TECHNICAL FIELD

The present disclosure relates to a control entity and method for controlling a converter circuit to imitate an electrical output characteristic of a synchronous machine. Further, the present disclosure relates to a system comprising such a control entity and the converter circuit. Furthermore, the present disclosure relates to a computer program and a storage medium.

BACKGROUND

The disclosure is directed to a converter circuit comprising a three phase DC-to-AC converter for providing a three phase AC voltage. For example, the converter circuit may provide the three phase AC voltage to an AC grid, such as mains. The term “electrical grid” may be used as a synonym for the term “grid”. The term “power converter” may be used as a synonym for the term “converter”.

SUMMARY

Nowadays, electric grids (AC grids) are facing a high penetration of renewable energy sources and, at the same time, reduction of traditional power plants generation. As a result the number of synchronous machines feeding an electric grid (i.e. providing voltage to the electric grid) is reducing. That is, generation of electrical power using synchronous machine(s) reduces. In the case of such power generation, a rotating mass kinetic energy is available, which may be used for frequency control. Nowadays an integration of power electronics technology for power generation takes place. Such power generation may be said to be static, i.e. there is no rotation as in a synchronous machine and, thus, no inertia is associated with such power generation based on power electronics technology.

From a power system level perspective, removal of synchronous machines results in that an aggregated inertia that is provided by multiple rotating synchronous machines (i.e., a buffer of rotating kinetic energy distributed along the power system) is being removed. The lack of inertia may have a negative effect on a power system frequency control because the balancing among generation and consumption becomes unfeasible. In view of the above, this disclosure aims to provide means allowing power electronics, such as a converter circuit, to achieve similar performance as a synchronous machine from a power system level perspective. An objective of this disclosure is providing means that allow power electronics, such as a converter circuit, to achieve a similar performance as the synchronous machines for frequency and voltage control.

These and other objectives are achieved by the solution of this disclosure as described in the independent claims. Advantageous implementations are further defined in the dependent claims.

A first aspect of this disclosure provides a control entity for controlling a converter circuit to imitate an electrical output characteristic of a synchronous machine. The converter circuit comprises a three phase DC-to-AC converter, and a filter comprising for each phase an inductor and a capacitor, which together are electrically connected in parallel to an output of the three phase DC-to-AC converter. The converter circuit is configured to provide, using a voltage across the capacitor, an output voltage at an output of the converter circuit. The control entity is configured to measure a current through the inductor and the voltage across the capacitor, control the voltage across the capacitor by controlling the current through the inductor, and control the current through the inductor by controlling, using the measured current and the measured voltage, an output voltage of the three phase DC-to-AC converter.

The three phase DC-to-AC converter may be referred to as “three phase inverter” or “three phase string inverter”. The three phase DC-to-AC converter may be configured to convert a DC power (DC voltage and/or DC current) to a three phase AC power (AC voltage and/or AC current). The three phase DC-to-AC converter may comprise three output terminals for the three different phases of the three phase AC power (providable by the DC-to-AC converter). The output of the DC-to-AC converter may comprise three output terminals for the three phases. The three phases may be referred to as “three electrical phases”. A respective inductor and capacitor of the filter may be electrically connected to each output terminal of the three output terminals for the three phases. A DC bus may provide DC power to the three phase DC-to-AC converter. The DC bus may receive DC power from renewable energy source(s) (e.g. photo voltaic (PV) plant(s) and/or wind power plant(s)) and/or battery storage system(s) (e.g. one or more batteries, optionally one or more rechargeable batteries). The three phase DC-to-AC converter may be or may comprise an actively switched DC-to-AC converter comprising at least one switch. The at least one switch may be at least on transistor, such as at least one bipolar junction transistor (BJT); at least one field effect transistor (FET), e.g. at least one metal oxide semiconductor FET (MOSFET); and/or at least one insulated gate bipolar transistor (IGBT). The control entity may be configured to control the three phase DC- to-AC converter of the converter circuit by controlling switching of the at least one switch. The three phase DC-to-AC converter may comprise one or more passive elements, such as one or more inductor(s) and/or capacitor(s), for power conversion and/or filtering.

