# Research Based on Modeling and Simulation of the Transient Regime in Controlled Switching with High Power Switches

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. The Switching Process

_{p}and C

_{p}, the arc energy decreases, and the cooling of the mechanism has a period which depends on the time constant of the circuit. In [18], it was demonstrated that the equation of the interruption time is presented in (1), where u

_{0}represents the constant arc voltage, which causes a resistive current [18].

_{p}, and on R

_{p}, is equal to zero. The transient recovery, at the appearance of the voltage between the circuit breaker contacts, presumes the charging of the C

_{p}capacity and causes the so-called time delay of the waveform, TRV [19].

_{arc}is steady-state arc resistance, the following can be derived from Equation (2):

_{0}is residual voltage on C

_{S}and C

_{t}and equivalent capacity $C=\frac{{C}_{S}{C}_{l}}{\left({C}_{S}+{C}_{l}\right)}$.

_{arc}and dR

_{arc}/dt, the following is obtained:

_{arc}, we can have three cases:

- If $\propto $R
_{arc}> R results in oscillations in which the amplitude increases, the system is unstable; - If $\propto $R
_{arc}< R, it is clear that the created regime is a depreciated regime; - If $\propto $R
_{arc}= R, a permanent oscillatory regime will result.

_{1}-main switch and an I

_{2}-auxiliary switch. Switching the I

_{2}to ON, it is possible to discharge the capacitor Co, which is initially loaded with the polarity from the figure. At the interruption of a short-circuit current i

_{c}(t) simultaneously with the switching I

_{1}to OFF, the switch I

_{2}is turned to OFF, so the intensity i(t) a of the current through the arc results from Equation (9).

_{k}(t) − i

_{c}(t),

## 4. Materials and Methods

#### 4.1. Simulation In Matlab of the Transient Regime of the SF6 Circuit-Breaker Commutation

ɸI = 0, resistive character,

ɸI∈(0,π/2], inductive character

#### 4.1.1. Simulation in Matlab of the Transient Regime of the SF6 Circuit-Breaker Disconnection

_{aper}(t) = I

_{def}·sin(φI

_{def})e

^{-}σ

^{t},

_{per}(t) = I

_{def}·sin(2πft − φI

_{def}),

_{aper}(t) + i

_{per}(t),

- i
_{aper}is the aperiodic component of the current in the transient regime; - i
_{per}is the periodic component of the current in the transient regime; - i(t) is the transient current, as the sum of the two components.

_{def}of the current I

_{def}represents the phase shift of the source and determines the load character, like in Equation (12). Based on the Equations (13)–(15), the components of the transient characteristic t∈(0,100) ms were obtained over time, as shown in Figure 9, using an inductive load, and as shown in Figure 10 for a capacitive load. In Figure 9, the voltage and current characteristic of a transient regime are represented, where σ = 0.01, so the defect is at a long distance and the periodic component of the current is equal to π/2, the amplitude of the defective current is I = 290.3 A. In this case, it is noted that the aperiodic component is above the horizontal axe where the transient current is found in the positive area.

_{def}= −π/2, the single-phase characteristic of the transient current I

_{def}= 290.3 A in the time interval t∈(0,100) ms, for a long distance defect, σsigma = 0.01 as in Figure 10, and it is found that the maximum transient current is negative [1].

_{def}= π/2, I

_{def}= 290.3 A; over time, t∈(−100,100) ms, for σ = 0.9, σ = 0.09, σ = 0.009 and σ = 0.0009.

_{breaker}= f (°C, V_DC, p), as shown in [31,32,33]. The calculation of the coefficient according to which the disconnection of the switch is studied is conducted based on measured values and saved in vectors. The coefficients will then be calculated by interpolation.

_{temp}(T) = 0.0026·T

^{2}− 0.0829·T + 21.482

_{temp}on the outdoor temperature on the disconnection of a circuit breaker.

- 2.

_{UDC}(UDC) = −0.2·UDC + 44

_{UDC}on the DC voltage supply on the disconnection of a circuit breaker.

- 3.

_{Ph}(P) = −0.3 P + 99

_{Ph}on the oil pressure on the disconnection of a circuit breaker.

_{breaker}parameter is made according to Equation (19) [35].

_{breaker}= C

_{temp}+ t

_{UDC}+ C

_{Ph},

_{1}= t

_{command}= 13 ms are presented.

_{1}= t

_{command}= 13 ms.

#### 4.1.2. Simulation in Matlab of the Transient Regime of the SF6 Circuit-Breaker Connection

_{temp}= f(T) on the connection of a circuit breaker is represented in Table 7. Taking into consideration the measured values, the equation which describes this dependency is presented in Equation (20).

_{temp}(T) = 0.0026·T

^{2}− 0.0829·T + 71.482

_{temp}on the outdoor temperature on the connection of a circuit breaker.

_{UDC}= f (UDC) on the disconnection of a circuit breaker is represented in Table 8. Taking into consideration the measured values, the equation which describes the dependency is presented in Equation (21).

