## Reactive power compensation project

Design of reactive power compensation panel is much different and not that simple like standard distribution panel. When dealing with such panels, there are dozen of parameters to specify and other things to take care of.

This article is the part of Mr. Jakub Kępka’s excellent thesis work on subject ‘**Reactive Power Compensation**‘. I haven’t read such a good work for a long time. Excellent.

The aim of project called „Reactive power compensation panel” was to design capacitor bank with **rated power of 200kVar and rated voltage of 400V** adapted for operation with mains, where higher order harmonics are present. The capacitor bank was to be power capacitor based with automatic control by power factor regulator.

**elements, dimensions, connections, cross section of the wires, capacitor protection**since it needs to be tested and accepted by certified laboratory.

Bearing above in mind, first thing to do is to investigate basic requirements for capacitor banks according to the polish standards. The most important standards, that were used during design process was:

- EN 61921:2005
- EN 60439-1:1999
- IEC 60831-2

EN 61921:2005 describes the general requirements for the capacitor bank. The most important of them are listed below:

**Access to the particular elements**within the capacitor bank should be easy, so that there is no problem to replace an element in case of failure**Index of protection**depends of the place of the installation of a capacitor bank. If the capacitor bank is to be placed in the same place as the main switchgear or utility room next to it, IP 20 is enough.**Section construction**– in a device for reactive power compensation particular sections can be determined, placing them in separate partitions or within the same cubicle.**Marking**– each capacitor bank has to have nameplate, which contains information about: manufacturer, identification number, date of manufacture, rated power in [kVar], rated voltage in [V], min and max ambient temperature, index of protection, short circuit strength in [A]

- Enclosure
- Arrangement of the elements
- Power capacitors and detuning reactors
- Contactors
- Protection
- Connection diagram

### 1. Enclosure

Having above information, it is possible to find fitting cubicle for the elements of the capacitor bank. Because the device is going to operate at the mains, where higher order harmonics are present, power capacitors must be protected by reactors. Each capacitor emits additional amount of heat as well as a reactor.

**in order to force the air flow inside the enclosure**which will cool the elements down.

The maximum temperature around the power capacitors cannot be higher than listed in table below.

Table 1 **– Thermal Conditions according to IEC 60831-2**

Maximum | 55°C |

Maximum average within 24h | 45°C |

Annual maximum average | 35°C |

Minimal | -25°C |

The issue of cooling is very important. Capacitors and reactors working in improper thermal conditions are exposed for danger of overheating and its life expectancy gets shorter.

**In order to avoid this, one needs to follow few rules, that will prevent unwanted effects. These are as follow (generally for switchgear cubicles):**

- The distance between air inlet and outlet should be possibly far in order to provide the maximum speed for the air stream.
- The dimension of the inlet should be at least 10% bigger than the outlet
- Vertical dimension of the inlet/outlet should be the bigger one
- Avoiding air flow at the right angle or zigzag line
- In case of forced cooling, ventilators should be placed at the bottom of the cubicle in order to launch a cold air into the switchgear.
- Choosing the fun, the real air flow should be considered, since theoretical one can be can be higher in terms of counterpressure effect

**7W per / kvar – for acceptor circuit**(capacitor and reactor).

**According to the formula:**

D = 0.3 × Ps [m^{3}/h]

D = 0.3 × (200 × 7) = 420 [m^{3}/h]

Where:

**D**– Minimal efficiency of ventilators**Ps**– Total power loss od acceptor circuit

Taking into account the rules above, following cubicle was selected:

Table 2 **– Enclosure dimensions**

Height [mm] | 2000 |

Width [mm] | 1050 |

Depth [mm] | 500 |

The photography below shows the interior of the cubicle:

As you can notice, there is no floor in this enclosure. This type of construction lets the air stream flow easily up to the top of the cubicle, which is slightly lifted up for better ventilation.

### 2. Arrangement of the elements

The arrangement of the elements inside the enclosure should be **easily available for maintenance and replacement**, and each element should be clearly marked according to the technical documentation.

In the project, in terms of the construction of the enclosure, following solution was taken into account (see figure 3 below).

**Elements no. 1,2**(violet font) these are the metal plates which constitute panels for contactors and protection equipment of particular sections of capacitor bank.**Element no. 3**represents the barrier between capacitor and reactor.

All the elements 1,2,3 come from the same manufacturer, taken from the same catalogue, in order to make easier construction of next device of similar type and decrease parts diversity.

