WO2013058722A1 - Method of compensation of reactive power in an alternating current power line - Google Patents

Method of compensation of reactive power in an alternating current power line Download PDF

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Publication number
WO2013058722A1
WO2013058722A1 PCT/UA2012/000092 UA2012000092W WO2013058722A1 WO 2013058722 A1 WO2013058722 A1 WO 2013058722A1 UA 2012000092 W UA2012000092 W UA 2012000092W WO 2013058722 A1 WO2013058722 A1 WO 2013058722A1
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Prior art keywords
current
power
compensation
reactive power
light
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PCT/UA2012/000092
Other languages
French (fr)
Inventor
Iurii N. Samoilenko
Valeriy S. Galuschak
Original Assignee
Samoilenko Iurii N
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Publication of WO2013058722A1 publication Critical patent/WO2013058722A1/en

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Classifications

    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
    • H05B45/00—Circuit arrangements for operating light-emitting diodes [LED]
    • H05B45/30—Driver circuits
    • H05B45/395—Linear regulators
    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
    • H05B45/00—Circuit arrangements for operating light-emitting diodes [LED]
    • H05B45/30—Driver circuits
    • H05B45/37—Converter circuits
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B20/00—Energy efficient lighting technologies, e.g. halogen lamps or gas discharge lamps
    • Y02B20/30—Semiconductor lamps, e.g. solid state lamps [SSL] light emitting diodes [LED] or organic LED [OLED]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Definitions

