Keywords

1 Introduction

Practically electrical power system network works smoothly by measuring current and voltage signals and decisions for relaying purposes are derived from these measurements. The relaying system works with a lower range of current (in amperes, not kA) and voltage (volts, not kV). So, currents and voltages magnitudes must be scaled to lower the levels and then fed to the meters and relays. This work can be done by Current Transformers (CTs) and Voltage Transformers (VTs). These measuring transformers are also electrically isolating the relaying system from the high range of power apparatus, which also provides safety for both human beings and the equipment. Considering this reason into account we can say that CTs and VTs are the measuring sensors for the relay. Based on the sensed quantity by these instruments, the decision-making block (relay) processes these signals and generates decision commands to circuit breakers, alarms, etc. The working quality of the current-based relaying scheme depends upon the authentic reproduction of the signal on the secondary side of the CT.

The CTs can be classified into measurement CTs and protection CTs [1]. Two types of CTs are classified as per ANSI/IEEE standards: Class T and Class C. Same as auxiliary CTs are used for circuit isolation to permit independent grounding and change in ratio to match current requirements.

Hooshyar et al. [2] proposed current differential function to detect the saturation of CT from the properties of the current signal wave shape. They have also considered mathematical morphological solutions based on wave shape properties of current derivatives, but practical implementation is remained left. After that, Hooshyar and Sanaye-Pasand [3] elaborated precise measurement of fault currents breached with decaying dc offset and CT saturation result confirmation throughout the system is perfect, even simulation results are also validated. Hooshyar and Sanaye-Pasand [4] involved CT saturation identification based on waveform analysis with the use of a variable-length window. Solak et al. [5] suggested transmission line differential relay immune to CT saturation based on a fuzzy adaptive concept. Results are highly validated with 5000 test data with 0% error in simulation on ATP software. Bertrand et al. [6] presented CT saturation calculations: IEC standards and nonconventional instrument transformers which give a general idea regarding the effect of CT saturation. dos Santos et al. [7] proposed the detection of CT saturation with the use of the distance between consecutive points in the plans formed by the secondary current samples and their different functions on EMTP software-based simulation with mathematical explanations. Moreover, THD-based CT saturation detection techniques are also adopted under transformer protection under various test conditions [8]. Various CT saturation effects are incorporated in transformer protection with adaptively shifting percentage biased characteristics under linear and non-linear load conditions [9,10,11].

Kuzhekov et al. [12] proposed a technique to compute the coefficient of the transient regime and the time-to-saturation of CT. However, the method depends only on the characteristics of CT and not on the external parameters of the 500 kV power system network. Vakhnina et al. [13] have presented a system of non-linear differential equations considering the non-linearity of the inductive resistances of the magnetization curve. The developed model considers the effect of DC offset on the saturation of the transformer core. However, other effects like over fluxing and remnant flux are not considered in the analysis. A novel scheme has suggested a technique using the dynamic current saturation with phasor estimation [14]. An index is calculated to compute the difference between the estimated current samples regenerated from the dynamic phasor and the actual current samples value. However, the noise and harmonics must be taken into consideration while estimating the phasor values of CT secondary signals.

A controlled voltage source (CVS)-based device is introduced in series with a relay to compensate for Current transformer (CT) saturation [15]. The suggested CVS produces a voltage change with time to cancel out the voltage induced across the CT burden. Therefore, the CT core flux remains undistorted and virtually constant during the power system faults. On the other hand, the asymmetry in the original waveform and the presence of DC decaying components may affect the operation of protective devices. Detection and resolution of CT saturation are important to eliminate the maloperation of the current-based protective relays. Haghjoo and Pak [16] have demonstrated least square error and artificial neural network-based compensation and reconstruction of the distorted secondary current waveform of CT. The suggested method can work for minor variations in system parameters and noisy environments.

Davarpanah et al. [17, 18] elaborated a saturation suppression approach for the CT as a fundamental concept with flux condition flag (FCF). Schettino et al. [19] offered a new method of CT saturation detection in the presence of noise, and signal-to-noise ratio (SNR). Smith and Hunt [20] elucidated CT saturation effects on coordinating time intervals based on partial differential loss of coordination. Hooshyar et al. [21] carried out several simulations on PSCAD software on a current derivative-based algorithm to detect saturation phenomenon in CT. Hooshyar and Sanaye-Pasand [22] detailed wave shape recognition technology to detect CT saturation. Esmail et al. [23] presented the detection of partial saturation and waveform compensation of CTs using the Kalman filtering technique. Also, three state Kalman filtering-based technique [24] provides better results than DFT based algorithm. Even under real-time monitoring of transformer special effects of CT saturations are also given distinctive consideration [25, 26].

