Bidirectional Charge Control of Series Resonant Converters.

Technical field

The present application generally relates to the field of electronics and more specifically to a method and circuit for power conversion employing bidirectional charge control.

Background

With the current electrification of society, isolated power conversion between two Direct Current, DC, sources with different voltage levels and bidirectional power flow plays a key role. Especially power converters that are able to handle a wide variety of voltage levels, both on the primary and secondary side of the converter, are of interest due to their flexibility in usage. In order to improve the usage of these converters, it is deemed important that the converters are able to handle highly dynamic behaviour, i.e. the imposed set point can be changed rapidly, while guaranteeing zero-voltage switching of all switches to improve Electro-Magnetic Interference, EMI, behaviour of the converter and decrease thermal stress on the switches.

Current state-of-the-art power conversion stages are primarily constructed using either the Dual-Active Bridge, DAB, converter or the Series- Resonant Converter, SRC, topologies. As the DAB is unable to provide an insightful method to provide both dynamic operation, without an additional bias current in the inductor, and including commutation without diminishing the open-loop accuracy of the control strategy, the focus lays on the SRC.

The isolated SRC converter is a converter in which two active semiconductor bridges, are connected by means of a circuit consisting of an inductor, a capacitor and optionally a transformer. The active semiconductor bridges can be of various types, the most used are the two-level half bridge - using a single phase leg composed of two semiconductors, the full bridge - using two of the described phase legs, and multi-level varieties of these two. Obviously, to obtain a functional circuit, at least one of the bridges needs to contain active switches, such as thyristors, MOSFET s or IGBTs.

The control of the SRC is a topic that has been handled extensively. To obtain fast dynamic response, the most promising control method for the SRC is Optimal Trajectory Control, OTC, which is a control strategy that utilizes a state-plane description of the circuit operation to obtain the optimal switching events. After the first uses of OTC, a variety of the method has been presented which allows obtaining pre calculated timing instants, expressed in the value of the voltage across the resonant capacitor. As such, at each zero crossing of the resonant current new switching events are calculated and optimal dynamic behaviour can be achieved.

OTC as presented originally does also support soft-switching of all switches, although it does not include the associated voltage commutation in the proposed equations. Improved version of OTC has been shown for a series-parallel series-resonant converter by using the energy displacements in the converter between two consecutive zero crossing of the resonant current. As such, the analysis includes commutation thereby guaranteeing zero-voltage switching of all switches. However, the proposed method requires an additional energy storage element and, additionally, the method as presented is restricted to unidirectional operation, which is a serious limitation.

The proposed invention describes the charge displacement in the converter in three simple, insightful equations that describe the exact behaviour of the converter. With these equations, bidirectional charge displacement is inherently possible, as is fast dynamic response due-to-the cycle-by-cycle. As the equations are all based on charge and energy in the converter, zero-voltage switching is described analytically, guaranteeing zero-voltage switching of all the switches. Moreover, due to the flexibility of the control strategy, it can be used for both half- and full- active bridges on the primary and secondary side and, if required, can easily be extended for multilevel operation. Additionally, the method allows the incorporation of non-linear capacitances, being present as the inherent parasitic capacitances of electronics switches or as capacitances which are added on purpose to reduce the slope of voltage transients in the semiconductor bridges.

Summary

The present disclosure will now be further elaborated with reference to the disclosed aspects and embodiments. It is understood that although the disclosure cites individual embodiments and/or examples, these embodiments can be combined with one another.

In a first aspect of the present disclosure, there is presented a method of operating a series resonant converter, wherein the series resonant converter is arranged for bidirectional power transfer between a primary side and a secondary side of the series resonant converter, wherein the series resonant converter comprises an active half bridge comprising active switching elements on each of the primary and secondary sides, wherein the method comprises the steps of determining a desired output charge displacement, based on a desired output power; determining switch on times for the active switching elements based on the determined desired output charge displacement; and activating the active switching elements at the determined switch on times.

Series resonant converters are known in the relevant technical field, and a standard architecture of such a series resonant converter is considered. Since a bidirectional power converter is considered, the applicants consider it relevant to refer to the two sides as a primary and a secondary side rather than referring to them as an input and an output. It is understood that either of the primary and/or secondary may function as the input and subsequently the other as the output.

The skilled person understands that active switching element may refer to any electronic component that is capable of being switched by means of a switching signal. In a preferable example, Metal Oxide Semiconductor Field Effect Transistors, MOSFETs, are considered. However they may be replaced by any suitable active switching element.

Similarly, the term active half bridge is also well known and understood in the relevant technical field.

