It’s all about reactive power… The four main means for the generation of reactive power are: Synchronous alternators Synchronous compensators (SC) Static var compensators (SVC) and Banks of static capacitors 1. Synchronous alternators Synchronous alternators are the main machines used for the generation of electrical energy. Besides, without going into technical details, by acting on […]

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]]>**The four main means for the generation of reactive power are:**

- Synchronous alternators
- Synchronous compensators (SC)
- Static var compensators (SVC) and
- Banks of static capacitors

**Synchronous alternators** are the main machines used for the generation of electrical energy.

They are intended **to supply electrical power to the final loads** through transmission and distribution systems.

Besides, without going into technical details, by acting on the excitation of alternators, it is possible to vary the value of the generated voltage and consequently to regulate the injections of reactive power into the network, so that the voltage profiles of the system can be improved and the losses due to joule effect along the lines can be reduced.

They are synchronous motors running no-load in synchronism with the network and having the only function **to absorb the reactive power in excess (under-excited operation)** or to supply the missing one (overexcited operation).

Where:

**E**= e.m.f. induced in the stator phases**V**= Phase voltage imposed by the network to the alternator terminals I : stator current**X**= Stator reactance_{s}

These devices are used mainly in definite nodes of the power transmission and sub-transmission network for the regulation of voltages and of reactive power flows. The use of synchronous compensators in power distribution networks is **not favourable from an economic point of view** because of their high installation and maintenance costs.

The considerable development of power electronics is encouraging the replacement of synchronous compensators with **static systems for the control of the reactive power** such as for example **TSC** (thyristor switched capacitors) and **TCR** (thyristor controlled reactors).

These are an electronic version of the reactive power compensation systems based on electromechanical components in which, however, the switching of the various capacitors is not carried out through the opening and closing of suitable contactors, but through the control carried out **by couples of antiparallel tyristors**.

TSC allow a **step-by-step control of the reactive power delivered by groups of capacitors**, whereas with TCR a continuous control of the reactive power drawn by the inductors is possible. By coupling a TSC with a TCR it is possible to obtain a continuous modulated regulation of the delivered/drawn reactive power.

From the point of view of applications, these devices are used above all in **high and very high voltage networks**.

A capacitor is a **passive dipole** consisting of two conducting surfaces called plates, isolated from one another by a dielectric material.

The system thus obtained is impregnated to prevent the penetration of humidity or of gas pockets which could cause electrical discharges.

The last generation capacitors are **dry-type** and undergo a specific treatment which improve their electrical characteristics. Using dry-type capacitors there is no risk of pollution because of the incidental leak of the impregnating substance.

**According to the geometry of the metal plates, it is possible to have:**

- Plane capacitors;
- Cylindrical capacitors;
- Spherical capacitors.

**The 4 main parameters which characterize a capacitor are:**

**The rated capacitance C**– the value obtained from the rated values of power, voltage and frequency of the

capacitor;**The rated power Q**– the reactive power for which the capacitor has been designed;_{n}**The rated voltage U**– the r.m.s. value of the alternating voltage for which the capacitor has been designed;_{n}**The rated frequency f**– the frequency for which the capacitor has been designed._{n}

When an alternating voltage is applied across the plates, the capacitor is subjected to charge and discharge cycles, during which it stores reactive energy (capacitor charge) and injects such energy into the circuit to which it is connected (capacitor discharge).

**Such energy is given by the following relation:**

where:

**C**is the capacitance;**U**is the voltage applied to the terminals of the capacitor.

Because of their capability of storing and delivering energy, capacitors are used as basic element for the realization of **power factor correction banks** (for all voltage levels) and of static devices for the regulation of reactive power.

In particular, the power factor correction capacitors used for low voltage applications are constituted by **single- phase components of metalized polypropylene film** and can be of the **self-healing type**.

In these capacitors, the dielectric part damaged by a discharge is capable of self-restoring; in fact, when such situations occur, the part of the polypropylene film affected by the discharge evaporates due to the thermal effect caused by the discharge itself, thus restoring the damaged part.

**Reference //** Power factor correction and harmonic filtering in electrical plants – ABB

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]]>Factory tests The remainder of the twelve factory tests are briefly summarized below. The details of the test set connections and formulas of some of the listed tests are already described in separatly published articles, and for the rest you are directed to ANSI/IEEE Standard C57.12.90 for these details. This list is not complete, there […]

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]]>The remainder of the twelve factory tests are briefly summarized below. The details of the test set connections and formulas of some of the listed tests are already described in separatly published articles, and for the rest you are directed to **ANSI/IEEE Standard C57.12.90** for these details.

This list is not complete, there are few tests missing, not mentioned here, like Turn ratio test or Measurement of voltage ratio and check of phase displacement, but you can find them also separatly published at EEP (use Search).

- No-Load Losses
- No-Load Excitation Current
- Load Losses and Impedance Voltage
- Dielectric Tests
- Switching Impulse Test
- Lightning Impulse Test
- Partial Discharge Test
- Insulation Power Factor
- Insulation Resistance
- Noise Measurement
- Temperature Rise (Heat Run)
- Short-Circuit Test

The tests measures the no-load losses at specified excitation voltage and a specified frequency. Sine-wave voltages are used unless a different waveform is inherent in the operation of the transformer.

The recommended method is the **average-voltage voltmeter method**, employing two parallel-connected voltmeters. One voltmeter is an average-responding but RMS calibrated voltmeter and the other voltmeter is a true RMS-responding voltmeter.

The test voltage is adjusted to the specified value as read by the average-responding voltmeters. The readings of both voltmeters are used to correct the no-load losses to a sine-wave basis.

This current is measured in the winding used **to excite the transformer with the other windings open-circuited**. It is generally expressed in percent of the rated current of the winding. No-load excitation current is not sinusoidal and contains, as we have seen, odd harmonics (predominantly third harmonic current).

The ammeter used to record the no-load excitation current is an RMS meter which reads the square root of the sum of the squares of the harmonic currents.

The transformer must be in a **specific state** before the load losses and impedance voltage are measured. The temperature of the insulating liquid must be stabilized and the difference between the top and bottom oil temperatures shall be less than 5°C.

The winding temperatures must be measured (using a resistance method) before and after the test **and the average taken as the true temperature**. The difference in the winding temperature before and after the test must not exceed 5°C.

**The two test methods for measuring load losses and impedance voltage are:**

- Wattmeter-voltmeter-ammeter method and
- Impedance bridge method.

