In this post, we will analyze the circuit below to synthetically test a circuit breaker (CB) in the event that the circuit breaker is open and closed. The idea is to solve the electrical transition mathematically, but the next approach will be based on simulation analysis of synthetic tests.
According to , synthetic tests are based on a two-part test performed in one pass. “The test is performed by connecting a moderate voltage source that supplies the full primary fault current with a secondary high voltage, low current source that provides a precisely timed high frequency high voltage pulse close to the natural zero current of the high current primary. The purpose of the synthetic tests is to reproduce conditions that accurately simulate the conditions inside the circuit breaker during periods of strong arcing and high voltage return” .
Many synthetic test schemes have been developed, but in practice they are all just variations of the basic voltage or current injection schemes :
1. Current injection method
This method is characterized by the injection of a current pulse supplied from a high voltage source.
The two main methods of current injection are:
- Parallel power injection circuit
Series current injection circuit
2. Voltage supply method
In practice, all testing laboratories more often use the parallel flow injection technique (Figure 1)  , detailed below:
The high-current source consists of:
- short circuit generator,
- Spare CB to protect the test generator,
- A series of current limiting chokes,
- To change gear,
- An isolation switch (IB) that isolates the power circuit from the high voltage circuit.
Part of the high-voltage circuit consists of:
- A high-voltage source consisting of a capacitor bank charged to a specified high voltage level. One side of the activated spark gap (TG) is connected in series with the capacitor.
- The other side of the trigger gap is connected to the reactor group for frequency adjustment.
- These shunt reactors are connected in series with the short-circuiting network of the TRV line (SLF), which consists of a combination of capacitors and shunt reactors connected in most cases in the classic configuration of the pi (π) circuit.
The schematic diagram of parallel current application, shown in Figure 1, is shown in a more simplified way in Figure 6 (in the red rectangular part of the circle of our original problem). The test starts by closing the ON (MS) switch, causing current to flow i1, from a high current source through IB and the test switch (TB). As the current approaches the zero crossing, the spark is activated at time t1(see figure 2) introduced current i.e2it starts to flow. Current and1+ w2flows through TB until time t2has been achieved. This is the time when mainstream1tends to zero and when I divide the two power sources. currently t3the injected current is intermittent and the high voltage supplied by the high voltage source gives the desired TRV which then appears across the terminals of the breaker under test.
IEC standard for transient recovery voltage (TRV) envelope.
The short-circuit test requires a circuit with a response specified in IEC standards  to control the TRV. The TRV produced as a result of the test must meet the specifications required by the standards.
The case of two parameters 
The case of four parameters 
Based on what we want to solve and what we have explained above regarding the CB synthetic tests, the parallel current injection model in MATLAB/Simulink is developed below (files can be emailed on request):
Based on ANSI/IEEE standard. C37  The operation of the parallel current injection circuit can be described as follows:
The test starts by closing the circuit breaker allowing the current to flow i1current through the choke limiting the current LC, additional CB in TB.
Before the interaction interval, the spark is activated at time t1, (see Figure 1) and current i2is injected and flows through the high voltage reactor Lw, TB.
Stroom by TBis and1not any more2by time t2when the auxiliary switch separates the power circuit from the voltage circuit.
The current through TB is i2by time t3when the TB breaks and the transient recovery voltage (TRV) is squeezed through the TB.
Figure 9 shows the stress in TB before and after fracture. As shown, an arc voltage appeared when the contacts were separated on the TB. Then, when zero current is reached, the TB fully opens its contacts while a very small amount of current flows through the TB.
Figure 10 shows the short-circuit current imposed on TB by the generator. The course of the short-circuit current was influenced by the DC and AC components in the tested circuit.
In the synthetic test, a current pulse is also injected for a few microseconds before the fault current reaches zero, creating a reverse voltage on the TB. Therefore, the capacitor bank must be fully charged before it can be used to provide injection current. Figure 11 shows the charging and discharging process of the capacitor bank.
Figure 12 shows the current drawn by the capacitor bank to provide a recovery voltage to TB after the auxiliary switch isolates the fault current from TB. The magnitude of the input current must be adjusted in such a way that the rate of change of the input current (di/dt) and the rate of change of the corresponding rated power current (di/dt)ulare equal at their current zero point. The start time of the current pulse is controlled so that the time when the arc is powered only by the introduced current does not exceed one quarter of the period of the introduced frequency .