The description with regard to the measurement and control of electrical variables/parameters is correspondingly valid for each phase of the three phases. The terms “variable” and “parameter” may be used as synonyms. In other words, with regard to a phase of the three phases the converter circuit may be configured to provide, using a voltage of the phase across the respective capacitor, an output voltage of the phase at an output of the converter circuit (e.g. at a respective output terminal of the converter circuit for the phase). The control entity may be configured to measure a current of the phase through the respective inductor and the voltage of the phase across the respective capacitor. The control entity may configured to control the voltage of the phase across the respective capacitor by controlling the current of the phase through the respective inductor. The control entity may configured to control the current of the phase through the respective inductor by controlling, using the measured current of the phase and the measured voltage of the phase, an output voltage of the phase of the three phase DC- to-AC converter.

The control by the control entity of the converter circuit allows the converter circuit to imitate an electrical output characteristic of a synchronous machine. As a result, the control entity according to the first aspect of this disclosure allows the converter circuit to achieve similar performance as a synchronous machine from a power system level perspective. For example, the control entity allows the converter circuit to achieve a similar performance as the synchronous machine for frequency and voltage control. With other words, the first aspect provides a control entity for controlling a converter circuit to imitate a performance (e.g. electrical performance) of a synchronous machine. The synchronous machine is an example of an electrical machine. The synchronous machine may take the role of a synchronous generator. The inductor and the capacitor being together electrically connected in parallel to the output of the three phase DC-to-AC converter is to be understood such that a voltage across the output of the three phase DC-to-AC converter equals to a sum of a voltage across the inductor and a voltage across the capacitor. In other words, the inductor and the capacitor may be said to be electrical connected in series, wherein the series connection is electrically connected in parallel to the output of the three phase DC-to-AC converter. The capacitor of the filter (for each phase) may play a pivotal role of an energy buffer of the imitated synchronous machine. The capacitor may be referred to as “output filter capacitor”. The terms “imitate”, “mimic” and “emulate” may be used as synonyms.

The control entity may be configured to control the three phase DC-to-AC converter such that the three phase DC-to-AC converter implements an AC voltage control over the capacitor for each phase of the filter.

Optionally, the converter circuit may comprise aDC-to-DC converter. The DC-to-DC converter may be configured to convert a first DC power (DC voltage and/or DC current) to a second DC power (DC voltage and/or DC current). The DC-to-DC converter may be or may comprise an actively switched DC-to-DC converter comprising at least one switch. The at least one switch may be at least on transistor, such as at least one bipolar junction transistor (BJT); at least one field effect transistor (FET), e.g. at least one metal oxide semiconductor FET (MOSFET); and/or at least one insulated gate bipolar transistor (IGBT). The control entity may be configured to control the DC-to-DC converter of the converter circuit by controlling switching of the at least one switch. The DC-to-DC converter may comprise one or more passive elements, such as one or more inductor(s) and/or capacitor(s), for power conversion and/or filtering.

An output of the three phase DC-to-DC converter, a capacitor and a DC-side (i.e. input) of the three phase DC-to-AC converter may be electrically connected to each other in parallel. The control entity may be configured to control the DC-to-DC converter such that the DC-to-DC converter controls, optionally regulates, a power flow from one or more electrical energy sources (e.g. renewable energy source(s), such as photo voltaic (PV) plant(s) and/or wind power plant(s), and/or battery storage system(s), such as one or more batteries, optionally one or more rechargeable batteries) and optionally a voltage (DC link voltage) across the aforementioned capacitor. The control entity may be implemented by software and/or hardware. Optionally, the control entity may be a device that may comprise a processor or processing circuitry configured to perform, conduct or initiate the various operations of the control entity described herein. The processing circuitry may comprise hardware and/or the processing circuitry may be controlled by software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as applicationspecific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. The device may further comprise memory circuitry, which stores one or more instruction(s) that can be executed by the processor or by the processing circuitry, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the processor or the processing circuitry, causes the various operations of the device (i.e. the control entity) to be performed. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device (i.e. the control entity) to perform, conduct or initiate the operations or methods described herein.

In an implementation form of the first aspect, the output of the converter circuit is electrically connected with a primary winding of a step up transformer; and a secondary winding of the step up transformer is electrically connected to an AC grid.