The next requirement for the reactors is to be placed above the capacitors, since they evolve much more heat than capacitors which is lighter and could go up causing the capacitor temperature to rise. If one wants to place the reactors in the same cubicle, they should be physically separated by a barrier.

That is what was mentioned in **EN 61921:2005 Section construction**.

In the project, the barrier was carried out

by means of a metal plate placed between capacitors and reactors.

### 3. Power capacitors and detuning reactors

The next step is to chose appropriate power capacitors. It means, that one needs to pay attention to its rated voltage and power. Since the capacitors will be working in series with reactors, what will cause the voltage at the capacitors’ terminals to rise.

**voltage of 1,1×U**longer than 8 hour per day. For this reason, there is a need to apply the power capacitors with the rated voltage higher than the voltage of mains.

_{n}By reason of this one must take under consideration a statement below:

**As the voltage rises or drops, the reactive power of the capacitor changes as well, according to the formula:**

where:

**Q**– calculated power of the capacitor_{R}**Q**– nominal power at rated voltage_{N}**U**– voltage of a mains_{S}**U**– rated voltage of capacitor_{N}

Project assumed rated power of the capacitor bank equal to **400V**. Let’s carry out an example calculation. Considering power capacitor with rated power of **20 kvar** and rated voltage of **440V** supplied by mains at **U _{n}=400V**.

This type of calculation is true, if there is no reactor connected in series with capacitor.

Once we know the total reactive power of the capacitors, **we can choose series of capacitors for PF correction**. There is 200kvar to be divided. Taking this into account, at his point, one needs to consider the number of capacitors that will be used.

However, before the capacitors will be chosen, one needs to take a closer look at the power factor regulators output number, and reactor which will change the total power of the section of capacitor bank.

#### 3.1 Acceptor circuit

Power electronic based devices have significant, negative influence on the power quality. Since its number is increasing nowadays, it leads to designing more and more capacitor banks, that are well prepared to work with distorted voltage and current.

**detuning reactors**, which are interconnected with capacitors within the circuit breaker (CB). Capacitor and reactor connected in series is referred to as an

**acceptor circuit**.

This connection is depicted in the picture below.

The capacitance and inductance of the series connected capacitor and inductor create a resonance circuit with the **natural frequency f _{r}**. For the frequencies below the f

_{r}, including 50Hz, circuit has capacitive behaviour, which makes possible compensation of inductive reactive power. For all the frequencies higher than natural frequency, acceptor circuit has inductive behaviour.

This prevents from the resonance phenomenon between the capacitor bank and supplying network.

In detuned filters, parameters L and C must have such a value, that the natural frequency value of the capacitor bank is smaller than the frequency of the lowest order harmonic present in the supplying electric network.

As an example, if it was found, that in the grid there are following harmonics: 5^{th}, 7^{th}, 11^{th}, 13^{th} the LC parameters has to be selected so that the resonance frequency is included in **range 174 – 210Hz (usually 189Hz)**. This type of filtering is being used in the automatic capacitor banks.

If one wants to consider operation of the capacitor bank without resonance reactors, the fact, that higher order harmonics sources can be either receivers from the spot, where the CB is installed or supplying network.

Before decision is made, whether install the reactors or not,

it is strongly recommended to make measurements at the place of CB installation, it the higher order harmonics are present in supplying current and voltage.

As one can notice, the reactors are very important part of capacitor bank, and they cannot be omitted in the designing process. They also cause the voltage rise of series connected capacitor. Increased voltage changes the power of the capacitor.

So, there is a row of calculations that are required to be carried out during designing process.

First of all, as mentioned above, basing on detailed network analysis, knowing the harmonic content in supplying voltage/current, **a detuning factor can be found**. Since the capacitor bank in the project has no determined particular network to operate with, but was built for demonstrations by the ELEKTROTIM company, it was assumed that it has to be able to work at resonance frequency of 189Hz.

**first step is to calculate the detuning factor**.

Detuning factor indicates the capability of the acceptor circuit to filtrate the higher order harmonics. It is denoted as p and expressed in percents. It can be defined as ratio of reactor’s reactance with respect to reactance of capacitor.

**However, it can be calculated basing on the network frequency and natural frequency of the circuit according to the formula:**

Typical range of higher order harmonic limiting includes 5th and 7th harmonic , which usually are present in mains and have the biggest share in supplying current.