These tests generally apply a reduced voltage to one set of windings with the other set of windings short-circuited. For three-winding transformers, these tests are repeated for each combination of windings taken two at a time.

These tests consist of **applied-voltage tests** and **induced-voltage tests**.

**Applied-voltage tests** apply a high voltage to all bushings of a winding, one winding at a time, with the other windings grounded. A 60 Hz voltage is increased gradually over 15 s and held for 40 s and reduced to zero over 5 s.

**Induced-voltage tests** apply a high voltage across a winding with the other windings open-circuited in order to test the quality of the turn-to-turn insulation. In order to prevent core saturation at the higher excitation voltage, the frequency of the induced-voltage test is increased (**typically around 120 Hz**). The induced voltage is applied for 7200 cycles or 60 s, whichever is shorter.

The switching impulse test applies **a switching impulse wave between each high-voltage line terminal and ground**.

The test series consists of one reduced voltage wave (50%– 70% of specified test level) followed by two full-voltage waves. Either positive or negative polarity waves, or both, may be used. A voltage oscillogram is taken for each applied wave. The test is successful if there is no sudden collapse of voltage. Successive oscillograms may differ **because of the influence of core saturation**.

The test sequence consists of **one reduced full wave**, **two chopped waves**, and **two full waves**. Tap connections are made with the minimum effective turns in the winding under tests and regulating transformers are set to the maximum buck position. Oscillograms are taken of each wave.

The general technique for interpreting the results is **to look for differences in the shapes of the reduced full wave** and the two full waves, which indicate turn-to-turn insulation failure.

Additional test criteria are found in **IEEE Std. C57.98-1993**. The impulse tests probably have the highest likelihood failures among all of the factory tests that are typically performed.

This test detects **radio-frequency (0.85–1.15 MHz) noise** generated from partial discharges within voids in the insulation. An applied voltage is gradually increased **until partial discharge starts to occur**, which is the inception voltage. The voltage is then decreased until the partial discharge stops, which is the extinction voltage.

The extinction voltage must be less than the operating voltage of the transformer; otherwise, once partial discharge starts in the field (due to some voltage transient), it would continue indefinitely and possibly cause damage or failure.

**Insulation power factor** is the ratio of the power dissipated in the insulation in watts to the apparent power (volt-amperes) under a sinusoidal voltage. The applied 60 Hz voltage of this test is generally lower than the operating voltage of the trans- former. **The Doble Test Set** is designed specifically to carry out this test.

Portable versions are used to measure the insulation power factor of transformers in the field. This test usually must be done by a trained technician. The test results are temperature-corrected to a reference temperature of 20°C.

This test applies a **high-voltage DC voltage** to one winding at a time with the other windings grounded. The leakage current is measured and the insulation resistance is calculated using Ohm’s law.

A **Insulation resistance test set** is designed specifically to carry out this test, and its meter is calibrated in megohms in order that the calculation may be avoided. The Megger as well as other manufacturers has a portable instrument that can easily carried around in the field.

**The noise measurement test** is carried out while the transformer is energized at rated voltage with all of the cooling equipment running. Room geometry can greatly affect the measurements, so it is preferable that the transformer be inside an anechoic chamber. However, if such a chamber is not available, no acoustically reflecting surface may be **within 3 m** of the measuring microphone other than the floor or ground.

The recording microphones are positioned in **1 m intervals around the perimeter of the transformer**, with no fewer than four (4) microphone positions for small transformers..

Sound power levels are measured over a specified band of frequencies. The sound power levels are converted into **decibels (dB).**

The transformer is energized at rated voltage **in order to generate core losses**. The windings are connected to a loading transformer that simultaneously circulates rated currents through all of the windings in order to develop load losses.

Naturally, the excitation voltage and the applied circulating currents are electrically 90° apart to minimize the KW requirements for this test. Nonetheless, a large power transformer can consume **up to 1 MW of total losses** and the heat run test is an expensive test to perform.

Therefore, in order to reduce the total expense, heat run tests are **normally performed on only one transformer** on a purchase order for multiple transformers, unless the customer chooses to pay for testing additional units.

The short-circuit test is generally reserved for a sample transformer **to verify the design of a core and coil assembly** unless the customer specifies that a short-circuit test be performed on transformers that are purchased.

The customer should be cognizant of **the ever-present risk of damaging the transformer** during short-circuit tests.

A low-voltage impulse (LVI) current waveform is applied to the transformer before and after the applications of short-circuit test. The ‘‘before’’ and ‘‘after’’ oscillograms of the LVI currents are compared for significant changes in waveshape that could indicate mechanical damage to the windings.

**Reference //** Power Transformers Principles and Applications – John J. Winders, Jr.

(Purchase from Amazon)

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]]>Transformer Price and Losses The Connection Losses and purchase price should be considered when deciding which transformer to purchase. The purpose of this technical article is to present a uniform approach that can be used to determine the dollar value of these losses over the life of the transformer. Below is typical wording of a transformer loss evaluation clause […]

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]]>Losses and purchase price should be considered when deciding which transformer to purchase. The purpose of this technical article is to present a uniform approach that can be used to determine **the dollar value of these losses** over the life of the transformer.

Below is typical wording of a transformer loss evaluation clause for insertion into bidding documents that specifies how losses will be evaluated.

- No-Load Losses
**$/kW 2450** - Load Losses
**$/kW 1304** - Auxiliary Losses
**$/kW 756**

The cost of losses for each transformer will be calculated by multiplying the appropriate dollars/kW values above by the **guaranteed load losses at 55°C rating** and no-load losses at **100% voltages**. This cost will be added to the bid price for evaluation.”

Using the loss evaluation factors given above, determine which manufacturer’s transformer has the lowest evaluated cost including losses.

Manufacturer A’s Transformer | Manufacturer B’s Transformer | |

Bid price | $424,500 | $436,000 |

No -load losses | 59 kW | 53 kW |

Load losses at 50 MVA (at 55°C temperature rise) | 224 kW | 218 kW |

Auxiliary losses (at 50 MVA 55°C temperature rise) | 2.0 kW | 2.5 kW |

Manufacturer A’s Transformer | Manufacturer B’s Transformer | |

Bid Price | = $424,500 | = $436,000 |

Total cost ofNo-load Losses | 59 kW (2450 $/kW) = $144,550 | 53 kW (2450 $/kW) = $129,850 |

Total cost ofLoad Losses | 224 kW (1304 $/kW) = $292,096 | 218 kW (1304 $/kW) = $284,272 |

Total cost ofAuxiliary Losses | 2.0 kW ( 756 $/kW) = $ 1,512 | 2.5 kW (756 $/kW) = $1,890 |

TOTAL COST // | = $862,658 | = $852,012 |

Although the transformer from Manufacturer A has the lowest bid price, it is obvious that the transformer from Manufacturer B has **the lowest evaluated total cost**.

