Bruce C. Smith

A review of iterative harmonic analysis for AC-DC power systems

Detailed models of a static power converter capable of representing the effects of AC and DC power system distortion, as well as harmonic modulation of the firing and commutation angles, are now becoming available. Using iterative techniques, such models are combined with linear harmonic penetration into AC network equivalents to provide accurate information about the power system harmonic content. This paper provides a critical review of the state-of-the-art in iterative harmonic analysis.

A Newton solution for the harmonic phasor analysis of AC/DC converters

The steady state equations that describe the power converter and DC system in the harmonic domain are solved by means of Newtons method, in a manner suitable for embedding in an iterative harmonic analysis of the complete power system. The solution includes the interaction of the power converter with the DC system, and the effect of variation in the firing and end of commutation angles caused by AC voltage and DC current harmonics. The convergence of Newtons method is investigated, and methods for accelerating the solution are implemented. Finally, the solution obtained is validated by means of time domain simulation.

Modelling of HVDC transmission systems in the harmonic domain

This paper describes an HVDC link modelled within the harmonic domain using a full Newton method for solution. The solution is rapid and robust for a variety of cases and shows excellent agreement with time domain simulation. The HVDC link is also modelled with an extended control system for realistic specification of the steady-state operating point.

Harmonic tensor linearisation of HVDC converters

The equivalent harmonic impedances associated with time-variant devices such as FACTS and HVDC power converters are in many cases phase-dependent. The second rank tensor is proposed as a means of performing the nodal analysis of networks incorporating phase-dependent admittances. A useful geometric interpretation of phase dependency is developed and applied to the calculation of the harmonic phase-dependent impedance of a HVDC power converter on the AC side.

A modular approach to the solution of the three-phase harmonic power-flow

This paper describes a modular algorithm for the solution of power systems containing active nonlinear devices such as power converters. The solution is a unified real-valued Newton method allowing simultaneous solution of electrical and nonelectrical variables. The algorithm is demonstrated using the reduced equivalent of a real power system which includes both load-flow busbars and a large uncontrolled rectifier. The solution process is fast, robust and exhibits excellent convergence.

A sequence components model of the AC/DC converter in the harmonic domain

In the steady state, the AC/DC power converter couples harmonics on the DC side with sequence component harmonics on the AC side. A solution for the power converter in sequence components may be more efficient than one in phase components. Since most other power system steady-state analysis is framed in sequence components, so too must the power converter analysis be-if a unified solution is to be achieved. However in order to model the commutation process, existing power converter models suitable for iterative steady-state analysis are necessarily framed in phase components. When the power converter steady-state is solved by Newtons method, the advantages of both frames of reference can be derived by a judicious use of the sequence transform, interfacing a Newton solution in sequence components, to a power converter model in phase components.

Linearised direct harmonic solution method for a back-to-back HVDC link

This paper presents a linearised direct harmonic solution for a back-to-back HVDC link operating in the steady state. Using perturbation analysis, small signal distortions are applied to each converter using a time domain model. This allows the transfers around and through the converters to be linearised around a base operating point. The transfers are then written in nodal form and combined with the system equations to form the HVDC link linearised tensor admittance matrix. The system can then be solved directly for any applied distortion and used to determine transfers through the link.

A graphical interface for interactive AC/DC system harmonic analysis

Detailed modelling of the harmonic cross-modulation process performed by a power converter, especially under unbalanced operation, is a difficult task. Although it can be achieved using time domain analysis, it is too slow for interactive work using PCs, and does not represent the frequency response of the components accurately. A fast accurate harmonic domain solution is therefore the best option. This paper presents an interactive program that combines the harmonic domain solution with pre- and post-processing graphics to analyse and display AC/converter/DC system harmonic interactions.

Harmonic evaluation of Benmore converter station when operated as a group connected unit

Three-phase harmonic measurements of a group connected generator-HVDC power converter unit were recently carried out at the Benmore end of the New Zealand HVDC link. This paper describes the test measurement procedures, the set up and configuration of the CHART instrumentation and presents the results which include measured waveforms and their harmonic contents in sequence components for a range of DC line currents. Dynamic simulation accurately predicts the harmonic current contents. The generator harmonic impedances are estimated from the measured and simulated terminal voltages and currents. The generator harmonic ratings for direct connections are also investigated.

Electromagnetic transient simulation

This chapter discusses electromagnetic transient simulation. The simulation of electromagnetic transients associated with HVDC schemes is carried out to assess the nature and likely impact of overvoltages and currents, and their propagation throughout both the AC and DC systems. Transient simulation is also performed for the purpose of control design and evaluation. Transients can arise from control action, fault conditions and lightning surges.