Covers the incorporation of AC DC converters and DC transmission in power system analysis.
Inspec keywords: load flow; power system harmonics; AC-DC power convertors
Other keywords: AC-DC converter; three-phase power; power flow solution; electromechanical stability; harmonic solution; transient converter simulation; electromagnetic transient simulation; harmonic flow; AC-DC power system analysis
Subjects: Power systems; Power convertors and power supplies to apparatus; Power transmission, distribution and supply
The three-phase bridge is the basic switching unit used for the conversion of power from AC to DC and from DC to AC. The valve numbers indicate the sequence of their conduction with reference to the positive sequence of the AC-system phases (R, Y, B). Two series-connected bridges constitute a 12-pulse converter group, the most commonly used configuration in high-voltage and large-power applications. Although the analysis described in this book relates specifically to the 12-pulse converter and a point-to-point DC link, the proposed algorithms can easily be extended to higher pulse converters and multiterminal AC-DC interconnections.
This chapter describes a variety of steady-state AC-DC converter models with varying degrees of complexity. The starting case is the fundamental-frequency model based on symmetrical operation, with perfect AC-current filters and DC-voltage smoothing. This model is used in the power flow solution considered in Chapter 3. The removal of the symmetry constraint is considered next, and a three-phase model is developed for use in more detailed power-flow analysis, a subject described in Chapter 5. The perfect filter and smoothing assumptions are then removed and the AC-DC converter is considered as a frequency modulator. A small-signal transfer-function model is described, capable of direct analysis of cross modulation effects at any frequency. This technique is used to simulate the mechanism of harmonic instabilities. The use of convolutions in the harmonic domain avoids the problems of aliasing associated with numerical FFT calculations, or the complexity of Fourier analysis. An additional advantage of the convolution analysis is that all of the equations are differentiable when decomposed into real and imaginary components, a feature which enables a straightforward implementation of a Newton's method solution in Chapter 4.
Power-flow analysis is used to determine the steady-state operating characteristics of the power-generation/transmission system for a given set of busbar loads. In this context, steady state means a time-independent condition which implicitly takes into account the final adjustment of the parameters involved in maintaining the specified operating condition at each bus, and the component-related capability constraints. In short-term studies, such as the system response to a change in load specification, the power-flow assessment is made without the assistance of generator-control adjustment. The term quasisteady state is used here when referring to such a condition. An assessment of the power-transfer capability of the DC link also considered in this chapter comes under this category.
This chapter describes the use of the Newton method to model the interaction between the converter and the AC and DC systems.
In this chapter, a three-phase power-flow and harmonic-converter model are combined and solved using both the sequential and unified Newton's methods. Interaction between the three-phase power flow and a three-phase harmonic converter model has been solved using both decoupled and full Newton methods. The decoupled method displays good convergence if a linearising shunt is present but is slow because the Jacobian matrices need to be recalculated and factorised at every iteration. The full Newton method (with constant Jacobian), is faster and displays more robust convergence. The decoupled method is compatible with any existing three-phase power flow, including a polar fast-decoupled type. A special but simple three-phase power flow is required for the unified method as the converter model must be framed in real variables. Overall, code for the unified method is shorter and less complicated, as there is only one set of sparse storage, mismatch evaluation, convergence checking, etc. The effect of not modelling the power-flow/distortion interaction is a moderate underestimate of unbalance in the power-flow solution, and a large underestimate of distortion at low order noncharacteristic harmonics in the converter model. The AC-DC iterative algorithm can easily be extended into a general purpose model with the capability of including several AC systems, DC systems, possibly with multiple terminals in each system, and all integrated with the power-flow equations. This is essentially a software engineering task, as each half pole contributes a block to the main diagonal of the system Jacobian matrix, with diagonal matrices coupling to other harmonic sources in the same system. The main task is to code the program so as to be versatile, easy to use and modular.
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.
This chapter contains a concise description of the synchronous-generator transient mechanical and electrical response to disturbances in the power system. The modelling of other system components is also discussed with emphasis on the AC-DC converters. The structure of a basic transient-stability program is then described with representation of the DC-link behaviour on the assumption that the link maintains continuous controllability during the disturbance; however, a check for the onset of commutation failure has been included as part of the solution. Prediction of such an event would indicate the limit of applicability of the algorithm and the need to adopt the more detailed stability simulation discussed in Chapter 8.
This chapter discusses electromechanical stability with transient converter simulation.
The generalised Newton-Raphson method is an iterative algorithm for solving a set of simultaneous equations in an equal number of unknowns. At each iteration of the N-R method, the nonlinear problem is approximated by the linear-matrix equation. The linearising approximation can best be visualised in the case of a single-variable problem. The Newton-Raphson algorithm will converge quadratically if the functions have continuous first derivatives in the neighbourhood of the solution, the Jacobian matrix is nonsingular and the initial approximations of x are close to the actual solutions. However, the method is sensitive to the behaviours of the functions fk(xm) and, hence, to their formulation; the more linear they are, the more rapidly and reliably Newton's method converges. Nonsmoothness, i.e. humps, in any one of the functions in the region of interest, can cause convergence delays, total failure or misdirection to a nonuseful solution.
This appendix discusses the short-circuit ratio.
This appendix discusses a simplified test system. To explain the mechanism of harmonic interaction, the inverter side of the CIGRE benchmark system is replaced by a constant DC voltage source E.
This appendix discusses the state-space analysis of a linear time-invariant network.
In this appendix, the numerical integration in AC-DC power system analysis is discussed.
In this appendix, a curve-fitting algorithm can be used to extract the fundamental-frequency data based on a least-squared error technique. It can be described by assuming a sinewave signal with a frequency of ω radians per second and a phase shift of φ relative to some arbitrary time To.