In addition to giving loss evaluation values, **the bid documents should also have penalty values** that the manufacturer is to be charged for every kilowatt by which the actual tested transformer losses exceed the guaranteed losses upon which the bids are evaluated.

It is important to have such penalty values in order to give an incentive to the manufacturers to provide the most accurate guaranteed loss values possible. The penalty values should be expressed in the same dollars per kW manner as the bid evaluation values but should be somewhat higher.

An increment of **approximately 20 percent** is recommended.

**The three different types of transformer losses that should be evaluated separately are: **

- Load losses (sometimes called copper or coil losses);
- No-load losses (sometimes called core or iron losses); and
- Auxiliary losses (electric fan losses, other such equipment losses).

**Load losses** are primarily from the **I ^{2}R losses in the transformer windings** and

**No-load losses** consist of the hysteresis and the eddy current losses in the iron core of the transformer and the I^{2}R losses in the windings due to the excitation current.

**Auxiliary losses** consist of the power necessary to drive the auxiliary cooling pumps and fans.

The formulae below yield the total costs of the losses that should be added to the purchase price of the transformer as shown in the example above:

Where:

**G**= peak ratio**K**= peak responsibility factor**SI**= the system capital investment in dollars per kilowatt required to supply the power losses of the transformer;**8760**= the number of hours in a year**EC**= the cost of energy in dollars per kilowatt-hour;**FCR**= fixed charge rate for capital investment expressed as a decimal in dollars per dollar of investment;**LFA**= the loss factor for auxiliary equipment;**LFT**= the transformer loss factor which is the ratio of average transformer losses to peak transformer losses;**TNLL**= the transformer’s guaranteed no-load losses in kilowatts;**TLL**= the transformer’s guaranteed load losses in kilowatts;**TAL**= the losses due to transformer auxiliary equipment in kilowatts

**The System Investment (SI) charge** is the cost of generation and transmission facilities per kilowatt necessary to supply the additional demand resulting from the transformer losses at the system peak.

Since a transformer located directly at a generating station does not require an investment in transmission facilities, the SI value used to evaluate the losses in the generating station transformer should be **less than the SI of a transformer** to be located at the receiving end of a transmission line.

One method for determining the SI value involves **adding the construction cost (dollars per kilowatt)** of a recently completed or soon to be completed generating station to the cost of the transmission facilities (dollars per kilowatt) required to connect the transformer to the plant.

If power is purchased rather than self-generated, the SI value can be determined **by dividing the demand charge in dollars per kW per year by the fixed charge rate (FCR)**. Since there is more than one method of evaluating the SI value, the method that is judged to yield the most realistic results should be used.

**The fixed charge rate (FCR)** represents the yearly income necessary to pay for a capital investment. FCR is expressed as a percentage of capital investment. The rate covers all costs that are fixed and do not vary with the amount of energy produced.

The rate includes interest, depreciation, taxes, insurance, and those operations and maintenance expenses that do not depend on system kilowatt-hours sold. The interest rate used should be the same as the interest rate of the loan acquired to purchase the transformers. If loan funds are not used, a blended rate of the interest earned on deposited funds should be used.

**The practice of including some operations and maintenance expenses in the fixed charge rate is a matter of judgment.** Some typical values for the components of the carrying charge rate are as follows:

Interest | 7.5% |

Depreciation | 2.75% |

Insurance | 0.60% |

Taxes | 1.00% |

Operations and Maintenance Carrying | 2.76% |

Carrying Charge Rate | 14.61% |

**The energy charge (EC)** is the cost per kilowatt-hour for fuel and other expenses that are directly related to the production of electrical energy.

Although the costs per kilowatt-hour will vary with the level of demand, a single energy charge representing an average cost per kilowatt-hour throughout the load cycle should be used for the sake of simplicity.

Equations 1 and 2 are based on the assumption that the energy charge remains constant throughout the life of the transformer. If power is purchased, EC will be the kWh (or energy) cost of power.

**The peak responsibility factor (K)** is intended to compensate for the transformer peak load losses not occurring at the system peak losses. This means that only a fraction of the peak transformer losses will contribute to the system peak demand.

**The value of K can be determined from:**

**NOTE:** It should be pointed out that K is squared in Equations 2 and 3 because K is a ratio of loads while losses are proportional to the load squared. Any value of K that seems appropriate can be used.

**The following are recommended values that appear to be reasonable.**

Transformer Type | K | K^{2} |

Generator Step-up | 1.00 | 1.00 |

Transmission Substation | 0.90 | 0.81 |

Disrtribution Substation | 0.80 | 0.64 |

**The transformer loss factor** is defined as the ratio of the average transformer losses to the peak transformer losses during a specific period of time. For the sake of simplicity, the equations assume that the transformer loss factor is a constant and that it does not change significantly over the life of the transformer.

**The transformer loss factor can be determined directly using the equation:**

LFT can also be approximated from the load factor (the average load divided by the peak load for a specified time period) using the empirical equation below:

Where:

Load factor is the ratio of the average load over a period of time to the peak load occurring in that period. The load factor is a commonly available system parameter. **The one-hour integrated peak value should be used.**

The peak ratio is defined by the equation:

For the peak annual transformer load, **the one hour integrated peak value should be used**. The purpose of the peak ratio is to relate the value of Equation 2 to the full rated transformer load and not to the peak transformer load that would otherwise result if G were not in the equation.

If the total kVA of all transformers is known for your system and the peak kW (or kVA) load is known, then the average peak ratio for your system would be:

**If the peak kW is known, but the peak kVA is unknown, assume a reasonable power factor on peak and calculate peak kVA as follows:**

kVA = kW / power factor

If the transformer being purchased has a peak ratio different from the average, use that value. If the transformer will be installed at a known substation, use the billing data and assumed load growth for that substation.

The equations above are based on the assumption that **the peak annual transformer load remains the same throughout the life of the transformer**. If the load on the transformer is expected to increase annually, then use a reasonable equivalent level yearly peak load value based on experience even though the expected peak loading value will increase every year.