This present disclosure covers all of the mentioned aspects for a series- resonant converter by applying a charge control method. The converter will operate in a cyclic, resonant current mode in which each cycle, the time interval between two consecutive zero-crossing of the resonant current, the charge displacement through the controlled port (either the primary or secondary DC source) is controlled by switching the switches at a predefined moment. The timing of these switching events is recalculated at every zero -crossing of the resonant current in order to facilitate highly dynamic operation of the converter. Moreover, bidirectional charge displacement is inherently possible, as the equations offer a natural transition between positive and negative charge displacement.

The invention uses charge control, all switching events and calculations are based on charge displacement and static charge present in the converter. This has never been done before and provides a control method that facilitates a series- resonant converter that is able to handle highly dynamic, bidirectional operation, while guaranteeing soft-switching of all switches, thereby facilitating higher efficiency and (more) EMI-friendly behaviour of the converter.

According to an example, the step of determining switch on times for the active switching elements is performed for each half cycle of a resonant current of the series resonant converter.

According to an example, the step of determining switch on times comprises determining the switch on times based on any of a charge displacement through a primary source of the series resonant converter; a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter; a charge displacement through a secondary source of the series resonant converter; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

It is therefore clear that the switching times of the relevant active switches are determined on the basis of a desired charge displacement.

According to a further example, the charge displacement through a secondary source of the series resonant converter is determined based on any of a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge displacement through a primary source of the series resonant converter; a primary voltage of the series resonant converter; a secondary voltage of the series resonant converter.

According to an example, the charge displacement through a primary source of the series resonant converter is determined based on any of a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge displacement through a secondary source of the series resonant converter; a primary voltage of the series resonant converter; a secondary voltage of the series resonant converter.

In an example, the method comprises the step of verifying that the charge displacement through a primary source of the series resonant converter is feasible based on any of a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

According to an example, the method comprises the step of verifying that the charge displacement through a secondary source of the series resonant converter is feasible based on any of: a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

According to an example, the method comprises the step of determining a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle based on any of: a charge displacement through a primary source of the series resonant converter; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter; a charge displacement through a secondary source of the series resonant converter; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

In a second aspect of the present disclosure, there is presented a series resonant converter arranged for bidirectional power transfer between a primary side and a secondary side of the series resonant converter, wherein the series resonant converter comprises an active half bridge comprising active switching elements on each of the primary and secondary sides, and wherein the series resonant converter comprises a controller arranged to: determine a desired output charge displacement through either the primary side or the secondary side, based on a desired output power; determine switch on times for the active switching elements based on the determined desired output charge displacement; and activate the active switching elements at the determined switch on times. It is noted that the definitions and advantages associated with the first aspect of the present disclosure being a method of operating the series resonant converter are also associated with the second aspect of the present disclosure.

In an example of the second aspect, the controller is further arranged to determine switch on times for the active switching elements for each half cycle of a resonant current of the series resonant converter.

According to an example of the second aspect, the controller is further arranged to determine the switch on times based on any of: a charge displacement through a primary source of the series resonant converter; a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter; a charge displacement through a secondary source of the series resonant converter; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

According to an example of the second aspect, the controller is arranged to determine the charge displacement through a secondary source of the series resonant converter based on any of a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge displacement through a primary source of the series resonant converter; a primary voltage of the series resonant converter; a secondary voltage of the series resonant converter.

According to an example of the second aspect, the controller is arranged to determine the charge displacement through a primary source of the series resonant converter based on any of: charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge displacement through a secondary source of the series resonant converter; a primary voltage of the series resonant converter; a secondary voltage of the series resonant converter.

According to an example of the second aspect, the controller is arranged to verify that the charge displacement through a primary source of the series resonant converter is feasible based on any of: a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

According to an example of the second aspect, the controller is arranged to verify that the charge displacement through a secondary source of the series resonant converter is feasible based on any of: a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle; a charge difference across a resonant capacitor of the series resonant converter at a beginning of a corresponding half-cycle; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter.

According to an example of the second aspect, the controller is arranged to determine a charge difference across a resonant capacitor of the series resonant converter at an end of a corresponding half-cycle based on any of a charge displacement through a primary source of the series resonant converter; a charge exchange between a primary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter; a charge displacement through a secondary source of the series resonant converter; a charge exchange between a secondary switch-node capacitance of the series resonant converter and a resonant capacitor of the series resonant converter. The present disclosure is described in conjunction with the appended figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.

In the appended figures, similar components and/or features may have the same reference label. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.

The above and other aspects of the disclosure will be apparent from and elucidated with reference to the examples described hereinafter.

