HARMONIC CALC TOOLBOX

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HARMONIC CALC TOOLBOX Powered By Docstoc
					             Harmonic Calculation Toolbox in
      Industry Application for Adjustable Speed Drive
            Lucian Asiminoaei, Frede Blaabjerg,                                                                        Steffan Hansen,
                Institute of Energy Technology,                                                                Danfoss Drives A/S,
                       Aalborg University,                                                                 DK-6300, Graasten, Denmark,
                DK-9220, Aalborg SE, Denmark,                                                                s.hansen@danfoss.com
                 las@iet.auc.dk, fbl@iet.auc.dk

Abstract–Previous to electrical installation of large power non-           estimated, and this approach provides an easy and fast
linear loads, a comprehensive design-study is often required in            software implementation.
order to determine if the overall installation complies with                This paper describes the development of calculation tools for
international regulations in respect to harmonics. Current THD,            estimation the six-pulse diode rectifier harmonics. The focus is
voltage distortion and power factor are just few parameters to be
                                                                           placed on estimation of line-side harmonic distortion when
aware off. This paper focuses on estimation of line-side harmonic
distortion when connecting one or multiple six-pulse diode                 connecting one or multiple six-pulse diode rectifiers to any
rectifiers to any supply transformer. Results are put into a               supply transformer.
practical PC software toolbox for harmonic estimation on real               Results are put into a practical PC software toolbox for
applications. Through a combination of an off-line database and            harmonic estimation on real applications. Using a combination
new interpolation techniques very good results have been                   of offline database and interpolation techniques very good
achieved. The final results obtained are very close to the                 results can be achieved. Comparisons between the toolbox
measurements on real applications and the toolbox can be used              results and real measurement validate the implementation.
for future ASD designs and installations.

Keywords – variable speed drive; harmonics analysis; load flow                                            II. SIX-PULSE RECTIFIER MODELS
analysis; power system harmonic; software tools.
                                                                            Four state of the art methods have been analyzed in [15] for
                       I. INTRODUCTION                                     modeling the six-pulse diode rectifier: ideal, table-based,
  Lately, end users of non-linear 3-phase equipment, such as               analytical and numerical. It is shown that a close correlation
Adjustable Speed Drives (ASD), require a detailed harmonic                 exists between the number of required parameters and the
calculation report for their application. Both harmonic voltage            accuracy of the result. And as expected, the more parameters
and current spectrum up to the 50th harmonic are requested.                are known, the more accurate results are obtained. Fig. 1
This involves both knowledge on the power system and the                   shows a comparison of measured and simulated line-currents
equipment level.                                                           of a six-pulse diode rectifier when the system parameters are
  For ASD’s the most used front-end topology is still the 6-               well determined.
pulse diode rectifier, due to well-known advantages such as,               10

high efficiency, low cost, robustness and reliability.                         8
                                                                                        measured

Unfortunately, even though the six-pulse diode rectifier has a                                             simulated


very simple circuit topology, calculation of the (harmonic)                    6
                                                                    I sa [A]




currents is not a trivial task. It is for example well known that
                                                                               4
the harmonic currents of the six-pulse diode rectifier are
heavily depending on the supply impedance and supply                           2

voltage quality (i.e. pre-distortion and unbalance) [1] – [7].
  Furthermore, as this paper will show, the harmonic current                   0
                                                                               0.01    0.012       0.014     0.016     0.018   0.02
                                                                                                       Time [s]
emission is also depending on the numbers and rating of the
                                                                               Fig. 1. Comparisons of measured and simulated line-current of the three-phase
connected rectifiers. Besides these aspects there is always a                         rectifier (2.2 kW). Time-domain and frequency-domain representation.
little lack of knowledge with respect to the system. Thus, the
estimation of the harmonic current emission in a certain point              In a context of practical use, to estimate the harmonic
is far beyond a simple engineering problem.                                distortion in a given industrial application, the table-based
  There are different approaches to calculate the harmonic                 model has the advantages of easy implementation in a
currents, some from the practical [10], others from the                    spreadsheet format, where the amount of data is highly
analytical point of view [12] or even combinations of both.                depending on the accuracy required.
  The achievement of this paper is to prove that using an                   The availability of a numerical simulator or programs like
empirical method correlated with analytical expressions the                Matlab “in the field” is a significant limitation for the
harmonic model of the rectifier part of ASD's can be                       analytical and numerical models. However, the analytical
                                                                           model may be compiled into a stand-alone PC-software