**The auxiliary loss factor** compensates for the transformer auxiliary equipment that operates during only part of the transformer’s load cycle. For a transformer with two stages of cooling:

The choice of the proper probabilities in the above equation is a matter of judgment based on historical system loading patterns. It is expected that the above probabilities under normal loading patterns will be extremely low.

Since energy use and losses associated with transformer auxiliaries are extremely small over the life of the transformer, they could be ignored. The capital cost associated with auxiliaries are significant and should be considered.

Download free MS Excel Spreadsheet for calculation of transformer losses

**Reference //** Guide for the Evaluation of Large Power Transformer Losses – United States Department of Agriculture – Rural Utility Service

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]]>Inputs for Coordination Calculation A 440 V 60 Hz switchboard feeds a 4-wire distribution board for small loads such as socket outlets. The switchboard has a fault making capacity of 100kA rms. After applying diversity factors to the loads the total load current is 90 A. Moulded case circuit breakers (MCCBs) rated at 16 A […]

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]]>A 440 V 60 Hz switchboard feeds a **4-wire distribution board** for small loads such as socket outlets. The switchboard has a fault making capacity of **100kA rms**. After applying diversity factors to the loads the total load current is **90 A**. Moulded case circuit breakers (MCCBs) rated at **16 A** and **32 A** are to be used for the loads.

The installation will use cables having copper conductors and XLPE insulation. The cable from the switchboard to the distribution board is **20 metres in length**.

A typical load cable is **15 metres in length** and will carry a current of **29 A** at a **power factor of 0.85** lagging.

**Ignore the presence of induction motors at the switchboard and find the following:**

- Rating of the incoming circuit breaker.
- Size of the incoming cable.
- Size of the load cable.
- Check that the MCCB coordination is complete.

**The following sequence will be used to calculate the results:**

- Choose the upstream MCCB at the switchboard and its settings
- Choose the incoming feeder cable
- Choose the downstream load MCCB and its settings
- Find the upstream fault source impedance
- Find the cut-off, or let-through, current from the switchboard
- Find the impedance of the incoming cable
- Find the impedance of the load cable
- Find the fault current at the distribution board, point B
- Find the fault current at the beginning of the load cable, point C
- Find the fault current at the end of the load cable, point D
- Check the peak making capacity and peak let-through capacity of the MCCBs chosen above
- Find the highestI-squared-t value for the upstream MCCB
- Calculate a suitable size for the load cable to satisfy the I
^{2}t duty - Calculate the volt-drop in the load cable
- Select the largest conductor size from the above calculations
- Plot the results (coordination curve)

From a manufacturer’s data sheet a **125 A MCCB with an adjustable 100 A thermal release** is chosen. The thermal release is set to **90 A** to match the total load.

From a manufacturer’s data sheet several cables can be compared for the same ambient conditions and laying arrangements. **Their details are:**

- 50 mm
^{2}cable, maximum current 124 A, R = 0.492, X = 0.110 ohms/km. - 70 mm
^{2}cable, maximum current 159 A, R = 0.340, X = 0.106 ohms/km. - 95 mm
^{2}cable, maximum current 193 A, R = 0.247, X = 0.093 ohms/km.

The **70 mm**^{2} cable is chosen since the rating of the 50 mm^{2} cable is just too low.

From a manufacturer’s data sheet a **32 A MCCB with an adjustable 32 A thermal release** is chosen. The thermal release is set to **29 A** to match its load.

For a prospective symmetrical fault current of **100 kA rms** the **upstream fault source impedance Z _{up}** is:

From a manufacturer’s data sheet a **125 A MCCB** has a **let-through current I _{p} of 25 kA peak** for a

The **impedance Z _{c1}** of the incoming cable is:

The **impedance Z _{c2}** of the incoming cable is:

From a manufacturer’s data sheet several cables can be compared for the same ambient conditions and laying arrangements. Their details are:

- 6 mm
^{2}cable, maximum current 33.8 A, R = 3.91, X = 0.130 ohms/km. - 10 mm
^{2}cable, maximum current 46.7 A, R = 2.31, X = 0.126 ohms/km.

The **6 mm**^{2} cable is chosen provisionally, since its rating is above the **32 A rating of the MCCB that feeds it**.

The **impedance Z _{c2}** of the load cable is:

From a manufacturer’s data sheet **the contact impedance** data for low voltage MCCBs are:

MCCB (Rating in Amps) | Resistance (in Ohms) | Reactanse (in Ohms at 60Hz) |

16 | 0.01 | neglect |

20 | 0.008 | neglect |

25 | 0.0065 | neglect |

32 | 0.005 | 0.000009 |

50 | 0.0027 | 0.000016 |

63 | 0.002 | 0.000025 |

80 | 0.0014 | 0.000042 |

100 | 0.0011 | 0.00007 |

125 | 0.0008 | 0.0001 |

160 | 0.00055 | 0.00015 |

200 | 0.0004 | 0.0002 |

250 | 0.00029 | 0.00027 |

320 | 0.0002 | 0.0004 |

Hence **the upstream MCCB impedance Z _{m1}** is

The **fault making current I _{fb}** is:

Where **V _{p}** is the line-to-neutral voltage. Locate

Hence the downstream MCCB impedance** Z _{m2} is 0.005+j0.000009 ohms**. Add this to

The fault making current **I _{fc}** is:

Locate **the point S** for** 17,443 A** on the prospective curve in Figure 1.

**Add Z _{c2} to Z_{fc}** to give the fault impedance

The **fault making current I _{fd}** is:

Locate **the point U for 3473 A** on the prospective curve in Figure 1.

The following manufacturer’s data are typical for **125 A** and **32 A MCCBs**:

MCCB Rating | Making capacity | Let-through capacity kA _{peak} (cut-off) | |

kA_{rms} | kA_{peak} | ||

32 A | 95 | 209 *** | 6.0 |

125 A | 132 | 290 *** | 25.0 |

******* Approximate values of the doubling factor taken to be **2.2**

Hence the peak making capacity of the **32 A MCCB** is well in excess of the let-through peak current of the **125 A MCCB**.

