Measurement of electrical energy

An electrical product, in accordance with its purpose, consumes (generates) active energy consumed to perform useful work. At constant voltage, current and power factor, the amount of energy consumed (generated) is determined by the ratio Wp = UItcosφ = Pt

where P = UIcosφ — active power of the product; t is the duration of the job.

The SI unit of energy is the joule (J). In practice, a non-systematic unit of measurement is still used for the watt NS hour (tu NS h). The relationship between these units is as follows: 1 Wh = 3.6 kJ or 1 W s = 1 J.

In intermittent current circuits, the amount of energy consumed or generated is measured by induction or electronically by electrometers.

Structurally, the induction counter is a microelectric motor, each revolution of the rotor corresponds to a certain amount of electrical energy. The ratio between the counter readings and the number of revolutions made by the engine is called the gear ratio and is indicated on the dashboard: 1 kW NS h = N revolutions of the disk.The gear ratio determines the counter constant C = 1 / N, kW NS h / rev; ° С=1000-3600 / N W NS s / rev.

In SI, the counter constant is expressed in joules, since the number of revolutions is a dimensionless quantity. Active energy meters are produced for both single-phase and three- and four-wire three-phase networks.

Rice. 1... Scheme for connecting measuring devices to a single-phase network: a — direct, b — a series of measuring transformers

A single-phase meter (Fig. 1, a) electric energy has two windings: current and voltage and can be connected to the network according to schemes similar to the switching schemes of single-phase wattmeters. To eliminate errors when turning on the meter and therefore errors in energy measurement, it is recommended in all cases to use the switching circuit of the meter indicated on the cover covering its outputs.

It should be noted that when the direction of the current in one of the coils of the meter changes, the disk starts to rotate in the other direction. Therefore, the current coil of the device and the voltage coil must be turned on, so that when the receiver consumes power, the counter rotates in the direction indicated by the arrow.

The current output, denoted by the letter G, is always connected to the supply side, and the second output of the current circuit, denoted by the letter I. In addition, the output of the voltage coil, unipolar with the output G of the current coil, is also connected to the side on the power supply.

When you turn on the measuring instruments through the measuring transformerTCurrent transformers must simultaneously take into account the polarity of the windings of the current transformers and voltage transformers (Fig. 1, b).

Meters are manufactured both for use with any current transformers and voltage transformers — universal, in the symbol designation of which the letter U is added, and for use with transformers whose rated transformation ratios are indicated on their nameplate.

Example 1. A universal meter with parameters Up = 100 V and I = 5 A is used with a current transformer with a primary current of 400 A and a secondary current of 5 A and a voltage transformer with a primary voltage of 3000 V and a secondary voltage of 100 V.

Determine the circuit constant by which the meter reading must be multiplied to find the amount of energy consumed.

The circuit constant is found as the product of the current transformer transformation ratio by the voltage transformer transformation ratio: D = kti NS ktu= (400 NS 3000)/(5 NS 100) =2400.

Like wattmeters, measuring devices can be used with different measuring converters, but in this case it is necessary to recalculate the readings.

Example 2. A measuring device designed for use with a current transformer with a transformation ratio kti1 = 400/5 and a voltage transformer with a transformation ratio ktu1 = 6000/100 is used in an energy measurement scheme with other transformers with such transformation ratios : kti2 = 100/ 5 and ktu2 = 35000/100.Determine the circuit constant by which the counter readings must be multiplied.

Circuit constant D = (kti2 NS ktu2) / (kti1 NS ktu1) = (100 NS 35,000) /(400 NS 6000) = 35/24 = 1.4583.

Three-phase meters designed for measuring energy in three-wire networks are structurally two combined single-phase meters (Fig. 2, a, b). They have two current coils and two voltage coils. Usually, such counters are called two-element.

Everything said above about the need to observe the polarity of the windings of the device and the windings of the measuring transformers used with it in the switching circuits of single-phase meters applies entirely to switching schemes, three-phase meters.

