDC equipment as well as the study of the impact of these equipment on the AC and DC networks.