Locate two points **P** and **Q** on the curve of the upstream MCCB as follows,

Point | Current in p.u. | Current in Amps | Time in seconds | I^{2}t |

P | 14 | 406 | 6 | 989016.0 |

Q | 602 | 17,450 | 0.0016 | 487204.0 |

**Hence I ^{2}t at P exceeds that at Q.**

For XLPE cables the **‘k factor’** for the I^{2}t is** 143**. The cross-sectional area A is:

The next standard cross-sectional area is **10 mm**^{2}.

The usual limit to volt-drop in three-phase cables feeding static loads is **2.5% at full load**.

Where, **I _{flc} = 29 A**,

which is well within the limit of **2.5%**.

Comparing the conductor sizes found in **13.** and **14.** gives the **larger as 10 mm ^{2}**, and this size should be used. Revise the calculation of the fault current

Add **Z _{c2}** to

The **fault making current I _{fd}** is:

The results are plotted in Figure 1.

**Refrence //** Switchgear and Motor Control Centres – Handbook of Electrical Engineering: For Practitioners in the Oil, Gas and Petrochemical Industry by Alan L. Sheldrake (Download here)

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]]>Motor starting operations The problems connected to motor starting operations are fundamentally linked to the type of motor which a determined motor operational torque “CM” offers, to the starting modality and to the connected load which has a determined load torque “C ”. A generic curve of the above mentioned quantities is shown in the Figure […]

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]]>The problems connected to motor starting operations are fundamentally linked to the type of motor which a determined **motor operational torque “C _{M}”** offers, to the starting modality and to the connected load which has a determined

The necessary **starting torque “C**_{a}” can be expressed as:

C_{a} = C_{M} – C_{L}

and shall be well calibrated to prevent it from being either too low, so as starting is not too long and heavy – which causes **risks of temperature rise for the motor** – or from being too high on the joints or on the operating machines.

A generic curve of the above mentioned quantities is shown in the **Figure 1** below.

The concept of **motor starting time “ta”** can be associated to this concept of properly calibrated starting and can be evaluated making reference to concepts linked to the motion dynamics, but also by introducing simplifying hypotheses which allows, however, an evaluation with a good approximation.

It is possible to relate the acceleration torque, expressed as a difference between the motor operational torque and the load torque, to the moment of inertia of the motor **“J _{M}”**, of the load

where the expression of **“dω”** assumes the following form:

and it is obtained by differentiating the well known expression for the motor angular speed:

Through simple mathematical operations and applying **the method of integral calculus**, it is possible to make the unknown quantity “ta” explicit by the following expression:

**To express the value of the acceleration torque, it is necessary to introduce some simplifications:**

**The first one** consists in considering an average value for the motor operational torque to be expressed as:

C_{M} = 0.45 x (C_{s} + C_{max})

where **C _{S}** represents the

**The second one** concerns the torque due to the load and which can be correct by applying the multiplying factor KL linked to the load typology as in Table 1 below.

**Table 1** – Values of factor K_{L}

Type of comparable loads | ||||

Load Coefficient | Lift | Fans | Piston Pumps | Flywheel |

K_{L} | 1 | 0.33 | 0.5 | 0 |

In order to better understand **the significance of the coefficient K _{L}** we associate to the type of load indicated in the table the torque characterizing the starting phase of the load by means of the following assumptions:

**Lift**= load torque constant during acceleration**Fans**= load torque with square law increase during acceleration**Piston pumps**= load torque with linear increase during acceleration**Flywheel**= zero load torque.

With these assumptions, **the acceleration torque can be expressed as**:

These hypotheses allow to obtain the motor starting time with the aid of the following formula

The starting time allows to define whether a normal or a heavy duty start must be realized and to choose correctly the protection and switching devices. The above mentioned parameters relevant to the motor are given by the manufacturer of the motor.

As an example, Table 2 below shows the values that these parameters can take for **three-phase asynchronous motors** of common use and typically present on the market. Obviously the parameters relevant to the load characterize each single application and must be known by the designer.

**Table 2** – Typical values of some electrical and mechanical parameters of a three-phase asynchronous motor

Making reference to the data of the above table, here is an example of calculation of the starting time of a motor, according to the **theoretical treatment previously developed**.

Three-phase asynchronous motor – 4 poles Frequency | 160 kW |

Frequency | 50 Hz |

Rated speed | 1500 rpm |

Speed at full load | 1487 rpm |

Moment of inertia of the motor | J_{M} = 2.9 Kgm^{2} |

Moment of inertia of the load | J_{L} = 60 Kgm^{2} |

Load torque | C_{L} = 1600 Nm |

Rated torque of the motor | C_{N} = 1028 Nm |

Inrush torque | C_{s} = 2467 Nm (C_{s }= 2.4 x 1028) |

Max. torque | C_{max} = 2981 Nm (C_{max }= 2.9 x 1028) |

Load with constant torque | K_{L} = 1 |

**C**_{acc }= 0.45 · ( C_{S} + C_{max}) – K_{L}· C_{L} = 0.45 · (2467 + 2981) – (1 · 1600) = **851.6 Nm**

**from which**

**t _{a}** = (2 · π · 1500 · (2.9 + 60)) / 60 · 851.6 =

Load with quadratic rising torque **K _{L} = 0.33**

**C _{acc}** = 0.45 · ( C

**from which**

**t _{a}** = (2 · π · 1500 · (2.9 + 60)) / 60 · 1923.6 =

For both typologies of load, the esteemed motor starting time results to comply with the instruction given by the manufacturer **regarding the maximum time admitted for DOL starting**. This indication can be also taken as a cue for a correct evaluation of the thermal protection device to be chosen.

**Reference //** Three-phase asynchronous motors: generalities and proposals for the coordination of protective devices – ABB

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]]>Current drawn by the insulation When DC voltage is applied to an insulation, the electric field stress gives rise to current conduction and electrical polarization. Consider an elementary circuit as shown in Figure 1 below, which shows a DC voltage source, a switch, and an insulation specimen. However, this current immediately drops in value, and […]

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]]>When DC voltage is applied to an insulation, the electric field stress gives rise to current conduction and electrical polarization. Consider an elementary circuit as shown in Figure 1 below, which shows a DC voltage source, a switch, and an insulation specimen.

When the switch is closed, the insulation becomes electrified and a **very high current flows** at the instant the switch is closed.

However, this current immediately drops in value, and then decreases at a slower rate until it reaches a nearly constant value.

