Power Quality. Guide for electrical design engineers. Power Quality. Mitigation of voltage unbalance

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1 Guide for electrical design engineers Power Quality Zbigniew Hanzelka GH-University of Science & Technology Mitigation of voltage unbalance U U = C = - = L U U = - U = - U Power Quality

2 Power Quality. ntroduction When the limit values of unbalance factor, specified in standards are exceeded, the use of symmetrizatin systems is required. symmetrizator should not cause significant active power losses during operation; it implies that the symmetrization process shall be carried out by means of reactive elements (LC) or using active methods (power electronic systems).. Symmetrization of the load currents The further analysis, using the method of symmetrical components, concerns the system node in the configuration as in Figure. n asymmetrical load (), symmetrical load (S) and compensator (K) are connected to substation busbars of phase voltage U, supplied from three-phase symmetrical system. COMPENSTOR (K) K K E E E U U U SYMETRC LOD (S) SYMETRC LOD () Fig.. Diagram of the analysed node Since the system of electromotive forces (E) and the supply line are symmetrical, it is assumed that the voltage unbalance at the load terminals is caused by the asymmetry of the load currents. t means that, if the asymmetry of the load currents is eliminated, the voltages at the point of the load connection form the symmetrical three-phase system. This is the case of the supply system protection, and the loads connected to it, against the asymmetry caused by asymmetrical currents of the load () and resulting asymmetrical voltage drops across the equivalent impedances of supply system (on assumption identical in all phases: Z= Z= Z). n obvious conclusion from Figure is that the voltage unbalance at PCC, caused by the load asymmetry, can be mitigated by reduction of the phase equivalent impedances (short-circuit impedances) i.e. by increasing the short-circuit capacity at the point of load connection, what in practice means connecting the load to the point of the system of higher voltage.. The natural symmetrization The first and the most basic operation of the symmetrization process is the arrangement of the actual load connections between the system phases, in such a way that the current unbalance factor (and hence the voltage unbalance factor) was the smallest possible value. n case of connecting a single load to the network, the level of unbalance (measured by the current unbalance factor for zero- or negative-sequence component) does not depend on phase-to-phase or phase-to-neutral voltage, where the load is connected. Similarly, when connecting two singleelement loads, the level of unbalance does not depend on which voltages the loads are connected. However, when these loads will have a different character then, in terms of the natural symmetrization (i.e. the symmetrization, which does not require any additional elements), it is important to take into account the character of the loads and phase angles of the voltages they are connected to.

3 EXMPLE Mitigation of voltage unbalance For the system of three loads on nominal voltage 8 V and powers, respectively: P = 7. kw, Q = 7. kvr (ind.); P = 7. kw, Q = 7. kvr (cap.); P = 7. kw, Q = delta-connected, supplied from three-phase x8/v network, determine the arrangement of their connections to the network phases, ensuring minimum value of the current unbalance factor. From the load active and reactive power the elements of its equivalent admittance can be determined, i.e.: the Q susceptance (B = U ) and conductance (G = P ) (Fig. ). U U N Load (P, Q) U N B G Y Hence: Fig.. The load (P - active power, Q - reactive power) and its equivalent admittance P Y G jb j Q 7. kw 7. kvr = + = = j = (.5 j. 5) S U U ( 8V ) ( 8V ) P Y G jb j Q 7. kw 7. kvr = + = + = + j = (.5+ j. 5) S U U ( 8V ) ( 8V ) P Y G jb j Q 7. kw kvr = + = + = + j =. S U U ( 8V ) ( 8V ) Variant Loads connected as in Fig. : Y Y Y Y = Y = Y = Y Y Y Fig.. Variant of load connection The current unbalance factor: k % ( ) a Y+ Y+ ay = % = % = 68. % () Y + Y + Y a= exp( j ) = + j a = exp( j ) = j