  0-7803-8269-2/04/$17.00 (C) 2004 IEEE.                        1628
application, where after the analytical model can provide                                                     Ultimately, harmonic data and all analytical expressions are
accurate harmonic estimation without prior table generation                                                 compiled using the Matlab programming into a graphical
even “in the field”.                                                                                        interface application where the user provides the input
  The circuit-based simulators have significant advantages                                                  parameters. Thus, for a given case the input parameters are
under non-ideal voltage conditions, as it must be recognized                                                used to search the database retrieving for the best-fitted
that the current of a diode rectifier is highly depending on the                                            information and estimating the harmonic currents based on a
supply voltage quality. Thus, it is recommended to use                                                      linear interpolation algorithm.
numerical simulators to predict the harmonic current distortion
of the diode rectifier at significant non-ideal conditions.                                                 B. Analyzing the basic circuit
However, this requires more detailed knowledge of the system
                                                                                                              Initially, a correlation between the toolbox diagram and the
parameters such as phase-angle of the harmonic voltage
                                                                                                            system should be established for simulation. This will help
distortion, harmonic impedance, resonance frequency, etc. In
                                                                                                            choosing the right parameters in the simulation to meet certain
the case that these parameters are not available, the table-
                                                                                                            requirements, i.e. acceptable data size and simulation time.
based or analytical models might be just as exact.
                                                                                                              The ASD is a typical three-phase capacitive smoothed
  Supported by the conclusions and experience of [15] it is
                                                                                                            rectifier containing an ac-inductance, a dc-reactance and a
chosen to let the harmonic calculation toolbox be based on a
                                                                                                            resistive load. Fig. 3 presents a Spice schematic used for
table-based model. Harmonic data (collected by simulating the
                                                                                                            simulations.
six-pulse diode rectifier) are pre-processed and saved in
                                                                                                              The relationship between the simulated circuit and the
databases. Furthermore, analytical expressions are used to
                                                                                                            toolbox circuit is done as following. The voltage ac-sources
reduce data size where applicable.
                                                                                                            represent the secondary side of the transformer (see Fig. 2).
  In this way, the developed tools keep the goal of accurate,
                                                                                                            The Lac and Rac components identify the cable and the
practical and easy to be implemented in PC software.
                                                                                                            transformer short-circuit impedance and the Rload component
                                                                                                            identifies the power rating of the rectifier.
                III. PRINCIPLE OF TOOLBOX DEVELOPMENT
                                                                                                              As these parameters can vary from case to case, eg.
A. General description                                                                                      transformer inductance, transformer rating, cable length, ASD
                                                                                                            rating, etc., it is necessary to establish a practical number of
  The toolbox is developed around a general power system
                                                                                                            parameters to express the line-side harmonic current since it is
diagram as shown in Fig. 2a. It includes a transformer, two sets
                                                                                                            known that all these have impact on the emission level.
of cables, a linear load and multiple connected drives. The
                                                                                                              Therefore, the harmonic current emission should be
drives consist of six-pulse front-end diode rectifiers. In real
                                                                                                            expressed as a function of multiple arguments as:
cases, the ASD could be supplied alone or most likely,
                                                                                                                                i h = f ( x1 , x 2 , x3 ...x n )         (1)
connected together with other ASDs at panel point, therefore the
toolbox allows parallel connection of different types of drives.                                            where: ih represents the characteristic harmonic currents of the
  Since the number of drives and their characteristic may vary                                                         six-pulse diode rectifier,
(i.e. nominal power, load, internal dc-link inductance,                                                             x1… xn are the arguments of the function.
supplementary ac-inductance) it is difficult to analyze the                                                  Having too many arguments (equivalent to as running the
system in a one-step iteration.                                                                             simulations in "all possible cases" with "all possible values")
 Instead of using a large and laborious harmonic analysis, a new                                            creates large memory storage requirements and excessive time
approach has been found in this paper by "splitting" the original                                           spent on simulation.
diagram into multiple simple diagrams, as shown in Fig. 2b.                                                  On the other hand, if the number of arguments is too small or
  Each system contains an equivalent model of the power system                                              not properly chosen, the consequence will be a lack of
and one single ASD. The ASD is separately analyzed using                                                    knowledge when the harmonic currents are required for a
circuit simulators and data are minimized and stored in                                                     given case.
databases for offline estimations later in the developed toolbox.                                            Therefore, previous to simulate the system, some
  The last step is to use the superposition principle and a                                                 assumptions should be made, like:
compensation factor (due to a reciprocal influence when the                                                 • the line voltage is balanced and sinusoidal,
drives are connected in parallel) in order to regroup the                                                   • the grid is purely inductive (Rac=0),
original diagram.                                                                                           • all passive components are linear, i.e. the resistance and
                                       Panel    Drive 1          ac-impedance
                                           ih             Grid                             Drive 1             inductance are constant at all frequencies.
       Transformer
                                                Drive 2                               ih
                                                                 ac-impedance                                                                D1       D3     D5
                        PCC                                                                                          Vsa                                           Ldc
                  Cable     Cable ih       ih             Grid                             Drive 2                         Lac      Rac
Grid                                            Drive 3
                                                                                      ih
                                           ih                    …                                                   Vsb   Lac      Rac                                  Cdc Rload

