Compared to the primary voltage the secondary voltage can be

8.3.3 Experimental instruments

The secondary voltage was measured through a Tektronix P6015 high-voltage probe with 1000:1 attenuation attached to a socket that is plugged to the end of the plasma antenna. The secondary current is measured by a Pearson 411 current transformer on the wire between the secondary coil and the plasma antenna. The electrical waveforms were recorded by a PicoScope 4824 digital storage oscilloscope with a sampling frequency of 100 MHz. A Keysight E4990A impedance analyzer with 20 Hz to 20 MHz frequency range is applied to measure the capacitance and inductance of electronic components in the plasma ignition system.

10.3.3.1 Case study 1

The proposed SVR scheme is applied to a real PV plant of a nominal power of 48 MVA connected to the high-voltage transmission grid. Each photovoltaic field (made of series and parallel connected photovoltaic modules) is connected to two centralized, that is, equipped with a unique MPPT, converters. The low-voltage converter outputs are raised to 20 kV via a double winding transformer in 45 “converter stations.” The output of each converter station is connected with the output of the nearby station forming four groups that are connected to a central station from where four medium voltage circuits are sent to a transforming station. In the transforming station, the four circuits are connected to the medium voltage side of a transformer that raises the voltage up to 132 kV that is the nominal voltage of the transmission line, where the PV plant is connected. The single-line diagram of the plant topology is shown in [41].

Simulations have been carried out assuming an initial vB,ref = 1.005 pu and the same reactive power injections from all generators. At t = 500 s, the reference voltage vB, ref step to 1.03 pu; consequently, the regulator imposes a new value of reactive power to be supplied by the generators. Fig. 10.14 shows the voltage profile at the point of delivery as well as the trajectory of the reactive power delivered by the generator expressed in pu with respect to its nominal power.

As expected, the proposed control allows distributing the reactive power equally among the generators of the power plant; furthermore, there is no steady-state error, the dynamic of the system does not show oscillations. The dynamic response of the proposed control scheme is thus very similar to that of an SVR installed in conventional power plants.

10.2.2.13 Tap changer

To keep the secondary voltages reasonably constant at the user's end when incoming voltage and/or load on the transformer changes, it is necessary to adjust the voltage ratio (i.e., turns ratio of the windings) of the transformer. This is achieved by operating the tap changing switch. There are two types of tap changers. One is the online tap changer (OLTC), in which tapping of the transformer can be changed automatically without disconnecting the transformer from the grid. The other is the off circuit tap changer (OCTC). In OCTC tap changers, the transformer has to be disconnected and the tap change has to be done. Depending on the voltage fluctuations of the grid, the requirements of the OLTC for the inverter duty transformer are decided. For power transformers, OLTC is followed in grid-connected solar PV systems depending on the voltage fluctuations of the grid voltage of the substation.

3.3.6.2 Secondary and tertiary voltage regulation

The principle of secondary voltage control consists in the control of voltages inside an area of the electrical network called “control area”. By employing control devices located in the respective area of the network in a coordinated way, the voltages are maintained within admissible limits. Voltage control is done online, in a closed loop, and assumes that interactions with neighboring areas are minimized. In a control area there is a large number of load nodes in which the evolution of voltage is representative for the evolution of voltage in the other load nodes of the area; thus, the voltage measurements will be made only in these nodes called “pilot nodes.”

The response time of this type of adjustment is between one minute and several minutes.

The tertiary control represents the global coordination action in the voltage values. It consists in determining the optimal voltage settings at the control devices. The aim is to maintain the reactive power flow between the various areas of the power system and to increase the stability limits of the system. The response time of this type of adjustment is of the order of tens of minutes.

In some power systems, only the tertiary control is adopted, seen as a static problem of reactive power-voltage optimization, treated in the open loop.

In this situation, the most common purpose is to identify the steady operating state with minimum power losses. Minimization of power losses modifies reactive power at generators to maintain voltage at appropriate levels across all system nodes.

13 Voltage error or ratio error

This is the error in the transformed secondary voltage as generally caused by the excitation current I1, and as shown in Figure 15.1. It is the variation in the actual transformation ratio from the rated and is expressed by

Voltage error=Kn.V2*−V 1*V1*×100%

*where

Kn = rated transformation ratio

V1 = actual primary voltage (r.m.s.)

V2 = actual secondary voltage (r.m.s.)

