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1 Close-Loop Control Design for a Three-Level Three-Phase Neutral-Point-Clampe Inverter Using the Optimize Nearest-Three Virtual-Space-Vector Moulation S. Busquets-Monge 1, J. D. Ortega 1, J. Boronau 1, J. A. Beristáin, an J. Rocabert 1 1 Dept. of Electronic Engineering Technical University of Catalonia Av. Diagonal Barcelona, Spain sergio.busquets@upc.eu Abstract This paper presents a close-loop control scheme for the three-level three-phase neutral-point-clampe c-ac converter using the optimize nearest-three virtual-spacevector pulsewith moulation, a moulation that prouces a low output voltage istortion with a significant reuction of the c-link capacitance. A specific loop moifying the moulating waveforms is introuce to rapily control possible perturbations in the neutral-point voltage balance. The remaining part of the control is analogous to the control for a two-level converter with an appropriate interfacing to the selecte moulation, incluing an online estimation of the loa isplacement angle at no extra cost. The close-loop control is esigne for the case of a renewable energy source connecte to the ac mains an its performance is analyze through simulation an experiments. I. INTRODUCTION Multilevel converter topologies [1]-[] have receive special attention uring the last two ecaes ue to their significant avantages in high-power meium-an-highvoltage applications. In these topologies, an compare to a two-level converter, the voltage across each semiconuctor is reuce, avoiing the problems of the series interconnection of evices, reucing the harmonic istortion of the output voltage, an improving the efficiency. But a larger number of semiconuctors are neee an the moulation strategy to control them becomes more complex. Among these topologies, the three-level three-phase neutral-point-clampe (NPC c-ac converter [3], in Fig. 1(a, is probably the most popular. The application of conventional moulation techniques to this converter causes a low frequency (aroun three times the funamental frequency of the output voltage, f o oscillation of the neutral-point voltage. This, in turn, increases the voltage stress on the evices an generates low orer harmonics in the output voltage. There have been many efforts to analyze this problem an efine a moulation strategy to solve it [4]-[14], therefore eliminating the nee to significantly increase the c-sie capacitance to minimize the voltage oscillation. Among them, the nearest-three virtual-space-vector (NTV pulsewith moulation (PWM [13], allows controlling the neutral-point voltage over the full range of converter output voltage an for any loa. The optimize nearest-three virtual-space-vector (ONTV PWM [14] also allows comprehensively controlling the neutral-point voltage but with a lower output voltage harmonic istortion in the case of linear-an-balance ac loas. The esign of a close-loop control scheme interfacing the ONTV PWM an correcting possible c-link capacitor voltage balance perturbations is not straightforwar. This paper presents a proposal for such control, focusing on a particular application, an the performance of the propose control scheme is verifie through simulation an experiments. II. OPTIMIZED NEAREST-TREE VIRTUAL-SPACE- VECTOR PWM Let us esignate ap, bp, cp, an, bn, cn the six inepenent converter phase uty-ratios, where xy refers to the uty ratio of the phase x connection to the c-link point y. Equation (1 reprouces from [14] the six expressions that efine the ONTV PWM in terms of these six inepenent converter phase uty-ratios in -q-0 coorinates (,, p0, n, nq, n0. n nq = = ( = tan ϕ m m θ π 3: p0 = π 3 < θ 4π 3: θ > 4π 3: p0 = θ π 3, θ > 5π 3 : π 3 < θ π : n0 = π < θ 5π 3 : n0 = = K sin Dept. of Electrical an Electronic Engineering Instituto Tecnológico e Sonora 5 e febrero 818, Ciua Obregón, Sonora, Mexico bantonio@itson.mx ( 3θ ( cos( θ π 3 sin( θ π 3 p0 = ( cos( θ sin( θ ( cos( θ π 3 sin( θ π 3 n0 = ( n cos( θ nq sin( θ ( n cos( θ π 3 nq sin( θ π 3 ( cos( θ π 3 sin( θ π 3 n where m ( [0, 1] an θ are the length an angle (with reference to axis α, aligne with vector V L1 corresponing to switching state n [13] of the reference vector, V ref, a rotating vector in the converter space