                                                                 ac-impedance
                       Other                                                                                               Lac      Rac
                                                          Grid                             Drive n                   Vsc
                       Loads                    Drive n
                                                                                      ih
                                           ih
                                                                                                                                             D4       D6      D2
                         (a)                                                    (b)
                          Fig. 2. System diagrams used in
            a) harmonic toolbox analyzes, b) individual study approach.                                           Fig. 3. Basic circuit layout of the simulated six-pulse rectifier.




                                                                                                     1629
 Furthermore, it is assumed that the diode rectifier is of the                     Therefore, even the harmonic currents are expressed as a
voltage-stiff type. This means that the dc-link capacitor is                      function of only three arguments, the simulation data are still
sufficient large to maintain a constant dc-link voltage. This is                  high. The consequences are the need of a large storage and
a fair assumption since most of the diode rectifiers used in                      difficult data handling.
today’s power electronic converters are of this type.                              The amount of data can be minimized by using an
 By investigating common applications it can be concluded                         interpolation algorithm and analytical expressions in the
that three arguments practically cover the requirements for                       toolbox.
calculating the harmonics.                                                         The 5th and the 7th harmonic currents are typically the weightiest
                   ih = f ( Lac , Ldc , Rload )              (2)                  harmonics in the current distortion. An approximation of these
 The arguments are expressed on a per unit basis of an                            with analytical expressions will bring significant errors.
initially established nominal power. Then simulations have                        Therefore, the 5th and the 7th harmonic currents are stored without
been run independently on the circuit in Fig. 3, varying one                      further minimization.
parameter and keeping the other constant:                                          Instead, higher harmonics are suitable for an analytical
• ac-reactance Lac, between 0% to 25% p.u.,                                       approach, because they have lower values and from the 11th
                                                                                  harmonic, the currents will have similar shapes.
• dc-link inductance Ldc, between 0 to 10% p.u.,
                                                                                    Fig. 5 presents as an example the 11th harmonic current.
• load, between 10% to 160% of nominal load.
                                                                                  These harmonic currents are depicted with respect to ac- and
 The results are the harmonic currents up to the 50th harmonic.
                                                                                  dc-link inductance at a load of 100%.
 Thus, based on the specified assumptions the harmonic
                                                                                   One can note the existence of 2 zones, namely the common-
currents can be expressed depending on these three input
                                                                                  and the spreading-zone. In the common-zone the currents are
parameters.
                                                                                  following the same curve and can be well fitted by an
                                                                                  analytical expression, based on an average method, a least
                                 IV. DATA ANALYSIS
                                                                                  square method or even using polynomial coefficients.
 As initially mentioned the toolbox uses for estimating the                        The spreading-zone is due to the low values of the ac- and
current harmonics a look-up table method. Therefore all                           dc-inductance, highly dependent on the value of the dc-link
harmonic data have to be achieved in advance. This can be                         inductance when the phenomenon of discontinuous
done in two steps, an individual ASD analysis followed by a                       conduction mode appears. Fig. 7 details the spreading-zone
system aggregation analysis.                                                      when the values of the ac- and the dc-inductance are smaller
                                                                                  than 1%. The currents cannot be fitted anymore with one
A. Individual analysis                                                            single curve, instead each current may be linearized and
                                                                                  simple expressions can be used for each.
 This section evaluates the line-side harmonic current                                                      40