A leakage inductor of the step up transformer is a physical parameter that well imitates an inductor of a synchronous machine of the same power. The primary winding of the step up transformer may be referred to as “primary side” or “low voltage primary side”.

In an implementation form of the first aspect, the output of each of multiple of the converter circuit is electrically connected with a primary winding of a step up transformer and a secondary winding of the step up transformer is electrically connected to an AC grid. The control entity may be configured to control, according to the control of the converter circuit, each of the multiple of the converter circuit.

With other words, multiple of the converter circuit may be connected with the primary winding of a step up transformer, wherein the output of each converter circuit is electrically connected with the primary winding of the step up transformer. The control entity may be configured to control, according to the control of the converter circuit, each of the multiple of the converter circuit to imitate an electrical output characteristic of a synchronous machine. This allows imitating a multi-phase synchronous machine. In other words, the equivalent synchronous machine may be conceived as a multi-phase synchronous machine, for which each converter circuit of the multiple of the converter circuit may feed a three phase section of the whole machine (i.e. number of terminals may be a multiple of three).

The term “multi-phase” in the term “multi-phase synchronous machine” may refer to a family of electrical machines for which the number of input terminals is greater than three. For example, in case ten converter circuits are connected with the primary winding of the step up transformer and each converter circuit has three input terminals for the three phases, then there are in total thirty input terminals. In this case, a 30-phase synchronous machine may be imitated.

In other words, the aforementioned implementation form of the first aspect allows imitating a multi-phase synchronous machine for which each converter circuit of the multiple of the converter circuit is configured to feed a section of the virtual machine. The control entity allows the multiple of the converter circuit (i.e. a group of converter circuits) to imitate a single multiphase electrical machine, i.e. a single multi-phase synchronous machine, instead of a group of unrelated three phase electrical machines. That is, the multi-phase electrical machine has a higher number of phases compared to the three phases of each three phase electrical machine. For this, the control entity may be configured to perform a distributed control (e.g. distributed voltage control) of the multiple of the converter circuit. That is, the control entity may be configured to control, according to the control of the converter circuit, each of the multiple of the converter circuit. Distributed control of the multiple of the converter circuit may mean that a group of local controllers may be implemented for each converter circuit (e.g. for the three phase DC-to-AC converter of each converter circuit). That is, there is not a sample-by-sample communication among the converter circuits. Therefore, a first converter circuit of the multiple of the converter circuit does not use an input current of a second converter circuit or an n-th converter circuit and so on (assuming that that n is an integer equal to or greater than two, n > 2.), but a control objective may be achieved for the overall system (i.e. the multiple of the converter circuit). Thus, the control entity allows controlling multiple of the converter circuit (i.e. multiple converter circuits) to work in a collaborative way offering at least one of frequency control service, voltage control at the point of connection (of the multiple converter circuits with the primary winding of the step transformer) and a synchronous machine like short-circuit ratio.

The distributed control (e.g. distributed voltage control) of the multiple of the converter circuit allows taking care of the power and individual voltage balancing, and a frequency generation implementation, accordingly. Since control (e.g. power and/or voltage control) of the voltage across the capacitor for the respective phase of the filter of the converter circuit (capacitor energy is proportional to square of its voltage across) may be performed, an internal frequency of each converter circuit may be generated as it would reflect the kinetic energy of a rotating machine.

Thus, generation of the internal frequency of the converter circuit (or of each of the multiple of the converter circuit) allows imitating/mimicking the synchronous machine. Since the three phase DC-to-AC converter of the converter circuit (or of each of the multiple of the converter circuit) is static (there is not a rotating mass), its energy function may be obtained as a model equivalent. The energy stored in the filter capacitor for each phase may be used as the one that plays the role of rotating energy. Thus, if this energy decreases (i.e. the amplitude of the voltage across the capacitor for the respective phase decreases) the frequency is to decrease. Implementing this in the converter circuit (or in each of the multiple of the converter circuit) by the control entity, the behavior of the converter circuit (or the multiple of the converter circuit) may match stability properties of a power system based on a synchronous machine or synchronous machines.

