In electric energy metering, incorrect wiring of current transformers can lead to inaccurate measurements of active power. However, it's also important to note that improper connections can affect the measurement of reactive power, which may result in incorrect readings for users. Below are several examples illustrating how wrong wiring impacts the measurement of reactive energy.
1. When the secondary polarity of all three-phase current transformers is reversed, the reactive power expressions for each phase become:
Qa = Ia * Ub * cos(90° + φa)
Qb = Ib * Uc * cos(90° + φb)
Qc = Ic * Ua * cos(90° + φc)
The total reactive power Q = Qa + Qb + Qc = - (IaUb sinφa + IbUc sinφb + IcUa sinφc).
If the three-phase system is balanced, then Q = -3IaUb sinφa.
Meanwhile, the actual reactive power Q’ = 3IaUb sinφa.
This means the reactive energy meter will reverse and show a value close to the normal reading.
2. If two-phase voltage components are incorrectly connected, such as phases A and C, the power expressions for each component change. For example:
Qa = Ia * Ub * cos(150° - φa)
Qb = Ib * Uc * cos(90° + φb)
Qc = Ic * Ua * cos(30° - φc)
Under balanced conditions, the sum of these values equals zero, so the reactive power meter does not rotate.
3. If two-phase current elements are incorrectly connected, like phases A and B, the power expressions become:
Qa = Ib * Ub * cos(30° + φa)
Qb = Ia * Uc * cos(150° + φb)
Qc = Ic * Ua * cos(90° - φc)
Again, under balanced conditions, the total reactive power sums to zero, and the meter remains stationary.
4. When both current and voltage elements are incorrectly connected, the reactive power expressions become more complex. For example:
Qa = Ic * Ub * cos(90° + φa)
Qb = Ib * Uc * cos(90° + φb)
Qc = Ia * Ua * cos(90° + φc)
In a balanced system, this results in a negative reading, causing the meter to reverse at the same speed as normal operation.
5. If the three-phase voltages are connected in a different sequence, such as A → B, B → C, and C → A, the power expressions for each phase become:
Qa = Ia * Uc * cos(150° + φa)
Qb = Ib * Ua * cos(150° + φb)
Qc = Ic * Ub * cos(150° + φc)
The total reactive power is calculated as 3IaUc cos(150° + φa), which leads to the meter reversing due to the cosine function being in the second or third quadrant.
6. If the three-phase voltages are connected in another sequence, such as A → C, B → A, and C → B, the expressions change again:
Qa = Ia * Uab * cos(30° + φa)
Qb = Ib * Ubc * cos(30° + φb)
Qc = Ic * Uca * cos(30° + φc)
Depending on the phase angle φa, the meter may under-read, over-read, or even stop rotating when φa = 60°.
7. These examples illustrate just a few scenarios of incorrect wiring affecting reactive power meters. In reality, there are many more possibilities. However, by understanding vector diagrams and applying similar analytical methods, engineers can accurately determine the correct reactive power and ensure proper billing for users, preventing measurement errors.
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