emission of single ASD, as a function of the prior established                                              35
                                                                                                                     Spreading
input parameters. The study is initially made with the load                                                            zone
                                                                                                            30
value set to 100%, expressing the harmonic currents as a
function of Lac and Ldc. Then the load variation is considered                                              25         Ldc=0%
                                                                                               i11/i1 [%]




and further harmonic dependencies are investigated.                                                         20           Ldc=1%
 An example is shown in Fig. 4, which gives the level of the                                                15
                                                                                                                           Ldc=2%
5th harmonic current (expressed in percentage of the                                                        10
fundamental current). Since this only shows the harmonic with                                                                                             Common
a load value of 100% the amount of data will be significant                                                 5
                                                                                                                          Ldc=10%
                                                                                                                                                           zone
when the load varies within the span from 10% to 160%.                                                      0
                                                                                                                 0           5             10             15   20    25
                                                                                                                                                Lac [%]
                                                                                             Fig. 5. Simulated 11th harmonic current dependence on
                                                                                                     ac- and dc-link inductance at 100% load.
                      90    80[%]

                      80
                                                                                                            60
                      70
                                                                                                            50                                  Ldc=0%
                      60
          i5/i1 [%]




                                           i5/i1
                                                                                               i11/i1 [%]




                                 40[%]                                                                      40
                      50                                                                                                         Ldc=0.2
                                  35[%]    Levels [%]
                                     30[%]                                                                  30
                      40                                                                                                    Ldc=0.4
                                         25[%]
                                                 20[%]                                                                      %
                      30                                                                                    20         Ldc=0.6
                                                         15[%]                                                         %
                      20                                                                                             Ldc=0.8
                                                                    0                                       10       %
                                                                       ]




                                                                                                                     Ldc=1%
                                                                    [%




                      10                                        5
                                                                    c




                                                                                                                 0           0.2           0.4      0.6        0.8    1
                                                                 Ld




                        0    5      10                        10
                                            15     20    25                                                                                 Lac [%]
                                      Lac [%]
                                                                                  Fig. 6. Simulated 11th harmonic current when Lac and Ldc are smaller than 1%
        Fig. 4. Three-dimensional view of the 5th harmonic current                                               at 100% load.
                versus Lac and Ldc in the ASD at 100% load.




                                                                           1630
                                                                                                                          14
                   Ih [%]
                                                                                                                                                                     Legend:
                     Ih max                                                                                                                                               Simulated harmonic currents
                                                Maximum value of                                                          12                                              Estimated harmonic currents
                                                the harmonic current
               k                                                                                                          10
                                                                                                                                                                                               Load

                                                Ldc=0%                                                                                                                                         10%




                                                                                                                  i5/i1 [%]
                                                                                                                              8
                     I(0,Ldc)
                                                                                                                                                                                            20%
                                                                         Average vector                                       6
                                  I(Lac, Ldc)
           (1-k)




                   Iavg (0)                                                                                                                                                         40%