When the arrangement comprising the multiple of the converter circuit and the step up transformer reaches steady- state the output voltages of the multiple of the converter circuit match and they may imitate (“build”) a counter-electromotive force (counter emf or back emf) behind the step-up transformer (i.e. at the secondary side/at the side of the secondary winding). That is, the AC grid (distribution grid) may see a synchronous machine at the secondary winding of the step-up transformer (i.e. at the secondary side of the step up transformer).

Having a large equivalent synchronous machine (i.e. an equivalent multi-phase synchronous machine) formed by the cooperation of the step up transformer and multiple of the converter circuit when controlled by the control entity allows providing benefits at a system level: for example, in case the multiple of the converter circuit are used in a power generation system, such as a large photo voltaic (PV) park, less but larger synchronous machines per power generation system may be imitated by controlling the converter circuits by the control entity. This may lead to an easy maintenance at power generation system level (i.e. power plant level). Further, the control of the converter circuits by the control entity allows better usage of short- circuit ratio of the step up transformer. The energy stored in the capacitor for each phase of the filter of the multiple converter circuits may be seen as a large buffer for energy for inertia and large short-circuit current provision during faults. Having a large equivalent synchronous machine allows a smart use of the physical system. That is, a leakage inductance of the step up transformer may well imitate inductance of an electrical machine. The leakage inductor of the step up transformer is a physical parameter that well imitates an inductor of a synchronous machine of the same power.

In an implementation form of the first aspect, a node between the inductor and the capacitor is electrically connected to the output of the converter circuit. The control entity may be configured to measure or estimate an output current flowing from the node to the output of the converter circuit, and use, in addition to the measured current and the measured voltage, the measured or estimated output current for controlling the output voltage of the three phase DC- to-AC converter.

In an implementation form of the first aspect, the node between the inductor and the capacitor is electrically connected via a second inductor to the output of the converter circuit; and the output current is the current through the second inductor.

With other words, the control entity may be configured to measure or estimate the current flowing (from the node to the output of the converter circuit) through the second inductor, and use, in addition to the measured current and the measured voltage, the measured or estimated current flowing through the second inductor for controlling the output voltage of the three phase DC-to-AC converter.

In an implementation form of the first aspect, the control entity is configured to compute a reference value for the current through the inductor using a reference value for an amplitude of the voltage across the capacitor and an amplitude of the measured voltage across the capacitor. The control entity may be configured to compute a reference value for the output voltage of the three phase DC-to-AC converter using the computed reference value for the current through the inductor.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the output voltage of the three phase DC-to-AC converter using a reference value for the phase angle of the voltage across the capacitor.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the output voltage of the three phase DC-to-AC converter by transforming the measured current through the inductor to a dq-frame using the reference value for the phase angle, inputting the dq-frame of the reference value for the current through the inductor which comprises the computed reference value for the current through the inductor as q-axis or d-axis, and the transformed measured current through the inductor to a controller transfer function, and transforming a value that is based on the output of the controller transfer function to an abc- firame using the reference value for the phase value.

With regard to the dq-frame of the reference value for the current through the inductor, the other axis (not being the computed reference value for the current through the inductor) of the q-axis and d-axis may be zero Amperes. In other words, the dq-frame of the reference value for the current through the inductor may comprise zero Amperes as the other axis (not being the computed reference value for the current through the inductor) of the q-axis and d-axis. The amplitude of the voltage across the capacitor may be controlled in one control loop and the phase angle/frequency of the voltage across the capacitor may be controlled in another control loop. Using transformation to the dq-frame allows combining the two aforementioned control loops in one control loop. Thus, all relevant information may be in one control loop. This allows simplifying the control by the control entity and, thus, the control entity.

The controller transfer function may be or may comprise a transfer matrix with non-zero decoupling terms. The transfer matrix may be a 2 by 2 matrix (2x2 matrix).

The computation of the reference value for the output voltage of the three phase DC-to-AC converter by the control entity may be referred to as current control loop (e.g. innermost current control loop). Namely, the current through the inductor may be controlled by controlling the output voltage of the three phase DC-to-AC converter. That is, the current control loop allows controlling, optionally regulating, the current delivered from the three phase DC-to-AC converter to the inductor of the filter.