Brief description of the drawings

Fig. 1 illustrates a series resonant converter according to the present disclosure.

Fig. 2 illustrates generic operating waveforms of the SRC.

Fig. 3 shows a state-plane trajectory of a resonant half-cycle.

Fig. 4 illustrates a non-linear capacitance of a MOSFET and an example of corresponding switch node capacitance.

Fig. 5 illustrates a state machine for both the primary and secondary side for positive current.

Fig. 6 illustrates three different steady-state state-plane trajectories with identical net charge transfers.

Fig. 7 illustrates the flow diagram for a method according to the present disclosure.

Fig. 8 illustrates example of steady-state state-plane trajectories for a number of charge displacements with a fixed Q _en d for light load operation.

Fig. 9 illustrates results of a simulation where all delays are neglected while commutation is included.

Fig. 10 illustrates results of a simulation where all delays and commutation are included. Fig. 11 (a) - (g) illustrate steady-state waveforms of the converter for different converter states.

Fig. 12 illustrates steady state waveforms of the converter for different converter states.

Fig. 13 (a) - (g) illustrate dynamic waveforms of the converter for different converter states.

Fig. 14 illustrates dynamic waveforms of the converter for different converter states.

Fig. 15 illustrates dynamic waveforms of the converter for different converter states.

Fig. 16 illustrates the state plane, the corresponding voltage across the resonant capacitor and the corresponding resonant current for various charge displacements.

Detailed Description

It is noted that in the description of the figures, same reference numerals refer to the same or similar components performing a same or essentially similar function.

A more detailed description is made with reference to particular examples, some of which are illustrated in the appended drawings, such that the manner in which the features of the present disclosure may be understood in more detail. It is noted that the drawings only illustrate typical examples and are therefore not to be considered to limit the scope of the subject matter of the claims. The drawings are incorporated for facilitating an understanding of the disclosure and are thus not necessarily drawn to scale. Advantages of the subject matter as claimed will become apparent to those skilled in the art upon reading the description in conjunction with the accompanying drawings.

The ensuing description above provides preferred exemplary embodiment(s) only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the preferred exemplary e bodi ent(s) will provide those skilled in the art with an enabling description for implementing a preferred exemplary embodiment of the disclosure, it being understood that various changes may be made in the function and arrangement of elements, including combinations of features from different embodiments, without departing from the scope of the disclosure.

Unless the context clearly requires otherwise, throughout the description and the claims, the words "comprise," "comprising," and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of "including, but not limited to." As used herein, the terms "connected," "coupled," or any variant thereof means any connection or coupling, either direct or indirect, between two or more elements; the coupling or connection between the elements can be physical, logical, electromagnetic, or a combination thereof. Additionally, the words "herein," "above," "below," and words of similar import, when used in this application, refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the Detailed Description using the singular or plural number may also include the plural or singular number respectively. The word "or," in reference to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list.

These and other changes can be made to the technology in light of the following detailed description. While the description describes certain examples of the technology, and describes the best mode contemplated, no matter how detailed the description appears, the technology can be practiced in many ways. Details of the system may vary considerably in its specific implementation, while still being encompassed by the technology disclosed herein. As noted above, particular terminology used when describing certain features or aspects of the technology should not be taken to imply that the terminology is being redefined herein to be restricted to any specific characteristics, features, or aspects of the technology with which that terminology is associated. In general, the terms used in the following claims should not be construed to limit the technology to the specific examples disclosed in the specification, unless the Detailed Description section explicitly defines such terms. Accordingly, the actual scope of the technology encompasses not only the disclosed examples, but also all equivalent ways of practicing or implementing the technology under the claims.

The SRC circuit is depicted in Fig. 1 which shows an isolated, series resonant converter with two active half bridges where the resonant capacitor is integrated in the capacitive divider on the primary side. It consists of an active half bridge, AHB, on both the primary (SPI - SP2) and a secondary AHB (Ssi - Ss2) in order to minimize driving circuitry complexity while achieving identical converter losses and volume. The AHBs are connected via a series resonant tank (L _res and C _res ) and a transformer (T _r ) that provides galvanic isolation between the primary and secondary side and is constructed with a turns ratio of N : 1.

The semiconductors in both the primary and the secondary bridge are shown with the non-linear, parasitic output capacitances and diodes inherently present due to the structure of the semiconductors. Moreover, both the primary AHB and the secondary AHB are connected to a voltage source, VPDC and VSDC respectively. All the corresponding values are presented in Table I.