4 Power Quality 4 Three-wire network voltages 4 Three-wire network currents Voltages [V] - Currents [] Time [s] Time [s] Fig. 4. Voltage waveforms: Example Variant Fig. 5. Current waveforms: Example Variant See Figures 4 and 5. Variant - Y = Y Y = Y Y = Y The current unbalance factor: k % ( ) a Y+ Y+ ay = % = % = 8. % () Y + Y + Y This is the minimal value of the current unbalance factor, which can be obtained connecting the impedances to phase-to-phase voltages in various configurations. This configuration has been taken for further considerations (Fig. 6). 4 Three-wire network currents Currents [] Time [s] Fig. 6. Waveforms of currents: Example Variant n cases, where the negative component cannot be sufficiently reduced solely by means of the more uniform distribution of the loads between phases, compensators are used. The purpose of the compensation systems is usually the elimination or mitigation of the negative- and zero-sequence component of currents at the point of connection of asymmetric load. Such process is called symmetrization. 4. Compensator/symmetrizator n the three wire MV systems, usually operated as the isolated neutral point or compensated systems, asymmetrical loads are connected on phase-to-phase voltages. n such case, there is no zero-sequence component of currents, therefore the symmetrization resolves into elimination or mitigation of the negative-sequence component. The LV systems are typically four-wire networks, with grounded neutral point, thus the negative-sequence and zerosequence components are present. The symmetrizator (K) is connected in parallel to the asymmetric load () (Fig. ). The symmetrizator causes the currents K, K, K, which adding to the load currents,,, result in the balanced system of the source currents,,, according to the equation: = + = + = a = + = a (7) K K K 4

5 Mitigation of voltage unbalance s the currents drawn from the network form a balanced system, therefore the negative-sequence and zero-sequence components are equal zero: ( ) ( ) = ( + a+ a ) = = ( + + ) = (8) The load to be balanced can be represented in general as a circuit of six elements in the star/delta connection (Fig. 4), where individual elements are connected to phase-to-neutral, as well as to phase-to-phase voltages. The impedances Z, Z, Z Z, Z Z (or admittances Y, Y, Y Y, YY ), which in the diagram represent the actual load, can be functions of time. Z ) Z ) ( Y ( Y Z ) Z ) ( Y ( Y Z ) Z ) ( Y ( Y Fig. 4. General diagram of the three-phase unbalanced load To establish the rules of compensation and symmetrization, the values of specified impedances should be assumed constant, and generally different from each other. This does not exclude considerations on their variability in time. These impedances can be regarded as a representation of the time-varying load, but only in the specific, selected instants of time the sampling instants. The set of such constant values of impedances represents the load at discrete instants of time. The compensation of asymmetric load will be understood as the compensation of reactive part of the positivesequence symmetrical component (reactive power compensation for the fundamental frequency) and of the zerosequence component (for three-phase, four-wire systems) and negative-sequence component for the fundamental frequency. mong various possible methods, the inductive-capacitive systems are of particular importance. Their practical applications are certain solutions of static follow-up compensators. 5. The compensator/symmetrizator parameters The symmetrization and compensation of the fundamental harmonic reactive current is a process, which in practice consists in connecting in parallel to the asymmetric load the asymmetric reactive elements (reactors, capacitors) of such values as to fulfil the conditions (9): ( ) ( ) K ( ) ( ) K () () K + = + = m + = (9) ( ) ( ) ( ) where:,, ( ) ( ) ( ), K, K, K are symmetrical components of the asymmetric load and compensator (index (K)) currents, respectively for the zero- (), positive- () and negative-sequence component; m () denotes the reactive part of the positive-sequence of the load current component (imaginary part in complex numbers notation); is the value of reactive current, which is the measure of the load non-compensating level permitted in the supply conditions by electrical power supplier. Thus, according to the presented notation, the processes of the reactive current compensation and symmetrization (for the zero-sequence and negative-sequence component) have been separated. 5

