Optmized pulse patterns with closed-loop realtime modification of switching transitions by means of linear controller

Abstract

A method for operating an electrical converter (2), the method comprising: calculating (61) a voltage reference (M) for the converter (2) in steady state from a desired electrical variable reference; determining (62) a precalculated pulse pattern (u*) from the calculated voltage reference (M) for the converter (2), wherein the precalculated pulse pattern (u*) is determined from a lookup table, wherein the precalculated pulse pattern (u*) comprises discrete voltage amplitude values changing at predefined switching instants; determining (63) an electrical variable tracking error by subtracting a measured electrical variable from the desired electrical variable reference; applying a linear controller (14) to calculate (64) a voltage increment (Δv) to be applied to the precalculated pulse pattern (u*) to track the desired electrical variable reference; modifying (65) the precalculated pulse pattern (u*) to obtain a modified precalculated pulse pattern (u), wherein modifying (65) is done by shifting switching instants (I) of the precalculated pulse pattern (u*) into shifted switching instants (II); applying (66) the modified precalculated pulse pattern (u) to semiconductor switches (25) of the electrical converter (2).

Description

[0001] METHOD AND DEVICE FOR OPERATING AN ELECTRICAL CONVERTER AND SYSTEM INCLUDING SAID DEVICE TECHNICAL FIELD

[0002] The present invention belongs to the field of control of electrical converters. More particularly, the invention relates to a method and device for operating an electrical converter, such as a voltage source converter (i.e. a high-power voltage source converter) based on precalculated pulse patterns. The invention also relates to a system including an electrical converter and the device for operating the same.

[0003] STATE OF THE ART

[0004] High-power electrical converters are used to convert voltages of different amplitudes and frequencies, such as AC and DC voltages, into one another. These converters use semiconductor switches which are switched according to specific patterns. The patterns are selected or obtained by a controller to achieve the required voltage conversion. The high-power semiconductor devices (i.e. switches) with which high-power mediumvoltage electronic converters work have a limited switching frequency (usually around 1 kHz) to reduce switching losses and operate within the converter thermal limits. To meet the grid code harmonic emission requirement while working with such low switching frequencies, precalculated pulse patterns can be used to control the converter, in particular to determine the switching orders for the semiconductor devices. The switching angles over a fundamental period are computed offline, and they are stored in a lookup table (LUT) for their use in real-time controllers. The precalculated pulse patterns are thus used to shape the spectrum of the currents and voltages of the converter.

[0005] Conventional linear control strategies calculate a voltage reference or modulation index reference every sampling period used to access the LUT. The calculated reference is used to select from the LUT the switching angles to be applied by the power converter. These control strategies have the disadvantage that slow controllers must be adjusted, as a consequence of which the converter dynamic performance is compromised, as reported for example in Rosado, L., Samanes, J., Gubia, E., & Lopez, J. (2023). Selective harmonic mitigation: Limitations of classical control strategies and benefits of model predictive control. IEEE Transactions on Industry Applications. This limitation of the converter dynamic performance when using precalculated patterns has also been analyzed in Holtz, J., & Beyer, B. (1995). Fast current trajectory tracking control based on synchronous optimal pulsewidth modulation. IEEE Transactions on industry applications, 31(5), Sept / Oct 1995, 1110-1120. When the operating point changes, theswitching sequence applied by the converter is pieced together from precalculated switching patterns for different modulation indexes. This causes a deviation from the optimal trajectory, called dynamic modulation error, which can lead to significant overcurrent.

[0006] To solve this problem, control strategies based on model predictive control (MPC) have been developed. In Holtz, J., & Beyer, B. (1995). Fast current trajectory tracking control based on synchronous optimal pulsewidth modulation. IEEE Transactions on industry applications, 31(5), Sept / Oct 1995, 1110-1120, a current tracking strategy for motor drives is proposed. The current fundamental component is controlled by a conventional proportional integral (PI) regulator that is used to load the required switching pattern in steady state. This pattern is used to calculate the reference current trajectory, and a tracking controller based on a deadbeat algorithm modifies the switching angles to obtain a fast dynamic response. As an alternative, a stator flux trajectory control is proposed in Holtz, J., & Oikonomou, N. (2005, October). Synchronous optimal pulsewidth modulation and stator flux trajectory control for medium voltage drives. In Fourtieth IAS Annual Meeting. Conference Record of the 2005 Industry Applications Conference, 2005. (Vol.

[0007] 3, pp. 1748-1791). IEEE. The stator flux reference trajectory is obtained from the precalculated pulse pattern, and the real flux is estimated using the machine model. The error is used in a trajectory controller that modifies the switching pattern to follow the stator flux reference.

[0008] More recently, model predictive pulse pattern control (MP3C), was proposed in Geyer, T., Oikonomou, N., Papafotiou, G., & Kieferndorf, F. D. (2011). Model predictive pulse pattern control. IEEE Transactions on Industry Applications, 48(2), 663-676, for motor drives, and it was later extended to a grid-connected static synchronous compensator (STATCOM) in Spudic, V., & Geyer, T. (2019). Model predictive control (MPC) based on optimized pulse patterns for modular multilevel converter STATCOM. IEEE Transactions on Industry Applications, 55(6), 6137-6149, to a grid-connected converter with L filter in US10312793B2, and to a grid-connected converter with LCL filter in US11967908B2. In this control strategy, a reference pulse pattern associated to a steady state operation point of the converter is selected from a first LUT, and the reference harmonic content corresponding to that pulse pattern is computed from a second LUT. From the harmonic content reference, a harmonic content error is determined. With the objective of correcting the harmonic content error, the reference switching pattern is modified online based on the minimization of a cost function.