Bidirectional charge control, BCC, is a control algorithm that uses a mathematical description of the converter to determine the required input to obtain the desired outcome. For BCC, the outcome is the realization of a predefined charge displacement through the converter between two consecutive zero crossing of the resonant current, i.e. during a half cycle. Therefore, converter operation is analysed for half-cycles where the current is positive (positive half-cycles) and half-cycles where the current is negative (negative half-cycles). As operation and derivation of the required inputs for a negative half-cycle are analogous to the positive half-cycle, the upcoming analysis is limited to positive half-cycles. As discussed, BCC targets to obtain a desired, predefined, net amount of charge displacement through the controlled port between two consecutive zero- current crossings, i.e. a half-cycle. Although applications where the charge displacement through the primary source should be controlled exist, the present disclosure limits the analysis to control of the charge displacement through the secondary source, i.e. ^ _^^^ . However, the equations can easily be rewritten for primary charge control. In order to obtain the desired charge displacement through the controlled port, the required inputs are to be derived. For the SRC, the required inputs, i.e. the switching events, are calculated in terms of the charge in the resonant capacitor. The change in charge is directly proportional to the charge displacement through the respective input ports. This results in direct control of the desired charge displacement through the input port. As mentioned, the switching events are a function of the charge difference across the resonant capacitor. The events consist of the OFF switching of the active switches, and for the primary and secondary AHB, respectively, and the ON switching of the complementary switch in the AHB i and for the primary and secondary AHB, respectively. Although the described charge events are described for an AHB, the functioning of BCC for active full bridges and/or multilevel operation of the discussed topologies is analogous. These events are shown in Fig. 2, which presents generic operating waveforms of a BCC operated SRC. Also shown is the charge on the resonant capacitor at the start of a half-cycle, and at the end of the half- cycle, i and the net charge displacement through the secondary source, ^ Fig.2 also shows the imposed voltage by the primary AHB and secondary AHB, respectively and the charge displacement through the secondary source, q _SDC . It is understood, that the commutation of the non-linear capacitances is exaggerated for enhanced visibility and understandability. An example is shown in Fig. 3, displaying the charge displacement in the resonant capacitor in a half cycle with all key events identified, the resonant current, the imposed voltage by primary and secondary AHB respectively when the switches are equipped with (the inherently present) non-linear capacitances, and the charge displacement through the secondary source. For the charge displacement through the secondary source, , the sign convention of I _C is used.

In order to reduce losses in the converter and decrease EMI of the converter, BCC facilitates soft-switching of the switches. Soft switching is achieved when switches are switched ON when zero voltage is applied across the switch, which in turn requires BCC to have circuit-assisted voltage commutation integrated. As a result, the node capacitances CP and Cs that represent the lumped output capacitances of the switches, i.e. are not (dis)charged by the switches but are rather (dis)charged by the resonant current i _res . As described in other prior art documents, zero-voltage switching, ZVS, is only achievable if the imposed voltage by the switching leg decreases for current flowing out of the switch-node. For the imposed voltages individually, this implies that V _P has to decrease at every switch action of the primary bridge for positive resonant current whereas vs should increase at every switching action of the secondary AHB.

For a positive half-cycle, the switching events for the primary AHB should result in a decreasing imposed voltage in order to facilitate ZVS. Thus, the positive half-cycle starts with the switch S _PI ON. When the charge difference across the resonant capacitor reaches is switched OFF and at QP2, when the natural transition to S _P 2 is finished, S _P 2 is turned ON. This switching pattern of the primary side is shown in Fig. 5. Fig. 5 illustrates the state-machine for both the primary and secondary side for positive current. The cycle is excited by a negative to positive zero crossing of the resonant current, i.e. when the i _res becomes positive, and ends with a positive to negative zero-crossing of the resonant current. In order to derive the required charge displacement to facilitate ZVS, Kirchoff’s current law is used to write the charge exchange between the primary switch-node capacitance (CP) and the resonant capacitor as which specifies that all charge that is required to commutate the primary switching leg, i.e. QCP , results in a change in the charge difference across the resonant capacitor of (QP2 - QPI ). However, when non-linear switch capacitances are assumed (in case of the output capacitance of switches, see Fig. 4(a) for the output capacitance of a switch and Fig. 4(b) for the corresponding switch-node capacitance and charge as a function of the imposed voltage VP). The required charge displacement to facilitate ZVS can then be rewritten into as depicted in Fig. 4(b). From (2) and (3) then follows

It shows that the commutation in terms of charge is solely dependent on the input voltage source V _PDC and the output capacitance of the switch(es).