vector plane that represents the esire funamental converter output threephase voltage. The expressions in (1 assume that axis of the -q-0 transformation of the phase uty-ratios is aligne with V ref. Variable ϕ is the ac loa/source isplacement angle an the optimum value of parameter K is a function of m an ϕ. In [14], expressions are provie to compute the value of K as a function of m an ϕ. Alternatively, a look-up table as a function of m an tan(ϕ can be generate to select the appropriate value of K on-line. Given the values of m, θ, an tan(ϕ, the uty ratios in -q-0 coorinates can be obtaine from (1 an the look-up table or expressions to compute K. Applying the inverse nq (1

2 -q-0 transformation, we then obtain the inepenent phase uty-ratios ap, bp, cp, an, bn, cn. From these uty ratios an assuming that the sequence within a switching cycle of connection of each phase to each of the c-link points is the symmetrical p-o-n-o-p, it is fairly straightforwar to generate the twelve switch control signals. III. CLOSED-LOOP CONTROL DESIGN The propose moulator an controller have been esigne an implemente for the particular system in Fig. 1(a. The purpose of the system is to sen the energy from a renewable energy source to the mains with unity power factor while also regulating voltage v. The close-loop control esigne is applicable to any system where the power source can be basically moele as a current source an the energy is sent to the mains, such as, for example, a win energy conversion system where the ac generator is connecte to a non-controlle boost rectifier. The iagrams of Fig. 1(b an Fig. 1(c summarize the propose controller an moulator structure, iscusse in etail next. A. Neutral-Point Voltage Control The ONTV PWM guarantees no low-frequency oscillations of v unb ue to the loaing conitions of the converter provie that the aition of line currents equals zero. Even if the loa presents a severe non-linearity, this will not affect the c-link voltage balance if we set K = 0. The occurrence of neutral-point voltage perturbations shoul however be consiere. Perturbations can occur if, for example, there is a leakage current flowing from the loa neutral to groun, causing that the aition of the three-phase currents be ifferent from zero. The noniealities, an specially the ifferences, in the switching behavior of the converter evices are another possible source of isturbances. As iscusse in [15], certain moulations have the property of naturally recovering the c-link voltage balance after a perturbation. The ONTV PWM with K = 0 oes not belong to this family of moulations. It oes not affect the balance of the c-link capacitors. If an unbalance exists at a given point in time, the ONTV PWM with K = 0 will preserve this unbalance (see Fig. (a. owever, the ONTV with K > 0 oes belong to the set of moulations that naturally recover the balance (see Fig. (b. The higher the value of K, the faster the system recovers the balance. Still, this natural recovery process is usually slow. The aition of ischarging resistors to the c-link capacitors also helps recovering the balance after a perturbation. Their resistance value is usually high, though, an the recovery process thanks to these resistors is also slow. Since all preexisting possible balance recovery processes o not seem to be effective/fast enough, an appropriate perturbation of the moulating waveforms that allowe speeing-up this process woul be helpful. Reference [7] shows that introucing a common-moe voltage into all three line-to-neutral output-voltage waveforms causes an unbalance in the ischarging of the c-link capacitors. This property can be use to spee-up the recovery process whenever a c-link voltage unbalance occurs. ere, this control mechanism is aapte to the ONTV PWM, leaing to an alternative scheme to guarantee the c-link capacitor voltage balance in the three-level three-phase NPC c-ac converter ifferent from other solutions presente [16]. The introuction of a common moe voltage can be one by aing an offset ( offset to all three ap an, bp bn, cp cn moulating waveforms. If we want to a an offset to the ap an waveform, we have three options: 1 We a the offset to ap. We subtract the offset from an. 3 We a part of the offset to ap an we