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103-434: STATCOMS are alternatives to other passive reactive power devices, such as capacitors and inductors (reactors). They have a variable reactive power output, can change their output in terms of milliseconds, and able to supply and consume both capacitive and inductive vars . While they can be used for voltage support and power factor correction, their speed and capability are better suited for dynamic situations like supporting

206-526: A resistor , an ideal capacitor does not dissipate energy, although real-life capacitors do dissipate a small amount (see Non-ideal behavior ). The earliest forms of capacitors were created in the 1740s, when European experimenters discovered that electric charge could be stored in water-filled glass jars that came to be known as Leyden jars . Today, capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth

309-471: A vacuum or an electrical insulator material known as a dielectric . Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on

412-484: A "Low voltage electrolytic capacitor with porous carbon electrodes". He believed that the energy was stored as a charge in the carbon pores used in his capacitor as in the pores of the etched foils of electrolytic capacitors. Because the double layer mechanism was not known by him at the time, he wrote in the patent: "It is not known exactly what is taking place in the component if it is used for energy storage, but it leads to an extremely high capacity." The MOS capacitor

515-518: A STATCOM's VSC operation is based on changing current flow to affect voltage, its voltage-current (VI) characteristics control how it operates. The VI characteristic can be divided into two distinct parts: a slopped region between its inductive and capacitive maximums, and its maximum operating points. While in the slopped region between its maximums, the STATCOM is said to be in voltage regulation mode, where it either supplies capacitive vars to increase

618-491: A STATCOM's effectiveness is not dependent on the voltage drop caused by the fault. While technically capable of responding to near zero voltage magnitudes, typically a STATCOM is set to ride through voltage drops of around 0.2 pu and lower, to prevent the STATCOM from causing a high over-voltage when the fault clears, and the voltage returns to normal. A STATCOM may also have a transient rating, where it can provide above its maximum current for very short time, allowing it to help

721-480: A dielectric of permittivity ε {\displaystyle \varepsilon } . It is assumed the gap d {\displaystyle d} is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of

824-615: A dynamic reactive power output is possible. This compares to a traditional, fixed capacitor or inductor, that is either off (0 MVar) or at its maximum (for example, 50 MVar). A similarly sized STATCOM would range from 50 MVar capacitive to 50 MVar inductive, in as small as 1 MVar steps. Since a STATCOM varies its voltage magnitude to control reactive power, the topology of how the VSC is designed and connected defines how effectively and quickly it can operate. There are numerous different topologies available for VSCs and power electronic based converters,

927-406: A fast, dynamic, and multi-quadrant source of reactive power, a STATCOM can be used for a wide variety of applications, however they are better suited for supporting the grid under fault or transient events or contingency events. One popular use is to place a STATCOM along a transmission line, to improve system power flow. Under normal operation the STATCOM will do very little, however in the event of

1030-428: A fault of a nearby line, the power that was being served is forced onto other transmission lines. Ordinarily this results in voltage drop increases due to increased power flow, but with a STATCOM available it can supply reactive power to increase the voltage until either the fault is removed (if temporary) or until a fixed capacitor can be switched in (if the fault is permanent). In some cases, a STATCOM can be installed at

1133-700: A finite amount of energy before dielectric breakdown occurs. The capacitor's dielectric material has a dielectric strength U d which sets the capacitor's breakdown voltage at V = V bd = U d d . The maximum energy that the capacitor can store is therefore E = 1 2 C V 2 = 1 2 ε A d ( U d d ) 2 = 1 2 ε A d U d 2 {\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}} The maximum energy

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1236-461: A fixed size, reactive power flow is controlled by the difference in magnitude of the two AC voltages. From the equation, if the STATCOM creates a voltage magnitude greater than the system voltage, it supplies capacitive reactive power to the system. If the STATCOM's voltage magnitude is less, it consumes inductive reactive power from the system. As most modern VSCs are made of power electronics that are capable of making small voltage changes very quickly,

1339-491: A flexible dielectric sheet (like oiled paper) sandwiched between sheets of metal foil, rolled or folded into a small package. Early capacitors were known as condensers , a term that is still occasionally used today, particularly in high power applications, such as automotive systems. The term condensatore was used by Alessandro Volta in 1780 to refer to a device, similar to his electrophorus , he developed to measure electricity, and translated in 1782 as condenser , where

