Current Measurement

SVC Control Components and Models

4.2 MEASUREMENT SYSTEMS

4.2.3 Current Measurement

106 SVC CONTROL COMPONENTS AND MODELS

Because of the saturation of the SVC coupling transformer, sometimes 2nd harmonic currents are injected into the system, causing the inception of 2nd harmonic voltage oscillations. This 120-Hz (f1) voltage component gets trans- lated to 60 Hz (f1 − f0), 120 Hz (2f0), 180 Hz (f0+f1), and 240 Hz (2f1) on the dc side of the voltage transducer. The 60-Hz frequency component in the control loop tends to augment the original 120-Hz oscillation in the system, leading to 2nd harmonic instability (see Section 5.4). To mitigate this effect, a notch filter tuned to 60 Hz is connected to the dc side.

Provided on the dc side of the voltage transducer are two additional notch filters: one tuned to 120 Hz, the other to 360 Hz. It may be recalled that the 360-Hz ripple is caused by the 6-pulse rectification process. There is a need to filter the 120-Hz frequency component; otherwise, it may generate a 3rd harmonic sideband-frequency component in the SVC bus voltage. The other high-frequency components, arising on the dc side and caused by the demodu- lation effect of the voltage transducers, are eliminated through a low-pass filter having a time constant in the range of 1–8 ms.

Furthermore, in series-compensated ac networks, the interaction between the series capacitors and shunt reactors results in the excitation of the shunt-reactor mode having a frequency in the range of several to 20 Hz. This mode is deci- sive in determining the controller stability. A much-improved SVC response is obtained by filtering this mode and is achieved by placing a high-pass filter with a break frequency of about 25 Hz on the ac side.

The total arrangement of filters in the voltage measurement system and the typical characteristics of the filters within the context of the Hydro-Quebec James Bay system SVC [18] are depicted in Fig. 4.10.

MEASUREMENT SYSTEMS 107

High-Pass 80- and 96- Hz Notch

ac-Side Rectifier dc-Side

ac Voltages From Potential Transformers

Harmonic Notch Low-Pass

V_{H meas}

Gain (pu) Gain (pu)

1 10 100 1000

0.01 0.1 1 10

1 10 100 1000

0.001 0.01 0.1 1

Figure 4.10 The filtering of measurement voltages (solid lines represent existing fil- ters; dashed lines represent additional filters needed for series-compensated ac lines).

A better option is to use a differentiating-current transformer (DCT) [28], which is an air-gapped-current transformer that supplies a voltage output with an extremely high burden resistance. An application of DCT is illustrated in Fig. 4.11, in which thedi

/

^{d t}signal is integrated to reconstruct the current signal and the integrator is reset at every firing instant when the thyristor valves are just commencing to conduct. An advantageous feature of this application is that any dc component in the actual current can be faithfully generated in the reconstructed signal. To prevent amplification of the fast interference pulses, a small despiking-lag circuit of time constant 200ms and a metal-oxide varistor (MOV) are connected at the output of DCT.

In many control applications, such as load compensation and voltage balanc- ing, the control strategies require the phasor quantities of positive- and negative- sequence currents and voltages. These quantities can be obtained by suitably transforming the instantaneous values of the currents or voltages. A general pro- cedure [32] for deriving the phasor components of thekth harmonic is described in the following text.

Let a sinusoidal signalx(t) be represented by Fourier series as

x(t)c C0

2 + 冱∞

冱

n冱c1 C_ncos(2pn f₀t+Jn) (4.25)

The kth harmonic phasor is then described by

108 SVC CONTROL COMPONENTS AND MODELS

di dt

Reset DCT

Oscillator Pulses SVC MV Bus

L

∫

i

Figure 4.11 The TCR current measurement using a differentiating-current transformer (DCT).

C_k cc_k/–J_k cc_k(cosJ_k+ sinJ_k) (4.26) Multiplying x(t) by a sinusoidal signal cos 2pf_rt, where f_r c k f₀ andk ∈ n, results in

x(t) cos(2pf_rt)c ck

2 cos(J_k) + 冱∞

冱

mc1冱,m⬆k

d_mcos(2pm f₀t+gm) (4.27) The first term on the right-hand side of Eq. (4.27) represents a dc term, whereas the second term corresponds to a series of sinusoids of frequencym f0c (n±k)f0. The magnitude and phase of these sinusoids are denoted by dm and gm, respectively. It follows from Eq. (4.22) that

2x(t) cos(2pfrt)cRe{Ck} + sinusoids (4.28) Also

2x(t) sin(2pfrt)c−Im{Ck} + sinusoids (4.29) where Re{C_k} and Im{C_k} represent the real and imaginary components of the kth harmonic phasor of signalx(t). The sinusoids in Eqs. (4.28) and (4.29) can be eliminated by an averaging filter, which averages over one time period of the smallest (n±k)f₀ frequency.

Ifx(t) corresponds to thea-axis current,i_a(t), then thekth harmonic phasor, I_a, is given by

I_acRe[I_a] +j Im[I_a]

c2ia(t) cos(2pfrt)−j2ia(t) sin(2pfrt) (4.30)

MEASUREMENT SYSTEMS 109 Equation (4.30) is strictly valid only after filtering out the sinusoids of Eqs.

(4.28) and (4.29). A similar expression, however, can be obtained for the kth harmonic phasor,Ib, that corresponds to theb-axis current, ib(t), as discussed in the text that follows.

The symmetrical component phasorsI1 andI2 are derived using the follow- ing phasor transformation:

[

^II12

]

^{c 12}

[

^{11 −jj}

] [

^IIab

]

^(4.31)

The real and imaginary components of thekth harmonic positive-sequence pha- sor are then given by

[

^Re{IIm{I11}}

]

^c

[

^{−cos(2pfsin(2pfrrt)t) cos(2pfsin(2pfrrt)t)}

] [

^iiab(t)(t)

]

^(4.32)

The corresponding negative-sequence phasor quantities are

[

^Re{IIm{I22}}

]

^c

[

^{−cos(2pfsin(2pfrrt)t) −−cos(2pfsin(2pfrrt)t)}

] [

^iiab(t)(t)

]

^(4.33)

The a, b components ia(t), ib(t) are obtained from the 3-phase quantities ia(t),ib(t), andic(t) using the transformation given by Eq. (4.1). Implementation of this measurement scheme is described in ref. [32].