subtract the remaining part from an. A simple an interesting strategy is to apply all the offset to the uty ratio to be reuce. Since uty ratios must be greater than zero, in case we reach the value of zero, the other uty ratio will be increase an amount corresponing to the part of the offset still not applie. This strategy allows minimizing the number of commutations, since it will maximize the occasions where a non-zero uty-ratio becomes zero. With reference to Fig. 1(c, this strategy can be formulate for phase x as ap = f 61 ( ap, an, offset ; an = f 6 ( ap, an, offset ; bp = f 63 ( bp, bn, offset ; bn = f 64 ( bp, bn, offset ; cp = f 65 ( cp, cn, offset ; cn = f 66 ( cp, cn, offset ; if ( offset 0 { if ( xn > offset { xn = xn offset xp = xp }else { xn = 0 xp = xp ( offset xn } }else { if ( xp > offset { xp = xp offset xn = xn }else { xp = 0 xn = xn ( offset xp } } The value of offset to be applie is etermine from the c-link capacitor voltage unbalance v unb = f 11 (, = = ( / by a compensator. This compensator must have a low-pass characteristic, in orer to only react to perturbations in the c-link voltage balance with frequencies lower than the switching frequency. (

3 Generic Renewable Energy Source p 3L-3P NPC inverter Mains L L a C 1 I v o i b L L b N C i c L L c n 1 switch control signals ap,, cn m, θ, tan(ϕ,,, v ab, Moulator offset, NLB i Controller a, i b v * Distributor (a f 1 v unb v o (s Limiter offset_max offset v * _ v (s i offset_min Non Linear-an-Balance Loa Detector NLB i * _max a-b-c i _ i * _min v i (s f _ v ref m max m i b -q -0 _ iq (s v refq f 4 φ m min θ i * q=0 i v f 3 v ab Positive-Slope Zero-Crossing Detector Reset t f 7 (b ψ i -q q i 1 i q1 f 5 tan(ϕ offset θ m tan(ϕ NLB Look-up table for K Eq. (1,, p0 n, nq, n0 1 -q a-b-c ap, bp, cp an, bn, cn f 6 ap, bp, cp an, bn, cn (c Fig. 1. System block iagram. (a Power stage plus control. (b Controller structure. (c Moulator structure.

4 vc1,vc (V vc1,vc (V t (s (a t (s (b Fig.. Natural c-link capacitor voltage balance recovery transient in the following conitions: V = 1500 V, m = 0.75, f o = 50 z, switching frequency f s = 5 kz, C 1 = C = 1 mf, an a wye connecte three-phase R-L loa (R L = 10 Ω, L L = 10 m. (a ONTV PWM, K = 0. (b ONTV PWM, K = B. Non Linear-an-Balance Loa Detector Whenever the loa is not linear an balance, we must set K = 0 in orer to maintain the neutral-point voltage control. This situation can be etecte by monitoring the maximum length of the line-current vector oscillation in -q coorinates, an if it goes beyon a given maximum, activating an latching a non linear-an-balance loa flag (NLB in orer to force K = 0 in the moulator. C. Reference Vector Computation From a close-loop control point of view, the key ifference between a two-level an a three-level c-ac converter is that the latter introuces the ynamics of the neutral-point voltage. We can assume that the neutral-point voltage is always balance thanks to the chosen moulation an the eicate control presente above. Then, the average moel of the three-level converter becomes equivalent to the moel of a two-level converter. ence, conventional control schemes an esign proceures for the two-level converter can be irectly applie to the three-level converter to obtain, from the sense variables, the reference vector length m an angle θ require by the moulator. For the particular application consiere here, the selecte control scheme is shown in Fig. 1(b. First, the clink voltage v = f 1 (, = is compare to the esire comman. The error is then processe by a compensator to prouce the i comman. Line currents an i b are sense an -q transforme. We o not nee to sense i c since we know i c = i b. The transformation is performe to axes -q -0, where axis is in phase with the vector of line-to-neutral mains voltages (V L-N. This vector has an angle ψ with reference to axis α (Fig. 3: ψ = f 7 ( t = ωo t π 3 = π f o π 3. (3 The an q components of the current are compare to their corresponing comman. The comman is zero to achieve a unity isplacement factor for the power transferre to the mains. Both an q channel errors are processe by their specific compensators. Finally, both channels are ecouple through f an f 3 : f ( iq, v = ( iq ωo LL v (4 f 3 ( i, v = ( i ωo LL