1442-452: A higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude – an AC "short circuit" or AC coupling . Conversely, for very low frequencies, the reactance is high, so that a capacitor is nearly an open circuit in AC analysis – those frequencies have been "filtered out". Capacitors are different from resistors and inductors in that the impedance

1545-614: A miniaturized and more reliable low-voltage support capacitor to complement their newly invented transistor . With the development of plastic materials by organic chemists during the Second World War , the capacitor industry began to replace paper with thinner polymer films. One very early development in film capacitors was described in British Patent 587,953 in 1944. Electric double-layer capacitors (now supercapacitors ) were invented in 1957 when H. Becker developed

1648-420: A new apparent power ( S ), measured in volt-amperes: The relationship between real power and apparent power is described by the power factor . With a purely resistive load, they are the same: the apparent power is equal to the real power. Where a reactive (capacitive or inductive) component is present in the load, the apparent power is greater than the real power as voltage and current are no longer in phase. In

1751-576: A similar capacitor, which was named the Leyden jar , after the University of Leiden where he worked. He also was impressed by the power of the shock he received, writing, "I would not take a second shock for the kingdom of France." Daniel Gralath was the first to combine several jars in parallel to increase the charge storage capacity. Benjamin Franklin investigated the Leyden jar and came to

1854-534: A substation, to help support multiple lines rather than just one, and help reducing the complexity of the protection on the line with a STATCOM on it. Depending on available control function, STATCOMs can also be used for more advanced applications, such as active filtering, Power Oscillation Damping (POD) , or even limited active power interactions. With growth of Distributed Energy Resources (DER) and Energy Storage , there has been research into using STATCOMs to aid or augment these uses. One area of recent research

1957-434: A total of five levels can be created. This creates a very crude sine wave, however PWM still offer less harmonic generation (as the pulses are still on all five levels). Three-level converters can also be combined with transformers and phase shifting to create additional levels. A transformer with two secondaries, one Wye-Wye and the other Wye-Delta, can be connected to two separate three-phase, three-level converters to double

2060-467: A voltage of one volt across the device. Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance. In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance

2163-469: A volume of water in a hand-held glass jar. Von Kleist's hand and the water acted as conductors and the jar as a dielectric (although details of the mechanism were incorrectly identified at the time). Von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine. The following year, the Dutch physicist Pieter van Musschenbroek invented

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2266-590: Is inversely proportional to the defining characteristic; i.e., capacitance . A capacitor connected to an alternating voltage source has a displacement current to flowing through it. In the case that the voltage source is V 0 cos(ωt), the displacement current can be expressed as: I = C d V d t = − ω C V 0 sin ⁡ ( ω t ) {\displaystyle I=C{\frac {{\text{d}}V}{{\text{d}}t}}=-\omega {C}{V_{0}}\sin(\omega t)} At sin( ωt ) = −1 ,

2369-400: Is a function of dielectric volume, permittivity , and dielectric strength . Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that

2472-471: Is added to represent the initial voltage V ( t 0 ). This is the integral form of the capacitor equation: V ( t ) = Q ( t ) C = V ( t 0 ) + 1 C ∫ t 0 t I ( τ ) d τ {\displaystyle V(t)={\frac {Q(t)}{C}}=V(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t}I(\tau )\,\mathrm {d} \tau } Taking

2575-408: Is approximately the same width as the plate separation, d {\displaystyle d} , and assuming d {\displaystyle d} is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of + Q {\displaystyle +Q} is placed on one plate and − Q {\displaystyle -Q} on

2678-447: Is defined as C = Q / V {\displaystyle C=Q/V} . Substituting V {\displaystyle V} above into this equation C = ε A d {\displaystyle C={\frac {\varepsilon A}{d}}} Therefore, in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between

2781-419: Is defined in terms of incremental changes: C = d Q d V {\displaystyle C={\frac {\mathrm {d} Q}{\mathrm {d} V}}} In the hydraulic analogy , voltage is analogous to water pressure and electrical current through a wire is analogous to water flow through a pipe. A capacitor is like an elastic diaphragm within the pipe. Although water cannot pass through

2884-419: Is due to possible loss of synchronicity and cooling). The footprint of a STATCOM is smaller, as it does not need large capacitors used by an SVC for TSC or filters. Capacitor In electrical engineering , a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as

