determination of synchronous generator parameters

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determining parameter values is replaced by a numerical ... subtransient reactance to be obtained. ... salient-pole synchronous generator are given in Fig. 1.
18th INTERNATIONAL SYMPOSIUM on POWER ELECTRONICS - Ee 2015 NOVI SAD, SERBIA, October 28th - 30th, 2015

DETERMINATION OF SYNCHRONOUS GENERATOR PARAMETERS USING THE FIELD CURRENT WAVEFORM Bogdan Brković, Dragan Petrović, Radenko Vasić* University of Belgrade, School of Electrical Engineering, Belgrade, Serbia *Drinsko-Limske Hidroelektrane, Bajina Bašta, Serbia 1

Abstract: In this paper, a method for identification of synchronous generator parameters using sudden short circuit test data is proposed. Standard methods are usually graphical and rely on armature current waveforms to obtain the transient parameters. The approach presented here uses the field current waveform instead. The traditional graphical approach for determining parameter values is replaced by a numerical procedure, based on a simple and effective algorithm which minimizes the sum of squared errors. The accuracy of the presented method has been verified experimentally verified using test results from a 100 MVA synchronous generator at HPP Bajina Basta. Key Words: synchronous generator/parameters/field current/numerical procedure/algorithm/sum of squared errors

procedures involving least-squares optimization. Such procedures often exhibit convergence issues, since they are based on differential calculus. In this paper, field current data from the sudden three phase short circuit test will be used in order obtain transient parameters. This approach allows for all reactances and short circuit time constants except for the subtransient reactance to be obtained. Using the field current waveform can sometimes be advantageous, since armaure currents are usually measured using current transformers which are subject to saturation, whereas field current is measured using shunt resistors. Another convenience when using field current is the absence of the double frequency component, which can sometimes compromise the accuracy of results obtained using armature currents. The standard graphical approach is replaced by an original numerical least-squares optimization procedure. Parameter values obtained using the graphical and numerical approach show good agreement. Furthermore, the field current waveform obtained from the analytical expression is compared with the recorded waveform in order to demonstrate the accuracy of the suggested method.

1. INTRODUCTION Exact knowledge of steady-state and transient parameters of large synchronous generators is demanded in modern power systems. Current standards suggest several test procedures for determination of synchronous generator transient parameters [1, 2]. These methods are mostly geometrical, and thus subject to human error. In an attempt to improve or replace the standard methods, various non-standard test procedures have been developed over the years. In [3, 4], methods for deriving open-circuit transient parameters from load-rejection tests are described. Determination of short-circuit transient parameters using blocked-rotor step response is suggested in [5]. This method is particularly convenient, since it can be performed at standstill. An online parameter estimation technique using an observer for damper currents is suggested in [6]. Numerical methods using curve-fitting procedure on armature currents obtained from sudden 3-phase short-circuit test are described in [7, 8]. A similar approach, only aimed at small synchronous generators, is suggested in [9]. Most numerical methods rely on standard mathematical

2. GENERATOR MODELING The d- and q-axis dynamic equivalent circuits of a salient-pole synchronous generator are given in Fig. 1. Parameters of the equivalent circuits are well-known, and it is therefore unnecessary to elaborate them here. Using these circuits and the appropriate terminal conditions, the analytical expression for field current following a sudden three-phase short circuit is obtained as [10]:  X  Xd   i f (t )  I f 0 1  d  Xd    t  (1)   t  T   t  T  Td  Td Ta KD KD e  e  1   e  cos 0 t  .  T      T d d    

1

The expression is comprised of an aperiodic (DC) component:

Corresponding author: Bogdan Brković E-mail: [email protected] Phone: +381 11 3218 364

1

Ra

ω0ψq Ra ω0ψ+q +

Lσa Lσa

uf

id

uf +

id

if

iD

id+iD+if id+iD+if ud

if_fit.m

+ iD

PAR = [Xdprim_0, Tdprim_0, Tdsec_0, Ta_0, TKD_0]

if

RD RD

Rf

STEP = k*PAR

Lσf

CRIT = SUMSQR(IF_GUESS, IF ) CRIT_OLD = CRIT N_STALL = 0

Rf

pψd

ud

IF_GUESS = GUESS(t,PAR)

pψd

Lmd

LσD

Lmd

LσD

Lσf

CONDITION = 0

PAR_FINAL = PAR

a) Ra

Ra ω0ψd

ω0ψd

Lσa + Lσa

+

iq iQ

uq

uq

pψq

CONDITION ≠ 0

PRINT OUTPUT PARAMETERS

iq

iq+iQ

YES

iq+iQ

RQ

i=1

iQ

NO NO

i≤N

PLOT CURRENT WAVEFORMS

RQ

YES

pψq

PAR1(i) = PAR(i) + STEP(i) PAR2(i) = PAR(i) - STEP(i)

Lmq

Lmq

LσQ

LσQ

IF_GUESS1 = GUESS(t,PAR1) IF_GUESS2 = GUESS(t,PAR2)

CRIT1 = SUMSQR(IF_GUESS1, IF ) CRIT2 = SUMSQR(IF_GUESS2, IF )

b) Fig. 1. Equivalent circuits of a synchronous generator: a) d-axis; b) q-axis t  T X   i fdc (t )  I f 0 d e Td   1  KD  T  Xd   d   and a periodic (AC) component:

  t    e Td  ,    

i=i+1

CRIT1