Active, reactive and apparent power: formula, measurement, how indicators are measured

Power is an important factor in assessing the performance of electrical equipment in a power grid. The use of its limit values ​​can lead to network overloads, emergency situations and equipment failure. In order to protect oneself from these negative consequences, it is necessary to understand what active reactive and apparent power is.

Determination of power

The power that is actually consumed or used in the AC circuit is called active power, in kW or MW. Power that constantly changes direction and moves, both in the direction of the circuit and reacts to itself, is called reactive, in kilovolts (kVAR) or MVAR.

Obviously, power is consumed only with resistance. A clean inductor and a clean capacitor do not consume it.

In a pure resistive circuit, the current is in phase with the applied voltage, while in a pure inductive and capacitive circuit, the current is displaced by 90 degrees: if an inductive load is connected to the network, it loses voltage by 90 degrees. When a capacitive load is connected, the current is shifted by 90 degrees in the opposite direction.

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In the first case, active power is created, and in the second, reactive power.

Power triangle

Apparent power is the vector sum of active and reactive power. Full power elements:

• Active, P.
• Reactive, Q.
• Complete, S.

Reactive power does not work, it is represented as an imaginary axis of a vector diagram. Active power works and is the real side of the triangle. From this principle of power decomposition, it is clear in what the active power is measured. The unit for all types of power is watt (W), but this designation is usually assigned to the active component. Apparent power is conventionally expressed in VA.

The unit for the Q component is expressed as var, which corresponds to reactive volt-ampere. It does not transfer any clean energy to the load, however it performs an important function in electrical networks. The mathematical relationship between them can be represented by vectors or expressed using complex numbers, S = P + j Q (where j is the imaginary unit).

Calculation of energy and power

The average power P in watts (W) is equal to the energy consumed by E in joules (J) divided by the period t in seconds (seconds): P (W) = E (J) / Δ t (s).

When the current and voltage are 180 degrees out of phase, PF is negative, the load supplies power to source (an example would be a house with rooftop solar panels that supply power to power system). Example:

• P is 700W and the phase angle is 45.6;
• PF is cos (45, 6) = 0.700. Then S = 700 W / cos (45, 6) = 1000 V⋅A.

The ratio of active to apparent power is called power factor (PF). For two systems carrying the same amount of resistive load, the system with the lower PF will have higher circulating currents due to the electricity being fed back. These high currents create high losses and reduce the overall transmission efficiency. A circuit with a lower PF will have a higher total load and higher losses for the same amount of resistive load. PF = 1, 0 when there is phase current. It is zero when the current leads or lags the voltage by 90 degrees.

For example, PF = 0.68 and means that only 68 percent of the total supplied current is actually doing work, the remaining 32 percent are reactive. Utility providers do not charge consumers for their jet losses. However, if there is an inefficiency at the source of the client's load that causes PF to fall below a certain level, utilities services may charge customers to cover increases in power plant fuel use and degradation of line performance networks.

Full S characteristics

The formula for the apparent power depends on the active and reactive power and is presented as an energy triangle (Pythagoras theorem). S = (Q 2 + P 2) 1/2, where:

• S = full (measured in kilovolt-amperes, kVA);
• Q = reactive (reactivity in kilovolts, kVAR);
• P = active (kilowatt, kW).

It is measured in volt-amperes (VA) and depends on the voltage multiplied by the total incoming current. This is the vector sum of the P and Q components, which tells you how to find the total cardinality. Single-phase network: V (V) = I (A) x R (Ω).

P (W) = V (V) x I (A) = V ² (V) / R (Ω) = I ² (A) x R (Ω).

Three-phase network:

The voltage V in volts (V) is equivalent to the current I in amperes (A) times the impedance Z in ohms (Ω):

V (V) = I (A) x Z (Ω) = (|I| x |Z |) ∠ ( θI + θZ ).

S (VA) = V (V) x I (A) = (|V| x |I |) ∠ ( θV — θI ).

Active P

This is the power that is used to operate, its active part, measured in watts, is the force consumed by the electrical resistance of the system. P (W) = V (V) x I (A) x cos φ

Reactive Q

It is not used for networking. Q is measured in volt-amperes (VAR). An increase in these values ​​leads to a decrease in the power factor (PF). Q (VAR) = V (V) x I (A) x sin φ.