Ajaei et al. [27] explicated compensation of the CT saturation. They are using Least Estimation Square (LES) filtering technology for the current waveform and make validation through PSCAD™ software, and they introduce Minimum Estimation Error Tracking (MEET). Now a day, artificial intelligence is incorporated to improve the accuracy of any system protection section of the power systems. Many classifiers [28,29,30,31] and regression techniques are adopted to discriminate CT saturation conditions under various parameter considerations and variations. Even in transmission line protection various abnormalities and advance protection systems are elaborate nicely [32, 33] to avoid power system stress and unwanted blackout.

CT saturation is affected by various parameters and comprehensive knowledge is required to analyze or discriminate those conditions. Otherwise, the power system protective scheme may malfunction under unwanted power system abnormalities.

2 Saturation Problem in Current Transformer (CT)

CT is a specially designed transformer for the higher rating of fault current capturing. So, in CT, there are special designs for core manufacturing. Core saturation normally occurs due to the core characteristics and material used for manufacturing. Saturation is a basic physical phenomenon of CT under excessive current or burden. This singularity occurs when the combined magnetic flux is so powerful that all magnetic domains of core material are allied in one direction and thus do not allow for any further intensification in the flux. The electromechanical conversion principle states that the secondary output of CT is closely related to the changing coupled magnetic flux. That’s why the conventional transformer and regular CT do not operate on DC supply. Along with fundamental AC, a small transient DC is applied to the primary of the CT, however, this DC does not replicate on the secondary side of CT. This DC transient current merely produces unidirectional flux and thus contributes to core saturation.

Saturation of the CT is caused by the non-linear nature of the electromagnetic core. Thus, the output signal of CT will be severely distorted whenever the core flux density enters the region of saturation. During this situation, two components of flux are set up in the core: (1) Alternating flux ΦAC which is propositional to the fundamental frequency component of the fault current and (2) Transient flux ΦDC which is induced by the DC decaying component of the fault current. The second component ΦDC is a function of CT primary and secondary circuit time constants. Primary CT is connected to the power system network and hence primary constant. The time constant of the secondary circuit is defined by the burden impedance and leakage impedance on the secondary side.

The factors affecting CT saturation are: (a) Secondary burden, (b) Primary current, (c) Asymmetry in the primary current, and (d) Remnant flux in the core of the CT.

For simplicity, let us accept that initially at t = 0 the magnitude of flux in core of CT is zero. Then using the Faraday’s law, one can find the flux setup in the core of transformer as per below equation:

$$ V_2 = N_2 \frac{{{\text{d}}\phi }}{{{\text{d}}t}} $$
(1)
$$ \begin{aligned} \phi (t) - \phi (0) & = \frac{1}{N_2 }\int\limits_0^t {v_2 {\text{d}}t} \\ & = \frac{RI_0 }{{N_2 }}\tau \left( {1 - e^{\frac{ - t}{\tau }} } \right) \\ & = \frac{LI_0 }{{N_2 }}(1 - e^{\frac{ - t}{\tau }} ) \\ \phi (t) & = \phi (0) + \frac{LI_0 }{{N_2 }}(1 - e^{\frac{ - t}{\tau }} ) \\ & = \frac{LI_0 }{{N_2 }}(1 - e^{\frac{ - t}{\tau }} ) \\ \end{aligned} $$
(2)

The peak value of flux in the core which exponentially increases to

$$ \phi_{{\text{dc}}}^{\max } = \frac{LI_0 }{{N_2 }} $$

as

$$ t \to \propto = \frac{L}{N}\frac{V_m }{{\left| Z \right|}} = \frac{V_m }{{\left| Z \right|}} = \phi_{{\text{dc}}}^{\max } $$
(3)

Here, the flux as derived in Eq. (3) is unidirectional, unlike flux induced by sinusoidal ac voltage. The flux set up in a practical CT core during transient conditions is the addition of AC flux and DC flux.

The ac flux induced in core can be derived by replacing operator \(\frac{{\text{d}}}{{{\text{d}}t}}\) by \(j\omega\).