The abc-frame generated from the value that is based on the output of the controller transfer is the reference value for the output voltage of the three phase DC-to-AC converter. The abc- frame may comprise or be a pulse-width modulation (PWM) reference for setting PWM pulses or signals that may be used for controlling the three phase DC-to-AC converter, in case the three phase DC-to-AC converter is controlled using PWM pulses or signals. The control entity may be configured to control the three phase DC-to-AC converter using PWM pulses or signals.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the output voltage of the three phase DC-to-AC converter by transforming the voltage across the capacitor to a dq-frame using the reference value for the phase angle, inputting the output of the controller transfer function and the transformed voltage across the capacitor to a state-feedback active damping unit, and transforming an output of the statefeedback active damping unit to the abc-frame using the reference value for the phase value.

The abc-frame generated from the output of the state-feedback active damping unit is the reference value for the output voltage of the three phase DC-to-AC converter. The abc-frame may comprise or be a pulse-width modulation (PWM) reference for setting PWM pulses or signals that may be used for controlling the three phase DC-to-AC converter, in case the three phase DC-to-AC converter is controlled using PWM pulses or signals. The control entity may be configured to control the three phase DC-to-AC converter using PWM pulses or signals. The state-feedback active damping unit may be used for stability purposes, i.e. it may improve stability.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the current through the inductor by computing a difference between the amplitude of the measured voltage across the capacitor and the reference value for the amplitude of the voltage across the capacitor, and inputting the computed difference to a controller transfer function configured to compute, using the inputted difference, the reference value for the current through the inductor. The computation of the reference value for the current through the inductor by the control entity may be referred to as counter-electromotive force control loop (counter emf control loop or back emf control loop, e.g. distributed counter/back emf control loop). This allows controlling the amplitude of the voltage across the capacitor. In particular, this allows the control entity regulating the amplitude of the voltage across the capacitor itself (i.e. perform a voltage control) and regulating a buffer of energy that may play a similar role as kinetic energy in a synchronous machine rotation (i.e. inertia for frequency control action).

The controller transfer function may comprise a proportional controller (e.g. proportional gain). In other words, the control entity may be configured to input the computed difference to a proportional controller configured to compute, using the inputted difference, the reference value for the current through the inductor.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the amplitude of the voltage across the capacitor by an equalization that corrects, using the measured or estimated output current, a main reference value for the voltage across the capacitor.

In case the converter circuit (optionally the multiple of the converter circuit) is used in a power generation system, such as a photo voltaic (PV) plant or wind power plant, the main reference value may be set at power generation system control level (i.e. power plant control level). The control entity may receive the main reference value for the voltage across the capacitor (e.g. from a user or operator, such as a user or operator of the power generation system). The main reference value for the voltage across the capacitor may be constant or a slowly changing parameter that slowly changes compared to the control of the converter circuit by the control entity. The main reference value may be referred to as “central reference value”.

In an implementation form of the first aspect, the control entity is configured to correct the main reference value for the voltage across the capacitor by inputting an amplitude of the measured or estimated output current to a low pass filter transfer function configured to emulate an equalizing resistor, and subtracting an output of the low pass filter transfer function from the main reference value. The term equalizing resistor may be referred to as “virtual equalizing resistor”. In other words, the control entity may be configured to correct the main reference value with an equalization action, wherein the equalization uses the amplitude of the measured or estimated output current and passes it through a low pass filter transfer function configured to emulate an equalizing resistor. The transfer function allows considering bandwidth limitation (e.g. below 5 Hz) for avoiding interaction with one or more other control loops. That is, the counter-electromotive force control loop (counter emf control loop or back emf control loop), which may be performed by the control entity, may be a back emf control with an active equalization for power sharing among converter circuits (e.g. in case of multiple of the converter circuit connected to a primary winding of a step-up transformer, i.e. to the same step-up transformer primary). The amplitude of the measured or estimated output current in combination with the low pass filter transfer function allows actively sharing the power among the multiple converter circuits, in case the control entity controls multiple of the control circuit (wherein each of the multiple of the control circuit may be connected to a step up transformer). The amplitude of the measured or estimated output current may be a magnitude proportional to delivered torque and power in a synchronous machine (e.g. synchronous generator), of which the electrical output characteristic or performance may be imitated by the control entity controlling the converter circuit.