6 Power Quality For the load as in Fig. 4, the relations, describing the values of the negative- and zero-sequence symmetrical components can be written as follows (according to (8)): ( ) ( ) = U ( Y + ay + a Y ) a Y + Y + ay ( ) U Y a = ( + Y + ay ) (b) f the expressions () are not identically equal zero, and the asymmetry level is inadmissibly high, the load symmetrization is needed and can be made by connecting a symmetrization-compensating device with elements BK BK, BK, connected to the phase-to-neutral voltages and BK BK, BK, connected to the phase-to-phase voltages. The problem resolves into finding the compensating susceptances, which in connection with the admittances to be compensated will constitute a symmetric load. The relations, where the parameters of symmetrizator/compensator are expressed as a function of the equivalent impedances (admittances) of the load to be compensated/symmetrized, will be presented further in this paper. This is particularly useful when designing a symmetrizator. The symmetrizator parameters can be expressed as a function of other quantities, which describe a compensated load, i.e.: the current symmetrical components, values of phase currents or powers, instantaneous values of phase voltages and currents, etc. 6. Symmetrization of a star-connected load with neutral conductor elimination of the zero-sequence symmetrical component n this case the process of compensation comprises of two stages. The first one concerns the elimination of the zero-sequence symmetrical component elimination of the current in neutral conductor. The configuration in Fig. 5 has been taken for further considerations; it is distinguished by the minimum value of the current unbalance factor (the values of elements as in the EXMPLE ). (a) Y Y N Y EXMPLE Fig. 5. Three-phase four-wire network - star-connected load U= V U = a V U = av = UY = (. 5+ j, 5) = ( + j) = UY = ( 5. 6 j4. 6) = UY= ( j9. 5) ( ) N The current in neutral conductor: = = + + = ( 5. 6 j6. 6) where ( ) is the current zero-sequence symmetrical component. The negative-sequence symmetrical component: ( ) = ( + a + a) = (. 4+ j. 5) 6

7 Mitigation of voltage unbalance () The positive-sequence symmetrical component: = ( + a+ a ) = The current unbalance factor: k % ( ) = % = 5% () Y Y Y B K B K N Fig. 6. The elimination of the zero-sequence component (EXMPLE ) [] 4 Supply network currents [] 4 Supply network currents - - [] [s] current in neutral conductor 4 - [] [s] current in neutral conductor [s] Fig. 7. Waveforms of currents: EXMPLE before the elimination of zero-sequence component [s] Fig. 8. Waveforms of currents: EXMPLE after the elimination of zero-sequence component The elimination of the current zero-sequence component is performed by means of the two-element symmetrizator in the example configuration as in Fig. 6. Supply network currents: = U( Y + jbk ) = U( Y + jbk ) = U Y The condition for the current in neutral conductor to become zero takes form: Hence: + + = Reactive part of neutral current: m( + + ) = and ctive part of neutral current: Re( + + ) = Substituting the numerical values: B K -.5 = and.5 + B K.8.5B K = 7

8 Power Quality Hence: BK =. 789S BK =. 789S YΣ= Y + jbk = (. 5 j. 89) S YΣ= Y+ jbk = (. 5+ j. 89) S Y = Y + jb =. S Σ K = UYΣ = (. 5 j. 89) = ( j6. 58) = UYΣ = (. 6 j. 75) = UYΣ = ( + j9. 5) + + The current zero-sequence component has been eliminated (Fig. 8). 7. Symmetrization a three-wire load 7.. Symmetrization of a delta-connected load compensation and symmetrization of the admittance Y compensation of the reactive part of the load admittances B G G G G = B B = B + B + K B K G = + B G G G + + B = B + B + B K G G = + + B + B = B + B + G G () compensation and symmetrization of the admittance Y compensation and symmetrization of the admittance Y symmetrization of the load n practice, the susceptances of a static compensator perform both processes simultaneously, that means symmetrization and reactive current compensation and then the resulting values of the susceptance are defined by (), where B represents the permissible level of non-compensation. s it results from (), the three susceptances that are necessary for reactive current compensation and symmetrization can be expressed through real and imaginary components of the load admittance. The first elements of the right side of the relation () represent the components of the compensation susceptances, necessary for the compensation of the imaginary part of the adequate load admittance. The second element represents the components of the compensator that are necessary for the symmetrization of the real parts of the load admittance. These relations clearly indicate that the process of compensation can also be treated as an activity concerning each of the interphase load admittances separately. E.g. for the load Y compensation of the imaginary part is achieved through parallel connection of a susceptance (-B ) followed by symmetrization of the remaining part of such a single interphase load by connecting the symmetrizing susceptances respectively: (G / ) for the voltage U and (-G / ) for the voltage U. The compensation process of such a load with its indication diagrams has been presented in Fig. 9. For a symmetric system of supply voltages of positive sequence, such a circuit is equivalent to three star-connected resistors, each of them having a conductance G. 8