As discussed, the secondary side can only achieve soft switching of the switches when the imposed voltage by the secondary AHB, vs, increases with every switching event for a positive half-cycle. Therefore, the secondary bridge starts with Ss2 ON. When the charge difference between the terminals on the resonant capacitor reaches Qsi , the switch is turned OFF. After the commutation the charge difference reaches Qs2 and Ssi is turned ON. The relation between Qsi and Qs2 can be derived analogously to the commutation on the primary side so that where

The switching pattern of the secondary side is shown in Fig. 5.

As discussed, the target is to control the charge displacement through the controlled input port. Therefore, the charge displacement through the secondary source is described as a function of the key events (predefined charge differences across the resonant capacitor). Therefore, the direction of the charge displacement through the converter is analyzed. At the start of the half-cycle, as Ss _å is ON, a positive resonant current results in a positive current flowing through the secondary source. As a result, the charge displacement through the secondary source is directly proportional to the difference in the charge in the capacitor, such that where N is required to integrate the winding ration of the transformer and the fraction ½ is a result of the half-bridge configuration, and where Q _Cs denotes the commutation charge.

In a similar manner, the analysis shows that there is no charge displacement through the secondary source during commutation. With S _sl ON though, the charge displacement is in the opposite direction of the charge displacement in the series-resonant network. The net charge displacement through the secondary source over an entire half-cycle is then described as

In which the difference in Q _S1 and Q _S2 is the required charge to fully commutate the secondary switching leg(s), i.e.

The charge displacement through the primary source is described analogously as

In order to derive the switching events, the energy in the converter at the start and at the end of the half-cycles are related through energy conservation. It is comprised by the net amount of energy that is displaced through the primary and secondary side, and the change in energy in the capacitor over a half-cycle. This is all summarized by which is the energy balance for the SRC between two consecutive zero-current crossings. It states that the total amount of energy displaced through the primary and secondary side source over a half-cycle is equal to the increase in energy in the series- resonant network.

Equation (10) describes the energy balance of the series-resonant converter over a half cycle. In steady state, however, an additional constraint is imposed on the converter, i.e. the swing in the charge difference across the resonant capacitor should be zero on average over a half-cycle so that Q _Cend = -Qinit _■ This eliminates any offset of the resonant capacitor charge and therefore reduces the stress on the capacitor. Equation (10) is then rewritten for steady state into (11) which gives the relation between in steady-state. Therefore, at the start of every resonant half-cycle, both input voltages are measured.

When (9) and (8) are considered with the added constraint, i.e. Qend = -Qinit, it shows that the amount of charge displaced through the input ports merely depend on the switching event on the corresponding side: where (4) and (5) define the relation between Q _PI and Q _P 2 and Qsi and Q _S 2, respectively. As a result, Q _end (and thus Qi _nit ) has no impact on the charge displacement. However, as shown in Fig. 6, it does impact the RMS current in the series resonant network. By minimizing the inductor current, the efficiency can be maximized. Fig. 6 illustrates the steady-state state-plane trajectory for an identical charge transfer (QSDC = -50 μC ) for various Qi _nit (and thus Q _end ) with exaggerated commutation for enhanced visibility and understandability. Fig. 6 shows that minimizing the current is achieved when the swing in charge difference on the capacitor is also minimized. Therefore, Q _end is chosen to facilitate the desired and required charge displacement through the sources. In order to encompass all possible operating ranges, i.e. bidirectional power flow and buck or boost operation, Q _end is determined by

This defines the steady state condition for every set of input parameters thereby guaranteeing zero voltage switching, minimization of the RMS current and the desired charge displacement through the controlled input port.

Each resonant half-cycle starts with acquiring the latest data for the input parameter, the supply voltages and the initial charge difference across the resonant capacitor, i.e. as indicated in Fig. 7, which illustrates the flow diagram for the used equations required to derive the proper switching events. As the key target is to operate at minimum RMS current in the series-resonant network, each half-cycle is targeted to end in the steady-state conditions for the desired charge displacement.

As such, the charge displacement through the controlled input port, Q _Sdc , is then limited to two options available to realize the steady-state conditions. The first one takes Q _SDC as the key objective, both during dynamic operation and steady-state operation of the converter. As such, when a new set point is imposed, Q _SDC is realized (if possible), resulting in a two-cycle behaviour to achieve steady-state conditions while guaranteeing the desired charge displacement Q _Sdc . This solution is possible and achieved with the proposed equations, but is lengthy and therefore not described in detail. The second alternative is to target the steady-state objective directly, so that the emphasis in the half-cycle after the new setpoint is imposed is on realizing the steady-state conditions.