Hence phasor relationship between phase \(\overline{V}_2\) and \(\overline{\phi }_{ac}\) is given by

$$ \overline{\phi } = \frac{{\overline{V}_2 }}{j\omega N_2 } $$
(4)

If, \(V_2 (t) = V_m \sin \left( {\omega t + \phi } \right)\), then

$$ \phi_{{\text{ac}}} = \frac{V_m }{{\omega N_2 }}\sin (\omega t + \phi - \frac{\pi }{2}) $$
(5)

The maximum value of ac flux is given by

$$ \phi_{{\text{ac}}}^{\max } = \frac{V_m }{{\omega N_2 }} $$

However, \(V_m = R_2 I_0^{\max }\)Hence,

$$ \phi_{{\text{ac}}}^{\max } = \frac{{R_2 I_0^{\max } }}{\omega N_2 } $$

And peak value of the total flux is given by

$$ \phi_{{\text{ac}}}^{\max } + \phi_{{\text{dc}}}^{\max } = \frac{V_m }{{\omega N_2 }} + \frac{{LI_0^{\max } }}{N_2 } $$
(6)

In practice, if this flux crosses the knee point flux in the core, then the CT core will saturate as shown in Fig. 1.

Fig. 1
A line graph depicts the secondary induced e m f in volts versus the secondary exciting current. The curve rises and then becomes almost constant.

CT saturation curve

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While CT is operating in a saturation region, the primary current would not reliably be transformed into a secondary current. It has been observed that the secondary current is trimmed and may lead to the relay maloperation and under the worst condition relay fail to operate. It has been proved that the core saturation does not start instantly after the inception of the fault. Thus, the fast operating relay can decide to detect the fault at that particular time before CT saturation. Else, a slow-acting relay generates a wrong decision and creates a glitch in the operation of the power system network. Thus, it is necessary to evaluate the parameters of CT and its saturation effect under varying power system scenarios.

2.1 CT Oversizing Factors

Characteristically, the cross-section of the CT core would be selected so that \(\phi_m^{{\text{ac}}}\) on B-H curve should be near the knee point (Fig. 1). Oversizing the core is the understandable way to avoid the saturation of CT by dc flux so that, for the given flux \((\phi_{{\text{ac}}}^{\max } + \phi_{{\text{dc}}}^{\max } )\) the equivalent flux density B remains below the knee point. Hence, the factor

$$ \frac{{(\phi_{{\text{ac}}}^{\max } + \phi_{{\text{dc}}}^{\max } )}}{{\phi_{{\text{ac}}}^{\max } }} $$

is known as the core-over sizing factor.

$$ \begin{aligned} {\text{Core}} - {\text{over}}\;{\text{sizing}}\;{\text{factor}} & = 1 + \frac{{\phi_{{\text{dc}}}^{\max } }}{{\phi_{{\text{ac}}}^{\max } }} \\ & = 1 + \frac{LI_0 /N_2 }{{RI_0 /\omega N_2 }} \\ & = 1 + \frac{\omega L}{R} \\ & = 1 + \frac{X}{R} \\ \end{aligned} $$
(7)

Here, X/R is the reactance to resistance ratio of the power system network line parameter X/R ratio. This X/R ratio is approximately 10 for a 220 kV transmission line. Thus, the core size of the instrument transformer should be a factor of 11. Similarly, for a 400 kV line typical value of this ratio will be 20. This suggests that the necessity of core oversizing is around 21 times the actual core design. This amount of oversizing of the core is practically not possible. Thus, the important decision is such that, protection engineers should bare the saturation problem and find an alternative solution to mitigate it.

2.2 Minimizing the Effects of CT Saturation

Generally, the performance specification for protective relays only covers operation at fundamental frequency sinusoidal currents. A rule of thumb frequently used in relating to minimizing the CT saturation effects is to select a CT with a C voltage rating at least twice that required for the maximum steady-state symmetrical fault current [34].

2.3 Time-to-Saturation

It can be observed that the distortion in the secondary signal begins a certain amount of time after the fault inception. Time-to-saturation is a measure of time just after the inception of fault in the power system by which the secondary current accurately reproduces the primary current as per the CT ratio. Time-to-saturation can be determined systematically based on the given power system parameters and saturation factor of CT. Time-to-saturation is important in the design and application of protective CTs. The time-to-saturation of a CT is determined by the following parameters:

  • Asymmetry in fault current

  • Severity of fault current

  • Remnant flux in the CT core

  • Burden of the secondary circuit

  • Knee point (Saturation) voltage

  • Turns ratio of CT.

2.4 Carefulness in CT Selection

Proper selection of a CT is required for a good protection scheme operation.