2987-475: Is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field. The current I ( t ) through any component in an electric circuit is defined as the rate of flow of a charge Q ( t ) passing through it. Actual charges – electrons – cannot pass through the dielectric of an ideal capacitor. Rather, one electron accumulates on

3090-442: Is generally around 5%, to keep the system voltage within 5% of its nominal value. When operating at either of its maximums, the STATCOM is said to be in a VAR control mode, where it's supplying or consuming its maximum reactive output. Unlike a traditional SVC, whose capacitive reactive output is linearly dependent on the voltage, a STATCOM can supply its maximum capacitive rating for any voltage. This offers an advantage over SVCs, as

3193-956: Is the time constant of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially . In the case of a discharging capacitor, the capacitor's initial voltage ( V Ci ) replaces V 0 . The equations become I ( t ) = V C i R e − t / τ 0 V ( t ) = V C i e − t / τ 0 Q ( t ) = C V C i e − t / τ 0 {\displaystyle {\begin{aligned}I(t)&={\frac {V_{Ci}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{Ci}\,e^{-t/\tau _{0}}\\Q(t)&=C\,V_{Ci}\,e^{-t/\tau _{0}}\end{aligned}}} Impedance ,

Static synchronous compensator - Misplaced Pages Continue

3296-419: Is the imaginary unit and ω is the angular frequency of the sinusoidal signal. The − j phase indicates that the AC voltage V = ZI lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc. Impedance decreases with increasing capacitance and increasing frequency. This implies that

3399-422: Is the unit of measurement for apparent power in an electrical circuit . It is the product of the root mean square voltage (in volts ) and the root mean square current (in amperes ). Volt-amperes are usually used for analyzing alternating current (AC) circuits. In direct current (DC) circuits, this product is equal to the real power , measured in watts . The volt-ampere is dimensionally equivalent to

3502-482: Is the capacitance for a single plate and n {\displaystyle n} is the number of interleaved plates. As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. Every pair of adjacent plates acts as a separate capacitor; the number of pairs is always one less than the number of plates, hence the ( n − 1 ) {\displaystyle (n-1)} multiplier. To increase

3605-407: Is the charge stored in the capacitor, V {\displaystyle V} is the voltage across the capacitor, and C {\displaystyle C} is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between

3708-800: Is then I (0) = V 0 / R . With this assumption, solving the differential equation yields I ( t ) = V 0 R e − t / τ 0 V ( t ) = V 0 ( 1 − e − t / τ 0 ) Q ( t ) = C V 0 ( 1 − e − t / τ 0 ) {\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{0}\left(1-e^{-t/\tau _{0}}\right)\\Q(t)&=CV_{0}\left(1-e^{-t/\tau _{0}}\right)\end{aligned}}} where τ 0 = RC

3811-563: Is virtual inertia: the use of an energy source on the DC side of a STATCOM to give it an inertia response similar to a synchronous condenser or generator. Fundamentally, a STATCOM is type of static VAR compensator (SVC), with the main difference being that a STATCOM is a voltage-sourced converter while a traditional SVC is a current-sourced converter . Historically, STATCOM have been costlier than an SVC, in part due to higher cost of IGBTs), but in recent years IGBT power ratings have increased, closing

3914-408: The condenser , a term still encountered in a few compound names, such as the condenser microphone . It is a passive electronic component with two terminals . The utility of a capacitor depends on its capacitance . While some capacitance exists between any two electrical conductors in proximity in a circuit , a capacitor is a component designed specifically to add capacitance to some part of

4017-484: The watt : in SI units , 1 V⋅A = 1 W. VA rating is most used for generators and transformers, and other power handling equipment, where loads may be reactive (inductive or capacitive). For a simple electrical circuit running on direct current , the electrical current and voltage are constant. In that case, the real power ( P , measured in watts ) is the product of the current ( I , measured in amperes ) and

4120-501: The 1990s and had the ability to switch both on and off at higher power levels, the first STATCOMs began to be commercially available. These devices typically used 3-level topologies and pulse-width modulation (PWM) to simulate voltage waveforms. Modern STATCOMs now make use of insulated-gate bipolar transistors (IGBTs), which allow for faster switching at high-power levels. 3-level topologies have begun to give way to Multi-Modular Converter (MMC) Topologies, which allow for more levels in