9 Mitigation of voltage unbalance The above considerations illustrate the well known Steinmetz rule of symmetrization, according to which any singlephase active load (or active-reactive one, after its equivalent susceptance has been compensated), connected e.g. between phases - (Fig. 9), can be symmetrized by means of reactive elements LC of such values, that the currents fulfil the relations (). = = () The obtained relations () transform any three-phase asymmetric load into the symmetric, resistive or resistiveinductive load with a defined level of reactive current. For a symmetric system of supply voltages of positive sequences the generated circuit is equivalent (for B = ) to three, star connected resistors, each having a conductance value G = G + G + G. The condition for the compensator elements selection can also be expressed as a function of the phase reactive powers of an asymmetric load: Q + Q = Q + Q = Q + Q = Q () K K K Q, Q, Q - the load phase reactive powers, Q K, Q K, Q K - the compensator phase reactive powers, Q - assumed non-compensating level. For the compensator delta-connected elements, the interphase reactive powers can be determined with respect to the load phase reactive powers, according to the relations: QK = Q Q + Q + Q QK =+ Q Q Q + Q () Q = Q + Q Q +Q K G = G C = = L = C G L (a) (b) 9

10 Power Quality U U = C = - = L U U = - U = - U EXMPLE (c) Fig. 9. (a) single-phase system before the symmetrization; (b) single-phase system with the symmetrizator; (c) phasor diagram, which illustrates the process of symmetrization For the loads configuration as in the EXMPLE Variant, susceptances of the delta-connected symmetrizator/ compensator are: BK = B ( G G) =. S BK = B ( G G) =S BK = B ( G G) =. S The sign + preceding the susceptance denotes its capacitive character, the sign - the inductive character. The capacitance of the capacitor connected between phases - is determined from the relation: C K = BK S F f =. π π 5Hz 67. μ The inductance of the reactor connected between phases - is determined from the relation: L K = = 5mH πfb π 5Hz. S K The load and compensator are shown in Fig.. fter connecting the compensator/symmetrizator: * * * = = ( j. ) 4. 89exp( j )

11 Mitigation of voltage unbalance * * * = = (. 945 j7. 988) 4. 87exp( j ) * * * = = ( j7. 987) 4. 87exp( j ) The phase currents of supply network constitute the three-phase symmetrical system. * * Y B K * Y B K Y B K * * * Fig.. Delta-connected asymmetric load with the symmetrizator 4 Three-wire network voltages Voltages [V] Time [s] 8 Three-wire network currents 6 4 Currents [] Time [s] Fig.. Voltage and current waveforms (EXMPLE )