Therefore, during transient analysis, first the steady state condition for Q _end is determined through (11) and (13), which is then defined as the objective for the corresponding half-cycle. as an upper limit, whereas the lower limit is

Q _SDC is then, for the current half-cycle, limited accordingly.

As (14) defined the maximum/minimum QSDC, it should be limited accordingly. This has as a consequence that during the transient half-cycle the desired charge displacement is possibly not met, but has the advantage that the converter is in steady state, and in its most efficient operating state, in a single half-cycle.

Although the limited QSDC does not meet the desired charge displacement, it comes as close as possible, given the constraints. The unknown parameter for the current cycle is then QPDC. AS all the remaining parameters of the energy balance as presented in (10) are already determined, and should be valid for every half-cycle, Q _PDC can be calculated accordingly as

This is defined as the amount of charge that should be displaced through the primary source to achieve both the desired QSDC and Q _end for the current half-cycle. However, this is the theoretical value and it should be verified that the value is feasible within the defined charge displacement in the series-resonant network.

As there is an upper and lower bound on the charge displacement through the secondary source, the charge displacement through the primary source is also limited by

As such, Qp _DC is limited to these values. Due to possible change in Q _Pdc , it should again be verified that the energy balance is preserved. Either QSDC and/or Q _end should be adjusted to realize the proper energy balance. As Q _end is the key target for transient half-cycles rather than the displaced charge through the secondary source, Q _SDC is adjusted to

The final step is then to calculate all parameters and the switching events are to be calculated as

The flow diagram of equations usage in BCC is summarized in Fig. 7. It must be stressed that the flow diagram is used in both steady-state and dynamic operation and results in a deadbeat control that minimizes the current in the series- resonant network while achieving the desired charge displacement through the secondary source.

Low-power operation: One of the advantages of BCC is the inherent property that it uses a variable frequency to minimize the resonant current and charge displacement for varying inputs. As a result, reducing the secondary power flow towards zero leads to a higher switching frequency. The proposed control strategy in as presented previously in the present disclosure though, leads to an undesirable high switching frequency at low power, limited by the resonance occurring between the switch-node capacitances and the resonant inductor. In order to restrain the switching frequency while guaranteeing ZVS of all switches, reactive power is used. As displayed in Fig. 6, a larger then required by (13) can still result in the desired charge displacement through the secondary source. As such, a restriction on the minimum results in suboptimal behaviour of the converter at reduced power and thus at low(er) resonant current, it also facilitates ZVS of all switches. An example is shown in Fig. 8, displaying three steady-state state-planes for Q _S D _C = -10 μC , -5 μC , and 0 μC . It shows three trajectories that each facilitate ZVS of all switches, at the cost of an increased resonant current. However, as is shown in the upcoming sections, the resonant current at these operating points is relatively low with respect to maximum power flow.

EXPERIMENTAL RESULTS

The present disclosure targets the improvement of the dynamic behaviour of the series-resonant converter by using a new control method, i.e. bidirectional charge control. Therefore, in Section II the theoretical analysis of the control method is discussed. This analysis is restricted to an ideal situation where measurements have infinite bandwidth, zero processing time and no other non idealities present. This section describes the required additions to the presented control strategy to overcome the mentioned non-idealities. Moreover, the realization of a prototype and corresponding measurements are shown and discussed.

As mentioned, bidirectional charge control is a control method that targets a pre-defined charge displacement through the secondary or primary source. Therefore, charge displacement through the resonant tank should be monitored. A disadvantage of this control parameter is that charge displacement is not a quantity that is directly measurable, it requires post-processing of a quantity that is directly measurable. A quantity that is directly measurable and that is closely related to charge displacement, is the voltage across the resonant capacitor. By using a NP0/C0G, the relation between the charge displacement is linear and all important events, i.e. Q _init , and Q _e n _d , ^are rewritten into an equivalent voltage across the resonant capacitor, and V _end respectively. Other (non-)linear capacitor type are also applicable for bidirectional charge control, but then the charge- voltage relation should be described in look-up tables/polynomials/etc.

Although the derivation is shown as charge based, an identical analysis solely based on voltages across the resonant capacitor leads to an identical result. Considering an ideal situation, an example of charge displacement (QSDC = -50 μC ) is displayed in Fig. 9. It shows the state-plane trajectory in Fig. 9(a), the voltage across the resonant capacitor, and resonant current versus time in Fig. 9(b) and Fig. 9(c) respectively. Included in the figure is the start-up of the converter, as the voltage across the resonant capacitor starts at 0 V, in which the steady-state condition is achieved in a single half-cycle, as clearly shown by the state-plane trajectory. Moreover, in Fig. 9(a), the trajectory of an identical charge displacement in the opposite direction (QSDC = 50 μC ) is shown, displaying symmetric steady-state behaviour. Transient operation (start-up in the shown example) though, results in different behaviour with the same result, i.e. V _end .