**The current drawn by the insulation may be analyzed into several components as follows:**

- Capacitance charging current
- Dielectric absorption current
- Surface leakage current
- Partial discharge current (corona)
- Volumetric leakage current

The **capacitance charging current** is high as the DC voltage is applied and can be calculated by the formula:

**C**represents charging current**R**represents absorption current_{A}**R**represents volumetric leakage current (dielectric loss)_{L}

**where:**

**i**is the capacitance charging current_{e}**E**is the voltage in kilovolts**R**is the resistance in megohms**C**is the capacitance in microfarads**t**is the time in seconds**e**is Napierian logarithmic base

The charging current is a **function of time** and will decrease as the time of the application of voltage increases. It is the initial charging current when voltage is applied and therefore not of any value for test evaluation.

**Test readings should not be taken until this current has decreased to a sufficiently low value.**

The **dielectric absorption current** is also high as the test voltage is applied and decreases as the voltage application time increases, but at a slower rate than the capacitance charging current. This current is not as high as the capacitance charging current.

The **absorption current** can be divided into two currents called reversible and irreversible charging currents. This reversible charging current can be calculated by the formula:

i_{a} = VCDT^{−n}

**where:**

**i**is the dielectric absorption current_{a}**V**is the test voltage in kilovolts**C**is the capacitance in microfarads**D**is the proportionately constant**T**is the time in seconds**n**is a constant

The **irreversible charging current** is of the same general form as the reversible charging current, but is much smaller in magnitude. The irreversible charging current is lost in the insulation and thus is not recoverable.

Again, sufficient time should be allowed before recording test data so that the revers- ible absorption current has decreased to a low value.

The surface leakage current is due to the **conduction on the surface of the insulation** where the conductor emerges and points of ground potential.

This current is not desired in the test results and should therefore be eliminated by carefully cleaning the surface of the conductor to eliminate the leakage paths, or should be captured and guarded out of the meter reading.

The partial discharge current, also known as corona current, is caused by overstressing of air at sharp corners of the conductor due to high test voltage. This current is not desirable and should be eliminated by the use of stress control shielding at such points during tests.

This current does not occur at lower voltages (below 4000 volts), such as insulation resistance test voltages.

The volumetric leakage current that flows through the insulation volume itself is of primary importance. This is the current that is used to evaluate the conditions of the insulation system under test. Sufficient time should be allowed for the volumetric current to stabilize before test readings are recorded.

The total current, consisting of various leakage currents as described above, is shown in Figure 2.

**Reference //** Electrical Power Equipment Maintenance and Testing – Paul Gill

(Purchase from Amazon)

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]]>Efficient joints in copper busbar conductors Efficient joints in copper busbar conductors can be made very simply by: Bolting Clamping Riveting Soldering Welding Bolting and clamping are used extensively on-site. Shaped busbars may be prefabricated by using friction stir welding. 1. Bolted joints (most common) Bolted joints are formed by overlapping the bars and bolting […]

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]]>**Efficient joints in copper busbar conductors can be made very simply by:**

Bolting and clamping are used extensively on-site. Shaped busbars may be prefabricated by using friction stir welding.

Bolted joints are formed **by overlapping the bars** and **bolting** through the overlap area. They are compact, reliable and versatile but have the disadvantage that holes must be drilled or punched through the conductors, causing some distortion of the current flow in the bar.

Bolted joints also tend to have **a less uniform contact pressure** than those made by clamping but, despite these issues, bolted joints are very commonly used and have proven to be **reliable**.

They can be assembled on-site without difficulty.

Clamped joints are formed **by overlapping the bars** and applying an **external clamp** around the overlap. Since there are no bolt holes, the current flow is not disturbed resulting in lower joint resistance. The extra mass at the joint helps to reduce temperature excursions under cyclic loads.

Well-designed clamps give an even contact pressure and are **easy to assemble**, but take up more space than a bolted joint and are **more expensive** to manufacture.

Riveted joints are similar to bolted joints. They can be efficient **if well made**. It is difficult to control the contact pressure. They cannot easily be dismantled or tightened in service and they are difficult to install.

Soldered or brazed joints are **rarely used for busbars** unless they are reinforced with bolts or clamps since heating under short-circuit conditions can make them both mechanically and electrically unsound.

Welded joints are made **by butting the ends of the bars and welding**. They are compact and have the advantage that the current-carrying capacity is unimpaired, as the joint is effectively a continuous copper conductor. However, it may not be safe or desirable to make welded joints **in situ**.

Welding of copper is discussed in **Copper Development Association Publication 98**, Cost-Effective Manufacturing: Joining of Copper and Copper Alloys (Download here).

In principle, a clamped or bolted joint is made by bringing together two flat surfaces under controlled (and maintained) pressure, as shown in Figure 6.

The resistance of a joint is mainly dependent on two factors:

- The streamline effect or
**spreading resistance, R**, due to the diversion of the current flow through the joint_{s} - The contact resistance or
**interface resistance of the joint, R**._{i}

Rj = R_{s}+ R_{i}

This applies specifically to **direct current applications**. Where alternating currents are flowing, the changes in resistance due to skin and proximity effects in the joint zone must also be taken into account.

**Reference //** Copper for Busbars – Guidance for Design and Installation – Copper Development Association (Download guidance)

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]]>General about DC motors Separate field excitation DC motors are still sometimes used for driving machines at variable speed. These motors are very easy to miniaturize, and essential for very low powers and low voltages. They are also particularly suitable, up to high power levels (several megawatts), for speed variation with simple, uncomplicated electronic technologies […]

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]]>Separate field excitation DC motors are still sometimes used **for driving machines at variable speed**. These motors are very easy to miniaturize, and essential for very low powers and low voltages.

They are also particularly suitable, up to high power levels (**several megawatts**), for speed variation with simple, uncomplicated electronic technologies for high performance levels (variation range commonly used from 1 to 100).

Their characteristics also enable accurate torque regulation, when operating as a motor or as a generator. Their nominal rotation speed, which is independent of the line supply frequency, **is easy to adapt by design to suit all applications**.

They are however **less rugged** than asynchronous motors and **much more expensive**, in terms of both hardware and maintenance costs, as they require regular servicing of the commutator and the brushes.

**A DC motor is composed of the following main parts:**

This is a **non-moving part of the magnetic circuit** on which a winding is wound in order to produce a magnetic field. The electro-magnet that is created has a cylindrical cavity between its poles.

This is **a cylinder of magnetic laminations** that are insulated from one another and perpendicular to the axis of the cylinder. The armature is a moving part that rotates round its axis, and is separated from the field coil by an air gap. Conductors are evenly distributed around its outer surface.