[0009] However, the previous predictive (MPC) strategies have some drawbacks for grid-connected applications since the system parameters must be known to properlycalculate the harmonic content reference. This implies knowledge of the grid impedance, which is generally unknown. In addition, the control parameters in MPC strategies are adjusted by simulation, as there are no linear models available to adjust the system dynamics. Finally, these strategies involve a high computational burden, which makes solving the optimization problem in short sampling periods a major challenge.

[0010] Therefore, there is need of an improved control strategy for electrical converters, such as for grid-connected applications.

[0011] DESCRIPTION OF THE INVENTION

[0012] The present disclosure provides a control strategy for electrical converters (i.e. high-power electrical converters), such as grid-connected converters, that overcomes the limitations of conventional linear control strategies combined with precalculated pulse patterns, namely, a limited dynamic response, without requiring transitioning to model predictive control strategies.

[0013] A first aspect of this disclosure relates to a method for operating an electrical converter. The method comprises:

[0014] calculating a voltage reference for the converter in steady state from a desired electrical variable reference;

[0015] determining a precalculated pulse pattern from the calculated voltage reference for the converter, wherein the precalculated pulse pattern is determined from a lookup table, wherein the precalculated pulse pattern comprises discrete voltage amplitude values changing at predefined switching instants;

[0016] determining an electrical variable tracking error by subtracting a measured electrical variable from the desired electrical variable reference;

[0017] applying a linear controller to calculate a voltage increment to be applied to the precalculated pulse pattern to track the desired electrical variable reference;

[0018] modifying the precalculated pulse pattern to obtain a modified precalculated pulse pattern, wherein modifying is done by shifting switching instants tx* of the precalculated pulse pattern into shifted switching instants tx, wherein

[0019] tjx= tjx*+ Δtjx, wherein:

[0020] x denotes the phase a, b, c;

[0021] j is a natural number in [1, nx], nxbeing the number of switching angles for phase x comprised within a correction horizon, Tc; andt is dependent on the voltage increment calculated to track the desired electrical variable reference;

[0022] applying the modified precalculated pulse pattern to semiconductor switches of the electrical converter.

[0023] The method may be implemented in hardware and / or software in a controller.

[0024] The electrical converter is in general a three-phase converter. Therefore, the former method steps are applicable to each of the three phases. In particular, a voltage reference and a precalculated pulse pattern are calculated for each phase.

[0025] The electrical variable may be a current, a voltage, a flux, an active power or a reactive power.

[0026] The voltage reference calculated for the converter in steady state from a desired electrical variable reference is for example, but not limiting, a fundamental voltage reference.

[0027] In a particular embodiment, the electrical converter is connected to an electric grid. As mentioned, the electrical variable under control may be a current, a voltage, a flux, an active power or a reactive power. When, in a particular example, the electrical variable is a current, the voltage reference is calculated from a current reference and from a component of the voltage measured at a point of common coupling of the electric grid. The electrical variable tracking error and the voltage increment to be applied, are typically calculated in axes αβ or dq, depending on the linear controller being used.

[0028] The method requires a lookup table (LUT) in which previously computed pulse patterns are stored. The precalculated pulse patterns comprise discrete voltage amplitude values which change at predefined switching time instants, which represent time instants at which the semiconductor switches of the converter must switch to shape the currents and voltages of the converter. Therefore, precalculated pulse patterns are used to control the converter.

[0029] The precalculated pulse pattern may be calculated to eliminate certain harmonics (selective harmonic elimination patterns), or to minimize the amplitude of certain harmonics or the total harmonic distortion (THD) (Selective Harmonic Mitigation patterns), or to limit semiconductor losses, or to reduce the common mode voltage, or to attenuate harmonic distortion present in an electric grid.

[0030] The switching time instants defined in a pulse pattern are usually represented as angles (for example between 0° and 360° (between 0 and 2TT rad), representing a completecycle or period). The relationship between angle and time is given by: = w0At, for phase x. Therefore, switching instants can be indifferently expressed in time (time change At) or in angle (angle change A0). From the LUT having precalculated pulse patterns, the switching angles (i.e. a specific pattern) associated with a desired voltage (i.e. voltage reference) are selected. Thus, the switching angles over a fundamental period are computed offline, and they are stored in a lookup table (LUT) for their use in real-time in a controller. Thus, when later a pulse pattern is modified by timeshifting switching instants in the pulse pattern, this implies adjusting the angles of the pulse pattern, such that the voltage reference for the converter is tracked and an electrical variable tracking error is corrected by the timeshifted switching instants. Switching angles and switching time instants are related through the period length of the actual frequency, ω0.

[0031] The voltage reference for the converter in steady state from which the precalculated pulse pattern is determined (i.e. selected from the LUT) is for example a modulation index calculated from a desired electrical variable reference. For example, the modulation index, used to access the LUT, may be calculated every sampling period. The calculated reference (i.e. modulation index) is used to select from the LUT a suitable pulse pattern which should enable to reach the desired electrical variable reference. In other words, based on a voltage reference, which for example may be provided as a modulation index, one precalculated pulse pattern is selected, so that when the semiconductor switches of the converter are subsequently switched at the switching angles imposed by the pulse pattern, the desired electrical variable reference can be reached. In general, a different modulation index per phase is calculated. In particular implementations, the same modulation index can be used for all phases.

