Analysis of Ferroresonance Mitigation Effectiveness in Auxiliary Power Systems of High-Voltage Substations

Abstract

Ferroresonance in power networks is a dangerous phenomenon, which may result in overcurrents and overvoltages, causing damage to power equipment and the faulty operation of protection systems. For this reason, the possibility of the occurrence of ferroresonance has to be identified, and adequate methods need to be incorporated to eliminate or reduce its effects. The aim of this paper is to evaluate the effectiveness of ferroresonance damping in auxiliary power systems of high-voltage substations by selected damping devices. Laboratory experiments, the results of which created bases for the development of models of selected damping devices, are presented. These models were used to simulate the effectiveness of ferroresonance damping in an auxiliary power system of a 220/110 kV substation in the EMTP-ATP program. The analyses showed that control systems with different algorithms of operation are used in damping devices. This knowledge is important when selecting parameters and settings of the applied damping devices for a given network and the disturbances in it. The presented research results have proved the effectiveness of commercially available damping devices, provided their parameters are correctly coordinated with the settings of the power system protection.

1. Introduction

The first publications on ferroresonance appeared at the beginning of the 20th century, e.g., an article by C. W. Baker in 1911 titled “Double Voltages in Circuits having Capacity and Inductance” in The Electric Journal, 1911, volume 8, page 1102 [1,2]. Ferroresonance can be observed in electrical circuits where capacitances and nonlinear inductances occur [3]. In the case of power networks, these are inductances of devices containing ferromagnetic cores, e.g., voltage transformers, shunt reactors or power transformers. For example, publication [4] analyzed ferroresonance induced by switching processes in a circuit consisting of the nonlinear inductance of a distribution transformer and the capacitance of a supply power cable. Ferroresonance involving voltage transformers has, among other aspects, been the subject of research presented in publications [5,6]. The importance of the problem has led to practical aspects of ferroresonance becoming the subject of IEEE [7] and CIGRE [8] guidelines.

Ferroresonance can seriously disturb the operation of power networks. For example, publication [9] investigated ferroresonance-induced overvoltages and overcurrents in the medium-voltage and low-voltage distribution networks of photovoltaic rooftop systems. In another case, the analogous effects of ferroresonance, but in relation to a wind turbine generator, were the subject of a publication [10]. This is due to the saturation of ferromagnetic cores of devices, leading to significant overcurrents in their windings (mainly voltage transformers), and consequently to thermal damage to their insulation [11,12]. Other effects of ferroresonance are temporary overvoltages and the distortion of phase voltages. Such effects have, among others, been the subject of simulation studies using the EMTP-ATP program [13] or the PSCAD program [14]. In addition to this, ferroresonance can be also responsible for protection system malfunctions, as presented in publication [15].

No unambiguous criteria of occurrence and universal ways to counteract ferroresonance have been defined so far. For this reason, ferroresonance occurrence should be predicted individually for a given network. Research presented in this paper focuses on ferroresonance, which can occur in an auxiliary power system of a high-voltage (HV) substation [16]. A typical schematic of such a system is shown in Figure 1. The system is fed from a medium-voltage (MV) winding of an HV1/HV2/MV transformer (TRp) and includes the following components: a cable line (C1), a medium-voltage switchgear with voltage transformers (VTs), another cable line (C2) and an MV/LV transformer (TRa).

As the neutral point of the system is isolated, parallel ferroresonance is possible. This stems from the parallel connection of the nonlinear magnetizing inductances of voltage transformers and transformers with the shunt capacitances of cable lines. Ferroresonance occurrence is determined by the relationship between the values of nonlinear inductances and linear capacitances, with the necessary condition, i.e., the occurrence (even temporary) of saturation of the ferromagnetic core, for example, due to switching. As previously mentioned, ferroresonance creates a dangerous disturbance condition for power equipment; therefore, suitable measures and methods to prevent and eliminate this phenomenon have to be incorporated. Due to the wide range of values of the resultant capacitances of power networks, in practice, ferroresonance cannot be prevented by individual shaping of the magnetization characteristics of transformers and voltage transformers.