                                                                                                                              4                                          60%
                                                  α                                                                                                   100%     80%
                                                              Iavg (1)                                                            Load 180%
                                                                                          Iavg (2)
                                                                                                                              2
                              0       Lac                 1                          2
                                                       Lac [%]
     Fig. 7. Analytical expression found for the higher harmonic current,                                                     0
                                                                                                                              0            5          10               15              20               25
                                                                                                                                                           Lac [%]
                        starting with the 11th harmonic.
                                                                                                                                  Fig. 8. Simulated and estimated 5th harmonic current
 This paper has found a convenient way to combine the                                                                                       with respect to the load variation.
analytical approaches for both the spreading- and common-                                                    Even the harmonic currents are still expressed as a three-
zone. Fig. 7 depicts the analytical representation. For Lac                                                 dimensional function (3), the database is reduced by storing
higher than 1%, the 11th harmonic currents are fitted by the                                                only two dependencies (Lac and Ldc) while the third one (the
average curve (referred to as the average vector).                                                          load) being analytically reconstructed using (4) and (5).
 For Lac smaller than 1%, the dc-link inductance (Ldc) comes                                                 Fig. 8 provides a comparison of the simulated and estimated
into an equation. Eq. (3) gives the value of 11th harmonic                                                  5th harmonic currents. Solid lines represent the 5th harmonic
currents when both Lac and Ldc are smaller than 1%.                                                         currents as a function of Lac and Load. Dashed lines represent
        I11 = I avg (1) + (1 − Lac )(1 − Ldc )(I h max − I avg (1) ) (3)                                    the current estimation using (5) and the function of the current
where: Iavg(1) is the first value of the average vector,                                                    depending on Lac at 100% load. The comparison reveals a
        Ih max is the maximum value among all currents,                                                     good approximation if the load is between 20% and 160% of
        Lac and Ldc are the ac- and dc-inductance.                                                          the nominal power which are values that practically cover
 Thus, the entire set of 11th harmonic currents is reduced to                                               most cases.
one point (the maximum value of the current) and one curve.                                                  In this way, the initial desire to keep minimum data for
A simple estimate gives that the database was reduced up to                                                 storage and a simple implementation for analytical expressions
90% of the initial amount (ten curves are fitted only by the                                                can be fulfilled, and simultaneously having the harmonic
average vector curve).                                                                                      estimation at an acceptable accuracy.
 Even further minimization can be done using polynomial
coefficients. The presented approach has the advantage of being
compiled into one function. Then the function is identical for all                                          B. Aggregation of the system
higher harmonic currents due to the similarity of the shape.                                                  After estimating the harmonic currents in the individual
 Until now the load has had a value of 100%. As initially                                                   cases, the initial approach must be reconsidered. The initial
established, the load also influence on (3) and consequently,                                               intention of simply adding the harmonic currents from every
the simulations should also include the load variation as well.                                             ASD can not solve the problem, because the results obtained
This will lead to a further increase of the database.                                                       only consider the drive connected alone to the power supply.
 For that reason, further effort has been done to compress (3)                                              Typically, many ASD's are connected to the same line.
even more. This can be achieved if studying the effect of the                                               Therefore, a correction factor should be considered due to the
load variation on the harmonic levels.                                                                      parallel connection. The correction factor is related to the
 It was noted that the load variation has the same effect as                                                common section of the inductance (Lac) situated in front of the
changing the Lac value into a new value, correlated with the                                                ASD's.
new load. Changing the per-unit base calculation of Lac will                                                  The investigation is done considering one drive as the
give this correlation by calculating the base impedance and Lac                                             analyzed drive, and then simulations are performed to record
as (4), (5).                                                                                                the harmonic evolution of this, when another drive is
                                                       Z base ( nom ) (4)                                   connected in parallel.
                        U2                  2
                                        U nom
         Z base ( new) = nom =                       =                                                        A simplified toolbox diagram of parallel-connected drives is
                         Pnew       Pnom ⋅ Load         Load                                                shown in Fig. 9. Under the assumption that the linear load
                       Lac ( new) = Lac ( nom ) ⋅ Load                (5)                                   does not contribute to the harmonic content, it is eliminated
where: Unom is the nominal voltage of the drive,                                                            from the diagram leaving the drives alone to share the cable
   Load is the new load of the drive, in percentage,                                                        and transformer impedance.
   Pnom and Pnew are the nominal power and the new power,                                                     The drive analyzed for harmonics is denoted by P1, while Pn-1
   Zbase(nom), Zbase(new) are base of the impedance at Pnom, Pnew                                           stands for all other parallel drives. They both share the same
   Lac(nom), Lac(new) are per-unit ac-inductances.                                                          ac-inductances in front (transformer and cable).




                                                                                                     1631
                                                                         Drives                                         10
                                                                                        ASD 1
                                                       Panel                                      P1                         9
                                                                                                                                                         Lac=0.5%

                                                                     ih
                                                                                                                             8
          Transformer                                                                    ASD 2
                                                           ih
                              ex , er          Cable                 ih                                                      7
  Grid
                                                                                         ASD 3                               6




                                                                                                                      KLac
                                                                                                                                                         Lac=1%
                                                                     ih                           Pn-1
                                                                                                                             5

                                                                                                                                                         Lac=2%
                                                                                         ASD n                               4
                                                                                                                                                         Lac=3%
                                                                     ih                                                      3