[0032] In certain circumstances, for example when the operating point of the converter changes, if the switching instants (also referred to as switching angles) imposed by the precalculated pulse pattern are directly applied to the semiconductor switches, a desired dynamic response is not obtained. For this reason, the selected precalculated switching pattern must be modified online. This is done by applying a closed-loop control, to improve the dynamic response to transients (changes of reference or perturbations) and to guarantee that the reference electrical variable is tracked. This closed-loop control calculates modifications required in a selected, precalculated pulse pattern.

[0033] Unlike in other methods for operating an electrical converter, such as the one disclosed in US10312793B2, which modifies the pulse pattern taking into account harmonic content references stored in a second lookup table (these harmonic content references model the behaviour of the electrical converter when a specific pulse pattern is appliedto the converter) and solving an optimization problem by minimizing a cost function, the proposed method uses voltage values calculated by a linear control to modify the precalculated pulse pattern by modifying the switching angles (in general, for each of the three phases) comprised within a defined correction horizon, Tc, of certain time length, in order to track the desired electrical variable reference. In other words, the switching angles comprised within the defined correction horizon are modified as a function of the voltage increment calculated by the linear control. The voltage increment is in turn obtained taking into account an electrical variable tracking error obtained by subtracting a measured electrical variable from the desired electrical variable reference.

[0034] Finally, the precalculated pulse pattern selected from the LUT is modified by timeshifting switching instants such that the voltage reference for the converter is tracked and the electrical variable tracking error is corrected by the timeshifted switching instants.

[0035] The method ensures a stable operation of the converter, and it allows to properly track the desired electrical variable reference. Furthermore, it maintains the benefits of using a precalculated pulse pattern regarding compliance with harmonic emission requirements, while achieving a fast dynamic response. The use of a linear controller has the advantage that a linear model can be developed to adjust the controller, which simplifies the adjustment of the control method for different systems. Additionally, this method can be easily implemented in a real-time control platform, and it can be executed online with a reduced computational burden.

[0036] In embodiments of this disclosure, timeshifts are applied in a time window equal to the correction horizon, Tc.

[0037] In embodiments of this disclosure, for each of the phases a, b, c of the converter, the switching instants of each of the na, nb, ncswitching angles comprised within the correction horizon, Tc, are shifted by the following increment:

[0038] T

[0039] Δtja= −K (2Tc) / (VDCnaΔuja) Δvα

[0040] T

[0041] Δtjb= K (Tc) / (VDCnbΔujb) (Δvα− √3Δvβ)

[0042]

[0043] 1VDCncAujv 7

[0044] wherein:

[0045] VDCis a DC link voltage of the converter (2),

[0046] Δujadenotes a switching transition for switching angle j for phase a,

[0047] Δujbdenotes a switching transition for switching angle j for phase b,AUj denotes a switching transition for switching angle j for phase c,

[0048] Δvαdenotes a voltage increment calculated by the linear controller in α axis, Δvβdenotes a voltage increment calculated by the linear controller in β axis, K is a coefficient of the Clarke transformation matrix.

[0049] In embodiments of this disclosure, the method further comprises applying the following constraints:

[0050] ln,-T1s < — tL1a-I '- T1min < — tLa2 + ' T1min < —... < — tLnaa-I- T1min < — tLnaa*+1

[0051] kTs≤ t1b+ Tmin≤ t2b+ Tmin≤ ... ≤ tnb+ Tmin≤ tn+1b*kTs≤ t1c+ Tmin≤ t2c+ Tmin

[0052]

[0053] 1min < —... < — tLncc-I- T1min < — tLnc*c+1 wherein

[0054] Tminis a minimum turn-on time of the semiconductor switches,

[0055] kTsis an actual sampling instant,

[0056] tn+1x*represents a first switching instant outside the correction horizon Tcin phase x.

[0057] In embodiments of this disclosure, the modified precalculated pulse pattern is applied to semiconductor switches of the electrical converter at each sampling period.

[0058] A second aspect of this disclosure refers to a device (i.e. a controller) for controlling an electrical converter, the controller comprising:

[0059] means for calculating a voltage reference for the converter in steady state from a desired electrical variable reference;

[0060] means for determining a precalculated pulse pattern from the calculated voltage reference for the converter, wherein the precalculated pulse pattern is determined from a lookup table, wherein the precalculated pulse pattern comprises discrete voltage amplitude values changing at predefined switching instants;

[0061] means for determining an electrical variable tracking error by subtracting a measured electrical variable from the desired electrical variable reference;

[0062] a linear controller for calculating a voltage increment to be applied to the precalculated pulse pattern to track the desired electrical variable reference;means for modifying the precalculated pulse pattern to obtain a modified precalculated pulse pattern, wherein modifying is done by shifting switching instants t * of the precalculated pulse pattern into shifted switching instants t, wherein

[0063] tjx= tjx*+ Δtjx, wherein:

[0064] x denotes the phase a, b, c;

[0065] j is a natural number in [1, nx], nxbeing the number of switching angles for phase x comprised within a correction horizon, Tc; and

[0066] t is dependent on the voltage increment calculated to track the desired electrical variable reference;

[0067] means for applying the modified precalculated pulse pattern to semiconductor switches of the electrical converter.

[0068] Any linear control strategy can be used to compute the voltage increment to be applied to the precalculated pulse pattern in order to track the electrical variable reference. For example, the linear controller may be a proportional integral (PI) controller or a plurality of PI controllers; or a proportional resonant (PR) controller or a plurality of PR controllers; or any other linear controller or combination of linear controllers.

[0069] The same advantages of the first aspect of the disclosure are applicable to the second aspect of the disclosure.

[0070] A third aspect of the disclosure refers to a power converter system comprising an electrical converter and a controller according to the second aspect.