The search for effective solutions to eliminate ferroresonance in electricity networks is an important and current research problem. This is reflected in numerous publications. Various methods are used, but in practice, most commonly, ferroresonance is eliminated with the use of damping resistors connected to the secondary windings of voltage transformers (Figure 2). In power networks with a non-solidly earthed neutral point, the damping resistor (R_DD) is connected in the circuit of the open-delta connection (D₁–D₂) of additional windings of da-dn voltage transformers (VTs). These additional windings are used for measuring the zero-sequence component (3U₀) of phase voltages U_V1, U_V2 and U_V3 [17,18]. The 3U₀ voltage is one of the input signals for earth fault protection (EFP). In the state of normal operation of the network, 3U₀ ≅ 0 V, while in the state of disturbance, e.g., an earth fault or ferroresonance, 3U₀ increases. If this increase was caused by a fault, it should be eliminated by earth fault protection (EFP), and if it was caused by ferroresonance, it should be suppressed by an R_DD resistor of an appropriately selected value.

The suppression of ferroresonance is possible for R_DD ≤ R_DDmax [19]. The lower the R_DD value is, the faster the process proceeds. The value of R_DDmax depends on the parameters of the network and voltage transformers. On the other hand, this resistance should meet the condition R_DD ≥ R_DDmin, where R_DDmin is the minimum value of resistance resulting from the permissible load capacity of the voltage transformer windings and the amount of energy released in the resistor. In order to ensure the most effective damping of ferroresonance, it is desirable to use resistors with the lowest possible values (even of the order of a few Ω), but then, they cannot be permanently connected to terminals D₁–D₂. Therefore, advanced damping devices are used, the operation of which is adjusted to the operating condition of the network by means of appropriate control, e.g., using IGBT transistors [20]. In this way, when ferroresonance occurs, the resultant value of the circuit resistance is automatically changed from a high level to a low level. In the state of normal network operation, the device has significant resistance, which does not create high loads on the voltage transformers. The results of research in this area (e.g., [21]) are leading to the construction of devices which have practical applications in electrical power networks. The devices presented in [22,23] are examples of such commercial solutions.

The aim of this paper is to evaluate the effectiveness of ferroresonance damping in auxiliary power systems of high-voltage substations by selected damping devices. Laboratory experiments, the results of which created bases for the development of models of selected damping devices, are presented in Section 2. These models were used to simulate the effectiveness of ferroresonance damping in an auxiliary power system of a 220/110 kV substation (Section 3).

The analyses showed that control systems with different algorithms of operation are used in damping devices. The originality of the scientific contribution is the development of models for these algorithms and their application in the EMTP-ATP simulation program. This knowledge is important when selecting parameters and settings of the applied damping devices for a given network and the disturbances in it.

2. Experimental Studies of Damping Devices and Their Effectiveness

2.1. Testing of Damping Devices

The idea of ferroresonance damping (Figure 2) lies in switching a resistor with a resistance value R_DD ≤ R_DDmax to terminals D₁–D₂. The higher the effectiveness of ferroresonance damping is, the smaller the value of R_DD resistance is. The value of R_DDmax depends on many factors, among which, the shape of the characteristic I_V = f(U_V) of voltage transformers (VTs) is of special importance. As the amount of energy dissipated must be limited, the connection of the resistor to terminals D₁–D₂ cannot be permanent.

In commercially available devices, the resistor is activated when the threshold voltage (U_tr) is exceeded with a time delay (t_d), for a time dependent on the rated power of the applied resistor. Due to this, the damping device can be miniaturized and installed in low-voltage auxiliary circuits on a 35 mm DIN-rail. Typical values of voltage (U_tr) are 20 ÷ 30 V, and times (t_d) range from 0 to 5 s.

Limiting the amount of energy dissipated is achieved in different ways. On the basis of the research (Figure 3) carried out by authors, two types were distinguished: A-type and B-type. In A-type devices (Figure 4), the damping resistor is a thermistor, so that the limitation of time (I_DD) of current flow depends on its value of I_DD. In B-type devices (Figure 5), the R_DD suppression resistor is pulse-activated by the control unit (CU).

Tests on these devices were carried out for varying values of U_DD voltages. They consisted of closing the switch (S) and recording the waveforms of U_DD voltages and I_DD currents by the digital recorder (DR), such as those shown in Figure 4 and Figure 5. On the basis of these recordings, the parameters of the tested devices, which are relevant for the evaluation of the damping efficiency, were determined. The measured parameters of these devices are shown in

Table 1. Measured parameters of analyzed FDD.