4223-513: The Inductor or transformer δ {\displaystyle \delta } : Phase-Angle difference between V S {\displaystyle V_{S}} and V R {\displaystyle V_{R}} With δ {\displaystyle \delta } close to zero (as the STATCOM provides no real power and only consumes a small amount as losses) and X {\displaystyle X}

Static synchronous compensator - Misplaced Pages Continue

4326-428: The capacitor for each step depends on the DC needs. If a DC bus is needed (for an HVDC tie or a STATCOM with synthetic inertia ) then only two IGBTs are needed per capacitor level. If a DC bus is not needed, and there are benefits to connecting the three phases into a delta arrangement to eliminate zero sequence harmonics , four IGBTs can be used to surround the capacitor to bypass or switch it in at either polarity. As

4429-546: The capacitor has a maximum (or peak) current whereby I 0 = ωCV 0 . The ratio of peak voltage to peak current is due to capacitive reactance (denoted X C ). X C = V 0 I 0 = V 0 ω C V 0 = 1 ω C {\displaystyle X_{C}={\frac {V_{0}}{I_{0}}}={\frac {V_{0}}{\omega CV_{0}}}={\frac {1}{\omega C}}} X C approaches zero as ω approaches infinity. If X C approaches 0,

4532-575: The capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0 , it follows from Kirchhoff's voltage law that V 0 = v resistor ( t ) + v capacitor ( t ) = i ( t ) R + 1 C ∫ t 0 t i ( τ ) d τ {\displaystyle V_{0}=v_{\text{resistor}}(t)+v_{\text{capacitor}}(t)=i(t)R+{\frac {1}{C}}\int _{t_{0}}^{t}i(\tau )\,\mathrm {d} \tau } Taking

4635-411: The capacitor is the inductor , which stores energy in a magnetic field rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance  L . A series circuit containing only a resistor , a capacitor, a switch and a constant DC source of voltage V 0 is known as a charging circuit . If

4738-687: The capacitor resembles a short wire that strongly passes current at high frequencies. X C approaches infinity as ω approaches zero. If X C approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies. The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source: I = − I 0 sin ⁡ ( ω t ) = I 0 cos ⁡ ( ω t + 90 ∘ ) {\displaystyle I=-I_{0}\sin({\omega t})=I_{0}\cos({\omega t}+{90^{\circ }})} In this situation,

4841-465: The capacitor's charge capacity. Materials commonly used as dielectrics include glass , ceramic , plastic film , paper , mica , air, and oxide layers . When an electric potential difference (a voltage ) is applied across the terminals of a capacitor, for example when a capacitor is connected across a battery, an electric field develops across the dielectric, causing a net positive charge to collect on one plate and net negative charge to collect on

4944-413: The capacitor. Since the separation between the plates is uniform over the plate area, the electric field between the plates E {\displaystyle E} is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area

5047-438: The charge and voltage on a capacitor, work must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field. If the voltage on the capacitor is V {\displaystyle V} , the work d W {\displaystyle dW} required to move a small increment of charge d q {\displaystyle dq} from

5150-412: The circuit. The physical form and construction of practical capacitors vary widely and many types of capacitor are in common use. Most capacitors contain at least two electrical conductors , often in the form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, or an electrolyte . The nonconducting dielectric acts to increase

5253-430: The conclusion that the charge was stored on the glass, not in the water as others had assumed. He also adopted the term "battery", (denoting the increase of power with a row of similar units as in a battery of cannon ), subsequently applied to clusters of electrochemical cells . In 1747, Leyden jars were made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between

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5356-609: The control system, allowing an SVC to detect and react to faults to better support the system. The thyristor dominated the FACTs and HVDC world until the late 20th century, when the IGBT began to match its power ratings. With the IGBT, the first voltage-sourced converters and STATCOMs began to enter the FACTs world. A prototype 1 MVAr STATCOM was described in a report by Empire State Electric Energy Research Corporation in 1987. The first production 100 MVAr STATCOM made by Westinghouse Electric

5459-487: The cost of adding 2, 3 or even 4 additional STATCOMs. It also adds little to no redundancy, as the switching pattern is too complex to accommodate the loss of one STATCOM. As the idea of the three-level converter is to add additional levels to better approximate a voltage sine wave, another topology called the Modular Multi-level Converter (MMC) offers some benefits. The MMC topology is similar to