When a finite bandwidth of the measurement and driving circuitry of the switches is included, the response of the system is altered. This is shown in Fig. 10, displaying the state-plane trajectory in Fig. 10(a), and the voltage across the resonant capacitor and resonant current versus time in Fig. 10(b) and Fig. 10(c) respectively. It shows that steady-state operation is still achieved, but at the cost of a higher resonant current and voltage across the resonant capacitor. Moreover, the steady state operation is, unlike the ideal situation, not achieved in a single cycle, but additional cycle(s) are required. To overcome the finite bandwidth of the measurement(s), a mathematical model is included in the software platform that uses the delayed measurement signals to predict the real-time, and even a prospective, voltage across the resonant capacitor. With the predicted voltage, it is possible to control the switches in such a fashion that it overcomes the delays present in the hardware, and potentially in the software.

As discussed, there are non-idealities that influence the obtained behaviour of bidirectional charge control on the converter with respect to the ideal model. Another key nonideality is processing time. Every half-cycle new switching levels are calculated based on the actual voltage across the resonant capacitor at the start of the corresponding half-cycle.

As such, the calculations to determine the switching levels of that specific half-cycle are performed after the start of that half-cycle. As shown in Fig. 6, combinations of (input) parameters for which switching levels are identical to V _mit are possible, requiring switching directly after the zero-current crossing. As the calculations are performed after the zero-current crossing, that specific switching level is yet unknown.

Therefore, some margin is added to V _en d (and thus Q _en d) in (13) so that the switching levels as determined in (18) give enough slack to perform all calculations between Vmit (and thus Qmit) and the consecutive switching level. This is also visualized in Fig. 6, where the bottom trajectory represents the trajectory when ideal processing time is assumed and the middle trajectory represents (an exaggerated) trajectory in which margin is added to facilitate processing time.

First, the steady-state behaviour of the converter at QSDC = -100 μC is analyzed, as depicted in Fig. 11. It shows the steady-state behaviour of both possible modes of the converter, i.e. buck mode (VPDC > NVSDC), boost mode (VPDC < NVSDC), and nominal operation of the converter.

Displayed are the state-plane trajectories (Fig. 11(a)), the voltage across the resonant capacitor (Fig. 11(b), 11(d), and 11(f)) and the resonant current (Fig. 11(c), 11(e), and 11(g) ) as a function of time. The state-plane shows that the form of the trajectory heavily depends on the voltage ratio of the input and output voltage. Operation of the converter in buck mode, the radius of the circles differ, as does the exact switching levels. In Boost stage however, Vend is no longer determined by QSDC, but is rather proportional to QSDC as dictated by (11) and (13). As such, a smaller ratio (VPDC : NVSDC) leads to a larger V _en d (and thus Qend). It also shows, as supported by the time dependent figures, stable operation in steady-state and zero- voltage switching of all switches. When operation is required in which no net charge is displaced through the secondary source, i.e. QSDC = 0 μC , waveforms as displayed in Fig. 12 are obtained.

The state-plane trajectory (Fig. 12(a)) shows that all operating modes results in the minimum voltage swing across the resonant capacitor and only reactive charge is displaced in the converter. This reactive charge does lead to a limit on the maximum switching frequency and zero-voltage switching of the switches. This is confirmed by Fig. 12(b) and Fig. 12(c) displaying the voltage across the resonant capacitor and resonant current versus time, respectively. For brevity, as all graphs display similar results, the time-dependent figures are limited to nominal operating primary and secondary voltages.

As discussed, bidirectional charge control is able to handle dynamic operation in a half-cycle. Such dynamic operation is shown in Fig. 13, displaying the step from zero net charge displacement to QSDC = -100 μC . Displayed are the state- plane trajectories for all operating modes (buck/boost) in Fig. 13(a), the corresponding voltages across the resonant capacitor for the different operating modes in Fig. 13(b), 13(d), and 13(f), whereas the resonant currents are displayed in Fig. 13(c), 13(e), and 13(g). As visible in the state-plane trajectories, the charge displacement is increased in a single half-cycle, but steady-state operation is only achieved after two half-cycles.

