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Sum of Vector Current Calculator
Application of Sum of Vector Current Principle
doblePRIME bushing monitor (formerly Doble IDD ) and Dynamic Rating bushing monitors were based on the sum of vector current principles. The sum of vector current is zero (0) in a balance symmetrical three phase electric system. So any non-zero summation of vector current would be an indicator that something in CONDENSER BUSHING insulation system is deteriorating. Any future increasing trend in the summation of vector current is also a clue for deterioration of condenser bushing insulation system.
What about if the three phase load current are not symmetrically balance, meaning your electrical system is experiencing unbalance loading condition? Will the sum of vector current algorithm still valid if the logic is based on a symmetrically balance system? In my understanding of Dynamic Rating answer, their algorithm is still valid because during commissioning they have balancing circuit to normalize any unknown sources of leakage current by adjusting each bushing balancing circuit to zero (null).
Source: White Paper : On-Line Bushing Monitoring and Comparison to Off Line Testing.
For doblePrime IDD bushing monitor (formerly Doble IDD) answer, their algorithm is still valid because they are using machine learning algorithm, training for one day, one week, one month and one year to observe the pattern of operation of a healthy bushing's leakage current even there is a load unbalance in your electrical system. Then using the trained value of leakage current to calculate the power factor and capacitance of a healthy bushing. These calculated bushing power factor and capacitance will be used as the reference to compare any events that exceeded these reference value of power factor or capacitance.
Source: doblePrimeOverview literature.
What about if the bushing manufacturer are different in H1,H2, and H3 or X1, X2, and X3 will the sum of vector current principle still valid? In my understanding of Dynamic Rating answer, their algorithm is still valid because during commissioning they have balancing circuit to normalize any unknown sources of leakage current by adjusting each bushing balancing circuit to zero (null).
Source: White Paper : On-Line Bushing Monitoring and Comparison to Off Line Testing.
" During commissioning the null meter is balanced to zero. The purpose of the balancing circuit is to take into account the differences in system voltages and phase fluctuations and bushing characteristics. As a defect develops the complex conductivity of the bushing insulations changes and the current and its phase angle in of the phases also changes. Therefore, the null meter will no longer null."
Source: White Paper : On-Line Bushing Monitoring and Comparison to Off Line Testing.
" Many bushing defects are temperature and voltage dependent. When testing off-line, the bushing is at ambient conditions and only 10 kV is applied. With on-line monitoring, higher voltages are applied and elevated temperatures are presents.
Top oil temperature is used as a relative temperature measurement for the temperature of the bushing. Approximately 60% of the bushing temperature comes from the oil. "
Source: White Paper : On-Line Bushing Monitoring and Comparison to Off Line Testing.
USING GEOGEBRA FOR DATA VIZUALIZATION OF SUM OF VECTOR
Four Vectors Addition - click here
As you can see the sum of vector u + v + w is zero in a balance symmetrical system. Vector u represents A-Phase, Vector v represents B-Phase and use as a reference. and Vector w represents C-Phase.
Phasor Vector Rotation starts from from 0 ° which is vector B-Phase, then rotates in CCW direction towards A-Phase, and finally C-Phase.
Frequently refer to as Phase Rotation is BAC
Remember the phasor rotation starts from 0 ° moving counter clockwise until it reaches 360 ° it can be displayed as 0 or 360 value. Therefore 0 ° and 360 ° is describing the same vector direction.
BAC phasor rotation seems to be associated with transmission line layout. For example from left to right (B-phase line-left, A-phase line, C-phase line-right) and from top to bottom ( B-phase line-top, A-phase line , C-phase line-bottom)
By Apolinario "Sam" Ortega, 07 December 2018, Created with GeoGebra
Given a polar coordinate of a point
∠ ° , meaning the radius is 690 and the angle is 0 degree. Counter clockwise rotation of the angle (CCW rotation) is the default rotatation.
DEFAULT ROTATION IS COUNTER CLOCKWISE FROM POSITIVE X-AXIS BECAUSE IT CORRESPONDS TO CARTESIAN COORDINATE
Compute its equivalent rectangular coordinate or cartesian coordinate:
ANSWER ( , )
Given a rectangular coordinate of a point in Cartesian coordinate system.
( , )
Solve for its equivalent polar coordinate.
DEFAULT ROTATION IS COUNTER CLOCKWISE FROM POSITIVE X-AXIS BECAUSE IT CORRESPONDS TO CARTESIAN COORDINATE
0 ° and 360 ° is describing the same vector direction.
ANSWER: ∠ °
Approximation of bushing leakage Tap Current in mA using formula
Formula Recall: Bushing tap current in mA = V LG ( in kV) * 2 π* f * C1 ( in pF)
Credit to: Doble Engineering
conversion of kV and pF are done in the algorithm.
| Line to Ground Voltage for 230 kV Line-Line Voltage, in kV = | in kV |
| 2 π = | |
| frequency in Hz = | |
| Latest off-line capacitance, C1 reading in picoFarad = | in pF |
| Approximate bushing tap current in milliAmpere = | in mA |
| Line to Ground Voltage in kV for 550 kV nominal = | 317.55 kV |
| Line to Ground Voltage in kV for 525 kV nominal = | 303.12 kV |
| Line to Ground Voltage in kV for 500 kV nominal = | 288.68 kV |
| Line to Ground Voltage in kV for 345 kV nominal = | 199.19 kV |
| Line to Ground Voltage in kV for 230 kV nominal = | 132.79 kV |
| Line to Ground Voltage in kV for 69 kV nominal = | 39.85 kV |
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