ACDC Power System Analysis
Covers the incorporation of AC DC converters and DC transmission in power system analysis.
Inspec keywords: load flow; power system harmonics; ACDC power convertors
Other keywords: ACDC converter; threephase power; power flow solution; electromechanical stability; harmonic solution; transient converter simulation; electromagnetic transient simulation; harmonic flow; ACDC power system analysis
Subjects: Power systems; Power convertors and power supplies to apparatus; Power transmission, distribution and supply
 Book DOI: 10.1049/PBPO027E
 Chapter DOI: 10.1049/PBPO027E
 ISBN: 9780852969342
 eISBN: 9781849194396
 Page count: 408
 Format: PDF

Front Matter
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1 Introduction
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The threephase 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 ACsystem phases (R, Y, B). Two seriesconnected bridges constitute a 12pulse converter group, the most commonly used configuration in highvoltage and largepower applications. Although the analysis described in this book relates specifically to the 12pulse converter and a pointtopoint DC link, the proposed algorithms can easily be extended to higher pulse converters and multiterminal ACDC interconnections.

2 The ACDC converter in steady state
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This chapter describes a variety of steadystate ACDC converter models with varying degrees of complexity. The starting case is the fundamentalfrequency model based on symmetrical operation, with perfect ACcurrent filters and DCvoltage 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 threephase model is developed for use in more detailed powerflow analysis, a subject described in Chapter 5. The perfect filter and smoothing assumptions are then removed and the ACDC converter is considered as a frequency modulator. A smallsignal transferfunction 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.

3 The power flow solution
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Powerflow analysis is used to determine the steadystate operating characteristics of the powergeneration/transmission system for a given set of busbar loads. In this context, steady state means a timeindependent condition which implicitly takes into account the final adjustment of the parameters involved in maintaining the specified operating condition at each bus, and the componentrelated capability constraints. In shortterm studies, such as the system response to a change in load specification, the powerflow assessment is made without the assistance of generatorcontrol adjustment. The term quasisteady state is used here when referring to such a condition. An assessment of the powertransfer capability of the DC link also considered in this chapter comes under this category.

4 The harmonic solution
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This chapter describes the use of the Newton method to model the interaction between the converter and the AC and DC systems.

5 Threephase power and harmonic flow
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In this chapter, a threephase powerflow and harmonicconverter model are combined and solved using both the sequential and unified Newton's methods. Interaction between the threephase power flow and a threephase 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 threephase power flow, including a polar fastdecoupled type. A special but simple threephase 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 powerflow/distortion interaction is a moderate underestimate of unbalance in the powerflow solution, and a large underestimate of distortion at low order noncharacteristic harmonics in the converter model. The ACDC 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 powerflow 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.

6 Electromagnetic transient simulation
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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.

7 Electromechanical stability
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This chapter contains a concise description of the synchronousgenerator transient mechanical and electrical response to disturbances in the power system. The modelling of other system components is also discussed with emphasis on the ACDC converters. The structure of a basic transientstability program is then described with representation of the DClink 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.

8 Electromechanical stability withtransient converter simulation
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This chapter discusses electromechanical stability with transient converter simulation.

Appendix I: Newton Raphson method
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The generalised NewtonRaphson method is an iterative algorithm for solving a set of simultaneous equations in an equal number of unknowns. At each iteration of the NR method, the nonlinear problem is approximated by the linearmatrix equation. The linearising approximation can best be visualised in the case of a singlevariable problem. The NewtonRaphson 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 f_{k}(x_{m}) 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.

Appendix II: The shortcircuit ratio (SCR)
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This appendix discusses the shortcircuit ratio.

Appendix III: Test systems
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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.

Appendix IV: Statespace analysis
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This appendix discusses the statespace analysis of a linear timeinvariant network.

Appendix V: Numerical integration
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In this appendix, the numerical integration in ACDC power system analysis is discussed.

Appendix VI: Numerical integration
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In this appendix, a curvefitting algorithm can be used to extract the fundamentalfrequency data based on a leastsquared 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 T_{o}.

Back Matter
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