Table 3 **– Detuning factor and corresponding resonance frequency**

Detuning factor p% | 5% | 5.76% | 7% | 12,5% | 14% |

Resonance frequency f_{R} | ≈224Hz | ≈210Hz | ≈189Hz | ≈141Hz | ≈134Hz |

Since the detuning factor for the project was given as **p=7%**, one knows that the capacitor bank needs to be equipped with reactors. For this reason, some calculations have to be performed, in order to fit the power of the capacitors and its rated voltage taking into account reactive power of a detuning reactors. This power has to be considered when resultant power of capacitor bank section is being determined.

First, **capacity of the capacitor** has to be found basing on the rated power and rated voltage value of the capacitor, according to the formula:

where:

**f**– frequency,**Qcn**– rated reactive power of capacitor,**Ucn**– Rated voltage of capacitor,**C**– capacitance of the capacitor

In compliance with the project assumptions, **for p=7%** and taking into account value of C calculated above, one can determine capacitive and inductive reactance:

**Resultant reactance of acceptor circuit is:**

Having calculated the values above, one can find phase inductance of the reactor:

as well as the current forced by the capacitor:

The reactor connected in series will step the voltage at the capacitor terminals up what can found by following formula:

All above calculations allow to find out, what is the reactive power of the capacitor bank, when the voltage across its terminal has changed:

In the next step, the **reactive power of detuning reactor** will be calculated:

Then, the **resultant power of the acceptor circuit** is going to be:

Table 4 **– Results of calculation**

C | X_{C} | X_{L} | X_{CB} | L_{R} | I_{S} | U_{C} | Q_{RE} | Q_{L} | Q_{RES} |

μF | Ω | Ω | Ω | mH | A | V | kvar | kvar | kvar |

329 | 9,86 | 0,68 | 9 | 2,16 | 25,65 | 430 | 19,11 | 1,34 | 18 |

In the table above all the results of calculation are listed. Since, as mentioned above, capacitor bank working with the mains where higher order harmonics are present, **needs to be equipped with reactors, which affect the total reactive power value of the capacitor bank**.

In order to find the total rated power of the capacitor bank including reactors, all the calculations above has to be carried out. Data taken for the calculations above:

Table 5 **– Data for calculation**

Capacitor | ||

Rated power | Q_{cn} | 20 kvar |

Frequency | f_{n} | 50 Hz |

Rated voltage | U_{cn} | 440 Volts |

Other | ||

Mains rated voltage | U_{n} | 400 Volts |

Detuning factor | p | 7% |

The rated voltage of the capacitor that was taken for calculations is not random, since it is known, that reactor will increase the voltage across the capacitor terminals according to formula above **U _{c}=U_{s} (1-p)**.

Taking resultant reactive power of acceptor circuit and denoting it as **Q _{RES}** and rated power of the capacitor

**Q**, one can find the ratio:

_{cn}The idea to determine the **coefficient M** is to make easier finding the total capacitor bank rated power when equipped with reactors. For the project:

**the total power of the capacitors that are used in capacitor bank will be bigger**, than assumed rated power of CB. It arose due to reactors connected with capacitors in series. Since voltage will be increased at the capacitor terminals, up to the 430V, overrated capacitors had to be used with the nominal voltage of 440V.

However, nominal power of the capacitor is reached at its rated voltage, so i.e. **20kvar at 440V**. If the mains voltage is 400V, capacitor nominal voltage 440, and reactor cause voltage change at the capacitor terminals as well as launch additional reactive power to the circuit, all the calculations introduced in this article must be done.

#### 3.2 Number and type of capacitors

Once coefficient M was calculated as well as the total power of the capacitors that needs to be installed, one may consider how many capacitors should be selected. At this point, it is important to match the capacitor which will be the first one in the series. However, before it happens, **the “series of type” has to be explained**.

Power factor regulators are manufactured with 6 or 12 outputs. It means that maximum 6 or 12 power capacitors can be switched on or off.

**Let`s take a closer look at the series below:**

- 1:1:1:1:1:1…
- 1:2:2:2:2:4…

1:1:1:1:1:1… – The first series (case a.) says, that in a capacitor bank there are **six capacitors with the same rated power**. This uniform staging allows to switch the capacitor on without waiting until it is discharged and ready to be switched on one more time. The first number in the series (representing multiplication of rated power of a capacitor) has to be chosen very carefully.