  • the present invention relates to electrical engineering and, primarily to methods and devices for compensation and controlling power factor in converters or inverters and particularly deals with methods for compensation of power in alternating current power lines of industrial enterprises and/or individual consumers, used for meeting the requirements of a power supply system for reactive power consumption.
  • a method for connecting a reactive power compensator comprising several parallel compensating components to operating voltage is known from RU, 2342759, C2.
  • compensating components K1-K3 are first successively connected to an operating voltage (U) with the use of a control unit (CU) through a swamp resistance (R), and then without the swamp resistance.
  • a connected compensating component (K1 ) use is made of an active component (K1) with at least one controlled reactive power element, for example with a thyristor controlled resistance (TCR).
  • TCR thyristor controlled resistance
  • a device for compensating reactive power comprising a capacitor bank and a protective device against overvoltage connected in parallel to the capacitor bank is further known from RU,66620,U1.
  • This device is provided with a voltage measuring unit having its input connected to the input of the capacitor bank, while the output of the control unit is connected to a switching unit, its switching parts being included in the capacitor bank circuit consisting of three capacitors having different capacities with the ratio of their reference values 0,8:1 ,0:1 ,2.
  • This device is quite complicated. It is intended to be used in high-voltage networks and, respectively, solves the problem of compensating reactive power in such networks.
  • RU, 79741 , U1 discloses a lighting source in the form of a light- emitting diode, comprising a voltage down-converter connected through a bridge rectifier to at least one light-emitting diode, and a capacitor filter plugged in between the bridge rectifier and the light-emitting diode in parallel to the latter.
  • the voltage down-converter (1 ) is made up of a chain of capacitors connected in series, and at least one of them, which is a power take-off capacitor, is connected to the diode bridge rectifier.
  • the operation of the proposed light-emitting diode light source is characterized by an ultra-low active energy consumption, but this operation is not stable in transient states, particularly during short-time multiple repeated switching on - switching off.
  • US, 4647837 discloses a reactive power compensator comprising a current converter bridge circuit with semiconductor switches in the form of transistors or fully controlled thyristors installed in the bridge arms.
  • a capacitor is installed in the alternating-current circuit of the bridge connected to the power line, while the bridge in the direct-current circuit is bridged over a reactor.
  • each network feeder is provided with a current converter bridge, in which the input circuit at the side of the power line comprises a capacitor 3, and the output current of the current converter bridge is passed through a load in the form of an oscillating LC-circuit connected to the direct current outputs of the bridge, while as bridge switches use is made of thyristors, which results in control by the capacitor current.
  • an object of the present invention is to provide a method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line, which would result in quite simple compensation of inductive reactive power in consumer power lines with the inductive reactive power of light-emitting diodes without commutation losses and, at the same time, due to the light emission by light-emitting diodes in the course of operation, would also result in providing an additional function of general lighting when implementing the present method, due to the use of at least one light-emitting diode as a device controlling the input circuit of the current converter bridge with the current parameters.
  • the present objected is achieved by a method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line, comprising mounting in each network feeder of a current converter bridge, in which the input circuit at the side of the power line comprises at least one capacitor, and passing the output current of the current converter bridge through a load controlling the current passing through this capacitor.
  • a method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line comprising mounting in each network feeder of a current converter bridge, in which the input circuit at the side of the power line comprises at least one capacitor, and passing the output current of the current converter bridge through a load controlling the current passing through this capacitor.
  • at least one light-emitting diode is used as a load.
  • the output current of the current converter bridge passed to the light-emitting diode is first smoothed by a resistor capacitor filter connected to the output poles of this bridge, and then passed through a current regulator and a current-limiting resistor connected in series, at the same time, in order to configure voltage at the current regulator control gate the use of a reference resistor connected in parallel to the light-emitting diode is preferred.
  • Fig.1 shows a schematic view of a device for the use of the method according to the invention
  • Fig.2 shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a smoothing filter, a current regulator and a current-limiting resistor is provided;
  • Fig.3 - shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a surge suppressor;
  • Fig.4 - shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a smoothing inductor;
  • Fig.5 shows a schematic view of connecting three identical devices for the use of the method according to the invention in a three-phase electrical network.
  • Figs.1 to 4 show different devices for the use of this method.
  • Fig.1 shows a device for compensating reactive power in alternating-current power lines consuming such power, for example in such power lines like lighting networks or electrical networks in consumer's industrial facilities.
  • Each feeder (phase) of a power line 1 has a current converter bridge 2, wherein, in the input circuit at the side of the power line 1 , two capacitors 3, 4 connected in series are provided, the capacitor 3 being shunted by a high-ohmic discharge resistor 5, connected by one end to one of the poles of the bridge 2 and being used to configure the value of current flowing through a load, while the capacitor 4 is mounted between the poles of the input circuit of the bridge 2 in parallel to the power line 1 and is used to configure the voltage level on the current converter bridge 2.
  • At least one light-emitting diode 6 is installed (Fig.1 shows one light-emitting diode, and Fig. 2 to 4 show a group of the light-emitting diodes 6 connected in series).
  • the number of light-emitting diodes 6 is chosen based on the luminous flux needed for lighting the vicinity. In the course of flow of the rectified current, the light-emitting diode 6 flashes and lights the vicinity. Flow of the current through the capacitor 3 results in the creation of capacitive reactive power, and according to the proposed solution inductive reactive power in a consumer network will be compensated with capacitive reactive power, which increases the power factor (Cos ⁇ ), and, at the same time, such a compensator may serve as a lighting source.
  • the output current is smoothed by the capacitor filter 7 preferably comprising a capacitor 8 mounted in parallel between the poles of the output circuit of the bridge 2 (for example, a high- capacity electrolytic capacitor), such a capacitor being shunted by a resistor 9 and thermistor 10 connected in series.
  • the output current of the filter 7 is further passed through a current regulator 1 1 and a current-limiting resistor 12 connected in series, while a reference resistor 13 is connected in parallel to the light-emitting diode, which configures voltage on the current regulator 1 1 control gate.
  • the EH series chip or an HV analogue may be used.
  • Such an arrangement allows to smooth rectified current pulses and, at the same time, to maintain the current reference value through the light-emitting diodes 6.
  • a surge suppressor 14 is connected in parallel to the filter 7.
  • a smoothing inductor 15 in included in the input circuit of the current converter bridge 2 in parallel to the capacitor 4 configuring voltage on the current converter bridge (Fig. 4).
  • a scheme of plugging in a device 16 for compensating reactive power in a three-phase electrical network according to the invention is shown in Fig.5.
  • Each of the devices 16 is plugged in its own phase (feeder), which results in uniform compensation of reactive power with regard to the phases.
  • the reactive power produced by the device has a character of capacitive reactive power and is calculated based on formula (1 ):
  • inductive reactive power is compensated with capacitive reactive power, which results in an increase of the power factor (Cos ⁇ ), and, at the same time, due to light emission by the light-emitting diodes, such a method also provides for functioning of the device as a general lighting source.