  • Maximum load current and the rating of CT must be perfectly matched. As an example, if the max continuous load current is 900 A, a 1000:5 A CT may be suitable but a 500:5 A CT is not acceptable.

  • Magnitude of fault current (maximum) should be less than 20 times the rated current of CT. For example, 1000:5 A CT can be used, so long as the burden on the CT and maximum primary fault current are below 20,000 A.

  • The voltage rating of CT should be compatible with knee point in saturation characteristic. For example, 1000:5 C100 would give a linear response, up to 20 times rated current provided CT burden is kept below (100/20 * 5 = 1 Ω). With higher burdens than 1 Ω, this CT can only be used if the maximum current is limited to 20 times the rated current.

3 Consequences of CT Saturation on Protective Relays

3.1 Impact of CT Saturation on Electromechanical Relays

The operation of an electromechanical relay cannot be projected for non-sinusoidal currents without detailed knowledge of the operating principles of the relay. The operation of electromechanical relays is related to the RMS value of current applied to the relay coil. However, during saturation, distorted current other than fundamental frequency components produce phase-shifted fluxes which may perform differently and produce unwanted torque in the relay.

3.2 Impact of CT Saturation on Static/Digital Relays

These types of relays either receive an analog current signal directly as an input or analog to digital converters is used. Depending on the construction, analog-type static relay reacts to an average value of current after applying filters. The digital relays response mainly depends on the technique used for current estimation and the software used for the same.

3.3 Impact of CT Saturation on Differential Relays

In a power system, a differential relay is the most sensitive and important protective scheme for the unit protection medium to large equipment. Differential relay’s basic purpose is to operate under internal fault only whether it is severe or else. And it remains inoperative under any type of external affairs, abnormalities, or severe external faults. In the differential relay, the CT saturation effect depends on the burden offered by different types of relays and on the intensity of the fault. The design and settings of differential relay should be such that it successfully operates during internal fault even in presence of distorted waveforms. The more dominant suffering is the possible maloperation of differential relays for external faults due to CT saturation. Moreover, percentage differential characteristic-based differential relays have some immunity to mis-operation on severe external faults because their operating characteristic needs a substantial ratio of operating current to restraining current. Furthermore, advanced techniques based on artificial intelligence may aid significant contributions to early and severe CT saturation detection incorporated in existing percentage differential relays.

4 System Diagram and Parameters

Where RG and XG are the Resistance and reactance of the generator, respectively, the generator is further connected to the bus and a CT with the relay is shown in the diagram, R1 and X1 are the line parameters, and the line is again connected to the load side bus and the supply is given through that bus to the load.

Figure 2 shows a one-line diagram of a typical power system for simulation modeling. In which a star grounded generator supplies power to a 3-phase load through a medium-length transmission system. CT observes the whole system continuously and gives a signal to the relaying system to make decisions and generate trip signals under faulty conditions. In case of fault occur in the system breaker must operate via the tripping signal of the relay.

Fig. 2
A circuit diagram in which a grounded generator supplies power to a 3-phase load through a current transformer and a series of resistors and inductors.

Single line diagram of a portion of power system

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The detailed parameters of the system are given in Appendix.

5 Results Related to CT

A wide range of parameters is considered for testing and confirming analysis. Results show that due to the CT saturation effect and CT ratio mismatch, a current difference is generated between primary and secondary protective CTs. FIA generate decaying DC component.

5.1 Result for the Various Condition of CT (Normal and Saturation Condition)

$$ \begin{aligned} {\text{Core}} - {\text{over}}\;{\text{sizing}}\;{\text{factor}} & = 1 + \frac{{\phi_{{\text{dc}}}^{\max } }}{{\phi_{{\text{ac}}}^{\max } }} \\ & = 1 + \frac{LI_0 /N_2 }{{RI_0 /\omega N_2 }} \\ & = 1 + \frac{X}{R} \\ & = 1 + \frac{\omega L}{R} \\ \end{aligned} $$

Figure 3a–c shows the effect of the variation of X and R, with the fault inception angle is 0.515 (second) consider so \(\phi_{{\text{ac}}}^{\max } = \phi_{{\text{dc}}}^{\max }\). Due to this there is no offsetting effect is seen. But, due to an increase in inductance and resistance, the current effect and DC offset effect is also appearing in Fig. 3a–c.

Fig. 3
Three graphs plot fault current versus time curves for C T primary and secondary current for different values of inductance and resistance.