Parameter	FDD Type A	FDD Type B
RDD (Ω)	6.6	12.0
tDD (s)	tDD = 22,130 × (UDD)−2.2	0.18
TDD (s)	N/A	18.5
td (s)	0	0.4; 1.4; 2.4; 3.4
Utr (V)	30	20; 25; 30

R_DD—resistance of damping resistor, t_DD—equivalent operating time or pulse duration, T_DD—time between pulses, t_d—time delay, U_tr—threshold voltage, U_DD—voltage on FDD terminals.

. Furthermore, the determined parameters formed the basis for the development of the computer models of these devices (Section 3). These models were used in the investigation performed in the EMTP-ATP simulation program.

2.2. Investigations in a Laboratory System of the Effectiveness of Ferroresonance Damping Devices

The effectiveness of damping devices was tested in a laboratory system visualized in Figure 6. The system is a model of a medium-voltage power network with an isolated neutral point. The system consists of the following components:

• Regulated three-phase source of voltage (autotransformer PS), 0–250 V;
• Regulated capacities C_E (0–150 nF), representing the earth capacity of the network;
• Factory-made low-voltage models of medium-voltage transformers (VTs) with a primary winding 173 V/$\sqrt{3}$, secondary windings 110 V/$\sqrt{3}$ and additional windings 100 V/3;
• Computer-controlled switch F simulating an earth fault which is switched off after time t_F;
• The analyzed damping device (FDD) attached to terminals D₁–D₂ in a series of windings da-dn of voltage transformers (VTs) (open-delta connection);
• A digital recorder (DR) (class A portable power quality analyzer NP45 [24]) for measuring and recording analyzed currents and voltages.

Ferroresonance was invoked by closing switch F (Figure 6) and then allowing it to automatically open after a preset time (t_F). The assumed switching sequence illustrates the origin of an earth fault in a real medium-voltage power network and its elimination by the power system protection.

The investigations were carried out for different values of capacitance, C_E; voltages, U_PS; and for two selected FDD damping devices (A-type and B-type). Transient voltage and current waveforms were recorded in the laboratory model (Figure 6).

• Phase voltages U_V1, U_V2 and U_V3 in the voltage transformer’s primary windings;
• Phase currents I_V1, I_V2 and I_V3 in the voltage transformer’s primary windings;
• The tripled zero-sequence component of phase voltages 3U₀ = U_V1 + U_V2 + U_V3 (voltage in terminals D₁–D₂ of open-delta);
• The current I_DD in the open-delta connection–current of the FDD.
• The recorded voltages and currents waveforms created bases for determining the possibility of the occurrence of ferroresonance in the analyzed system. Moreover, it was possible to assess the effectiveness of operation and ferroresonance damping by selected FDD devices.

Figure 7 shows exemplary graphs of voltages (3U₀) and currents (I_V) recorded for U_PS = 100 V, time t_F = 500 ms and capacitance C_E = 5 ÷ 75 nF. As can be seen, the occurrence of the earth fault results in a steady-state voltage (3U₀) with a maximum value of approximately $\sqrt{2}$ 100 V, duration t_F. Due to the saturation of the transformer cores, rapidly damped currents with peak values of up to about 50 A flow in the primary windings A–N. It can also be observed that capacitances (C_E) practically do not affect the values and shapes of voltages and currents during a fault.

Capacitances (C_E) have a significant effect on the transient states after the fault has been eliminated. For the capacitance C_E = 5 nF (Figure 7a), the voltage (3U₀) and currents (I_V) are damped shortly after the elimination of the fault. For capacitances C_E = 25 nF (Figure 7b) and C_E = 50 nF (Figure 7c), the character of the recorded curves changes, which is due to the excitation of the ferroresonance. These curves illustrate the negative effects of this phenomenon, i.e., which are persistent voltage (3U₀) and significant overcurrents (I_V), which can result in thermal damage to the insulation of the primary windings of the voltage transformers. However, for capacitance C_E = 75 nF (Figure 7d), the ferroresonance phenomenon is spontaneously suppressed, which, unlike the curves representing capacitance C_E = 5 nF, has a lower oscillation frequency.

Figure 8 and Figure 9 show the curves of voltages and currents, demonstrating the effectiveness of the considered FDDs (Table 1) in situations of ferroresonant oscillations excited for capacitances C_E = 25 nF and C_E = 50 nF. Switched to terminals D₁-D₂, the FDDs affect the course of this phenomenon, causing the expected attenuation of voltages and currents after a fault is off.