To distinguish the elements from each other in three-phase meters, the outputs are additionally designated with numbers simultaneously indicating the sequence of the phases of the supply network connected to the outputs. Thus, to the conclusions marked with numbers 1, 2, 3, connect phase L1 (A), to terminals 4, 5 — phase L2 (B) and to terminals 7, 8, 9 — phase L3 (C).

The definition of meter readings included in transformers is discussed in Examples 1 and 2 and is fully applicable to three-phase meters. Note that the number 3, which stands on the panel of the measuring device in front of the transformation coefficient as a multiplier, speaks only of the need to use three transformers and therefore is not taken into account when determining the constant circuit.

Example 3… Determine the circuit constant for a universal three-phase meter used with current and voltage transformers, 3 NS 800 A / 5 and 3 x 15000 V / 100 (the form of the record exactly repeats the record on the control panel).

Determine the circuit constant: D = kti NS ktu = (800 x 1500)/(5-100) =24000

Rice. 2. Schemes for connecting three-phase meters to a three-wire network: a-directly for measuring active (device P11) and reactive (device P12) energy, b — through current transformers for measuring active energy

It is known that when changing power factor at different currents I can obtain the same value of UIcos with active powerφ, and, therefore, the active component of the current Ia = Icosφ.

Increasing the power factor results in a reduction in the current I for a given active power and therefore improves the utilization of transmission lines and other equipment. With a decrease in the power factor at a constant active power, it is necessary to increase the current I consumed by the product, which leads to an increase in losses in the transmission line and other equipment.

Therefore, products with a low power factor consume additional energy from the source. ΔWp required to cover losses corresponding to the increased current value. This additional energy is proportional to the reactive power of the product and, provided that the values ​​of current, voltage and power factor are constant over time, it can be found by the ratio ΔWp = kWq = kUIsinφ, where Wq = UIsinφ — reactive power ( conventional concept).

The proportionality between the reactive energy of an electrical product and the additional generated energy of the station is maintained even when the voltage, current and power factor change over time. In practice, reactive energy is measured by a unit outside the system (var NS h and its derivatives — kvar NS h, Mvar NS h, etc.) using special counters that are structurally completely similar to active energy meters and differ only on the switching circuits of the windings (see Fig. 2, a, device P12).

All calculations involved in determining the reactive energy measured by the meters are similar to the above calculations for active energy meters.

It should be noted that the energy consumed in the voltage winding (see Fig. 1, 2) is not taken into account by the meter, and all costs are borne by the electricity producer, and the energy consumed by the current circuit of the device is taken into account from the meter, i.e. the costs in this case are attributed to the consumer.

In addition to energy, some other load characteristics can be determined using power meters. For example, according to the readings of reactive and active energy meters, you can determine the value of the weighted average tgφ load: tgφ = Wq / Wp, Gwhere vs — the amount of energy taken into account by the active energy meter for a given period of time, Wq — the same , but taken into account by the reactive energy meter for the same period of time. Knowing tgφ, from trigonometric tables find cosφ.

If both counters have the same gear ratio and circuit constant D, you can find tgφ load for a given moment.For this purpose, for the same time interval t = (30 — 60) s, the number of revolutions nq of the reactive energy meter and the number of revolutions np of the active energy meter are read simultaneously. Then tgφ = nq / np.

With a sufficiently constant load, it is possible to determine its active power from the readings of the active energy meter.

Example 4… An active energy meter with a gear ratio of 1 kW x h = 2500 rpm is included in the secondary winding of the transformer. The meter windings are connected through current transformers with kti = 100/5 and voltage transformers with ktu = 400/100. In 50 seconds the disc made 15 revolutions. Determine the active power.

Constant circuit D = (400 NS 100)/(5 x 100) =80. Taking into account the gear ratio, the counter constant C = 3600 / N = 3600/2500 = 1.44 kW NS s / rev. Taking into account the constant scheme C '= CD = 1.44 NS 80= 115.2 kW NS s / rev.

Thus, n turns of the disks correspond to the power consumption Wp = C'n = 115.2 [15 = 1728 kW NS with. Therefore, the load power P= Wp / t = 17.28 / 50 = 34.56 kW.