Abstract

Method of compensation of reactive power in an alternating current power line The invention relates to electrical engineering and, primarily to methods and devices for compensation and controlling power factor in converters or inverters and particularly deals with methods for compensation of reactive power in. power lines of. industrial enterprises or individual consumers of this power, used for meeting the requirements of a power supply system for reactive power consumption. The claimed method lies in providing each feeder of a power line with a current converter bridge 2 having, in the input circuit at the side of the power line (1), at least one capacitor (3) and in passing the output current of the current converter bridge (2) through a load controlling the current passing through this capacitor (3). The novel feature of the method is that at feast one light-emitting diode (6) is used as a load. Various modifications of the present method are disclosed which allow optimizing the compensation process. In the course of use of the claimed method for compensation of reactive power in consumer's power line, inductive reactive power is compensated with capacitive reactive power of a lighting source, thus the power factor (Cos φ) increases, and, at the same time, due to light emission by the light-emitting diodes, the compensator serves as a general lighting source.

Description

METHOD OF COMPENSATION OF REACTIVE POWER IN AN ALTERNATING
CURRENT POWER LINE
FIELD OF THE INVENTION
The present invention relates to electrical engineering and, primarily to methods and devices for compensation and controlling power factor in converters or inverters and particularly deals with methods for compensation of power in alternating current power lines of industrial enterprises and/or individual consumers, used for meeting the requirements of a power supply system for reactive power consumption.
BACKGROUND ART
A method for connecting a reactive power compensator comprising several parallel compensating components to operating voltage is known from RU, 2342759, C2. According to this known method, in order to connect a reactive power compensator to operating voltage (U), compensating components (K1-K3) are first successively connected to an operating voltage (U) with the use of a control unit (CU) through a swamp resistance (R), and then without the swamp resistance. As a connected compensating component (K1 ) use is made of an active component (K1) with at least one controlled reactive power element, for example with a thyristor controlled resistance (TCR). Even though this method allows to prevent unacceptable high adverse effects on operating voltage, it can not but avoid losses of active power in the swamp resistance.
A device for compensating reactive power, comprising a capacitor bank and a protective device against overvoltage connected in parallel to the capacitor bank is further known from RU,66620,U1. This device is provided with a voltage measuring unit having its input connected to the input of the capacitor bank, while the output of the control unit is connected to a switching unit, its switching parts being included in the capacitor bank circuit consisting of three capacitors having different capacities with the ratio of their reference values 0,8:1 ,0:1 ,2. This device is quite complicated. It is intended to be used in high-voltage networks and, respectively, solves the problem of compensating reactive power in such networks.
RU, 79741 , U1 discloses a lighting source in the form of a light- emitting diode, comprising a voltage down-converter connected through a bridge rectifier to at least one light-emitting diode, and a capacitor filter plugged in between the bridge rectifier and the light-emitting diode in parallel to the latter. The voltage down-converter (1 ) is made up of a chain of capacitors connected in series, and at least one of them, which is a power take-off capacitor, is connected to the diode bridge rectifier. Since pure resistance is not present in a voltage down-converter, the operation of the proposed light-emitting diode light source is characterized by an ultra-low active energy consumption, but this operation is not stable in transient states, particularly during short-time multiple repeated switching on - switching off.
US, 4647837 discloses a reactive power compensator comprising a current converter bridge circuit with semiconductor switches in the form of transistors or fully controlled thyristors installed in the bridge arms. A capacitor is installed in the alternating-current circuit of the bridge connected to the power line, while the bridge in the direct-current circuit is bridged over a reactor.
Since fully controlled switches are commuted at high current and voltage values, this results in significant commutation losses and increasing the weight and size of the device.
The closest prior art is constituted by the method for compensation of reactive power in industrial and/or individual/consumer alternating-current power lines described in the patent RU,45572,U1. According to this method, each network feeder is provided with a current converter bridge, in which the input circuit at the side of the power line comprises a capacitor 3, and the output current of the current converter bridge is passed through a load in the form of an oscillating LC-circuit connected to the direct current outputs of the bridge, while as bridge switches use is made of thyristors, which results in control by the capacitor current.
Use of this method is also associated with commutation losses. It is charactertised by unstable operation in transient states and limited use. SUMMARY OF THE INVENTION
Thus, an object of the present invention is to provide a method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line, which would result in quite simple compensation of inductive reactive power in consumer power lines with the inductive reactive power of light-emitting diodes without commutation losses and, at the same time, due to the light emission by light-emitting diodes in the course of operation, would also result in providing an additional function of general lighting when implementing the present method, due to the use of at least one light-emitting diode as a device controlling the input circuit of the current converter bridge with the current parameters.
The present objected is achieved by a method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line, comprising mounting in each network feeder of a current converter bridge, in which the input circuit at the side of the power line comprises at least one capacitor, and passing the output current of the current converter bridge through a load controlling the current passing through this capacitor. According to the invention at least one light-emitting diode is used as a load.