Table 15.5. Recommended limits of voltage and phase displacement errors, applicable for all types of measuring VTs (only electromagnetic and capacitor VTs). (A residual VT is basically a protection VT)

As in IEC-60044-2

Note

Transformer Regulation

It is important to ensure that the secondary voltage of the transformer does not drop below the specified range, and therefore the transformer regulation needs to be checked, based on the reactance and expected maximum loading, as follows:

Vpu=I1(Re.cosΦ2+Xe.sinΦ2)V1

where E1, primary electromotive force (EMF).; E2, secondary EMF; I1, primary current; I2, secondary current; Ro, no-load resistance; V1, primary voltage; V2, secondary voltage; Xe, equivalent reactance of the primary and secondary windings referred to the primary circuit; Xo, no-load reactance; Ze, equivalent impedance of the primary and secondary windings referred to the primary circuit; Ф1, phase angle between I1 and V1 and Ф2, phase angle between I1 and V2.

Voltage transformers

The main requirement in protection is that the secondary voltage should be a true reflection of the primary voltage under all conditions of fault. It is usual with electromagnetic v.t.s to apply additional delta-connected windings (Figure 35.7) to give a measure of the residual voltage at the point of connection. The three voltages of a balanced system summate to zero, but this is not so when the system is subject to a single-phase earth fault. The residual voltage in this case is of great value for protective gear practice as a means of detecting or discriminating between earth fault conditions. The residual voltage of a system is measured by connecting the primary windings of a three-phase v.t. between the three phases and earth, and connecting the secondary windings in series or ‘open delta’. The residual voltage is three times the zero sequence voltage. To measure this component it is necessary for a zero sequence flux to be set up in the v.t., and for this to be possible there must be a return path for the resultant summated flux: the v.t. core must have unwound limbs linking the yokes (Figure 35.7). If three single-phase units are used (as is common for e.h.v. systems), each phase unit has a core with a closed magnetic circuit, so that the above consideration does not arise.

An alternative, avoiding the cost of a HV voltage transformer, is to use the secondary voltages from a.v.t. on the LV side of a power transformer, the voltage drops in which are compensated by the addition or subtraction of voltages developed by c.t.s in the delta of the power transformer. The v.t.s and c.t.s must be provided with tappings if the power transformer is equipped with tap-changing gear, and arranged for automatic selection with the main tappings.

For high-voltage systems the capacitor voltage divider gives a cheaper (but less accurate) device than its electromagnetic counterpart. A typical divider for 400 kV has a total capacitance of 1500–2000 pF, with about 34000 pF between the tapping point and earth, to give about 13.5 kV across the primary of the intermediate transformer, the secondary of which gives 63.5 V (phase to neutral).

6.3.2 Interposing voltage transformers

Voltage transformer accuracy is not the only source of secondary voltage error. This also occurs due to lead resistance (see Section 6.3.4 of this chapter). The sum of these two errors in the incoming and running supply will not be the same at the synchronising equipment, particularly if the lengths of the connecting cables and hence lead resistances are significantly different. Clearly it is important for synchronising purposes that the errors in the measured voltages are as small as practicable. However, there is a further reason why this is important should the two supplies become electrically connected. Although the direct interconnection of VT secondaries is not permitted, with preventive steps taken internally and externally to the synchronising equipment, there remains a small risk that this might occur through a fault or sneak circuit. In this instance, the transformer with the higher of the two secondary voltages would contribute to the load of the transformer with the lower secondary voltage in the same way that power transformers share load in parallel. If the voltage difference is small, this condition would probably remain undetected during normal service with fuse protection. Complications may arise for protection, metering, etc., which may also involve other circuits.

To reduce the voltage error in the incoming and running supply, an interposing voltage transformer (which also provides DC electrical isolation) is installed between the VT secondary and the synchronising equipment, as shown in Fig 12.22. Tappings are provided to facilitate a certain amount of on-site voltage adjustment. With nominal system voltage, each interposing VT tapping is selected to indicate 63.5 V ±1% at the synchronising equipment with the switch both open and closed. With a voltage selection scheme this includes each alternative source of running supply.