  Fig. 9. Diagram of the parallel connection of ASD. P1 is the drive under                                                   2
     investigation and P2, P3… Pn are grouped into a generic drive Pn-1.                                                                                 Lac=8%
                                                                                                                         1
  The diagram presented in Fig. 9 can be reduced to a new                                                                -1.5    -1    -0.5   0   0.5      1
                                                                                                                                                  log10(Pn-1/P1)
                                                                                                                                                                 1.5   2   2.5   3   3.5

equivalent diagram, by grouping the drives into a generic Pn-1
                                                                                                              Fig. 11. Compensation characteristics for Lac due to the parallel connection of
drive, as suggested by the dashed line.
                                                                                                                                                 ASD's.
  This paper investigates the harmonic changes of the analyzed
drive P1 when the power drawn by Pn-1 varies. By conducting a                                                 • The THDi of the P1 in the stand-alone case (referred to as
series of simulations, the study concludes that the rating of the                                                standalone-THDi) was obtained with respect to the ac-
Pn-1 influences the P1 harmonic emission.                                                                        inductance (Lac).
  Simulations have been run, independently changing:                                                          • Then, the focus is to get the value of the ac-inductance,
• ac-reactance Lac, between 0% to 25% p.u.,                                                                      which gives the same effect in harmonic distortion as the
• Pn-1 power, between 0.1 to 2000 times the power of P1.                                                         parallel connection. This can be done using both
  It is worth to mention, that for all simulated cases, the P1                                                   characteristics, stand-alone-THDi and parallel-THDi, to
drive had no change in parameter values (load, nominal                                                           obtain a function of Lac vs. Pn-1/P1.
power, component values, etc.).                                                                               • The last step is to normalize this function in order to obtain a
  The simulations gave the value of the harmonic currents.                                                       multiplication (compensation) factor for the ac-inductance.
Furthermore, as an overall index on the harmonic changes, the                                                  The compensation factor is shown in Fig. 11.
Total current Harmonic Distortion (THDi) has been computed.                                                    To find the compensation factor for a given case it is just as
The results are displayed in Fig. 10, and represent the THDi of                                               simple as establishing the power ratio of the considered drive
the drive P1, with respect to the power ratio (the ratio of Pn-1/P1                                           and the value of the ac-inductance situated in front of the drive.
powers).                                                                                                      By using the curves in Fig. 11, the correction factor is found,
  Even no changes have been done in the P1 parameters, the                                                    which then is multiplied with the value of the ac-inductance
results show that the harmonic content of the P1 changes                                                      (Lac) to obtain the new value of the Lac. The new value is then
because of the influence of the parallel drive. This conclusion                                               used to retrieve the harmonic currents from the databases
leads to the idea of reevaluating the harmonic values obtained                                                stored in the individual simulations.
in the stand-alone simulations with a compensation factor due                                                  The conclusion of this study is that when several drives are
to the parallel connection. The compensation factor is                                                        connected in parallel, a reciprocal influence appears between
correlated with the value of the Lac-inductance.                                                              each other because of sharing the same transformer and line
The development of the compensation factor is done by:                                                        impedance. This influence decreases the harmonic currents
• The THDi from P1 in the parallel connection (referred to as                                                 compared to those calculated in the stand-alone case.
    parallel-THDi) was obtained with respect to the power ratio                                               However, a compensation factor can be found to correct the
    Pn-1/P1.                                                                                                  current values, allowing a superposition principle finally to be
                    45
                           Lac=0.5%
                                                                                                              applied.
                    40


                    35
                                                                                                                                      V. TOOLBOX IMPLEMENTATION
                           Lac=1%
                    30
                                                                                                               The goal is to obtain a practical harmonic toolbox. Based on
         THDi [%]




                           Lac=2%
                    25
                           Lac=3%
                                                                                                              the selected simulation parameters, the implementation only
                           Lac=4%                                                                             cares about choosing the right inputs for the toolbox to have a
                    20
                                                                                                              practical relation (i.e. nameplate numbers rather than catalog
                    15                                                                                        datasheets).
                           Lac=8%
                    10
                                                                                                               The inputs to the toolbox are:
                                                                                                              • the transformer data consists of nominal power, short-
                    5
                    -1.5     -1     -0.5   0      0.5      1       1.5     2      2.5   3   3.5                  circuit impedance and secondary voltage,
                                                                                                              • cables are characterized by length, material and number of pairs,
                                                    log10(Pn-1/P1)

                             Fig. 10. Simulated THDi of the P1 drive                                          • the linear load is defined by linear power and cos(ϕ),
                         as a function of power ratio and ac-inductance.