5562-538: The current is out of phase with the voltage by +π/2 radians or +90 degrees, i.e. the current leads the voltage by 90°. When using the Laplace transform in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the s domain by: Z ( s ) = 1 s C {\displaystyle Z(s)={\frac {1}{sC}}} where MVAr The volt-ampere ( SI symbol : VA , sometimes V⋅A or V A )

5665-402: The derivative and multiplying by C , gives a first-order differential equation : R C d i ( t ) d t + i ( t ) = 0 {\displaystyle RC{\frac {\mathrm {d} i(t)}{\mathrm {d} t}}+i(t)=0} At t = 0 , the voltage across the capacitor is zero and the voltage across the resistor is V 0 . The initial current

5768-429: The derivative of this and multiplying by C yields the derivative form: I ( t ) = d Q ( t ) d t = C d V ( t ) d t {\displaystyle I(t)={\frac {\mathrm {d} Q(t)}{\mathrm {d} t}}=C{\frac {\mathrm {d} V(t)}{\mathrm {d} t}}} for C independent of time, voltage and electric charge. The dual of

5871-439: The device. When a UPS powers equipment which presents a reactive load with a low power factor, neither limit may safely be exceeded. For example, a (large) UPS system rated to deliver 400,000 volt-amperes (400 kVA) at 220 volts can deliver a current of 1818 amperes (these are RMS values). VA ratings are also often used for transformers; maximum output current is then VA rating divided by nominal output voltage. Transformers with

5974-480: The diaphragm, it moves as the diaphragm stretches or un-stretches. In a circuit, a capacitor can behave differently at different time instants. However, it is usually easy to think about the short-time limit and long-time limit: The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of A {\displaystyle A} separated by a uniform gap of thickness d {\displaystyle d} filled with

6077-401: The dielectric for the first capacitors. Paper capacitors, made by sandwiching a strip of impregnated paper between strips of metal and rolling the result into a cylinder, were commonly used in the late 19th century; their manufacture started in 1876, and they were used from the early 20th century as decoupling capacitors in telephony . Porcelain was used in the first ceramic capacitors . In

6180-428: The durations of the pulses, the effective magnitude of the voltage waveform can be controlled. Since PWM still only produces square waves, harmonic generation is quite significant. Some harmonic reduction can be achieved by analytical techniques on different switching patterns; however, this is limited to controller complexity. Each level of the two-level converter also generally comprises multiple series IGBTs, to create

6283-507: The early years of Marconi 's wireless transmitting apparatus, porcelain capacitors were used for high voltage and high frequency application in the transmitters . On the receiver side, smaller mica capacitors were used for resonant circuits . Mica capacitors were invented in 1909 by William Dubilier. Prior to World War II, mica was the most common dielectric for capacitors in the United States. Charles Pollak (born Karol Pollak ),

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6386-442: The electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called parasitic capacitance . For some simple capacitor geometries this additional capacitance term can be calculated analytically. It becomes negligibly small when

6489-476: The foils. The earliest unit of capacitance was the jar , equivalent to about 1.11 nanofarads . Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of wireless ( radio ) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance . More compact construction methods began to be used, such as

6592-477: The gap. The response time of a STATCOM is shorter than that of a SVC, mainly due to the fast-switching times provided by the IGBTs of the voltage source converter ( thyristors cannot be switched off and must be commutated). As a result, the reaction time of a STATCOM is one to two cycles vs. two to three cycles for an SVC. The STATCOM also provides better reactive power support at low AC voltages than an SVC, since

6695-419: The grid under fault conditions or contingency events . The use of voltage-source based FACTs device had been desirable for some time, as it helps mitigate the limitations of current-source based devices whose reactive output decreases with system voltage. However, limitations in technology have historically prevented wide adoption of STATCOMs. When gate turn-off thyristors (GTO) became more widely available in

6798-403: The increase in losses it caused. They also became less effective as higher voltage transmissions lines moved loads further from sources. Fixed, shunt capacitor and reactor banks filled this need by being deployed where needed. In particular, shunt capacitors switched by circuit breakers provided an effective means to managing varying reactive power requirements due to changing loads. However, this