The interposing VTs have a ratio between primary and secondary windings of 110/63.5 V (63.5/63.5 V at transmission voltage) and have a minimum rating of 25 VA with a maximum limit of 50 VA, except at transmission voltage where this is reduced to 36 VA. It is, however, preferred that a single rating is used throughout the synchronising scheme for interchangeability reasons. Voltage adjustment is in steps of 0.5 V over the range 0 to +5 V above rated secondary voltage. The tappings may be divided between the primary and secondary windings as convenient. The transformers in general comply with BS3941 [2] accuracy Class 1.0; i.e., percentage voltage error ±1%, phase displacement ±40 minutes, at any voltage between 80% and 120% of rated voltage and with burdens of between 25% and 100% of rated burden at a power factor of 0.8 lagging, except that the range of voltage error is between 5% and 100% of rated burden at unity pf. To ensure that saturation does not occur during over-voltage conditions, the transformer knee point must not be less than three times the rated voltage. As an additional safety precaution, an earthed electrostatic screen is fitted between the primary and secondary windings.

33.3.5 Impedance voltage

The impedance voltage of a transformer can be defined as that voltage required to circulate full-load current in one winding with the other winding(s) short-circuited. It comprises a component to supply the IR drop and another to overcome the e.m.f. induced in leakage inductance. On larger transformers the resistance component is usually negligible and the percentage value of the impedance is the ratio between total magnitude of the leakage flux and the main flux in the core. The leakage flux is a function of the winding ampere-turns and of the area and length of the paths of the leakage flux. By adjustment of these parameters the transformer can be designed for a range of reactances. The most economical arrangement of core and windings results in a ‘natural’ value of reactance. This value can be varied to some limited extent without any great influence on the cost and performance of the transformer. Interleaving the windings and so reducing the effective area of the leakage paths will reduce reactance. High reactance requirements usually result in greater stray load loss, because of the necessarily greater leakage flux.

It is usual to express the leakage impedance Z of a transformer as a percentage (or per-unit) value. The per-unit value is IZ/V, and the percentage value is 100 (IZ/V), where I and V refer to the full-load current and rated voltage of one of the windings, and IZ is the voltage measured at rated current during a short-circuit test on the transformer. In the case of a transformer with tappings, the impedance is conventionally expressed in terms of the rated voltage for the tapping concerned.

33.3.5.1 Regulation

The regulation is the difference between the no-load and full-load secondary voltages expressed in terms of the former, with constant primary voltage. The difference is the result of voltage drops due to resistance and leakage reactance; it is proportional to load but is strongly influenced by the load power factor. Figure 33.16 gives a diagram to show the voltage drop IZ in the leakage impedance Z of the transformer (as obtained from a short-circuit test). The regulation is a maximum when the load phase angle ϕ is equal to the angle θ in the impedance triangle of R, X, and Z. If the load is leading reactive, the regulation is reduced; it may even be reversed so that the secondary voltage rises on load. Formulae (IEC 60076) for the regulation ɛ of a two-winding transformer on full-rated load, in terms of the percentage IR drop voltage ɛr and the percentage reactance voltage ɛx are:

Figure 33.16. Regulation

(33.1)ɛ=ɛr cosϕ+ɛxsinϕ+(ɛxcosϕ−ɛrsinϕ) 2/200%

for transformers having impedance voltages up to 20% and

is a simplified expression for cases in which the impedance voltage does not exceed 4%. For unity p.f. load, (33.1) reduces to ɛ = ɛr + ɛx2/200 and (33.2) reduces to ɛ = ɛr.

Turns Ratio

The relationship between the magnitude of the primary voltage (Vp) to the secondary voltage (Vs) is directly related to the number of turns in the primary (Np) to the number of turns in the secondary (Ns). This is expressed mathematically as

VpVs=NpNs

Figure 1-2 depicts a simple transformer. The primary and secondary wires are identified by the standard letter and numbering system. High-voltage (primary) wires are marked with a “H” and low-voltage wires with “X.” The turns ratio would be expressed as 2:1, and this would be a step-down transformer. If 480 volts were applied to the primary, the secondary voltage would be 240 volts. If 240 volts were applied to the primary, the output would be 120 volts.

Reversing conditions and having 240 turns on the primary and 480 turns on the secondary would make the device a step-up transformer. Applying 480 volts on the primary would result in 960 volts on the secondary. The turns ratio would then be 1:2.

Most transformers rated above 3 kVA can be used either as step-down or step-up service. Standard transformers below 2 kVA have compensated windings and should not be used in reverse. These transformers have a winding ratio that provides a rated voltage to a rated load.

The source voltage can be connected to either the “H” leads or to the “X” terminals. The primary of the transformer can be either set of terminals, depending on whether the transformer is operated as a step-up or step-down device.