v. The outcome of both channels is the an q components of V ref. Through f 4 we obtain the V ref length m (moulation inex an angle φ (with reference to axis : m = f φ = f 41 4 ( vref, vref q = vref vref q 1 ( v, v = tan ( v v. ref refq refq ref Angle θ can then be obtaine by simply aing ψ an φ (Fig. 3. This is the angle that will be use to perform the transformation of the uty ratios from 1 -q to a-b-c coorinates within the moulator. D. Online Estimation of tan(ϕ To implement the ONTV PWM we nee an estimate of tan(ϕ. Angle ϕ correspons to the angle between the vector of funamental line currents an V ref. ence, the value of tan(ϕ can be compute online by simply sensing the line currents, applying the 1 -q 1 transformation, an using (6 (in the case of non linear-an-balance loas, the c values of the 1 an q 1 components can be use. Since, in general, the controller alreay requires sensing the line currents, the implementation of the ONTV PWM oes not require aitional sensors. ( i, i = i i. (5 tan( ϕ = f 5 1 q1 q1 1 (6 V 0 θ ψ V ref 1 φ V S1 V L-N V L1 Fig. 3. Location of vectors V ref an V L-N with reference to axis α. α

5 IV. SIMULATION AND EXPERIMENTAL RESULTS Simulations have been carrie out in Simulink with close-loop switching an average moels of the system. For the experimental valiation, the controller an moulator blocks have been implemente using a PowerPC (SPACE 1103 an the istributor block using a FPGA (Altera EPF10K70. Fig. 4(a emonstrates the avantage of introucing the neutral-point voltage control. The simulation has been performe in the same conitions as in Fig. (a. Fig 4(b shows the perturbe uty-ratio pattern uring the transient. Fig. 5 epicts the goo performance achieve with this control in the experiments. In Fig. 5(a, the control effort is negligible: offset In Fig. 5(b, offset The complete control has been teste through simulation in the conitions of Fig. 6. These results have been obtaine with the complete close-loop switching moel for a step in voltage comman v * from 800 V to 750 V. We can observe that there is no unbalance of the c-link capacitor voltages before, uring, an after the step transient, as expecte (Fig. 6(a. Since the ONTV PWM alreay guarantees this balancing, the effort of the eicate control is minimal ( < offset < In Fig. 6(b we can observe that the power conversion is achieve with unity isplacement factor, as intene. Fig. 7 shows the experimental results obtaine with an emulator of a win energy conversion system connecte to the ac mains (Fig. 1(a. The voltage of a win mill generator is connecte to the inverter c-link through a set of three line inuctances (L S an a three-phase ioe rectifier. A constant torque of 10 Nm is applie to the generator shaft to emulate the win torque. A step in v * from 340 V to 300 V is force, proucing a variation of the rotor spee from 1577 rpm to 1396 rpm. The controller employe is efine in (7. The results show an overall goo performance of the complete control, which guarantees the c-link capacitor voltage balance an unity isplacement factor uring the entire transient. o v ( s ( s i iq ( s ( s = = 1000 = 500 = 1000 ( s π 0.01 s ( s π 5 ( s π 5 s ( s π 500 ( s π 5 s ( s π 500 ( s π 5 s ( s π 500 [ offset_min, offset_max ] = [ 0.1, 0.1] * * [ i, i ] = [ 10, 10] _min [ m, m ] = [ 0, 1]. min _max max V. CONCLUSIONS A close-loop control scheme for the three-level threephase NPC c-ac converter using the ONTV PWM has (7 been presente. The selecte moulation allows using small c-link capacitors leaing to an improve performance of the close-loop system. A specific control loop has been esigne to spee-up the recovery from neutral-point voltage perturbations. The remaining part of the control is analogous to the control for a two-level converter, with an appropriate interfacing to the selecte moulation, incluing an online estimation of the loa angle at no extra cost. The goo performance of the propose control has been verifie through simulation an experiments. REFERENCES [1] J. Roríguez, J. Lai, an F. Peng, Multilevel inverters: a survey of topologies, controls an applications, IEEE Trans. In. Electron., vol. 49, pp , Aug. 00. [] L. Demas, T.A. Meynar,. Foch, an G. Gateau, Comparative stuy of multilevel topologies: NPC, multicell