[0071] In some embodiments, the electrical converter is connected to an electric grid. The electrical variable under control may be a current, a voltage, a flux, an active power or a reactive power. When, in a particular example, the electrical variable is a current, the voltage reference is calculated from a current reference and from a component of the voltage measured at a point of common coupling of the electric grid.

[0072] The method and device (controller) work on-line (i.e. in real time). This means that, every sampling period, the electrical variable to be controlled is measured, and the electrical variable reference is provided by an external control loop. Based on these signals (provided values thereof), a precalculated pulse pattern is determined, and it is modified based on a voltage increment calculated to track the desired electrical variable reference. The modified switching instants are applied to the semiconductor switches of the electrical converter every sampling period, which is usually around tens or hundreds of microseconds.Additional advantages and features of the disclosure will become apparent from the detailed description that follows and will be particularly pointed out in the appended claims.

[0073] BRIEF DESCRIPTION OF THE DRAWINGS

[0074] To complete the description and in order to provide for a better understanding of the invention, a set of drawings is provided. Said drawings form an integral part of the description and illustrate an embodiment of the invention, which should not be interpreted as restricting the scope of the invention, but just as an example of how the invention can be carried out. The drawings comprise the following figures:

[0075] Figure 1 shows a power converter system having a three-phase three-level NPC converter connected to the grid.

[0076] Figure 2 shows an exemplary precalculated pulse pattern that can be applicable to one phase of the NPC converter of Figure 1, according to a particular embodiment of the disclosure.

[0077] Figure 3 shows a block diagram representing a control strategy to control the current of a converter according to an embodiment of the disclosure.

[0078] Figure 4 shows a phasor diagram of the power converter system for one phase according to an embodiment of the disclosure.

[0079] Figure 5 schematically shows an example of modification of a switching instant in one phase, applicable to the semiconductor switches of the converter of Figure 1.

[0080] Figure 6 shows a flow diagram of a method for operating an electrical converter according to embodiments of the disclosure.

[0081] DESCRIPTION OF A WAY OF CARRYING OUT THE INVENTION Figure 1 schematically shows a power converter system 1 having an electrical converter 2 (in particular, a voltage source converter 2) connected to the electric grid 3 at a point of common coupling (PCC) 4. In particular, the exemplary voltage source converter 2 is a three-phase three-level neutral point clamped (NPC) voltage source converter. The goal of converter 2 is to convert the DC voltage provided by the DC link into AC voltage at the output o2_x(o2_ao2_bo2_c) of each phase branch. The three phases are represented as a, b, c (generically, x denotes the phase). Therefore, ixis the converter current of a generic phase x, with x = a, b, c. In other words, ixis the current provided by converter 2in phase x. At the output O2_xof each phase branch, through which converter current ixcirculates, there is an inductive output harmonic filter 5 used to filter out the converter harmonics. The harmonic filters 5 are generally denoted by Lh. The inductance Lh of the harmonic filters 5 is in general the same for the three phases. Lgdenotes the grid inductance. In general, the grid inductance Lgis the same for the three phases. VPCCXis the voltage at the PCC for phase x. vgxis the grid voltage for phase x. VDC is the DC link voltage. The exemplary DC link shown in Figure 1 is a split DC link with a neutral point between two DC link capacitors, each of which has a voltage of VDC / 2 at its terminals. The voltage source converter 2 has semiconductor switches 25 which must be switched according to specific patterns to achieve the required voltage conversion. To meet the grid code harmonic emission requirement while working with low switching frequencies, the voltage source converter 2 uses precalculated pulse patterns to determine the switching orders (time instants which trigger the switching from one voltage level to another voltage level) for the semiconductors. These switching instants are calculated with the objective of minimizing the amplitude of certain voltage harmonics and / or the total harmonic distortion (THD). Precalculated pulse patterns comprise discrete voltage amplitude values which change at predefined switching instants. Precalculated pulse patterns are associated to a steady state operation point of the converter 2 and are used to reach a desired voltage reference.

[0082] As a matter of example, Figure 2 shows a precalculated pulse pattern uxfor one phase (phase x) of the converter 2. This pattern represents the output voltage of each phase with respect to the midpoint of the DC link. This precalculated pulse pattern represents the desired converter output voltage of phase x, vx, normalized with respect to

[0083]

[0084] vx

[0085] ux= vx / (VDC / 2)

[0086] In a three-level converter as the one shown in Figure 1, the converter output voltage can take three different values, VDC / 2, 0, and −VDC / 2. The precalculated pulse pattern models a voltage level for every phase to be output by the converter 2. At switching instants, represented in Figure 2 by instants (represented by angles) at which there is a change from one voltage level (VDC / 2, 0, and −VDC / 2) to another one, the voltage level of a phase x has to be switched to another level. The switching instants between levels, usually expressed as angles, are computed offline. The offline-computed switching angles are stored in a lookup table for their use by an online controller. The switching angles are then converted to switching time instants based on the period length of the actual frequency.Therefore, the power converter system 1 comprises a controller 10, schematically illustrated in Figure 3, for controlling the triggering or switching of the semiconductor switches 25 of the converter 2. In particular, the controller 10 modifies the precalculated pulse patterns in such a way that a component of the current (current reference) is tracked. For example, the fundamental component of the current is tracked. In other words, a voltage precalculated pattern will be modified in such a way to move or adjust time instants indicating when the output voltage has to be switched to another level. Figure 3 schematically shows the power converter system 1 of Figure 1 and a controller 10 designed to control the semiconductor switches of the schematically represented electrical converter 2. In particular, the shown controller 10 is based on current control. In other words, it is aimed at controlling the output current i (ia, ib, icfor each phase in Figure 1) of the converter 2. The controller 10 therefore implements a control strategy applied to control the output current of the converter 2. The main blocks or stages required by controller 10 are described with reference to Figure 3.