_{UDC}(UDC) = −0.2·UDC + 44

**t**on the DC voltage supply on the connection of a circuit breaker.

_{UDC}- 4.
- The oil pressure dependency of time coefficient C
_{Ph}= f(P) on the connection of a circuit breaker is represented in Table 9. Taking into consideration the measured values, the equation which describes the dependency is presented in Equation (22).

_{Ph}(P) = −0.3·P + 99

_{Ph}on the oil pressure on the connection of a circuit breaker.

_{1}= t

_{command}= 5 ms.

## 5. Simulation Results, Industry Implementation and Related Discussion

#### 5.1. Simulation Results

#### 5.2. Industry Implementation

- The current monitoring function, which is carried out by displaying the station’s single-phase operation scheme in dynamic coloring mode as well as the electrical operating parameters of the equipment and installations that comprise the transformation station.
- The function of viewing information and detail screens, which can be achieved by accessing both the control screens and the dedicated surveillance screens for the existing units.
- The operator function, which includes connecting and disconnecting the user, transferring the remote control between levels of remote control and displaying the level at which it is, and inserting indicator boxes.

#### 5.2.1. Controlled Disconnection of the Load Based on the Command-and-Control System, Using a Circuit Breaker

- a static label reading “Switch maneuver”;
- a dynamic “Cancel” button for closing the window;
- two confirmation buttons for turning on the circuit breaker (“Disconnection” and “Controlled disconnection”).

- a static label with the word “Disconnect”;
- a „Cancel” button for closing the window;
- a confirmation button labeled as “Save Data” that allows the circuit breaker to be opened and data to be saved from the moment of controlled opening.

#### 5.2.2. Controlled Connection of the Load Based on the Command-and-Control System, Using a Circuit Breaker

- a static label with the words “Choice Circuit Breaker operation”;
- a dynamic “Cancel” button for shutting down the window;
- two confirmation buttons for selecting the circuit breaker operation (“Synchronized connection” and “Non-synchronized connection”);
- a dynamic “Controlled connection” button for using the controlled connection of the load;
- two confirmation buttons for activating the circuit breaker operation (“Activate Synchronizing” and “Un-activate synchronizing”).

- a static label with the word “Connection”;
- a “Cancel” button for closing the window;
- a confirmation button labelled as “Save Data” that allows the circuit breaker to be opened and data to be saved from the moment of controlled opening.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Rp | parallel resistance |

Cp | parallel capacitance |

Δt | interruption time |

Δt_{R} | interruption time caused by resistance |

Δt_{C} | interruption time caused by capacitance |

i_{L} | inductivity current |

u_{arc} | arc voltage |

i_{arc} | arc current |

R_{arc} | arc resistance |

C_{s} | source capacitance |

C_{l} | load capacitance |

I_{1} | main switch |

I_{2} | auxiliary switch |

Ro, Lo and Co | elements of oscillator branch |

v(t) | input voltage |

i(t) | input current |

φv | voltage phase shift |

φi | current phase shift |

f | frequency |

t_{delay} | delay time |

t_{breaker} | disconnected time |

t_{arc} | arc time |

t_{prearc} | prearc time |

i_{aper} | the aperiodic component of the current |

i_{per} | the periodic component of the current |

I_{def} | the amplitude of the current |

T | temperature |

P | oil pressure |

C_{temp} | temperature time coefficient |

t_{UDC} | DC voltage supply time coefficient |

C_{Ph} | oil pressure time coefficient |

t_{command} | connection/disconnection time command |

t_{disconnect} | disconnection time |

HVCB | high voltage circuit breaker |

GIS | gas insulated substations |

TRV | transient recovery voltage |

POW | point-on-wave |

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**Figure 3.**Modelling of the electric arc: (

**a**) electric scheme of the circuit; (

**b**) current variation [1].

**Figure 4.**The mathematical model used [1].

**Figure 6.**Disconnecting operation of circuit breaker with a control system: 1—disconnected command, 2—identify the zero point of the current, 3—delay time, 4—command to the breaker disconnected coil, 5—disconnected time, 6—separate contacts; 7—arc time, 8—end of the current flow.

**Figure 7.**Connecting operation of circuit breaker with a control system: 1—connected command, 2—identify the zero point of the voltage, 3—delay time, 4—command to the breaker connected coil, 5—connected time, 6—touch contacts; 7—beginning of current flow, 8—prearc time.

**Figure 11.**The voltage and current variation for inductive load, ɸIdef = π/2, Idef = 290.3 A; over time, t∈(−100,100) ms for σ = 0.9, σ = 0.09, σ = 0.009 and σ = 0.0009.

**Figure 12.**Dependency of

**C**on the outdoor temperature on the disconnection of a circuit breaker.

_{temp}**Figure 13.**Dependency of t

_{UDC}on the DC voltage supply on the disconnection of a circuit breaker.

**Figure 15.**The simulation of monophasic power supply system on the disconnecting process of the circuit breaker on t

_{1}= t

_{command}= 13 ms.

**Figure 16.**Transient uncontrolled switching diagram for inductive load, ɸIdef = π/2, Idef = 290.3 A, σ = 0.005, t

_{disconnect}= 31.221 ms.