inverter an SMC with IGBT, in Proc. IEEE Inustrial Electronics Soc. Conf., vol. 1, 00, pp [3] A. Nabae, I. Takahashi, an. Akagi, A new neutral-point clampe PWM inverter, IEEE Trans. In. Applicat., vol. IA-17, pp , Sept./Oct [4] S. Ogasawara, an. Akagi, Analysis of variation of neutral point potential in neutral-point-clampe voltage source PWM inverters, in Proc. IEEE In. Applicat. Soc. Annu. Meeting, 1993, pp [5] R. Rojas, T. Ohnishi, an T. Suzuki, PWM control metho for NPC inverters with very small c-link capacitors, in Proc. IPEC- Yokohama, 1995, pp [6] M. Cosan,. Mao, D. Borojevic, an F. C. Lee, Space vector moulation of three-level voltage source inverter, in Proc. VPEC Seminar, 1996, pp [7] C. Newton, an M. Sumner, Neutral point control for multi-level inverters: theory, esign an operational limitations, in Proc. IEEE Inustry Applications Soc. Annu. Meeting, 1997, pp [8] D.. Lee, S. R. Lee, an F. C. Lee, An analysis of mipoint balance for the neutral-point-clampe three-level VSI, in Proc. IEEE Power Electronics Specialists Conf., vol. 1, 1998, pp [9] N. Celanovic an D. Boroyevich, A comprehensive stuy of neutralpoint voltage balancing problem in three level neutral-point-clampe voltage source PWM inverters, IEEE Trans. Power Electron., vol. 15, pp. 4 49, Mar [10] Z. Tan, Y. Li, an M. Li, A irect torque control of inuction motor base on three-level NPC inverter, IEEE Power Electronics Specialists Conf., vol. 3, 001, pp [11] J. Pou, D. Boroyevich, an R. Pinao, New feeforwar spacevector PWM metho to obtain balance ac output voltages in a threelevel neutral-point-clampe converter, IEEE Trans. Power Electron., vol. 49, pp , Oct. 00. [1] Q. Song, W. Liu, Q. Yu, X. Xie, an Z. Wang, A neutral-point potential balancing algorithm for three-level NPC inverters using analytically injecte zero-sequence voltage, in Proc. IEEE Applie Power Electronics Conf., vol. 1, 003, pp [13] S. Busquets-Monge, J. Boronau, D. Boroyevich, an S. Somavilla, The nearest three virtual space vector PWM a moulation for the comprehensive neutral-point balancing in the three-level NPC inverter, IEEE Power Electron. Lett., vol., pp , Mar [14] S. Busquets-Monge, S. Somavilla, J. Boronau, an D. Boroyevich, A novel moulation for the comprehensive neutral-point balancing in the three-level NPC inverter with minimum output switching frequency ripple, in Proc. IEEE Power Electronics Specialists Conf., 004, pp [15].. T. Mouton, Natural balancing of three-level neutral-pointclampe PWM inverters, IEEE Trans. In. Electron., vol. 49, pp , Oct. 00. [16] J. Pou, P. Roríguez, V. Sala, S. Busquets-Monge, an D. Boroyevich, Algorithm for the virtual vectors moulation in threelevel inverters with a voltage-balance control loop, in Proc. European Conference on Power Electronics an Applications, 005, pp. 1-9.

6 ap vc1,vc (V ap, an an t (s (a t (s (b Fig. 4. Dc-link capacitor voltage balance recovery transient in the same conitions as in Fig. (a but with the eicate neutral-point voltage control activate. (a Dc-link voltages an. (b Phase a inepenent uty-ratios. (a Fig. 5. Neutral-point voltage control performance in the following conitions: ONTV PWM, K = 0, V = 140 V, m = 0.75, f o = 50 z, f s = 5 kz, C 1 = C =1.1 mf, R L = 16.5 Ω, an L L = 5 m. (a Control tune to achieve v unb = 0 V. (b Control tune to achieve v unb = 5 V. (b v an / 10 vc1, vc [V] van / 10 [V], ia [A] t (s t (s (a (b Fig. 6. Simulation results for a step in comman v * at time = 0.1 s in the following conitions: I = 1.5 A, C 1 = C = 400 µf, L L = 5 m, V an = V bn = V cn = 30 V rms, f o = 50 z, an f s = 5 kz. (a Dc-link voltages an. (b Mains voltage v an an line current.

7 , (a v uv v vw v wu i u i v i w (b (c v an i b i c ( Fig. 7. Experimental results for a step in comman v * from 340 V to 300 V (variation of rotor spee from 1577 rpm to 1396 rpm. Conitions: Rectifie win mill generator voltage, constant torque applie to the generator shaft = 10 Nm, L S = 1.5 m, C 1 = C = 1.1 mf, L L = 10 m, V an = V bn = V cn = 75 V rms, f o = 50 z, an f s = 5 kz. (a Dc-link voltages an [5 V/iv]. (b Generator line-to-line voltages v uv, v vw, an v wu [150 V/iv]. (c Generator currents i u, i v, an i w [ A/iv]. (, i b an i c [3 A/iv]. (e Mains voltage v an [30 V/iv] an line current [5 A/iv]. (e