[0087] In block 11 (reference voltage calculation block), a voltage reference for the converter 2 in steady state is calculated, such that a desired current reference, i*, is injected into the PCC 4. For example, a fundamental voltage reference is calculated, such that a desired fundamental current reference is injected. Therefore, an input for block 11 is a desired fundamental current reference i*. For example, the desired fundamental current reference, i*, can be calculated by an external control loop (not shown) of the DC link, or from given reference values of active and reactive power. How to calculate the desired fundamental current reference, i*, is out of the scope of the present disclosure. Another input for block 11 is the fundamental component vpcc.f of the voltage VPCC measured at the PCC 4. The voltage at the PCC is measured and its fundamental component vpcc.f is extracted with filter 12. From the fundamental voltage reference for the converter 2 in steady state, calculated in block 11, a modulation index, M, and an angle <|) are obtained. In an embodiment, the fundamental voltage reference of the converter 2 is calculated at block 11 by solving the phasor diagram of the power converter system 1, which is shown in Figure 4 for one phase. In this figure, VPCCis the phasor of the fundamental voltage at the PCC 4, vpcc.f. The fundamental component of the voltage at the PCC 4, vpcc.f, is obtained by applying a filter 12 to the voltage measurement. For example, filter 12 can be implemented by a second order generalized integrator (SOGI) filter. In Figure 4, 7* is the phasor of the fundamental current reference, i*,

[0088]

[0089] = Rh+ j iω0Lh, where Rhis the series resistance of the inductance of the converter 2 (the series resistance Rhis not shown in Figures 1 and 3 for clarity), and >0is the grid fundamental angular speed. Rh,Lhand ω0are known. Finally, V* is the phasor of the voltage reference of the converter 2 (to be calculated in block 11), and 5 is the angle of phase difference between the voltage reference of the converter and the fundamental voltage at the PCC. By solving the phasor diagram, the voltage to be applied by the converter (voltage reference of the converter) is obtained. From VPCC, ~Z^ and 7*, the voltage reference phasor, 7*, of the converter 2 is calculated by

[0090]

[0091] y* = vPCCj + zhi*.

[0092] From the voltage reference phasor, 7*, of the converter 2, the modulation index, M, and the angle of the voltage reference, cf), are obtained. The modulation index is calculated as

[0093] M =

[0094]

[0095] VDC / 2

[0096] and the angle of the voltage reference, cf), is the sum of the angle 5 and the angle of the fundamental voltage at the PCC (obtained from the measured vpcc.f). The angle <() needs to be obtained to subsequently calculate the number of switching instants within a correction horizon na, nb and nc. In other words, angle <() is used to calculate the number of switching instants within a correction horizon.

[0097] At block 11, the phasor diagram of the power converter system 1 is solved for the three phases. Figure 4 represents the phasor diagram of the power converter system generically without specifying any one of the three phases, but a specific diagram should be used for each phase. Thus, the modulation index M and voltage reference angle <() of each phase are obtained.

[0098] Then, at block 13 (pulse pattern LUT), a precalculated pulse pattern, u*, an example of which is given in Figure 2, is selected from a lookup table (LUT). This is done by providing the modulation index, M, which is used to access the LUT. A precalculated pulse pattern, u*, corresponding to the provided modulation index, M, is selected.

[0099] The precalculated pulse pattern, u*, comprises discrete voltage amplitude values which change at predefined switching instants (represented as angles in Figure 2). The precalculated pulse pattern, u*, is the output of block 13. This is the pulse pattern that the converter 2 must apply in steady state to inject the desired fundamental current reference, i*, into the PCC 4. The application of the precalculated pulse pattern, obtained at block 13 using the modulation index, M, also ensures compliance with the harmonic emission requirement. However, when the operating point of the converter changes, directly applying the precalculated pulse pattern does not allow to obtain the desireddynamic response. Therefore, to properly track the current reference, the precalculated pulse pattern is modified.

[0100] A closed-loop control is included to track the desired fundamental current reference, i*, and achieve a fast dynamic response during transients. This closed-loop control is based on block 14, which implements a linear controller. The linear controller 14 is fed with a current tracking error,

[0101]

[0102] The current tracking error, £t, is calculated at stage or means 16 by subtracting the measured converter current, i, (ia, ib, icin Figure 1) from the desired fundamental current reference, i*:

[0103] £i = i* — i.

[0104] The linear controller 14 then calculates a voltage increment, Av, to be applied to the precalculated pulse pattern, u*, to track the current reference, i*. At block 14, the current can be controlled in different ways. For example, the current can be controlled using a proportional integral controller (PI controller) in a synchronous reference frame, or dq axes, or it can be controlled in a stationary reference frame, or op axes, using a proportional resonant controller (PR controller). For example, if a PI controller in the synchronous reference frame is used to control the current, the current tracking error is expressed in dq axes, £dq, and the voltage increment to be applied is also calculated in dq axes as follows:

[0105] Avd<?= £dq

[0106]

[0107] If, in another example, the current is controlled in the stationary reference frame using a PR controller, the current tracking error is expressed in op axes,

[0108]

[0109] , and the voltage increment to be applied is calculated by the PR controller in op axes:

[0110] R- IKiS0

[0111] = £aP

[0112] 0KiK[S

[0113]

[0114] V s'2+a>^

[0115] Kp, Tn, and

[0116]

[0117] are the design parameters of these controllers, which are adjusted to obtain the desired dynamic response.