**Figure 17.**Transient switching diagram for inductive load, ɸIdef = π/2, Idef = 290.3 A, σ = 0.005, t

_{command}= 50.121 ms, t

_{disconnect}= 77.375 ms.

**Figure 18.**Transient switching diagram for capacitive load, ɸIdef = π/2, Idef = 290.3 A, σ = 0.005, t

_{command}= 32.221 ms, t

_{disconnect}= 57.697 ms.

**Figure 19.**Transient switching diagram for capacitive, resistive and inductive load, ɸI

_{def}= −π/2; 0; π/2, for I

_{def}= 290.3 A, σ = 0.005, t

_{command}= 180.021 ms, t

_{dconnect}= 203 ms.

**Figure 20.**Dependency of

**C**on the outdoor temperature on the connection of a circuit breaker.

_{temp}**Figure 23.**The simulation of monophasic power supply system on the connecting process of the circuit breaker on t

_{1}= t

_{command}= 5 ms.

Parameters | Min. | Typ. | Max. |
---|---|---|---|

Frequency [Hz] | 48 | 50 | 52 |

Voltage control [V] | 187 | 242 | 255 |

Voltage connect control [V] | 187 | 242 | 255 |

Voltage disconnect control [V] | 154 | 241 | 255 |

Hydraulic pressure [bar] | 0 | 355 | 400 |

T [°C] | C_{temp} (ms) |
---|---|

40 | 21.5 |

20 | 22 |

0 | 22.5 |

−20 | 23 |

−30 | 24 |

−40 | 31 |

U Control (V) | t_{UDC} (ms) |
---|---|

UDC | |

187 | 6.6 |

192 | 5.6 |

203 | 3.4 |

209 | 2.2 |

221 | −0.2 |

232 | −2.4 |

241 | −4.2 |

252 | −6.4 |

255 | −7 |

Oil Pressure (bar) | C_{Ph} (ms) |
---|---|

310 | 6 |

316 | 4.2 |

321 | 2.7 |

326 | 1.2 |

333 | −0.9 |

337 | −2.1 |

342 | −3.6 |

346 | −4.8 |

350 | −6 |

Parameters | Values |
---|---|

Temperature [°C] | 23 |

Ucc [V] | 242 |

P [bar] | 330 |

tT | 21 |

tucc | −4 |

tp | 0 |

t5 | 17 |

t1 | 13 |

t2 | 26 |

Equation | Parameters | Values |
---|---|---|

i(t) = 0 | t2 | 26 |

t = f(T,U,P) | t5 | 17 |

SP2 = 1000/f/3 | sp2 | 10 |

nrp = t5/SP2 + 1 | Nrp | 2 |

t7 = t2 + nrp*SP2 | t7 | 46 |

t4 = t7 − t6 | t4 | 29 |

t3 = t4 − t2 | t3 | 3 |

T [°C] | C_{temp} (ms) |
---|---|

40 | 71.5 |

20 | 72 |

0 | 72.5 |

−20 | 73 |

−30 | 74 |

−40 | 81 |

U Control (V) UDC | t_{UDC} (ms) |
---|---|

187 | 6.6 |

192 | 5.6 |

203 | 3.4 |

209 | 2.2 |

221 | −0.2 |

232 | −2.4 |

241 | −4.2 |

252 | −6.4 |

255 | −7 |

Oil Pressure (bar) | C_{Ph} (ms) |
---|---|

310 | 6 |

316 | 4.2 |

321 | 2.7 |

326 | 1.2 |

333 | −0.9 |

337 | −2.1 |

342 | −3.6 |

346 | −4.8 |

350 | −6 |

Parameters | Values |
---|---|

Temperature [°C] | 18 |

Ucc [V] | 238 |

P [bar] | 325 |

tT | 71 |

tucc | −4 |

tp | 2 |

t5 | 69 |

t1 | 5 |

t2 | 11 |

Equation | Parameters | Values |
---|---|---|

i(t) = 0 | t2 | 11 |

t = f(T,U,P) | t5 | 69 |

SP2 = 1000/f/3 | sp2 | 10 |

nrp = t5/SP2 + 1 | nrp | 8 |

t7 = t2 + nrp*SP2 | t7 | 96 |

t4 = t7 − t6 | t4 | 27 |

t3 = t4 − t2 | t3 | 38 |

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**MDPI and ACS Style**

Panoiu, C.; Ciulica, D.; Panoiu, M.; Mezinescu, S.
Research Based on Modeling and Simulation of the Transient Regime in Controlled Switching with High Power Switches. *Machines* **2021**, *9*, 99.
https://doi.org/10.3390/machines9050099

**AMA Style**

Panoiu C, Ciulica D, Panoiu M, Mezinescu S.
Research Based on Modeling and Simulation of the Transient Regime in Controlled Switching with High Power Switches. *Machines*. 2021; 9(5):99.
https://doi.org/10.3390/machines9050099

**Chicago/Turabian Style**

Panoiu, Caius, Dumitru Ciulica, Manuela Panoiu, and Sergiu Mezinescu.
2021. "Research Based on Modeling and Simulation of the Transient Regime in Controlled Switching with High Power Switches" *Machines* 9, no. 5: 99.
https://doi.org/10.3390/machines9050099