In an implementation form of the first aspect, the control entity is configured to estimate a value of an amplitude of the estimated output current at a current point in time by computing a difference between a value of an amplitude of the measured current through the inductor at the current point in time and a value of the amplitude of the estimated output current at a point in time directly before the current point in time, inputting the computed difference to an estimator model that models charging and discharging of a capacitor, computing a difference between a reference value for the voltage across the capacitor at the current point in time and an output of the estimator model, and inputting the computed difference to a controller transfer function configured to compute, using the inputted difference, the value of the amplitude of the estimated output current at the current point in time.

The controller transfer function may comprise a proportional controller (e.g. proportional gain). In other words, the control entity may be configured to input the computed difference to a proportional controller configured to compute, using the inputted difference, the value of the amplitude of the estimated output current at the current point in time. The capacitor of which charging and discharging is modelled by the estimator module may be the capacitor of the filter. The estimator model may be referred to as “estimator”. Optionally, the estimator model is based on modelling the capacitor by a simplified DC-equivalent (which may be set in a dq-frame) that may consider input and output currents with regard to the capacitor and how those charge and discharge the capacitor.

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the phase angle by inputting a reference value for the frequency of an AC grid to an integration unit, wherein the output of the integration unit is the reference value for the phase angle.

The computation of the reference value for the phase angle by the control entity may be referred to as frequency control loop (e.g. distributed frequency control loop).

In an implementation form of the first aspect, the control entity is configured to compute the reference value for the frequency of the AC grid by an equalization that corrects, using the measured or estimated output current, a main reference value for the frequency of the AC grid.

The control entity may receive the main reference value for the frequency of the AC grid (e.g. from a user or operator, such as a user or operator of the power generation system). The main reference value (central reference value) for the frequency of the AC grid may be constant (e.g. a constant parameter proportional to the rated frequency, usually 50 Hertz (Hz) in a European AC grid or 60 Hz in the US). Alternatively, the main reference value for the frequency of the AC grid may be a slowly changing parameter. For example, in case the converter circuit (optionally the multiple of the converter circuit) is used in a power generation system, such as a photo voltaic (PV) plant or wind power plant, the main reference value for the frequency of the AC grid may be a slowly changing parameter set by a power generation system control (i.e. power plant control), e.g. some values close to the rated frequency settings (set by 50 Hz or 60 Hz). The main reference value for the frequency of the AC grid may be a constant or slowly changing parameter (slowly changing compared to the control of the converter circuit by the control entity) as an acting parameter for a slower frequency control scheme (compared to the control of the converter circuit by the control entity) at the power generation system level (i.e. the power plant level), e.g., primary, secondary or tertiary frequency control executed from the power generation system level. In an implementation form of the first aspect, the control entity is configured to correct the main reference value for the frequency of the AC grid by inputting an amplitude of the measured or estimated output current to a low pass filter transfer function configured to emulate an equalizing resistor, and subtracting an output of the low pass filter transfer function from the main reference value.

For example, in case the output of each of multiple of the converter circuit being electrically connected with a primary winding of a step up transformer and an equal active current sharing is achieved, in steady-state, the amplitude of the measured or estimated output current may be used or employed for a frequency droop control/function. A main objective of droop control is that the multiple converter circuits working in grid-forming reach the same frequency in steadystate, and this frequency is also a good information of the kinetic energy stored in each of the multiple converter circuits. Using the amplitude of the measured or estimated output current and the low pass filter transfer function allows computing the reference value for the frequency of the AC grid that coincides to all the multiple converter circuits. This allows emulating well an operation of a power system based on multiple synchronous generators.

In order to achieve the control entity according to the first aspect of this disclosure, some or all of the implementation forms and optional features of the first aspect, as described above, may be combined with each other.