The total current flowing through the TB during the synthetic test is shown in Figure 13. The most important part of the result of this simulation is the injection current effect, as shown in Figure 14. It is recommended  that the frequency for the injected. The current must be between 300 and 1000 Hz. The limits depend mainly on the characteristics of the arc voltage.
The final analysis of the synthetic simulation should show a tuberculosis failure result. If power is not restored, the TB has failed as a troubleshooting device. Figure 15 shows that the TB does not isolate the fault as this allows the fault current to reactivate while the fault current continues to flow through the TB after interruption.
The results obtained by simulating the synthetic test were performed by instantaneous injection. Basically, the current injection method and the voltage injection method are the same. As mentioned earlier, the only difference is that the output of the high-voltage source is introduced through the open contacts of TB after the short-circuit current is interrupted. In order to carry out the simulation, it is recommended to model both test methods. However, the voltage injection method is not very popular as a test method because it requires a very precise voltage injection time.
Basically, the main disadvantage of a true synthetic test is that these tests are primarily a single loop test where it is still very difficult to quickly reconnect with extended arc times. Another disadvantage is that this method is not suitable for testing switches whose impedance is connected in parallel with the switch contacts. In this case, it is likely that full recovery voltage will not be achieved due to power limitations of the high voltage source .
To simulate a short circuit trip, the test breaker is modeled to reclose after tripping to demonstrate that the breaker will not clear the short circuit. The arc does not extinguish when the contacts open, while the circuit breaker maintains the flow of the short-circuit current.
Appendix: Explanation of the elements of the developed model
As mentioned, the synthetic test consists of two main parts: a current source and a voltage source. The current source is a short-circuit current source with the maximum possible current. It has a large current at low voltage. In the case of a voltage source, it is a high voltage and low current power supply. In the actual synthetic test, the voltage source is a fully charged capacitor bank before it can be used for testing. For simulation purposes, this capacitor can be modeled as a DC voltage source. The spark gap can be modeled as a controlled timer switch because in an actual synthetic test, the spark is triggered by a specially controlled circuit. An additional circuit is used to control the spark, which is activated at the desired moment and just before the short-circuit current reaches its natural zero.
Purpose: to provide the energy consumed during the test (high current flowing through the TB for a short time). For the purposes of the simulation, the generator is modeled as an alternating current source with impedance RL.
Notes: Transient and subtransient reactances should be as low as possible to ensure maximum short-circuit current (leakage flux should be minimal, and individual windings should be connected as close to each other as possible) .
Purpose: To protect the equipment on the test bench from the effects of a TB that does not interrupt the short-circuit current.
Auxiliary circuit breaker
Purpose: To isolate the power source from the high voltage source, which should exceed the circuit breaker under test.
Make a change
Purpose: to apply the short-circuit current at the desired time during the test. This switch is used to connect the generator to the test circuit at a precise point in the voltage waveform, and high-speed operation is necessary to ensure precision at the closing point. The preload during disconnector closing should be minimal as it may affect the compliance of the check point on the wave .
Purpose: It is located between the generator and the transformer (amplifies the voltage from the voltage source to the secondary side. There is no need to use it if the voltage source already had the desired capacity) along with resistors to test the circuit for checking currents within limits before the current arrives circuit power factor 
Test Broker (TB)
Destination: tested switch. It can be single phase or poly phase depending on the synthetic test circuit used.
TRV project wheel
Purpose: To control the reverse voltage transient (TRV) and reverse voltage rise rate (RRRV).
Charged capacitor bank (high voltage source)
Purpose: high voltage power supply to the test switch. Capacitor banks rated up to hundreds of MVAR are required for circuit breaker testing in switching capacitor installations, and are also used for no-load testing of overhead lines and cable circuit breakers. Capacitors are also needed to control the circuit's natural frequency during normal short-circuit tests . The capacitor bank model provides a voltage of 800 kV.
Purpose: to apply high voltage to TB at the desired moment. It controls the moment of injection on the current and voltage diagrams.
Artificial Short Line (SL)
Purpose: To simulate the short-circuit distance on the overhead line from the switchgear, i.e. to simulate different conditions for single wires and bundles. Most test stations use a dummy line consisting of several series-parallel combinations of inductance and capacitance.
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