Space Vector Modulation in Voltage Sourced Three Level Neutral Point Clamped Inverter
Three Level Voltage Sourced Neutral Point Clamped Inverter 3-Level Neutral Point Clamped (NPC) inverter is one of the DC/ACconverters with partitioned dc-link by diode clamps. The diode clamps are locatedsuch that each phase voltage is produced with respect to neutral point, which isactually the mid-point of dc-link. Since each phase voltage is produced with respectto neutral point (Z), the line-to-line voltages form a balanced three phase set for theload. Dc-link voltage is distributed such that two equal valued capacitors share thetotal dc-link voltage. For the three level operation there will be two capacitior toshare the dc-link, meaning that each capacitor has voltage value E which is half oftotal dc-link voltage value. With the changing switching schema each phase voltage (phase - neutral) canhave three different voltage level. One of them is called P state, for this statecorresponding phase has a voltage level of E. The second state is called O state,which corresponds to zero voltage on a phase. The last state is called the N statewhich corresponds to -E voltage on a phase. Since each phase voltage has threelevels, the line-to-line voltages has five different voltage levels, namely +2E,+E,0,-E,-2E. With this voltage kind of voltage waveform, one can easily say that the mostdominant voltage harmonic for this scheme should be larger than 10th harmonic. Inaddition to that information, naturally the voltage harmonics may lay aroundswitching frequency and its integer multiplications. This kind of topology gives uslower dv/dt values than the traditional 2 level inverters with same dc-link value.However, one of the most challenging drawback is that the user should keep theupper and lower side capacitor voltages the same. The three level NPC topology isas shown in figure 1.
Figure 1 : 3 Phase NPC Space Vector Modulation Space Vector Modulation (SVM) technique is a bit more complex andchallenging method than carrier based Pulse Width Modulation (PWM) techniques.To introduce SVM, let me remember some points about three phase systems. Thethree phase voltages at any instant ,actually, forms a space vector which is rotatingaround cartesian coordinates with an angular frequency 2*pi*f, f being systemfrequency. This space vector has a constant magnitude and its phase changing intime with the integral of angular frequncy stated. Please think that an observersitting on the origin of cartesian coordinates sees this space vector as I stated before.What about an observer on a frame which is rotating with the same angular speedwith the space vector? Actually the observer in synchronously rotating frame seesthis vector space as constant in time. Knowing these concepts, our controller shouldbe like an observer sitting in a fixed frame on cartesian coordinates. Suppose ourobserver has two point of views which are direct and quadrature axes. Theinstantaneous values of direct and quadrature axes represents the direct andquadrature components of the Space Vector for the 3 phase voltage. We are using a
transformation called Clarke transformation (or alpha-beta transformation) in orderto create a 2 phase representation of 3 phase voltage such that their space vectorscoincide each other. Space Vector Modulation technique creates a fixed valued reference spacevector which is rotating with angular frequency of w. And to use this technique, thewhole space is divided into 6 sectors and each sector is divided into 4 regions for 3-level operation. The corresponding divisions are shown in figure 2. Figure 2 - Space Vector Modulation Divisions Note that each position in dq space is represented a voltage state for phases a,band c. For example Sector 1, Region II is enclosed with three space vectors100(V1),210(V7) and 221(V2), meaning ONN,PON and PPO. To get a referencespace vector using these three vectors in Sector 1 - Region II, these three vectorsstates should be applied some defined time intervals of Ta,Tb and Tc respectivelyso that the following equation holds. The time intervals Ta, Tb and Tc are calledDwell Times. Vref * Ts = V1 * Ta + V7 * Tb + V2 * Tc , where Ts is switching periodUsing our fixed space vectors, we can form any reference vector at any instant. Bythis way, for every period Ts we should calculate the direct and quadraturecomponenets of reference vector and find in which sector and region the referencevector lies. After we find the exact location of reference vector, we know whichvectors are used for composing a reference for the corresponding section and region;thus, if we apply these vectors with the duration of calculated Dwell Times, we canform the required reference space vector. The calculation of Dwell Times are statedbelow in figure 3;
Figure 4: Dwell Times Formulas In figure 4, Dwell Times calculations are stated, in these equations theta valuewill be the angle of corresponding sector and it must be between 0 and 60 degrees.The theta value for each sector is as stated below; theta_Sector = theta_Reference - (Sector_Number - 1) * PI / 3Also for the formulation in Dwell Times, there is another variable calledmodulation index, Ma. This modulation index is used for creating a reference withdifferent magnitudes. Ma = sqrt(3) * Vref / Vd , where Vd is DC-LINK voltage 0 <= Ma <= 1 , range of modulation index Spece Vector Modulation Sequence Design In previous sections, I mentioned how reference space vector is composed andhow we can realize it using Dwell Times. After calculation of Dwell Times, onecan ask that in which sequence we can apply the space vectors. This is actually oneof the important parts of control system, because switching sequence determinessome key points like even voltage distribution of dc link capacitors or eliminationof even harmonics.
At the beginning, I said that there are 3 levels for each phase at any instantand since we have three phases, there are 27 different switching state for theinverter. All of this states corresponds to a space vector in figure 1. These spacevectors are used to form the reference space vector which is rotation at a speed of wand has a constant magnitude which is determined by the modulation index Ma.Actually, some of the states corresponds to the same space vector. The whole tablefor the space vectors are as stated in figure 5. Figure 5 : Space Vectors I will mention one of the switching sequences called Seven-Segmentswitching sequence, which is actually the one I used for my application. Theswitching sequence is shown in figure 6.
Figure 6 : Seven-Segment Switching Sequence for Sector 1 - Region IV Figure 7 represents the locations of Space Vectors. Figure 7 : Space Vector Positions The Inverter Results PSCAD Simulation with topology in figure 1. Ma = 1 frequency = 50 Hz For SVM Control Block FORTRAN codes contact me email@example.com
Figure 8 : Output Voltage and Current Waveforms Figure 9 : FFT for Vab/Vd for load sideREFERENCE : WU, B. High-Power Converters and AC Drives. 2006