[0118] The voltage increment Av, and the precalculated pulse pattern, u*, obtained in block 13, are inputs to a pulse pattern modification block 15. The angle of the voltage reference, 4), is also an input to the pulse pattern modification block 15. In block 15, the control action or average voltage correction (voltage increment Av) calculated by the linear controller 14 is transformed to modifications of the switching angles of the precalculatedpulse pattern, u*, which results in a modified pulse pattern, u, at the output of block 15. In general, a specific modified pulse pattern, u, is obtained per phase.

[0119] To perform the modifications of the switching angles (or corresponding switching time instants), a correction horizon, Tc, of certain time length, is defined. Within the defined correction horizon, and for each of the three phases, there is a certain number of switching angles: there are naswitching angles for phase a, nb switching angles for phase b and ncswitching angles for phase c, wherein na, nb and ncare natural numbers. The angles comprised within the correction horizon, Tc, are modified by applying the voltage increment calculated by the linear control 14, that enables to track the desired fundamental current reference.

[0120] The required average voltage correction is divided between the switching angles that fall within a correction horizon, Tc, which is usually selected as corresponding to several sampling periods, such as more than one sampling period, or more than two sampling periods, or more than five sampling periods. This means that all the switching angles comprised within the correction horizon, Tc, are modified by a same absolute value, so that the required voltage correction is applied within the correction horizon. The modifications of the switching angles that fall within a next sampling period are applied by the electrical converter 2 (in particular, applied to the semiconductor switches), and, at the next sampling instant, the average voltage correction performed by controller 10 is computed again over a shifted correction horizon, Tc. The time length of the correction horizon, Tc, is a design parameter, and it can be modified online according to the converter operating conditions.

[0121] Thus, the switching angles of the precalculated pulse pattern, u*, obtained in block 13, are slightly shifted forward or backward in time to apply the correction Av calculated by the linear controller 14, which is the required correction to track the current reference i*. Figure 5 schematically represents the approach followed in the modification of the switching angles. In particular, Figure 5 shows a portion of a precalculated pulse pattern of the type shown in Figure 2. In particular, Figure 5 shows a modification of a switching instant in phase a by a time Ata(from initial switching instant ta* to new, actual switching instant ta) according to an embodiment of the invention. “1” and “0” denote the voltage value before and after the switching.

[0122] If there is a switching angle in one phase, for instance phase a, in the correction horizon, Tc, and it is shifted by a time At“ as shown in Figure 5, the average value of the voltage correction applied to the precalculated pulse pattern in phase a in this horizon is:&va_ _Zoc2\u“At“,

[0123]

[0124] 2TC

[0125] where Au“ denotes the switching transition in phase a, for example Au“ = -1 in this case. At“ = ta- ta*, where ta* is the precomputed switching time of the precalculated pulse pattern, u*, and tais the actual switching time. Considering that there are naswitching angles in phase a within the correction horizon, Tc, the total average voltage correction in phase a is given by

[0126] na

[0127] Lva= — V Au“At.“

[0128] 2TCZJJ J

[0129]

[0130] j=i

[0131] The same applies to phases b and c. The total average voltage correction that is achieved in those phases by modifying the switching angles that fall within the correction horizon, Tc, is

[0132] Aub= - — V Au? At?

[0133] 2TCL-t] ]

[0134] j=i

[0135] ’k

[0136] &vc= - — V Au? At?

[0137] 2TCZJ] ]

[0138]

[0139] j=i

[0140] where nband ncare the number of switching angles of phases b and c within the correction horizon, Tc, Au? and Au? denote the switching transitions of those angles, and At? and At? are the time modification suffered by switching angle j for each phase (from initial switching instant t?* to new, actual switching instant t? or, from initial switching instant t?* to new, actual switching instant t?*, if a similar scheme as the one shown in Figure 5 is applied to phases b and c).

[0141] The linear controller 14 calculates the required voltage correction, and from the previous equations the required time increment for each phase, At, to be applied to the precalculated pulse pattern (to be added to t**) can be calculated to obtain the average voltage correction calculated by the linear controller.

[0142] In embodiments of the disclosure, we impose that all the switching angles in each phase are modified by a same absolute value, that is, |Atf | = ••• = |At, with x = a, b, c. Besides, in embodiments in which a three-level converter is used, the step size of all the switching transitions is ±1, that is, |Au*| = 1, SO each switching transition provides the same correction. Therefore, the total average voltage correction in each phase can be expressed asVDC

[0143] bva= - —naLufLtf

[0144]

[0145] 2TC1 1

[0146] vb= - —nb Au? At?

[0147] 2TCb J J

[0148] VDC

[0149] vc= - — ncAu? Atf

[0150] 2TCc 1 1

[0151] The total average voltage correction can be expressed in op axes by applying the Clarke transformation to the voltage correction in each phase:

[0152] 'n„Au“At“'

[0153] Av“ J J

[0154] LvaP = [C] Avb= -^£

[0155] C[C] n

[0156] 2Tbhubhtb

[0157] . Avc.

[0158]

[0159] nc^u J^t Jf.

[0160] In the previous equation, [C] is the Clarke transformation matrix, which is used to transform electrical signals from the abc to the op reference frame

[0161]

[0162] where K is the coefficient of the Clarke transformation matrix.