The A-type device (Figure 8) starts its operation without delay (time t_d = 0) when a fault and the resulting voltage (U_DD) increase occur. After the time t_F = 500 ms, after which, the fault is eliminated, no ferroresonant oscillations are observed in the presented plots. Thus, the A-type device meets the specified requirements, provided the fault time (t_F) is shorter than the device operation time (t_DD). If this is not met, the FDD will switch off during the short circuit, resulting in ferroresonance excitation, as shown in Figure 7b,c. For this reason, a time delay t_d > 0 is advisable in practice to effectively coordinate the interaction of the earth fault protection and FDDs.

In the case of the B-type device (Figure 9), the system is activated after time t_d = 1400 ms from the moment the fault occurred. As a result, the FDD is not burdened by the current (I_DD) during the fault, though the resulting ferroresonance lasting t_ferr = t_d − t_F = 900 ms is generated. After time t_d, the ferroresonance is suppressed as quickly as in the A-type device.

The relatively small R_DD values (a few to several ohms) and high values of I_DD currents (several to several dozen amperes) result in powers dissipated in the resistor of several hundred or even several thousand watts. The miniaturization of FDDs, however, results in limited energy-dissipation capabilities in the resistor (R_DD). This is illustrated in Figure 10a, where the curves of the voltage (3U₀) and current (I_DD) are shown for an A-type device, recorded for a double short-circuit. These plots show the elimination of ferroresonance after the first fault, though after the second one, the device is unable to damp ferroresonance oscillations due to the increase in the temperature of the thermistor. Such a situation justifies the purposefulness of introducing a delay (t_d) in the operation of the FDD. On the other hand, however, even with the introduction of a time delay t_d > 0, the operation of the B-type device may not be effective after the second fault, as illustrated in Figure 10b. However, unlike the A-type device, this inefficiency is due to the programmed timing sequence, in which the RDD resistor is activated cyclically with a period of TDD = 18.5 s. Thus, next time the RDD resistor is activated, the ferroresonance will be certainly damped, though its duration time will be of several seconds.

Due to the lack of thermal models of voltage transformers, it is not possible to determine whether such a long duration of ferroresonance will endanger them, or not.

The analysis of the test results presented in this section confirms that the commercially available ferroresonance damping devices are effective only to some extent. One should be aware of their limited capabilities when selecting the devices for real power systems and coordinating their operation with power system protection. The following section presents the results of simulation studies concentrating on the occurrence and elimination of ferroresonance in the auxiliary power systems of high-voltage substations, using the developed models of A-type and B-type FDDs.

3. Simulation Studies of Ferroresonance Damping Efficiency in an Auxiliary Power System of a 220/110 kV Substation

The subject of the study was a 15 kV auxiliary power system, shown in Figure 11. This system consists of the following elements:

• A 230/120/15.75 kV ATR autotransformer fed by systems PS1 and PS2;
• A TR 15.75/0.4 kV auxiliary transformer;
• Cable lines C1 and C2;
• Voltage transformers (VTs) with a ferroresonance damping device (FDD);
• Surge arresters SA1 and SA2.

The studies were conducted with the use of a simulation program, EMTP-ATP, where specific elements of Figure 11 were represented.

Transformers ATR and TR and cable lines C1 and C2 were represented with standard models available in EMTP-ATP software: the Hybrid Transformer Model (component XMFR in ATPDraw) and procedure Cable Constants (LCC object in ATPDraw).

A schematic of the voltage transformer (VT) model is shown in Figure 12a. The model consists of three nonlinear inductances (Xμ) with ideal IT transformers having the following ratio:

$$\mathsf{\vartheta }=\frac{15000 \mathrm{V}}{\sqrt{3}}:\frac{100 \mathrm{V}}{3}\approx 260:1$$

The inductances (Xμ) represent the magnetization characteristics (I(U)) of the VT cores shown in Figure 12b. In Figure 13, the magnetization characteristics of cores of the ATR autotransformer and TR transformer are compared. The secondary windings of the IT transformers are connected in an open-delta system.

A schematic diagram of the A-type FDD model is shown in Figure 14a. It consists of a 6.6 Ω RDD resistor and two switches, Sw1 (usually open) and Sw2 (usually closed), connected in series. The Sw1 switch is closed by a block implemented in ATPDraw, code 59, which is a model of an independent-time overvoltage relay with the following settings: threshold voltage (U_tr) and time delay (t_d). The input signal is the rms value of the voltage between terminals D1-D2 of the delta-open system of voltage transformers (Figure 12). On the other hand, switch Sw2 is opened by block, code 51, which is a model of inverse definite minimum time (IDMT) overcurrent relay with the EI (Extremely Inverse) characteristic, according to IEC 60,255 [25]. The B-type FDD model (Figure 14b) differs from its A-type equivalent only in the Sw2 switch control block.