The commutator is integral with the armature. The brushes are fixed. They rub against the commutator and thus supply power to the armature conductors.

When the field coil is energized, it creates a magnetic field (excitation flux) in the air gap, in the direction of the radii of the armature. This magnetic field “**enters**” the armature from the North pole side of the field coil and “exits” the armature from the South pole side of the field coil.

When the armature is energized, currents pass through the conductors located under one field coil pole (on the same side of the brushes) in the same direction and are thus, **according to Laplace’s law, subject to a force**.

The conductors located under the other pole are subject to a force of the same intensity in the opposite direction. The two forces create a torque which causes the motor armature to rotate (see Figure 1).

When the motor armature is powered by a DC or **rectified voltage supply U**, it produces **back emf E** whose value is:

E = U – RI

where **RI** represents **the ohmic voltage drop in the armature**.

The **back emf E** is linked to the speed and the excitation by the equation:

E = k ω Φ

Where:

**k**is a constant specific to the motor**ω**is the angular speed**Φ**is the flux

This equation shows that at constant excitation the **back emf E (proportional to ω) is an image of the speed**.

The torque is linked to the field coil flux and the current in the armature by the equation:

T = k Φ I

If the flux is reduced, **the torque decreases**.

**There are two methods for increasing the speed //**

1. Either **increase the back emf E**, and thus the supply voltage at constant excitation: this is known as “constant torque” operation.

2. Or **decrease the excitation flux**, and thus the excitation current, while keeping the supply voltage constant: this is known as **“reduced flux”** or **“constant power” operation**. This operation requires the torque to decrease as the speed increases (see Figure 2 below). However, **for high reduced flux ratios** this operation requires specially adapted motors (mechanically and electrically) to overcome switching problems.

** The operation of this type of device (DC motor) is reversible //**

If the **load opposes the rotation movement** (the load is said to be resistive), the device provides a torque and operates as a motor.

If the load is such that **it tends to make the device rotate** (the load is said to be driving) or it opposes the slow-down (stopping phase of a load with a certain inertia), the device provides electrical energy and operates as a generator.

The coils, armature and field coil are connected **in parallel or supplied via two sources with different voltages** in order to adapt to the characteristics of the machine (e.g.: armature voltage 400 volts and field coil voltage 180 volts).

The direction of rotation is reversed by inverting one or other of the windings, generally by inverting the armature voltage due to the much lower time constants. Most bidirectional speed drives for DC motors operate in this way.

The design of this motor is similar to that of the **separate field excitation motor**. The field coil is connected in series to the armature coil, hence its name. The direction of rotation can be reversed by inverting the polarities of the armature or the field coil.

This motor is mainly used for traction, in particular on trucks supplied by battery packs. In railway traction the **old TGV (French high-speed train)** motor coaches used this type of motor. More recent coaches use asynchronous motors.

This technology combines the qualities of the series wound motor and the shunt wound motor. **This motor has two windings per field coil pole.** One is connected in parallel with the armature. A low current (low in relation to the working current) flows through it. The other is connected in series.

It is an added flux motor if the ampere turns of the two windings add their effects. Otherwise it is a negative flux motor. But this particular mounting method is very rarely used as it leads to unstable operation with high loads.

Here we have an open DC motor with permanent magnet for the field. An old armature from a faulty hedge trimmer was used. As it was for a school project The following topics had to be covered.

**Chemical energy**– We used a lead acid battery**Kinetic energy**– We got the armature rotating**Noise**– We got audio from the speaker**Heating**– We got some heating in the armature, and commutator bars**Light**– We made a special LED driven via coil**Magnetic**– We established that the armature won’t rotate without the magnet underneath.

*Cant see this video? Click here to watch it on Youtube.*

**Reference //** Cahier technique no. 207 – Electric motors – Schneider Electric

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]]>Purpose of the test The purpose of the impulse voltage test is to secure that the transformer insultations withstand the lightning overvoltages which may occur in service. Testing equipment Impulse generator Where: C1 – Impulse capacitor Rc – Charging resistor Rs – Series resistor Ra – Low-ohmic discharging resistor for switching impulse, Rb – High-ohmic discharging resistor for […]

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]]>The purpose of the impulse voltage test is to secure that the transformer insultations **withstand the lightning overvoltages** which may occur in service.

Where:

**C**– Impulse capacitor_{1}**R**– Charging resistor_{c}**R**– Series resistor_{s}**R**– Low-ohmic discharging resistor for switching impulse,_{a}**R**– High-ohmic discharging resistor for switching impulse_{b}**F**– Main spark-gaps,_{1}…F_{n}**F**– auxiliary spark-gaps_{al}…F_{an}

The impulse generator design is based on the Marx circuit. The basic circuit diagram is shown on Figure 1 above. The impulse capacitors **C _{s}** (12 capacitors of 750 nF) are charged in parallel through the charging resistors

When the charging voltage has reached the requider value, breakdown of the spark-gap **F _{1}** is initiated by an external triggering pulse. When

**R _{a}** is separated from the circuit by the auxiliary spark-gap

Concequently the capacitors are discharged in series-connection. The **high ohmic discharge resistors R**_{b} are dimensioned for switching impulses and the low-ohmic resistors **R**_{a} for lightning impulses. The resistors R_{a} are connected in parallel with the resistors R_{b}, when the auxiliary spark-gaps break down, with a time dalay of a few hundred nanoseconds.

**This arrangement is necessary in order to secure the functioning of the generator.**

The required voltage is obtained by selecting a suitable number of seriesconnected stages and by adjusting the charging voltage. In order to obtain the necessary disscharge energy parallel or series-parallall connections of the generator can be used. In these cases some of the capacitors are connected in parallel during the discharge.

**Max. test voltage amplitudes: 2.1 MV lightning impulse. 1.6 MV switching impulse.**

Where:

**C**– Resulting impulse capacitance_{r}**R**– Resulting series resistance_{sr}**R**– Resulting discharge resistance_{ar}**L**_{r }L– Stray inductances_{p}**C**– Input capacitance of transformer_{i}**L**– Transformer inductance_{i}**C**– Capacitance of voltage divider_{1}**F**– Spark gaps of impulse generator_{1}**F**– Calibration sphere gap_{2}**R**– Protective resistor._{2}

The required impulse shape is obtained by selecting the series and discharge resistors of the generator suitably.