                                                                                                       1632
• drives are characterized by the nominal power, load and                                                                B. Harmonic calculation
   harmonic mitigation solution (ac-inductors, dc-coils,
                                                                                                                          The harmonic calculation starts by calculating the harmonic
   filters, etc.).
                                                                                                                         currents from each drive, then by summing all specific
 The electrical diagram used for toolbox implementation is
                                                                                                                         harmonic currents at the panel point, the calculation is
shown in Fig. 12.
                                                                        Linear Load                                      extended upstream to the transformer towards grid connection.
                                                         PCC                                                              The harmonic currents calculation are performed as:
                                                      Plin                                                               • the total ac-inductance is evaluated by summing the cable
         Transformer
                                                  cos(ϕ)
                                                                                                    Drives
                                                                                                                             and transformer inductances,
                                    Cable Trafo-Bus
  Grid           ex, er                                                Qsvc
                                                                                           Panel        Drive 1          • the ac-inductance (Lac) is expressed in per-unit basis of
                               ih
                                                ΣPLoad            ih                          ih                             each drive,
   vh                     vh                                                                            Drive 2
                                                                        Cable Bus-Panel   ih                             • based on the power ratio (the ratio between powers of the
                                                                                               ih
                                                                                                        Drive 3              current drive and the sum of the others) a correction factor
                                                             vh                   vh           ih                            is applied to the Lac value due to the parallel influence,
                                                                                                                         • based on the value of Lac and other ASD’s parameters, an
                                                                                                        Drive n
                                                                                                                             individual harmonic current assessment is performed by
                                                                                               ih
  Fig. 12. Electrical diagram used for harmonic toolbox implementation.                                                      retrieving the currents from internal databases,
                                                                                                                         • the harmonic currents at the PCC are calculated by
  In the implementation, there are two calculation flows, one to                                                             summing the individual currents coming from the drives,
compute the fundamental current and one to compute the                                                                   • different harmonic related indices are evaluated, i.e. THDi,
relative harmonic currents at different points. For the                                                                      TDD, PWHD, etc.
fundamental current the calculation flow is from the                                                                      Knowing the harmonic currents and cable impedance, next
transformer to the drives. For the harmonics the calculation                                                             steps are to compute voltage drop and total harmonic voltage
flow has the opposite direction, meaning from the drives to the                                                          distortion, which can easily be done [7], [8].
transformer.
                                                                                                                                           VI. TOOLBOX VERIFICATION
A. Fundamental current
                                                                                                                          In the final toolbox - Danfoss VLT MCT 31 harmonic
 A load-flow calculation can do the determination of the                                                                 calculation - the Matlab code has been compiled into a
voltages and currents in a power system network. The basic                                                               dynamic link library (DLL) and is called by a user friendly
schematic is displayed in Fig. 13.                                                                                       graphical interface as shown in Fig. 14. It should be
                                                              P LIN                                                      mentioned that despite that the toolbox is designed for
                     Power flow
                     P1, Q1
                                                             cos( ϕ )                                                    calculation with Danfoss ASD's only (both with 6-pulse and
                                                                                                                         harmonic filters) it is also possible to make the calculations
                                          I2                      PCC                                                    with non-Danfoss ASD's as long the drive parameters are
                                                                                       Q SVC
                                        Cable
                                                                                                                         known. Furthermore, all internal results are written out to a
                                       R1 X1                                                                             harmonic analysis report in Rich Text Format.
                                                                                  ΣP DRIVES
               V1                                      V2                                                                 In order to determine the accuracy of the approach, the
                                                                                   ΣQ DRIVES                             toolbox has to assure similar results as real measurements.
                                                                                                                          Good validations have been shown when comparing
  Fig. 13. Load-flow electrical diagram for harmonic toolbox calculation.
                                                                                                                         simulated and a real case current in the time-domain.
Knowing the active and reactive power (denoted by P1                                                                     However, since the target is to validate both, the acquired
respective Q1 in Fig. 13) and also the cable impedance                                                                   database and the implemented algorithm, validation with real
(denoted by R1 and X1), the problem is reduced to a simple                                                               applications are a must.
equation. The equation of voltage drop is given by:
                             R ⋅ P + X 1 ⋅ Q1               (6)
              ∆V = V2 − V1 = 1 1
                                   V2
This turns to be a quadric equation that has a solution as:
               1                                            (7)
          V2 =  V1 + V1 − 4(R1 ⋅ P + X 1 ⋅ Q1 ) 
                          2
                                                
               2                  1
                                                 
The current drawn can then easily be computed as:
                             S                              (8)
                       I2 = 1
                              3V2
 The algorithm for the fundamental voltages and currents is
continued sequentially up to the drives connection point (panel
point in Fig. 12).
                                                                                                                                  Fig. 14. Graphical interface from the harmonic toolbox.