Usually, it is dependent on the load fluctuation at the network the capacitor bank is going to operate with. It is important issue, since the next capacitor in the series has to be equal or integer multiplication of the one on the first place. The series has to be increasing.

1:2:2:2:2:4… – In case b. one can notice, that i.e. if the rated power of the first capacitor in the series is equal i.e. 10kvar, then, second one is 20kvar, and so on.

Once the total power of 220 kvar that is supposed to be distributed among certain number of capacitors, one should find out, what are the typical ratings of capacitors offered on the domestic and international market.

For the project purposes, the products of ZEZ SILKO company was bought, because they were competitive comparing to the other suppliers.

##### Characteristics of chosen capacitors

The company produces Capacitors in MKP and MKV systems. Both dielectric systems are **self−healing**. Metal plated layer is evaporated in case of the voltage breakdown. Formed insulating surface is very small and does not effected the functionality of the capacitor.

Capacitors windings are inserted into aluminum container. Container is equipped with the **overpressure disconnector**.

MKP capacitors are made of **one−side metalized PP film**. Contacting of the winding is performed by zinc spraying. This configuration is dry without impregnant. As for MKV capacitor, electrodes are of metallized paper on both sides and PP foil serves as a dielectric. The system is impregnated by mineral oil.

MKV capacitors are suitable for higher power loading and higher ambient temperature. In the meantime the capacitors are produced mainly in MKP system, MKV”.

Table 6 **– Capacitors that are being offered by ZEZ Silko**

Having at disposal the list of capacitors, it is possible to figure out its total number for the capacitor bank.

The first capacitor in the series will have a power of 20kvar.If the remaining power will be managed in a smart way, it will be possible to reduce the cost of the power factor regulator choosing the one, that has 6 outputs instead of 12.

##### Capacitor type description

Each capacitor by the company is described by the specific name such as **CSADG** or **CSADP**. In this notation, each letter indicates a feature of the capacitor:

Table 7 **– Capacitor type description**

Sequence of a letter | Feature | Letter | Description |

1 | Application | C | PF protection |

2 | Number of phases impregnat | S | Three phase without impregnat |

3 | Cooling case construction | A | Steel insulated case |

4 | Configuration protection degree | D | Built-in discharge resistor for indoor use IP20 |

5 | Dielectric system | G | MKP (metalized PP film, dry, gas filled) |

P | MKP (metalized PP film, dry, gel filled) |

In order to check, if the capacitors are suitable for reactive power compensation and match the project assumptions, one can decode the capacitor type description in compliance with Table 7.

**Basing on the two tables above, following capacitors were selected:**

- 1 capacitor – CSADG 1-0,44/20
- 5 capacitors – CSADP 3-0,44/40

### 4. Contactors

The last step is to select the **protection of the capacitors as well as the contactors**. In order to do so, one has to skim the catalogue cards of the manufacturers.

Contactors for the capacitor banks are specially designed, taking into account life expectancy of the contacts, as well as an extra module limiting the inrush current of the capacitor.

Table 8 – Contactor ratings by LG

In the table above, there are listed contactors from LG company. In order to select proper contactor for each capacitor, one needs to pay attention for the rated power that can be handled by the device at given rated voltage.

**capacitors of rated power of 20kvar and 40kvar**, following contactors were selected:

**MC – 32 and MC – 50**. The last column of the table shows, what type of module should be used for particular contactor. The module is available separately.

One also needs to supply the coils of the contactors with the voltage of 230V. It can be obtained by mounting the transformer with the ratio 400/230.

### 5. Protection

The short circuit protection of the capacitors is provided by the switch disconnectors. For the capacitors the fuse link rated current should be **1.6 time of the rated reactive current of the capacitor**.

I_{n}=Q / (U_{n}×√3)

where:

**U**– rated voltage of the mains,_{n}**Q**– rated power of the capacitor at rated mains voltage.

Not only capacitors should be protected against short circuit, but the whole capacitor bank as well. Usually, in the switchgear from which the CB is supplied, there is an additional circuit breaker for the capacitor bank.

**Its value should be selected as:**

- Standard capacitor bank :
**1,36 × I**_{n} - Overrated capacitor bank:
**1,50 × I**_{n} - Capacitor bank with reactors (n=4.3):
**1,21 × I**_{n}

The next important issue is to provide proper section of the wires and conductors, which has to be able to withstand at least 1,5 of the nominal reactive current.

