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Modelling of HVDC systemsThe representation of the dc systems requires consideration of the following:

Converter model DC transmission line/network model Interface between ac and dc systems DC system controls model

Representation of the converters is based on basic assumptions

Representation for power flow solutionFrom the analysis presented earlier the converter equations may be summarized as follows:Vdo = 32 BTEac

Vd = Vdo Cos 3 Xc Id B

Vd = Vdo Cos - 3 Xc Id B

= Cos-1 (Vd / Vdo)

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P = Vd Id = PacQ = P tan whereEac = RMS lineto-line voltage on HT busT = transformer turns ratioB = no. of bridges in seriesP = active powerQ = reactive powerXc =Lc =commutating reactance per bridge/phaseVd , Id= direct voltage and current per pole

For the purpose of illustration, we will consider a two terminal dclink. Using the subscripts r and i to denote rectifier and inverterquantities, respectively, the equation for a DC line having resistanceRL is given by

Vdr = Vdi + R L Id

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AC/DC interface at the HT bus

Figure. 8

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AC/DC interface at the HT bus cont

Here Eacr and Eaci are considered to be input quantities for thesolution of dc system equations. They are known from the previousstep in ac solution.Variables Pr ,Qr, Pi and Qi are considered to be the outputs from thesolution of the dc system equations. They are used in the nextiteration for solving the ac system equations. The dependent andindependent variables in the solution of DC equations depend onrectifier and inverter control modes. The three possible modes ofoperation are:Mode 1: rectifier on CC control; inverter on CEA controlMode 2: inverter on CC control; rectifier on CIA controlMode 3: rectifier on CIA control; inverter on modified characteristic.

In mode1, alternative inverter control functions are constant voltagecontrol and constant- control.

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The computations are further simplified using fast decoupled loadflow method in which the corrections to the bus voltage estimatesare found from solving the following equations:P/V = [B] Q/V = [B] Vwhere Pi, Qi are mismatches of real and reactive powers atbus i, and V are the correction vectors to bus angles andvoltages magnitudes. B and B are constant matrices ofappropriate sizes and consist of elements that are related to thereactances of the elements of the network.

While the modelling of DC systems for power flow is fairlystandard, the solution methodology varies. The sequential oralternating method which does not require major changes in thesoftware available for the power flow analysis of AC systems, iswidely used.

Power Flow Analysis in AC/DC Systems

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Solution of DC Load Flow

There are four basic variables per converter, Vd , Id , () and T. If the voltages at all the converters that form tree branches (in

addition to the conductances of the network) are specified, currentsat the remaining converters are specified, then it is possible to solvefor the remaining variables (voltages at the current controlledconverters and currents at the voltage controlled converters ).

Once this is done ,the power factor is computed from theappropriate equations.

The power and reactive power at each converter station are thenobtained from the use of corresponding equations.

The knowledge of the AC voltages allows the calculation of taps.

Solution of AC-DC power flowThe solution methodology for AC-DC power flow can be classified as

Simultaneous or unified Sequential or alternating

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Here x is the vector of dependent variables for DC system and R isthe vector of mismatches of DC system equations.

In the second approach, the AC and DC system equations aresolved separately and sequentially. The AC system is solved to some degree of convergence using asimple model for the DC system based on its last solution. The DC system is then solved using a simplified representation ofthe AC system. There are many variations of this approach

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a) Represent the AC system as a constant voltage, constantangle model at every converter and the DC system as aconstant active and reactive power source (or load) during theAC solution.

b) Represent the AC system by an uncoupled or coupledThevenins equivalent model during DC solution.

c) Represent the DC network as a P-Q load model with aJacobian term contribution that will adjust the expectedinjection from DC system for variations in the converter busAC voltages during AC solution. In this context, it may bementioned that constant current type of load representation(rather than constant P, Q) is found to be satisfactory. It is to be noted that if the taps are continuous and unlimited,

then there is no need for iteration between AC and DC solutions.

The initial calculations of P and Q at each converter are final andused for AC solution.

The voltages calculated from AC power flow are then used tocalculate transformer taps.

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If the taps are fixed or discrete and limited, the power flow solution hasto be carried out for the DC system to re-compute P and Q which isthen used for the AC solution. The tolerance for the largest mismatchS1 and S2 are different and S2

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Comparison between Simultaneous and Sequential Methods

Control for enhancement of AC System Performanceo The converters in effect appear to the AC systems as frequency-

insensitive load and this may contribute to negative damping ofsystem swings.

o Further, the DC links may contribute to voltage collapse duringswings by drawing excessive reactive power.

o Supplementary controls are therefore often required to exploit thecontrollability of DC links for enhancing the AC system dynamicperformance.

Following are the major reasons for using supplementary control of DClink: Improvement of damping of ac system electromechanical

oscillations. Improvement of transient stability. Isolation of system disturbance. Frequency control of small isolated systems. Reactive power regulation and dynamic voltage support.

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The supplementary controls use signals derived from the ACsystems to modulate the DC quantities.

The modulating signals can be frequency, voltage magnitudeand angle, and line flows.

The particular choice depends on the system characteristicsand the desired results.

REFERENCES[1] Prabha Kundur: Power System Stability and control, The EPRI PowerSystem Engineering Series, McGraw-Hill, Inc., 1994.[2] K. R. Padiyar: HVDC Power Transmission Systems: Technology andSystem Interaction, New Age International (P) Limited, Publishers, 1996.

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Cvkr_power Flow With Dc Link