6901-405: The inventor of the first electrolytic capacitors , found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline electrolyte , even when the power was switched off. In 1896 he was granted U.S. Patent No. 672,913 for an "Electric liquid capacitor with aluminum electrodes". Solid electrolyte tantalum capacitors were invented by Bell Laboratories in the early 1950s as

7004-413: The limiting case of a purely reactive load, current is drawn but no power is dissipated in the load. Some devices, including uninterruptible power supplies (UPSs), have ratings both for maximum volt-amperes and maximum watts. A common prefixed derived unit is "kilovolt-ampere" (symbol kVA). The VA rating is limited by the maximum permissible current, and the watt rating by the power-handling capacity of

7107-439: The line's inductance, and as transmission voltage increased throughout the 20th century, the higher voltage supplied capacitive reactive power. As operating a transmission line only at it surge impedance loading (SIL) was not feasible, other means to manage the reactive power was needed. Synchronous Machines were commonly used at the time for generators, and could provide some reactive power support, however were limited due to

7210-430: The mercury-arc valve was a high-powered rectifier , capable of converting high AC voltages to DC. As the technology improved, inverting became possible as well and mercury valves found use in power systems and HVDC ties. When connected to a reactor, different switching pattern could be used to vary the effective inductance connected, allow for more dynamic control. Arc valves continued to dominate power electronics until

7313-448: The most common ones are covered below. IGBTS are listed as the power electronics device below, however older devices also used GTO Thyristors. One of the earliest VSC topologies was the two-level converter, adapted from the three-phase bridge rectifier . Also referred to as a 6-pulse rectifier, it is able to connect the AC voltage through different IGBT paths based on switching. When used as a rectifier to convert AC to DC, this allows both

7416-621: The name referred to the device's ability to store a higher density of electric charge than was possible with an isolated conductor. The term became deprecated because of the ambiguous meaning of steam condenser , with capacitor becoming the recommended term in the UK from 1926, while the change occurred considerably later in the United States. Since the beginning of the study of electricity , non-conductive materials like glass , porcelain , paper and mica have been used as insulators . Decades later, these materials were also well-suited for use as

7519-409: The needed final voltage, so coordination and timing between individual devices is challenging. Adding additional levels to a converter topology has the benefit of more closely mirroring a true voltage sine wave , which reduces harmonic generation and improves performance. If all three phases of a VSC utilize its own two-level converter topology, the phase-to-phase voltage will be three levels (as while

7622-415: The negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the integral of the current as well as proportional to the voltage, as discussed above. As with any antiderivative , a constant of integration

7725-911: The negative to the positive plate is d W = V d q {\displaystyle dW=Vdq} . The energy is stored in the increased electric field between the plates. The total energy W {\displaystyle W} stored in a capacitor (expressed in joules ) is equal to the total work done in establishing the electric field from an uncharged state. W = ∫ 0 Q V ( q ) d q = ∫ 0 Q q C d q = 1 2 Q 2 C = 1 2 V Q = 1 2 C V 2 {\displaystyle W=\int _{0}^{Q}V(q)\,\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}VQ={\frac {1}{2}}CV^{2}} where Q {\displaystyle Q}

7828-437: The number of levels. Additional phase-shifted windings can be used to turn the traditional 6 pulses of a three-level to 12, 24, or even 48 pulses. With this many pulses and levels, the waveform better approximates a true sine wave, and all harmonics generated are of a much higher order that can be filtered out with a low-pass filter . While adding phase shifting to three-level converters improves harmonic performance, it comes at

7931-416: The other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a surface charge layer of constant charge density σ = ± Q / A {\displaystyle \sigma =\pm Q/A} coulombs per square meter, on the inside surface of each plate. From Gauss's law the magnitude of the electric field between

8034-514: The other plate. No current actually flows through a perfect dielectric . However, there is a flow of charge through the source circuit. If the condition is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike

8137-431: The output of power supplies . In resonant circuits they tune radios to particular frequencies . In electric power transmission systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in early digital computers, and still is in modern DRAM . Natural capacitors have existed since prehistoric times. The most common example of natural capacitance are

8240-668: The plates is E = σ / ε {\displaystyle E=\sigma /\varepsilon } . The voltage(difference) V {\displaystyle V} between the plates is defined as the line integral of the electric field over a line (in the z-direction) from one plate to another V = ∫ 0 d E ( z ) d z = E d = σ ε d = Q d ε A {\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}} The capacitance