One needs to remember,

that the control and cooling circuits also need protection. It is provided by the fuse links with rated current of 6A in compliance with technical documentation of PFR.

### 6. Connection diagram

#### 6.1 Main circuit

The next task, which designer has to handle is to create the **connection diagram** for all the elements that were selected to be used in the capacitor bank. The capacitor bank should has two technical drawings, namely, main circuit diagram and control circuit diagram.

**The main circuit diagram should provide information how to connect the capacitor bank to the supplying switchgear:**

There is three phase network incoming to supply the capacitor bank (Low Voltage switchgear). From the feeder, the incoming power is distributed through the bus bars mounted in the capacitor bank. The cross section of the bus bars is chosen so that it can easily withstand the current flowing through the device.

**the proper number of isolators holding the busbars**, since it determines short circuit strength of the device. In case of the capacitor bank, there are three insulators which gives short circuit strength of about 20 – 30kA.

The connection points (red dots) L1, L2, and L3 represents the point of connection of the capacitors and reactors with the bus bars.

The three cooper busbars (cross section 30×10 mm) L1, L2 and L3 are connected through the wires to the switch disconnectors **F1 – F6**. All switch disconnectors has the same current strength of **160A**, the only thing that differs them from each other is rated current of the fuse link.

The terminals **2,4,6** of each disconnector are connected to the **three phase reactor (D1 – D6)**. Each reactor has thermal protection (**contact 11 and 14**).

Next, the reactors are connected in series through the **contactors (K1 – K6)**. The terminals **A1 and A2** (coil of the contactor supplied by 230V AC source) trip the contacts of the contactor.

The second drawing “**Control diagram**” explains in details how to connect the contactor’s coils with and thermal protection of the reactors with the power factor regulator. The procedure of creating control circuit diagram will be shown in few steps in the next subsection.

#### 6.2 Control circuit

In order to connect all the control equipment and protection one needs a **terminal stripe**. Terminal stripe will cross all necessary wires in order to make the circuit work.

The terminal stripe needs to be provided together with the control circuit diagram for the wireman, who was going to connect the equipment. The bottom part of the terminal stripe is dedicated for the wires coming from :

- Current transformer
**l – CT**and**k – CT**from the supplying switchgear - Short circuit protection of regulator, ventilators
**(FS – 1…F2.4)**as well as for the reactors**(D1 – D6)**

**letter “R”**denotes the Power Factor Regulator i.e. “l – R “ is a connection of the terminal “l” of the current transformer with the terminal “l” on the power factor regulator and so on. W1 – W3 terminals are assigned to ventilators.

##### Extraction of terminal stripe

According to the terminal stripe, one can wire the circuit step by step.

First, on needs to use the phases L2 and L3 in order to supply the transformer **Tr 40/230V (250VA)**. The transformer is protected from short circuit by **two-pole switch disconnector F1** whit the fuse link of **6A**. At the output of the transformer, one gets the phase L (230V) and the neutral N.

**The transformer will supply the equipment which needs 230V AC source to operate, that are:**

- Ventilators
- Power factor regulator
- Coils of the contactors

The ventilators are controlled by the **thermostat T** which will turn them on when the temperature will rise above 35 degrees of Celsius. The phase L2 and L3 is connected to the power factor regulator through the **fuse FS2**.

The next picture will continue from the points 1, 2, 3, 4 and 5 at the very bottom of the figure above.

Starting from points 1,2,3,4 and 5 one continue designing the control circuit. The figure shows the layout of the **power factor regulator RMB 10.6**.

**The regulator has got three terminal stripes:**

- l, k, alarm
- L1, L2, L3, N
- C, 1 – 6

The terminals **“l”** and **“k”** provide connection for the current transformer mounted on the phase **L1** in the main switchgear. The input alarm is connected in series with the **lamp “LA”** mounted on the door of capacitor bank. The lamp will light up every time, when contact “ALARM” inside the power factor regulator will close down.

The second terminal stripes contains terminals L1, L2, L3 and N. The terminal L1 and N is connected to the phase L and neutral wire N of the transformer respectively. In this way, one provides the supply source for power factor regulator.

Phases L2 and L3 are connected to terminals L2 and L3 respectively. These terminals are responsible for the measuring of the voltage. Moreover, phases L1, L2 and L3 are leaded through the **switch WL1**. This solution lets disconnect the capacitor bank without disconnecting it at the main switchgear i.e. for the maintenance.