[0163] By solving the previous system of equations the time modifications, At, of the switching angles j (j being a natural number in [1, nx], nxbeing the number of switching angles for phase x comprised within the correction horizon, Tc) of the precalculated pulse pattern, u*, that are required to apply the voltage increment calculated by the linear controller, Av“^, for each phase a, b, c, are computed:

[0164] 2 T

[0165] bt? = -K- - Av“

[0166] 1VDCnaLuf

[0167] At / K - - - r (Ava- V3Av^)

[0168] VDCnbkub

[0169] T

[0170] btf=K — -C.r(Ava+ V3Av^)

[0171]

[0172] 1VDCncltfv 7

[0173] It is noted that the voltage increment calculated by the linear controller in axes ap, Av"^, is the output of the linear controller expressed in axes ap, irrespective of the linear controller being a proportional integral (PI) controller, a proportional resonant (PR) controller, or any other linear controller or combination of linear controllers.

[0174] Thus, the modified switching instants are given by

[0175]

[0176] + At /

[0177]

[0178] = tf* + AtJ

[0179] In embodiments of the disclosure, once the previous solution is obtained, the following constraints are applied.

[0180] nk-T1s < — tL1a-X- T1min < — tL2a-L ' T1min < —... < — tLnaa-L T1min < — tLnaa*+1

[0181] nj-T < i-b I m < t-b I m <... < tb-X- T < tb* -1s —L11min —L2 '1min — —Lni}1min — ‘-n^+lnk-Tls < — fL1c-X- T1min < — tL2c-X '- T

[0182]

[0183] 1min < — ■■■ < — fLncc-X- T1min < — tLnc*c+1 These constraints ensure that the correct sequence of the precalculated pulse pattern is maintained as well as the minimum turn-on time of the semiconductors, Tmin. Besides, switching instants cannot be moved into the past, which is enforced by imposing that the final switching times are greater than kTs, which is the actual sampling instant. Finally, switching instants cannot be moved beyond the first switching instant outside the correction horizon, which is denoted by t„*+1. If a switching instant violates a constraint, it is limited to the maximum modification allowed by the constraint.

[0184] This way, the modified pulse pattern, u, is obtained, from which the switching orders for the semiconductors of the NPC converter 2 are determined.

[0185] The modified pulse pattern, u, can then be applied to the semiconductor switches 25 of the voltage source converter 2 so that the converter 2 provides the required voltage conversion.

[0186] A method for operating an electrical converter according to this disclosure is shown in the flow diagram of Figure 6. In a first stage 61, a voltage reference for the converter in steady state is calculated from a desired electrical variable. The electrical variable may be, for example, a current, as is the case in the electrical converter of Figure 1.

[0187] Next, in stage 62, a precalculated pulse pattern u* is determined from the calculated voltage reference for the converter 2, wherein the precalculated pulse pattern u* is determined from a lookup table, wherein the precalculated pulse pattern u* comprises discrete voltage amplitude values changing at predefined switching instants.

[0188] Then, in stage 63, an electrical variable tracking error is determined by subtracting a measured electrical variable from the desired electrical variable reference.

[0189] In stage 64, a linear controller 14 is applied to calculate a voltage increment Av to be applied to the precalculated pulse pattern u* to track the desired electrical variable reference.Next, in stage 65, the precalculated pulse pattern u* is modified to obtain a modified precalculated pulse pattern u, wherein modifying is done by shifting switching instants t * of the precalculated pulse pattern u* into shifted switching instants t.

[0190] Finally, in stage 66 the modified precalculated pulse pattern u is applied to semiconductor switches of the electrical converter 2.

[0191] It is noted that in the electrical converter 2 of the embodiment shown in Figure 1 the electrical variable is a current and the voltage reference is calculated from a current reference and from a component of the voltage measured at a point of common coupling of the electric grid. Therefore, the controller 10 shown in Figure 3 is based on current control.

[0192] An electrical converter connected to an electric grid, as the one shown in Figure 1, can be controlled in different modes, which may require to control other electrical variables, such as voltage, flux, active power and reactive power. For example, in an electrical converter used in grid-forming operating mode, i.e. operating as a voltage source that imposes the voltage amplitude and frequency, the electrical variable to be controlled is a voltage. In this case, the voltage reference is calculated from an active and reactive power reference and from a measured active and reactive power based on a droop control, or a synchronous-machine-based control, or another grid-forming control method.

[0193] Another application of the present disclosure is for example the control of an electrical machine. In this application the electrical converter is connected to an electrical machine, the electrical variable can be either a current or a flux, and the voltage reference is calculated from a current or a flux reference.

[0194] The general diagram of the controller 10 is applicable to these other embodiments, in which in block 11 (reference voltage calculation block), a voltage reference for the converter in steady state is calculated, such that a desired electrical variable reference is achieved and the current tracking error, £t, is replaced by a corresponding electrical variable tracking error calculated by subtracting a measured converter electrical variable from a desired electrical variable reference. Then the linear controller 14 will calculate a voltage increment, Av, to be applied to the precalculated pulse pattern, u*, to track the concerned electrical variable reference.

[0195] In this text, the term “comprises” and its derivations -such as “comprising”, etc - should not be understood in an excluding sense, that is, these terms should not be interpreted as excluding the possibility that what is described and defined may include further elements, steps, etc.On the other hand, the disclosure is obviously not limited to the specific embodiment(s) described herein, but also encompasses any variations that may be considered by any person skilled in the art -for example, as regards the choice of materials, dimensions, components, configuration, etc.-, within the general scope of the disclosure as defined in the claims.