12 Power Quality 7.. Star-connected asymmetrical load The symmetrization of a star-connected load is analysed after star-to-delta transformation. Further procedure of the symmetrizator parameters selection is analogical as in section Static compensators Reactive power static compensators are widely used in transmission and distribution systems, cooperating with medium and large power, rapidly variable loads, which are the most disturbing for the electric power system. Static compensators can perform various tasks, such as compensation of the fundamental component reactive power, symmetrization and mitigation of voltage fluctuations (flicker). lso some active filters configurations have a capability of symmetrization. 8.. Static VR compensators The purpose of a compensator (with control and measuring system) is to measure adequate electric quantities of the load and generate in the compensator such currents, that the resultant load: compensator compensated load, as seen from the supply network, was symmetrical, and the fundamental harmonic reactive current drawn from the network did not exceed the value permitted in the supply conditions. Generally, static compensators are the systems, which comprise reactors and/or capacitors controlled by means of semiconductor circuits. They can be treated as the values of susceptances, controlled according to the needs of compensation/symmetrization. Thyristors in these systems are used as switches or phase-controlled elements. n practice various solutions of compensators are applied. mong the most often used compensators is the FC/TCR compensator with fixed capacitor and controlled (variable) reactor current Compensator/symmetrizator FC/TCR So-called FC/TCR circuits are the most commonly used static Vr compensators/stabilizers in industry. They are composed of a Fixed Capacitor (FC) connected in parallel to a Thyristor-Controlled-Reactor (TCR). FC is most commonly a passive filter, filtering the harmonic/harmonics of a load and/or of the TCR. This solution is an example of the indirect compensation method in which the sum of the basic () TCR current harmonic TCR() and the load reactive current O() is constant, and equals the FC current FC() (Fig. a). The TCR current waveform for three sampled control angles α is shown in Figure b (single-phase circuit). The control angle (with respect to the positive voltage zerocrossing) and the basic current harmonic of TCR can vary in each supply voltage half-cycle, within the range of values π α (, π ). With the increase of the angle α the fundamental harmonic of the reactor current decreases, what is tantamount to the increase of its equivalent inductive reactance for this harmonic and to the decrease in the fundamental harmonic reactive power, drawn by the reactor. The fundamental harmonic of the reactor current is expressed by the formula: m TCR() ( α ) = UBK = ( K () FC() ) = [ ( π α) sin ( π α) ] (4) π where: α control angle of the switch T thyristors, FC() capacitor current, TCR() (α) reactor current (fundamental harmonic), m - the reactor current amplitude for α = π. Thyristor are fully conducting for α = π/. B is the controlled K susceptance of the TCR step, its value is controlled by changing the conduction angle of thyristors. The resultant compensator current i k (t) is the sum of the capacitor and reactor currents: i () t = i () t + i () t (5) k FC TCR

13 Mitigation of voltage unbalance f the current in the reactor branch is equal zero (α = π), then the compensator feeds reactive power to the supply network and its current has a capacitive character. When thyristors are fully conducting, and the reactor power is greater than the capacitor power, the compensator draws reactive power and its current has an inductive character. The compensator current is controlled from FCmax to TCRmax in a continuous manner. The disadvantage of this system is generation of the current harmonics, which results from the phase control of thyristor switch (Fig. c). n the three-phase configuration (Fig. a) the single-phase TCR s (as in Fig. ) are delta-connected in parallel with fixed capacitors; together they constitute a triangle of equivalent phase-to-phase susceptances for the supply network (Fig. b). Their values vary independently and continuously as a result of changes in the control angles (α, α, α ). This way, the circuit implements the Steinmetz procedure in order to compensate and symmetrize the three-phase load. Fig.. (a) Conceptual diagram; (b) TCR current waveforms; (c) harmonics amplitudes per unit of basic current component amplitude L (α ) K α C B K L ( α) K L (α ) α C K B K B K α C (a) Fig.. Diagram of FC/TCR static compensator (b)