8343-451: The plates, the charge moving under the influence of the electric field will do work on the external circuit. If the gap between the capacitor plates d {\displaystyle d} is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value E = V / d {\displaystyle E=V/d} . In this case

8446-446: The plates. Since the area A {\displaystyle A} of the plates increases with the square of the linear dimensions and the separation d {\displaystyle d} increases linearly, the capacitance scales with the linear dimension of a capacitor ( C ∝ L {\displaystyle C\varpropto L} ), or as the cube root of the volume. A parallel plate capacitor can only store

8549-476: The positive and negative portion of the waveform to be converted to DC. When used in a VSC for a STATCOM, a capacitor can be connected across the DC side to produce a square wave with two levels. This alone offers no real advantages for a STATCOM, as the voltage magnitude is fixed. However, if the IGBTs can be switched fast enough, pulse-width modulation (PWM) can be used to control the voltage magnitude. By varying

8652-499: The ratios of plate width to separation and length to separation are large. For unevenly charged plates: For n {\displaystyle n} number of plates in a capacitor, the total capacitance would be C = ε o A d ( n − 1 ) {\displaystyle C=\varepsilon _{o}{\frac {A}{d}}(n-1)} where C = ε o A / d {\displaystyle C=\varepsilon _{o}A/d}

8755-753: The reactive power flow between the two points is given by: Q = V S ∗ ( Δ V ) X ∗ cos ⁡ ( δ ) {\displaystyle Q={\frac {V_{S}*(\Delta V)}{X}}*\cos(\delta )} where Q {\displaystyle Q} : Reactive Power V S {\displaystyle V_{S}} : Sending-End Voltage Δ V {\displaystyle \Delta V} : Magnitude difference in V S {\displaystyle V_{S}} and receiving end voltage V R {\displaystyle V_{R}} X {\displaystyle X} : Reactance of

8858-450: The reactive power from a STATCOM decreases linearly with the AC voltage (the current can be maintained at the rated value even down to low AC voltage), as opposed to power being a function of a square of voltage for SVC. The SVC is not used in a severe undervoltage conditions (less than 0.6 pu ), since leaving the capacitors on can worsen the transient overvoltage once the fault is cleared, while STATCOM can operate until 0.2–0.3 pu (this limit

8961-555: The reference voltage with respect to the slope and any other modes a STATCOM may have. A full PID system can be used, but typically the derivative component is removed (or set very low) to prevent noise from the system or measurements from causing unwanted fluctuations. A STATCOM may also have additional modes besides voltage regulation or VAR control, depending on specific needs of the system. Examples being active filtering of system harmonics or gain control to accommodate system strength changes due to outages of generation or loads. As

9064-534: The rise of solid-state semiconductors in the mid 20th century. As semiconductors replaced vacuum tubes, the thyristor created the first modern FACTs devices in the Static VAR Compensator (SVC). Effectively working as a circuit breaker that could switch on in milliseconds, it allowed for quickly switching capacitor banks. Connected to a reactor and switched sub-cycle allowed the effective inductance to be varied. The thyristor also greatly improved

9167-453: The same sized core usually have the same VA rating. The convention of using the volt-ampere to distinguish apparent power from real power is allowed by the SI standard. In electric power transmission and distribution , volt-ampere reactive ( var ) is a unit of measurement of reactive power . Reactive power exists in an AC circuit when the current and voltage are not in phase. The term var

9270-453: The static charges accumulated between clouds in the sky and the surface of the Earth, where the air between them serves as the dielectric. This results in bolts of lightning when the breakdown voltage of the air is exceeded. In October 1745, Ewald Georg von Kleist of Pomerania , Germany, found that charge could be stored by connecting a high-voltage electrostatic generator by a wire to

9373-623: The stored energy can be calculated from the electric field strength W = 1 2 C V 2 = 1 2 ε A d ( E d ) 2 = 1 2 ε A d E 2 = 1 2 ε E 2 ( volume of electric field ) {\displaystyle W={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(Ed\right)^{2}={\frac {1}{2}}\varepsilon AdE^{2}={\frac {1}{2}}\varepsilon E^{2}({\text{volume of electric field}})} The last formula above