Claims

CLAIMS1.- A method for operating an electrical converter (2), the method comprising:calculating (61) a voltage reference (M) for the converter (2) in steady state from a desired electrical variable reference;determining (62) a precalculated pulse pattern (u*) from the calculated voltage reference (M) for the converter (2), wherein the precalculated pulse pattern (u*) is determined from a lookup table, wherein the precalculated pulse pattern (u*) comprises discrete voltage amplitude values changing at predefined switching instants;determining (63) an electrical variable tracking error by subtracting a measured electrical variable from the desired electrical variable reference;applying a linear controller (14) to calculate (64) a voltage increment (Av) to be applied to the precalculated pulse pattern (u*) to track the desired electrical variable reference;modifying (65) the precalculated pulse pattern (u*) to obtain a modified precalculated pulse pattern (u), wherein modifying (65) is done by shifting switching instants tx* of the precalculated pulse pattern (u*) into shifted switching instants tx, whereintjx= tjx*+ Δtjx, wherein:x denotes the phase a, b, c;j is a natural number in [1, nx], nxbeing the number of switching angles for phase x comprised within a correction horizon, Tc; andAt / is dependent on the voltage increment (Av) calculated to track the desired electrical variable reference;applying (66) the modified precalculated pulse pattern (u) to semiconductor switches (25) of the electrical converter (2).2.- The method according to claim 1, wherein the electrical variable is a current, or a voltage, or a flux, or an active power, or a reactive power.3.- The method according to either claim 1 or 2, wherein the precalculated pulse pattern is calculated to eliminate certain harmonics, or to minimize the amplitude of certain harmonics and / or the total harmonic distortion, or to limit semiconductor losses, or toreduce the common mode voltage, or to attenuate harmonic distortion present in the electric grid.4.- The method according to any one of the preceding claims, wherein timeshifts are applied in a time window equal to the correction horizon, Tc.5.- The method according to any one of the preceding claims, wherein for each of the phases a, b, c of the converter (2), the switching instants of each of the na, nb, ncswitching angles comprised within the correction horizon, Tc, are shifted by the following increment:TAt? = K - - — -fA / - V3Av^1VDCnbAujv 7TΔtjb= K (Tc) / (VDCnbΔujb) (Δvα− √3Δvβ)1VDCncAujv 7wherein:VDCis a DC link voltage of the converter (2),Δujadenotes a switching transition for switching angle j for phase a,Δujbdenotes a switching transition for switching angle j for phase b,uj denotes a switching transition for switching angle j for phase c,vadenotes a voltage increment calculated by the linear controller in a axis, Av^ denotes a voltage increment calculated by the linear controller in p axis. K is a coefficient of the Clarke transformation matrix.6.- The method according to any one of the preceding claims, further comprising, applying the following constraints:!n,-Tls < — tL1a4- T1min < — tL2a4 '- T1min < — ■■■ < — tLnaa4- T1min < — tLnaa*+1 / cTs< fb i m < f-b I m < < fb i m. < fb*L11 1min —L21 1min — — ‘'nf,1 1mtn — nb+l< f-c I m < f-c*nk-T1s < — tL1c4- T1min < — tL2c4 '- T1min < — — ‘■nc1 1min — nc+l whereinTminis a minimum turn-on time of the semiconductor switches,kTsis an actual sampling instant,t *+1represents a first switching instant outside the correction horizon Tcin phase X.7.- The method according to any one of the preceding claims, wherein the modified precalculated pulse pattern (u) is applied to semiconductor switches (25) of the electrical converter (2) at each sampling period.8.- A controller (10) for controlling an electrical converter (2), the controller (10) comprising:means (11) for calculating a voltage reference (M) for the converter (2) in steady state from a desired electrical variable reference;means (13) for determining a precalculated pulse pattern (u*) from the calculated voltage reference (M) for the converter, wherein the precalculated pulse pattern (u*) is determined from a lookup table, wherein the precalculated pulse pattern (u*) comprises discrete voltage amplitude values changing at predefined switching instants;means (16) for determining an electrical variable tracking error by subtracting a measured electrical variable from the desired electrical variable reference;a linear controller (14) for calculating a voltage increment (Av) to be applied to the precalculated pulse pattern (u*) to track the desired electrical variable reference;means (15) for modifying the precalculated pulse pattern (u*) to obtain a modified precalculated pulse pattern (u), wherein modifying is done by shifting switching instants tx* of the precalculated pulse pattern (u*) into shifted switching instants tx, wherein tx= t** + At / , wherein:x denotes the phase a, b, c;j is a natural number in [1, nx], nxbeing the number of switching angles for phase x comprised within a correction horizon, Tc; andAt / is dependent on the voltage increment (Av) calculated to track the desired electrical variable reference;means for applying the modified precalculated pulse pattern (u) to semiconductor switches (25) of the electrical converter (2).9.- A power converter system (1), comprising:an electrical converter (2); anda controller (10) according to claim 8.10.- The power converter system (1) of claim 9, wherein the electrical converter (2) is connected to an electric grid.11.- The power converter system (1) of claim 10, wherein the electrical variable is a current and the voltage reference is calculated from a current reference and from a component of the voltage measured at a point of common coupling of the electric grid.12.- The power converter system (1) of claim 9, wherein the electrical converter (2) is operated in grid-forming operating mode.13.- The power converter system (1) of claim 12, wherein the electrical variable is a voltage and the voltage reference is calculated from an active and reactive power reference and from a measured active and reactive power based on a droop control, or a synchronous-machine-based control, or another grid-forming control method.14.- The power converter system (1) of claim 9, wherein the electrical converter (2) is connected to an electrical machine.15.- The power converter system (1) of claim 14, wherein the electrical variable is a current or a flux and the voltage reference is calculated from a current or a flux reference.

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