Surge arresters SA1 and SA2 mitigate the effects of ferroresonance, significantly reducing the surge values caused by it. The arrester model proposed by IEEE Working Group 3.4.11 was adopted for the analysis. Its schematic is shown in Figure 15. The values of elements of the surge arrester model are determined iteratively, following the procedure presented in [26].

Simulations have shown that one of the possible causes of ferroresonance is to clear an earth fault previously occurring between CB4 and transformer (TR) (Figure 11). Figure 16 shows phase voltages U_L1, U_L2 and U_L3 on substation busbars AS; the tripled zero-sequence voltage component (3U₀) of the phase voltages on the open-delta side of the voltage transformers (VTs); and currents I_V1, I_V2 and I_V3 in the primary windings of voltage transformers. It was assumed that the earth fault in the L1 phase occurs at time t = 0.1 s, causing a voltage increase on the undamaged phases L2 and L3, the appearance of 3U₀ voltage and an increase in currents I_V2 and I_V3 due to the saturation of the cores of the voltage transformers. This state lasts to t = 0.6 s, at which time, the CB4 circuit breaker is switched off by the earth fault protection. As a result, ferroresonance is excited in the system with the following consequences: ferroresonant overvoltages (voltages U_L1, U_L2 and U_L3) in the area between the ATR autotransformer and the CB4 open circuit breaker, the lasting and increasing 3U₀ voltage and the significant saturation of the core of one of the voltage transformers (current I_V2).

Figure 17 and Figure 18 show the selected voltages and currents illustrating the efficiency of ferroresonance damping by the analyzed A-type and B-type devices. These plots relate to the sequence in Figure 16.

Figure 17a shows the 3U₀ voltage and I_DD current in an A-type damping device operating immediately (t_d = 0 s) when the earth fault occurs at time t_F = 0.5 s. In this case, the ferroresonance is damped immediately after the earth fault is switched off. Figure 17b shows analogous plots, but for a doubled value of the earth fault time (t_F = 1 s). In this case, the ferroresonance was not damped because the FDD got disconnected before the earth fault was switched off at t = 1.1 s, as can be seen from the t_DD = f(I_DD) characteristic visualized in Figure 14a. Thanks to the use of an appropriate time delay in the operation of the FDD, the ferroresonance can be damped, as shown in Figure 17c for a delay time t_d = 0.5 s and a time t_F = 1 s.

Figure 18a shows the plots of the 3U₀ voltage and I_DD current in a B-type damping device, for the earth fault time t_F = 1 s and the delay time t_d = 0.4 s. When the earth fault is switched off, ferroresonance is damped only after time T_DD = 18.5 s (Table 1). For a longer time t_d > t_F, ferroresonance is damped immediately, as shown in Figure 18b for time t_d = 1.4 s.

4. Conclusions

Ferroresonance is a dangerous disturbance occurring in power networks; therefore, measures and methods to prevent and eliminate this effect should be sought for and applied. The most common method of eliminating ferroresonance is the use of damping resistors, connected to the secondary windings of voltage transformers. The most effective damping of ferroresonance can be achieved by using resistors with the preferably smallest possible values, even of the order of a few Ω. For this reason, it is the advanced damping devices, the operation of which is adjusted to the work condition of the network, which are used in practice.

The tests carried out on the selected damping devices allowed the essence of their operation to be clarified in detail, their most relevant parameters to be identified and, thus, models to be developed for use in simulation studies in the EMTP-ATP program.

The results of the investigation confirm that commercially available ferroresonance damping devices are effective only to some extent. One should be aware of their limited capabilities when selecting devices for real power systems and coordinating their operation with power system protection.

The simulation studies performed for the auxiliary power system of a 220/110 kV substation confirmed the applicability of the considered ferroresonance damping devices, but with the same constraints as found in the laboratory studies.

The damping device models developed are an important extension of the EMTP-ATP program, allowing them to be applied to other cases of ferroresonance in power grids, such as industrial grids.

This paper is the result of a scientific collaboration between the AGH University of Krakow (Department of Electrical Engineering and Power Engineering) and Technology and the Gdansk University of Technology (Faculty of Electrical and Control Engineering).