It is the most preferable that the output current of the current converter bridge passed to the light-emitting diode is first smoothed by a resistor capacitor filter connected to the output poles of this bridge, and then passed through a current regulator and a current-limiting resistor connected in series, at the same time, in order to configure voltage at the current regulator control gate the use of a reference resistor connected in parallel to the light-emitting diode is preferred.
It is also advisable to use a surge suppressor, in addition to the resistor capacitor filter, which provides protection for a light-emitting diode by cutting down voltage surges which occur in a power line, while a smoothing inductor should be mounted in the input circuit of the current converter bridge in parallel to the capacitor configuring voltage on the bridge. Such an operation of the method according to the invention and its preferred embodiments results in compensation of inductive reactive power in an industrial and/or individual consumer alternating-current power line with the inductive reactive power of at least one light-emitting diode or a circuit including the same, which is incorporated in the direct-current output circuit of the current converter bridge.
BRIEF DESCRIPTION OF THE DRAWINGS The invention is further described in more details with reference to the accompanying drawings where:
Fig.1 shows a schematic view of a device for the use of the method according to the invention;
Fig.2 shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a smoothing filter, a current regulator and a current-limiting resistor is provided; Fig.3 - shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a surge suppressor;
Fig.4 - shows an embodiment of the device for the use of the method according to the invention, in which the additional use of a smoothing inductor;
Fig.5 shows a schematic view of connecting three identical devices for the use of the method according to the invention in a three-phase electrical network.
THE BEST MODE FOR CARRYING OUT THE INVENTION
To illustrate the method of the present invention Figs.1 to 4 show different devices for the use of this method. Thus, Fig.1 shows a device for compensating reactive power in alternating-current power lines consuming such power, for example in such power lines like lighting networks or electrical networks in consumer's industrial facilities.
Each feeder (phase) of a power line 1 has a current converter bridge 2, wherein, in the input circuit at the side of the power line 1 , two capacitors 3, 4 connected in series are provided, the capacitor 3 being shunted by a high-ohmic discharge resistor 5, connected by one end to one of the poles of the bridge 2 and being used to configure the value of current flowing through a load, while the capacitor 4 is mounted between the poles of the input circuit of the bridge 2 in parallel to the power line 1 and is used to configure the voltage level on the current converter bridge 2.
In the output of the direct-current circuit of the bridge 2 according to the invention at least one light-emitting diode 6 is installed (Fig.1 shows one light-emitting diode, and Fig. 2 to 4 show a group of the light-emitting diodes 6 connected in series).
The number of light-emitting diodes 6 is chosen based on the luminous flux needed for lighting the vicinity. In the course of flow of the rectified current, the light-emitting diode 6 flashes and lights the vicinity. Flow of the current through the capacitor 3 results in the creation of capacitive reactive power, and according to the proposed solution inductive reactive power in a consumer network will be compensated with capacitive reactive power, which increases the power factor (Cos φ), and, at the same time, such a compensator may serve as a lighting source.
According to the invention various modifications of the claimed method may be made, which provide for optimal conditions for compensating reactive power in power lines consuming such power.
As shown in Fig. 2, before supplying rectified current to circuit of light-emitting diodes 6 in the output circuit of the bridge 2, the output current is smoothed by the capacitor filter 7 preferably comprising a capacitor 8 mounted in parallel between the poles of the output circuit of the bridge 2 (for example, a high- capacity electrolytic capacitor), such a capacitor being shunted by a resistor 9 and thermistor 10 connected in series. The output current of the filter 7 is further passed through a current regulator 1 1 and a current-limiting resistor 12 connected in series, while a reference resistor 13 is connected in parallel to the light-emitting diode, which configures voltage on the current regulator 1 1 control gate. As a regulator the EH series chip or an HV analogue may be used.
Such an arrangement allows to smooth rectified current pulses and, at the same time, to maintain the current reference value through the light-emitting diodes 6.
As shown in Fig.3, to protect the light-emitting diodes 6 from voltage surges which occur in a power line, a surge suppressor 14 is connected in parallel to the filter 7. In order to maintain optimal conditions for compensation and to protect against unstable current supply in the power line 1 , a smoothing inductor 15 in included in the input circuit of the current converter bridge 2 in parallel to the capacitor 4 configuring voltage on the current converter bridge (Fig. 4). A scheme of plugging in a device 16 for compensating reactive power in a three-phase electrical network according to the invention is shown in Fig.5. Each of the devices 16 is plugged in its own phase (feeder), which results in uniform compensation of reactive power with regard to the phases. The reactive power produced by the device has a character of capacitive reactive power and is calculated based on formula (1 ):
U2
Qc ^ c~ (1 )
where,
U- voltage in the compensated consumer's power line, Uc ;
Xc - capacitance calculated based on formula (2). Xc = 1/ 2TT f C, (2) where ,
f- alternating-current frequency in a consumer's power line;
C - capacity of the capacitor 3.
Since significant inductive reactive power is generated in consumer's power lines, due to the use of the proposed method for compensation of reactive power in consumer's power lines, such inductive reactive power is compensated with capacitive reactive power, which results in an increase of the power factor (Cos φ), and, at the same time, due to light emission by the light-emitting diodes, such a method also provides for functioning of the device as a general lighting source.