Network efficiency factor

PF is determined by the sizes of P and S, it is calculated by the Pythagorean theorem. The cosine of the angle between voltage and current (non-sinusoidal angle), the phase diagram of the voltage or current from the energy triangle are considered. The PF coefficient is equal to the absolute value of the cosine of the complex energy phase angle (φ): PF = | cosφ | The efficiency of the power system depends on the PF coefficient and it is necessary to increase it in order to increase the efficiency of use in the power system.

Capacitive and inductive loads

The stored energy in electric and magnetic fields under load conditions, such as from a motor or capacitor, causes a bias between voltage and current. As current flows through the capacitor, the build-up of charge causes the opposite voltage to develop across it. This voltage increases to a certain maximum, dictated by the structure of the capacitor. In a network with alternating current, the voltage across the capacitor is constantly changing. Capacitors are said to be a source of reactive loss and thus cause a leading PF.

Induction machines are among the most common types of loads in the power system. These machines use inductors or large coils of wire to store energy in the form of a magnetic field. When the voltage first passes through the coil, the inductor strongly resists this change in current and magnetic field, which creates a time delay with a maximum value. This leads to the fact that the current lags behind the voltage in phase.

Inductors absorb Q and therefore cause lagging PF. Induction generators can supply or absorb Q and provide a measure of Q and voltage control to the system operators. Since these devices have the opposite effect on the phase angle between voltage and current, they can be used to cancel each other's effects. This usually takes the form of capacitor banks used to counteract lagging PFs caused by induction motors.

Damping reactive influence in power grids

Active reactive and apparent power determines PF as the main factor for assessing the efficiency of electricity use in the power grid. If PF is high, then it can be said that electricity is used more efficiently in the power system. As the PF is bad or decreases, the power efficiency of the power system decreases. A low PF or a decrease in it is due to various reasons. There are special correction methods to increase PF.

The use of capacitors is the best and most effective way to improve network efficiency. A technique known as reactive compensation is used to reduce the apparent power flow to a load by reducing reactive losses. For example, to compensate for an inductive load, a shunt capacitor is installed close to the load itself. This allows the capacitor to consume the entire Q and not transmit them over the transmission lines.

This practice saves energy because it reduces the amount of energy it takes to do the same amount of work. In addition, it allows for more efficient transmission line designs using fewer conductors or fewer conductors with connectors and optimize the design of transmission towers.

To maintain the voltage in the optimal range and to prevent instability phenomena, at optimal locations throughout the network power systems, various phase control devices are installed, and various reactive methods are used management.

The proposed system divides the traditional method into voltage and Q control:

• voltage control to regulate the voltage of the secondary bus of substations;
• Q regulation to regulate the primary bus voltage.

In this system, two types of devices are installed in substations for interaction of voltage control and Q control.

Voltage and reactive power control

These are two aspects of the same impact that maintain reliability and facilitate commercial transactions on transmission networks. On an alternating current (AC) power system, the voltage is controlled by controlling the production and absorption of Q. There are three reasons why this kind of control is needed:

1. Power system equipment is designed to operate over a voltage range, typically ± 5% of the rated voltage. At low voltage, the equipment works poorly, bulbs provide less illumination, asynchronous motors can overheat and be damaged, and some electronic devices will not work generally. High voltages can damage the equipment and shorten its service life.
2. Q consumes transmission and generation resources. To maximize the real power that can be transmitted over the congested transmit interface, Q flows must be minimized. Likewise, producing Q can limit the actual power of the generator.
3. The motive reactivity in the transmission network incurs real power losses. To compensate for these losses, power and energy must be compensated.

The transmission system is a non-linear consumer Q depending on the system load. At very low load, the system generates Q to be absorbed, and at heavy load, the system draws a large amount of Q, which must be replaced. System Q requirements also depend on the generation and transmission configuration. Consequently, system reactive requirements change over time as load levels and load and generation patterns change.

System operation has three objectives for controlling Q and voltages:

1. It must maintain sufficient voltage throughout the transmission and distribution system for both current and unforeseen conditions.
2. Ensure that the overload of real energy flows is minimized.
3. Strive to minimize real power losses.

A volumetric energy system consists of many pieces of equipment, any of which can be faulty. Thus, the system is designed to withstand the failure of individual equipment while continuing to operate in the best interest of consumers. This is why the electrical system requires real power reserves to respond to contingencies and maintain Q reserves.