The last terminal stripe will **control the coils of the contactors**. The terminals 1 to 6 are connected to the coils of the contactors which trip the contacts in order to switch the capacitor on or off. They are followed by the **contacts D1 – D6**. These are responsible for the **thermal protection of the reactors**.

In case, when the temperature rise above the limit, that is safe for the reactors, the **contact “D”** of the reactor will switch off the circuit capacitor reactor .

Putting all these diagrams together,

one obtains complete control circuit diagram for the capacitor bank.

**Reference //** Master thesis: Reactive Power Compensation by Jakub Kępka and Supervisor PhD. Zbigniew Leonowicz at Wroclaw University of Technology

NICE STUDY,THX

Please can I receive the installation and instructions book pdf forms for power factor improvement in my email box

Hi Edward,

I need a unit Which Will Take Care of the Below Requirement

Need Your Advice to proceed, can you Direct Me how to?

Can even DIY this, with Your Support

Design capacitor bank with rated power of 30kVar and rated voltage of 230V adapted for operation with mains(India)

1) Aim & Goal: Power factor correction and Good Voltage regulation.

2) Why Power factor correction, may also be justified for mainly

Three reasons:

A. To improve voltage

B. To lower the cost of electric energy, when the electric utility rates vary with the power factor at the metering point

C. To reduce the energy losses in conductors

Incoming voltage Power Grid: 235-240 Volts

On Load: 225 Approx.

Floating Load of 20 – 30 Amperes Approx.

Capacitor banks (230 Volts)

Size of a compensation unit, (total reactive power of 30 KVR Projected)

or 25 KVR also can be Considered.

To be assembled with capacitors of equal size or of different size. A unit with a total reactive power of, ex: 10×3 or 15×2 0r 5x 6.

This unit Must have Relay (single phase Reactive power Manager) Capable of picking out the correct capacitor size by referring to the actual demand of reactive power directly to the Source.

the value of capacitance is 329 for combination of three capacitors in delta connection so if we want to get capacitance of each capacitor we divide 329 by 3, does it correct or i miss something? and what about inductance L in example does is for three coils together or for one coil ?

Very usefullinformation. Any information about HT Series reactor and Shunt reactor.

Dear sir,

Thank you for the article its informative, i have question sir….

This is with regards to the correct use of capacitor rated voltages. We have 440 volts motors…

The line voltage reaches 490 volts and the motor will no longer run. The normal voltage the motor keeps running is at the rate of 450v to 470v….we install a series of capacitor with a total of 300uf each line (line 1, 2, 3 respectively) with capacitor rated voltages at 450v volts but these series of capacitor after 8 days it burst out…my final question sir what is the correct capacitor rated voltages to be use with this power system….hope you can advice us whether we will use higher rated voltages of capacitors? Thank you

very good pc to us learners

Sir,

when 10 kvar 440V capacitor is measured, it is 82 mfd, according to the formula mentioned above , it has to be divided by 2 again, pls correct.

so much comprehensible and applicable.

Good. Useful for academician and practicing Engineer.

Dear Sir,

You have really thought me a lesson about power factor correction. My question are,

1. How do you select/chose capacitors in order to obtain Power Factor consistently above 0.9 and above, even at no load of Transformer for Capacitor Bank? If you can explain with diagrams and a typical case study.

2. How will one offer regular capacitor maintenance, areas of concern and when will a capacitor may be changed. in many cases one is faced with capacitor and space for replacement in existing compartment?

Can you build a new cabinet and attach?

Thank you.

deGraft Johnson I.E.

Best article i have read

It’s a nice article sir…can u please explain control scheme using timer and relay channel in detail.

iam still reading through the article.it very informative

This is a very nice article on CBs. However, I cannot understand how you end up with the results in table 4 as far as the various Qs are concerned.As per my understanding the formulas are as below.

QRE=Qrz =2*3.14*50*0.000329*430=44.45

QL= 3*2*3.14*50*0.00216*25.65=52.14

QS=QRES=Qrz-QL=-7.69

Above results are far from what are given in Table 4 unless I am missing something.

There is a mistake in the Qre and QL formula, it should be Uc^2 and Is^2 respectively, then:

Qre = 2*phi*fn*C*Uc^2

QL = 3*2*phi*fn*LD*Is^2