**The front time can be calculated approximately from the equation:**

T_{1} ≈ 2,5 · R_{sr} · (C_{i} + C_{1}) **(formulae 1)**

and the time to half value from the equation:

T_{2} ≈ k · √(L_{i} · C_{r}) **(formulae 2)**

The **factor k** depends on the quantities **R _{sr}**,

The impulse shape and the peak value of the impulse voltage are measured **by means of an oscilloscope and a peak voltmeter** which are connected to the voltage divider (Figure 3). The measuring range can be changed by shortcircuiting part of the high voltage capacitors or changing the low voltage capacitor of the divider.

Where:

**E**– Damped capacitive voltage divider**W**– Measuring cable (= wave impedance = Rp)**P**– Oscilloscope_{1}**P**– Peak voltmeter_{2}**R**– Terminal resistance of the measuring cable_{p}**R**– Damping resistor of voltage divider_{1}**C**– High voltage capacitor of voltage divider_{1}**C**– Low voltage capacitor of divider._{2}

The measuring circuit is checked in accordance with the standards (formulae 2) and (formulae 3). If necessary the sphere-gap calibration of the measuring circuit can be performed in connection with the testing according to the standard (figure 4 below).

The lightning impulse test is **normally applied to all windings**. The impulse testsequency is applied successively to each of the line terminals of the tested winding. The other line terminals and the neutral terminal are earthed (singleterminal test, Figure 4a and 4b).

Where:

**a, b**– 1-terminal testing**c**– 3-terminal testing**d**– 2-terminal testing**e**– test with transferred voltages**f**– neutranl terminal testing

When testing low voltage windings of high power the time to half-value obtained is often too short. However, the time to half-value can be increased by connecting suitable resistors (**R _{a} in Figure 4b**) between the adjacent terminals and earth.

According to the standard **IEC 76-3** the resistances of the resistors must be selected so that the voltages at the adjacent terminals do not exceed **75 % of the test voltage** and the resistance does not exceed **500 Ω**.

A delta-connected winding (and star-connected winding, unless the neutral is available) is also tested with an impulse test-sequence applied to the line terminals of the tested winding connected together, while the other windings are earthed (**three-terminal test, Figure 4c**).

For delta-connected windings the single and three-terminal testings can be combined by applying the impulse to two line terminals at a time, while the other line terminals are earthed (**two-terminal testing, Figure 4d**). In this case two phases are simultaneously tested in a single-terminal connection and one phase in a test connection corresponding to three-terminal testing.

The two- and three-terminal testings are not included in the standard, but they can be done if it is so agreed.

When the low voltage winding cannot in service be subjected to lighting overvoltages from the low voltage system (e.g. step-up transformers, tertiary windings) the low voltage winding may (by agreement between customer and manufackturer) be impulse tested simultaneously with the impulse tests on the high voltage winding with surges transferred from the high voltage winding to the low voltage winding (**Figure 4e, test with transferred voltages**).

According to IEC 76-3 the line terminals of the low voltage winding are connected to earth through resistances of such value (**resistances R**_{a} in Figure 4e) that the amplitude of transferred impulse voltage between line terminal and earth or between different line terminals or across a phase winding will be as high as possible but not exceeding the rated impulse withstand voltage.

**The resistance shall not exceed 5000 Ω.** The neutral terminal is normally tested indirectly by connecting a high-ohmic resistor between the neutral and earth (voltage divider Ra, Ru) and by appluying the impulse (**Figure 4d**) to the line terminals connected together.

The impulse test of a neutral terminal is performed **only if requested by the customer**.

For fault detection in single-terminal and two-terminal tests the neutral of star-connected windings are earthed via a **low-ohmic resistor (R _{u})**. The current flowing through the detection resistor during the test is rocorded by means of an oscilloscope. Evidence of insultaion failure arising from the test would be given significant discrepacies between the calibration impulse application and the full voltage applications in recorded current wave-shapes.

**Certain types of faults give rise to discrepancies in the recorded voltage wave-shapes as well.**

For fault detection in three-terminal tests and tests on the neutral terminal the adjacent winding is earthed through a low-ohmic resistor. The fault detection is then based on recording the capacitive current which is transferred to the adjacent winding.

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**Reference //** Testing of power transformers – ABB

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]]>Very low-impedance ground connection As is evident from the name, a solidly grounded system is one where the neutral of the system is directly connected to ground without introducing any intentional resistance in the ground circuit. A solidly grounded system clamps the neutral tightly to ground and ensures that when there is a ground fault […]

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]]>As is evident from the name, a solidly grounded system is one **where the neutral of the system is directly connected to ground** without introducing any intentional resistance in the ground circuit.

With appropriate choice of the type and number of grounding electrodes, it is possible to obtain a very low-impedance ground connection, sometimes **as low as 1Ω**.

A solidly grounded system **clamps the neutral tightly to ground** and ensures that when there is a ground fault in one phase, the voltage of the healthy phases with reference to ground does not increase to values appreciably higher than the value under the normal operating conditions.

**1. ** A fault is readily detected and therefore isolated quickly by circuit protective devices. Quite often, the protection against short circuit faults (such as circuit breakers or fuses) is adequate to sense and isolate ground faults as well.

**2. ** It is easy **to identify and selectively trip the faulted circuit** so that power to the other circuits or consumers can continue unaffected (contrast this with the ungrounded system where a system may have to be extensively disturbed to enable detection of the faulty circuit).

**3. ** No possibility of transient overvoltages.

**The main disadvantage** is that when applied in distribution circuits of higher voltage (5 kV and above), the very low ground impedance results in extremely high fault currents almost equal to or in some cases higher than the system’s three-phase short circuit currents.

This can increase the rupturing duty ratings of the equipment to be selected in these systems.

Such high currents may not have serious consequences if the failure happens in the distribution conductors (overhead or cable). But when a fault happens inside a device such as a motor or generator such currents will result in **extensive damage to active magnetic parts** through which they flow to reach the ground.

For these reasons, use of solid grounding of neutral is **restricted to systems of lower voltage (380 V/480 V)** used normally in consumer premises. In all the other cases, some form of grounding impedance is always used for reducing damage to critical equipment components.

*Cant see this video? Click here to watch it on Youtube.*

**Reference:** Practical Grounding, Bonding, Shielding and Surge Protection G. Vijayaraghavan, Mark Brown and Malcolm Barnes (Buy hardcopy from Amazon)

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