                                                                                                                  1633
  The first tests were conducted with a programmable power                                                   VII. CONCLUSIONS
supply (in order to get pure sinusoidal voltage) and a Danfoss
                                                                                    This paper presents a new harmonic calculation toolbox,
VLT 5032 (32 kVA). The drive were connected to the power
                                                                                   which can be used for designing new and existing installations
supply through a 30 m cable (100 mm2) and a 256 µH                                 with ASD's.
inductance simulating a 122 kVA transformer with 6.1% short                         The main focus has been on a table-based method that can be
circuit impedance. The supply was set to 400 V nominal                             put into a toolbox. In a context of practical use to estimate the
voltage and 50 Hz frequency.                                                       harmonic distortion in a given industrial application by e.g. a
In this particular case all relevant data are exactly known and                    sales engineer, the table-based model has the advantages of
the supply voltage is programmed to be a pure sinusoidal                           easy implementation into a spreadsheet format.
voltage. The toolbox calculations are therefore as expected                        However, several analytical expressions can reduce the "table
very close to the actual measurements as shown in Table I.                         dimension" and can provide an efficient way to be compiled
  Another test is on a real application, which is a water                          into a stand-alone PC-software application.
pumping station with only a single ASD, as it can be seen in                        Finally, the approach is validated by real measurements with
Fig. 15. Typical for an application like this, only limited data                   satisfactory results.
are available. The supply transformer has a nominal power of
200 kVA with an impedance of 5%. The cable between the                                                           REFERENCES
transformer and the ASD is approximately 10 m. The input
power of the ASD is measured to 48 kW. The dc-link                                 [1]   W. F. Ray, “The Effect of Supply Reactance on Regulation and Power
                                                                                         Factor for an Uncontrolled 3-Phase Bridge Rectifier with a Capacitive
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capacitor is 26.5%.                                                                [2]   W. F. Ray, R. M. Davis, I. D. Weatherhogg, “The Three-Phase Bridge
  Table II compares the actual measurements with the results                             Rectifier with Capacitive Load”, IEE Conf. Publ. No. 291, 1988, pp.
of the toolbox. Furthermore harmonic currents and voltages                               153-156.
are displayed, as results of toolbox calculation, in Fig. 16.                      [3]   M. Grötzbach, “Line Side Behavior of Uncontrolled Rectifier Bridges
                                                                                         with Capacitive dc Smoothing”, Proc. of EPE Conf., 1989, pp. 761 –
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                                                                                         Operation Mode”, Proc. of EPE Conf., 1993, pp. 707-712.
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     Fig. 15. Circuit diagram of the water pumping station with ASD.               [7]   S. Hansen, “Harmonic Distortion of Rectifier Topologies for Adjustable
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                                                                                         Benefit Analysis”, Proc. of NORpie Conf., 2000, Aalborg, Denmark,
  Harmonic Measured Toolbox             Harmonic Measured Toolbox
                                                                                         pp. 271-277.
   order h   [%]      [%]                order h   [%]      [%]
      i5     35.4    33.6                   i5      32     29.3                    [9]   D. E. Rice, “A Detailed Analyze of Six-Pulse Converter Harmonic
      i7     14.2    14.3                   i7     13.8    12.6                          Current”, IEEE Trans. on Industry Applications, Vol. 30, No. 2, 1994,
    THDi     39.6    38.3                 THDi      37     33.6                          pp. 294-304.
     v5       2.4      2.3                 v5       2.1      1.9                   [10] IEEE Std 519-1992 “IEEE Recommended Practice and Requirement for
     v7       1.3      1.4                 v7       1.2      1.1                        Harmonic Control in Electrical Power Systems“, IEEE, 1993, ISBN 1-
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                                                                                        Willey & Sons, 1995, ISBN 0-471-30576-6.
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               a) Harmonic currents. b) Harmonic voltages.




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