Claims

Claims
1. A method for compensation of reactive power in an industrial and/or individual consumer alternating-current power line, comprising mounting, in each network feeder, of a current converter bridge, wherein the input circuit at the side of the power line comprises at least one capacitor, and passing the output current of the current converter bridge through a load controlling the current passing through this capacitor, characterized in that at least one light-emitting diode is used as a load.
2. The method according to claim 1 , characterized in that the output current of the current converter bridge passed to the light-emitting diode is first smoothed by a resistor capacitor filter connected to the output poles of the bridge, and then passed through a current regulator and a current-limiting resistor connected in series, while a reference resistor connected in parallel to the light-emitting diode is used in order to configure voltage at the current regulator control gate.
3. The method according to claim 2, characterized in that, in addition to the resistor capacitor filter, a surge suppressor is plugged in, which provides protection to a light-emitting diode by cutting down voltage surges which occur in a power line
4. The method according to any of claims 1 to 3, characterized in that a smoothing inductor is mounted in the input circuit of the current converter bridge in parallel to the capacitor configuring voltage on the bridge.
PCT/UA2012/000092 2011-10-19 2012-10-17 Method of compensation of reactive power in an alternating current power line WO2013058722A1 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
UAA201112269 2011-10-19
UAA201112269A UA101888C2 (en) 2011-10-19 2011-10-19 Method for reactive power balance in ac mains

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WO2013058722A1 true WO2013058722A1 (en) 2013-04-25

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CN105024383A (en) * 2014-03-20 2015-11-04 深圳市科陆驱动技术有限公司 Capacitor switching method in reactive compensation
US9641063B2 (en) 2014-01-27 2017-05-02 General Electric Company System and method of compensating power factor for electrical loads
CN106793269A (en) * 2016-12-07 2017-05-31 横店集团得邦照明股份有限公司 One kind compensation drive device and its implementation
CN107947191A (en) * 2017-12-11 2018-04-20 国网宁夏电力公司电力科学研究院 Reactive power compensator and mutual inductor detection device
CN110336296A (en) * 2019-07-10 2019-10-15 云南电网有限责任公司昆明供电局 A kind of electric network reactive-load equipment configuration method based on subregion reactive balance index

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Publication number Priority date Publication date Assignee Title
US9641063B2 (en) 2014-01-27 2017-05-02 General Electric Company System and method of compensating power factor for electrical loads
CN105024383A (en) * 2014-03-20 2015-11-04 深圳市科陆驱动技术有限公司 Capacitor switching method in reactive compensation
CN105024383B (en) * 2014-03-20 2018-01-05 深圳市科陆驱动技术有限公司 Capacitor switching method in reactive-load compensation
CN106793269A (en) * 2016-12-07 2017-05-31 横店集团得邦照明股份有限公司 One kind compensation drive device and its implementation
CN107947191A (en) * 2017-12-11 2018-04-20 国网宁夏电力公司电力科学研究院 Reactive power compensator and mutual inductor detection device
CN110336296A (en) * 2019-07-10 2019-10-15 云南电网有限责任公司昆明供电局 A kind of electric network reactive-load equipment configuration method based on subregion reactive balance index
CN110336296B (en) * 2019-07-10 2022-10-21 云南电网有限责任公司昆明供电局 Power grid reactive equipment configuration method based on partition reactive power balance index

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