This is an effect of incomplete compensation of the delays present in the system. Firstly there is a limitation regarding the ADC, which has a finite bandwidth (20 MSPS). As such, to not overstress the computational effort of the FPGA, limits the used predictor in steps of roughly 60 ns. As overcompensation leads to a very nervous and potentially unstable system, a fraction of the delay is still present in the system. This results in the additional half-cycle required to reach steady-state performance.

Although that additional half-cycle is present, BCC still realizes the step from no net charge displacement to maximum power flow within a single half cycle and guaranteeing steady-state behaviour within two half-cycles.

As already shown, BCC is able to change the charge displacement from zero to maximum in a single half-cycle. It is also capable of charge reversal from QSDC = -100 μC to QSDC = 100 μC within a single cycle, as presented in Fig. 14. Shown are the state-plane trajectories for three different primary and secondary voltage configurations in Fig. 14(a), whereas the corresponding voltage across the resonant capacitor and the resonant current for nominal primary and secondary voltage are shown in Fig. 14(b) and Fig. 14(c), respectively. The trajectories show that steady-state operation after reversal of the maximum charge displacement is achieved in a single half-cycle for all three configurations. What it also shows, is asymmetry between positive and negative charge displacement. This is a result of the integration of energy losses in the circuit in the energy balance as presented in (11).

As such, negative charge displacement leads to an increase in the charge displacement through the primary source, QPDC, to overcome these losses with respect to a lossless system. For positive charge displacement though, Q _PDC is also increased but due to the sign (negative), this leads to asymmetry in QPDC, depending on the direction of the charge displacement.

Shown are the behaviour of the converter when a large increase of reversal or the charge displacement is imposed. When the amount of charge displacement is reduced however, this leads to momentarily increased current, as shown in Fig. 15. It shows the behaviour of the converter when the QSDC is reduced from 100 μC to -40 μC by means of the state plane trajectory (Fig. 15(a)), the voltage across the resonant capacitor (15(b)), and the resonant current (Fig. 15(c)). Due to the excess of energy that is present in the resonant capacitor, reactive currents are required to reach steady-state in a single half-cycle. Again, steady-state is not achieved within a single half-cycle due to the delays still present in the system.

Finally, Fig.16 displays a pre-defined cycle where every 2 ms a new setpoint is imposed. It shows the potential of BCC, with highly dynamic behaviour between various setpoints. What is also shows, is the variety in the achieved end voltages Vend for identical setpoints. This is due to the discretization of the measured voltage in the ADC, but also due to the accuracy of the ADC with only 9 1/2 bits available.

Moreover, the comparison of the measured voltage against the desired switching level (where rounding leads to significant differences) is also discrete resulting in more variety in the achieved end voltages. It must be stressed though, that each setpoint is maintained for more than 400 half-cycles. The series-resonant converter has proven to be an (isolated) DC/DC converter capable of perfectly handling wide primary and secondary voltages while providing zero-voltage switching of all switches. However, previously research has not yet provided a solution to low-load operation and bidirectional operation of the converter while simultaneously maintaining the highly dynamic capabilities and minimization of the resonant current inherently present in optimal trajectory control (OTC). Therefore the present disclosure focuses on the combination of highly dynamic capability, zero-voltage switching of all switches and bidirectional power flow for the series-resonant converter.

In order to combine the highly dynamic capability of the series- resonant converter with zero-voltage switching of all switches and bidirectional power flow, the present disclosure discussed a novel control strategy where charge displacement per half cycle, i.e. the time interval between two consecutive zero crossings of the resonant current, is controlled. Every half cycle, the charge displacement in the resonant tank is used to describe the desired switching events to guarantee soft switching of all switches and displacement of the desired charge through the predefined source, where the present disclosure focusses on the secondary source. As every half-cycle is controlled independently of other half-cycles, setpoints and varying primary and/or secondary voltages are processed the consecutive half-cycle. This results in highly dynamic behaviour while guaranteeing zero-voltage switching of all switches and bidirectional power flow.

The working of bidirectional charge control (BCC) has been shown experimentally. Non-idealities are present in the realization of the hardware, such as delays (finite bandwidth), losses, and computational processing time. These nonidealities are overcome through the use of a predictor and the integration of a small amount of reactive charge displacement, as shown in the presented verification. An improvement in the predictor is possible, resulting in lesser losses due to the corresponding reduced resonant current. The present disclosure presented bidirectional charge control for the series-resonant converter, a control method that realizes highly dynamic capability, zero-voltage switching of all switches and bidirectional power flow. It therefore provides an efficient and low-cost control strategy suitable for the next-generation, isolated DC/DC converters that should meet the economic aspects associated with and required for the greenification of both the energy and transport sector.