14 Power Quality 8... TSC/TCR (Thyristor Switched Capacitor/ Thyristor Controlled Reactor) n this configuration a capacitor bank is divided into the steps, switched by means of thyristor C switches, according to the compensation/symmetrization needs. Synchronization of the instant of switching with respect to the supply voltage waveform guarantees elimination of overvoltages and inrush currents, normally associated with capacitor switching. lso reduced are the values of current high harmonics, as related to the FC/TCR structure of the same nominal power STTCOM The newest solutions of compensating systems are the STTCOM devices, based on C/DC converters. The STTCOM compensator can be considered as a controlled voltage source (VS inverter in GBT or GTO technology) connected to the power supply system through the reactors (Fig. 4), or as an inertialess, three-phase synchronous machine, whose phase voltages their amplitude, phase and frequency are independently controlled. The reactive power/ current flow is controlled by means of the voltage amplitude control. Due to the independent control in each phase of the system, the compensator enables voltage symmetrization by elimination of the negative-sequence component. The relationship between the values and phase angles of the supply network voltages (U bus ) and the compensator output voltages (U VSC ) (before and after the reactor X r Fig. 4) determines the value and character (inductive or capacitive) of the compensator current (power). t the zero phase shift between voltages U bus and U VSC, only reactive current flows. When U bus < U VSC the current is capacitive, for U bus > U VSC the current is inductive (Fig. 5). This way the compensator can be a source or a load of reactive power. The STTCOM compensators are characterized with the following basic features: they can simultaneously perform combine functions of reactive power compensation, load symmetrization and filtering of harmonics, do not require use of passive components; their overall dimensions are several times smaller than those of SVC compensators of analogical power, compared to the TSC/TCR and FC/TCR system they have better dynamic properties, due to the development in power electronics their prices show a declining tendency. i i u x u x u bus i X r u bus u bus u vsc u vsc u vsc LOD VSC Fig. 4. Schematic diagram of a compensator (VSC) connected to the supply network u bus u bus <u vsc >u vsc Fig. 5. Phasor diagrams for different relations between U bus and U VSC 8.. Static series compensators The series compensator can be provided with an additional - aside from the load voltage control - function of symmetrization. The concept of such a compensator and block diagram of the example design is shown in Fig. 6. The series voltages applied to individual phases of the system - ΔU XSR, (X =,, ) can be expressed as the sum of two three-phase systems, which execute two independent processes: - Symmetrization. This function is performed by means of the three-phase system of series voltages, determined on the basis of the measurement of negative-sequence component of load voltages. n result of adding appropriate components of series voltages ( ΔU XS for x =,, ) to the source voltages, the symmetric system of voltages is obtained at the point B (Fig. 6). 4

15 Mitigation of voltage unbalance - Stabilization of the voltage positive-sequence component value. For this purpose, to the source voltages has to be added the symmetric system of series voltages ( ΔU XR for x =,, ), which guarantees an increase or reduction of the load voltages, according to the stabilization needs Fig. 6. Unbalanced system of the supply network voltages ΔU S ΔU SR ΔU R Balanced voltages system with controlled values U ΔU SR U U ΔU S ΔU R ΔU SR U U ΔU S ΔU R SUPPLY NETWORK VOLTGES COMPENSTOR U LOD Fig. 6. Procedure of symmetrization and control of the load voltages by means of the series compensator The example of a practical system, shown in schematic diagram in Fig. 7, of comprises three single-phase dc/ac PWM converters connected in series with the supply line through three single-phase transformers. The load voltages are measured and used for determination of the symmetrical components and hence to the determination of the converters switching patterns, which ensure obtaining the series voltages. t is also possible to employ a three-phase inverter with asymmetrical switching functions in individual branches of the converter. The symmetrization and control / regulation of the load voltage are then performed by means of controlling the amplitude and phase angle of reference voltages. 5

16 Power Quality ΔU SR ΔU ΔU SR rectifier Filters of the voltage symmetrical components U () U () Control system (U () ) reference (U () ) reference References Fig. 7. The schematic diagram of series system of stabilization symmetrization of the load voltage. NS C84.: 995, merican national standard for electric power systems and equipment voltage ratings.. Engineering Recommendation P9: Planning limits for voltage unbalance in the United Kingdom. The Electricity Council (U.K.), Gyugyi L., Otto R.., Putman T.H.: Principles and applications of static, thyristor-controlled shunt compensators. EEE Transactions Vol. PS 97, no 5, Sep./Oct EC 6--, 99: Electromagnetic compatibility-part : Environment-Section : Description of the environment - Electromagnetic environment for low-frequency conducted disturbances and signalling in public power supply systems. 5. EC 6--5, 995: Electromagnetic compatibility-part : Environment-Section 5: Classification of electromagnetic environments. 6. EC --, 995: Electromagnetic compatibility-part : Environment-Section : Compatibility levels for low-frequency conducted disturbances and signalling in public medium-voltage power systems. 7. EC 6-4-7, : Electromagnetic compatibility Part 4-7: Testing and measurement techniques Unbalance, immunity test. 8. EEE P59.: Guide for recorder and data acquisition requirements for characterisation of power quality events. 9. Miller J. E.: Reactive power controlled in electric systems. John Willey & Sons 98.. UE Guide to quality of electrical supply for industrial installations. Part 4: Voltage unbalance This publication is subject to copyright and a disclaimer. Please refer to the Leonardo ENERGY website. 6