9476-561: The surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field. An ideal capacitor is characterized by a constant capacitance C , in farads in the SI system of units, defined as the ratio of the positive or negative charge Q on each conductor to the voltage V between them: C = Q V {\displaystyle C={\frac {Q}{V}}} A capacitance of one farad (F) means that one coulomb of charge on each conductor causes

9579-423: The system better for larger faults. This rating depends on the specific design, but can be as high as 3.0 pu. To control the operation of a STATCOM when in voltage control mode, a closed loop , PID regulator is typically used, which allows for feedback on how changing the current flow is affecting the system voltage. A simplified PID regulator is shown, however a separate closed loop is sometimes used to determine

9682-500: The three phase have the same switching pattern, they are shifted in time relative to each other). This allows a positive and negative peak in addition to a zero level, which adds positive and negative symmetry and eliminates even order harmonics. Another option is to enhance the two-level topology to a three-level converter. By adding two additional IGBTs to the converter, three different levels can be created by have two IGBTs on at once. If each phase has its own three-level converter, then

9785-454: The three-level in that switching on various IGBTs will connect different capacitors to the circuit. As each IGBT "switch" has its own capacitor, voltage can be built up in discrete steps. Adding additional levels increases the number of steps, better approximating a sine wave. With enough levels, PWM is not necessary as the waveform created is close enough to a true voltage sine wave and generates very little harmonics. The IGBT arrangement around

9888-951: The vector sum of reactance and resistance , describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. Fourier analysis allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively X = − 1 ω C = − 1 2 π f C Z = 1 j ω C = − j ω C = − j 2 π f C {\displaystyle {\begin{aligned}X&=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}\\Z&={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}=-{\frac {j}{2\pi fC}}\end{aligned}}} where j

9991-590: The voltage from one side of the circuit to the other ( V , measured in volts ): For alternating current , both the voltage and current are oscillating. Instantaneous power is still the product of instantaneous current and instantaneous voltage, but if both of those are ideal sine waves driving a purely resistive load (like an incandescent light bulb), average power becomes (with subscripts designating average (av), peak amplitude (pk) and root mean square (rms)): More generally, when voltage and current are not in phase, these products no longer represent average power but

10094-501: The voltage or consumes inductive vars to lower the voltage. The rate at which it does this is set by the slope, which functions similar to a generator's droop speed control . This slope is programmable and can be set to a high value (to have the STATCOM regulate voltage like a traditional fixed reactive device) or to near zero, producing a very flat line and reserving the STATCOMs capacity for dynamic or transient events. The maximum slope

10197-562: The voltage waveform, reducing harmonics and improving performance. When AC won the War of Currents in the late 19th century, and electric grids began expanding and connecting cities and states, the need for reactive compensation became apparent. While AC offered benefits with transformation and reduced current, the alternating nature of voltage and current lead to additional challenges with the natural capacitance and inductance of transmission lines . Heavily loaded lines consumed reactive power due to

10300-568: Was installed at the Tennessee Valley Authority Sullivan substation in 1995 but was quickly retired due to obsolescence of its components. The basis of a STATCOM is a voltage source converter (VSC) connected in series with some type of reactance, either a fixed Inductor or a Power Transformer . This allows a STATCOM to control power flow much like a Transmission Line , albeit without any active (real) power flow. Given an inductor connected between two AC voltages,

10403-404: Was later widely adopted as a storage capacitor in memory chips , and as the basic building block of the charge-coupled device (CCD) in image sensor technology. In 1966, Dr. Robert Dennard invented modern DRAM architecture, combining a single MOS transistor per capacitor. A capacitor consists of two conductors separated by a non-conductive region. The non-conductive region can either be

10506-402: Was not without limitations. Shunt capacitors and reactors are fixed devices, only able to be switched on and off. This required either a careful study of the exact size needed, or accepting less than ideal effects on the voltage of a transmission line. The need for a more dynamic and flexible solution was realized with the mercury-arc valve in the early 20th century. Similar to a vacuum tube ,

10609-756: Was proposed by the Romanian electrical engineer Constantin Budeanu and introduced in 1930 by the IEC in Stockholm , which has adopted it as the unit for reactive power. Special instruments called varmeters are available to measure the reactive power in a circuit. The unit "var" is allowed by the International System of Units (SI) even though the unit var is representative of a form of power. Per EU directive 80/181/EEC (the "metric directive"),

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