Fault current versus time under change in inductance at inception angle 0.515 in second

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Now at inception angle at 0.5 (second) and R = 1 Ω and L = 0.1 H. DC offset current is clearly shown in Fig. 4.

Fig. 4
A graph plots a fault current versus time curve for C T primary and secondary current for resistance equals 1 Ohm and inductance equals 0.1 Henry.

Fault current versus time at fault inception angle at 0.5 s and R = 1 Ω and L = 0.1 H

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5.2 Effect of a High Burden on CT Saturation

Figure 5 clearly shows an effect of CT saturation after 1.5 cycles at a fault inception angle of 0.5 (second) when we apply a high burden on CT secondary.

Fig. 5
A graph plots a fault current versus time curve for C T primary and secondary current for resistance equals 10 Ohms and inductance equals 0.1 Henry.

Fault current versus time at fault inception angle at 0.5 (second) and R = 10 Ω and L = 0.1 H (with the high burden of CT)

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5.3 Effect of Remnant Flux

Figure 6a–d shows an effect of remnant flux on CT saturation, if remnant flux is lesser, then saturation of CT is occurred after a lesser time and it will reduce if remnant flux increases.

Fig. 6
Four graphs plot fault current versus time curves for C T primary and secondary current for remnant flux equals of 0.5, 0.9, 1, and 2 Tesla.

Effect of remnant flux on CT saturation, fault inception angle 0.5 (second), line R = 1 Ω and L = 0.1 H with burden 0.5 Ω

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We can easily see that at remnant flux 0.5 T at that time CT gets saturation after 0.75 cycles, at remnant flux 0.9 T at that time CT gets saturation after 0.60 cycles, at remnant flux 1 T at that time CT gets saturation after 0.35 cycle, and at remnant flux, 2 T at that time CT get saturation after 0.05 cycle.

5.4 Variation of Fault Inception Angle

Mostly it is seen that DC offset is not offered to change in waveform after its five-time of the time constants. The value of I0 can be formulated by setting the current to zero value \(t = t_0\). This infers that

$$ I_0 = - \frac{V_m }{{\left| Z \right|}}\sin (\omega t_0 + \varphi - \theta ) $$
$$ i(t) = \frac{V_m }{{\left| Z \right|}}\sin (\omega t + \phi - \theta ) - \frac{V_m }{{\left| Z \right|}}\sin (\omega t + \phi - \theta )e^{ - (\frac{t - t_0 }{\tau })} $$

Noticeably, the maximum amplitude of DC decaying current be subject to,

  • Fault inception time

  • The phase angle \(\phi\) of applied AC voltage

  • \(\left| Z \right|\) and \(\theta\) of power system/transmission line.

In the above analysis (Fig. 7) of fault inception at different times, a single-phase fault is considered. Looking to the waveform of Fig. 7 for different fault inception angles, it is concluded that

Fig. 7
Three graphs plot fault current versus time curves for C T primary and secondary current for F I A equals 0.525, 0.5, and 0.513.

Effect fault inception angle

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  1. 1.

    DC offset current may be absent, e.g., If \(\varphi = \theta\), \(t_0 = 0\) (see Fig. 7a)

  2. 2.

    The DC offset current can be positive or negative (see Fig. 7b–c).

6 Conclusion

Due to CT saturation, many protective schemes are malfunctioning in the existing power system. So, protective relays must be equipped with suitable CT saturation discrimination techniques to notice CT saturation (Based on the criteria that the CT can deliver 20 times rated secondary current without exceeding a 10% ratio error). Every protective CT must fruitfully transform the primary current into the secondary side without any distortion. However, considering the size of the core, secondary burden, and DC offset in primary current and external network parameters, saturation is likely to occur in the worst condition of the fault scenario. These parameters variation results in distortion of the waveform, current magnitudes dramatically drop, and secondary current contains harmonics. In absence of Im, CT works in ideal mode, and Is = NIp. However, the actual CT secondary current (Is) is subject to an error due to the presence of a high magnetization current (Im) during a severe fault condition. There are so many schemes available like Zero-Crossing Detection, Kalman filtering method, symmetric assessment window base system, signal to noise ratio, etc. to make Im = 0. In this article, the system is simulated in PSCAD™ for obtaining CT saturation and various typical waveform results are obtained during the variation in burden, different fault inception angles, the effect of remnant flux, and DC offset. It has been observed from the simulation results and waveform how CT behave during the different operating condition of the power system. The future objective is to determine the proper method or any mathematical morphology to detect saturation or reduce the CT saturation effect and implement it in real practice.