A second aspect of this disclosure provides a system. The system comprises a control entity according to the first aspect of this disclosure, as described above, for controlling a converter circuit to imitate an electrical output characteristic of a synchronous machine. The system comprises the converter circuit comprising a three phase DC-to-AC converter and a filter comprising for each phase an inductor and a capacitor, which together are electrically connected in parallel to an output of the three phase DC-to-AC converter. The converter circuit is configured to provide, using a voltage across the capacitor, an output voltage at an output of the converter circuit.

Optionally, the converter circuit may comprise a three phase DC-to-DC converter. An output of the DC-to-DC converter, a capacitor and a DC-side (e.g. input) of the three phase DC-to-AC converter may be electrically connected to each other in parallel. An input of the DC-to-DC converter may be configured to be electrically connected to one or more electrical energy sources (e.g. renewable energy source(s), such as photo voltaic (PV) plant(s) and/or wind power plant(s), and/or one or more batteries, optionally one or more rechargeable batteries). A main role of a circuit (may be referred to as internal circuit) comprising one or more batteries and/or any other energy storage system (i.e. any other one or more electrical energy sources) may be to assure that the DC-to-AC converter is able to deliver the active power and active current demanded (by a controller, e.g. the control entity).

In an implementation form of the second aspect, the system comprises a step up-transformer and multiple of the converter circuit. The output of each converter circuit of the system is electrically connected with a primary winding of the step up transformer; a secondary winding of the step up transformer is electrically connected to an AC grid; and the control entity is configured to control each converter circuit of the system.

The above description of the control entity according to the first aspect is correspondingly valid for the system according to the second aspect. For example the description of the converter circuit when describing the control entity of the first aspect may be valid for the converter circuit of the system.

The system of the second aspect and its implementation forms and optional features achieve the same advantages as the control entity of the first aspect and its respective implementation forms and respective optional features.

In order to achieve the system according to the second aspect of this disclosure, some or all of the implementation forms and optional features of the second aspect, as described above, may be combined with each other.

A third aspect of this disclosure provides a method for controlling a converter circuit to imitate an electrical output characteristic of a synchronous machine. The converter circuit comprises a three phase DC-to-AC converter, and a filter comprising for each phase an inductor and a capacitor, which together are electrically connected in parallel to an output of the three phase DC-to-AC converter. The converter circuit is configured to provide, using a voltage across the capacitor, an output voltage at an output of the converter circuit. The method comprises measuring a current through the inductor and the voltage across the capacitor, controlling the voltage across the capacitor by controlling the current through the inductor, and controlling the current through the inductor by controlling, using the measured current and the measured voltage, an output voltage of the three phase DC-to-AC converter.

In an implementation form of the third aspect, the output of the converter circuit is electrically connected with a primary winding of a step up transformer; and a secondary winding of the step up transformer is electrically connected to an AC grid.

In an implementation form of the third aspect, the output of each of multiple of the converter circuit is electrically connected with a primary winding of a step up transformer and a secondary winding of the step up transformer is electrically connected to an AC grid. The method may comprise controlling, according to the control of the converter circuit, each of the converter circuit.

In an implementation form of the third aspect, a node between the inductor and the capacitor is electrically connected to the output of the converter circuit. The method may comprise measuring or estimating an output current flowing from the node to the output of the converter circuit, and using, in addition to the measured current and the measured voltage, the measured or estimated output current for controlling the output voltage of the three phase DC-to-AC converter.

In an implementation form of the third aspect, the node between the inductor and the capacitor is electrically connected via a second inductor to the output of the converter circuit; and the output current is the current through the second inductor.

In an implementation form of the third aspect, the method comprises computing a reference value for the current through the inductor using a reference value for an amplitude of the voltage across the capacitor and an amplitude of the measured voltage across the capacitor. The method may comprise computing a reference value for the output voltage of the three phase DC-to-AC converter using the computed reference value for the current through the inductor.

In an implementation form of the third aspect, the method comprises computing the reference value for the output voltage of the three phase DC-to-AC converter using a reference value for the phase angle of the voltage across the capacitor. In an implementation form of the third aspect, the method comprises computing the reference value for the output voltage of the three phase DC-to-AC converter by transforming the measured current through the inductor to a dq-frame using the reference value for the phase angle, inputting the dq-frame of the reference value for the current through the inductor which comprises the computed reference value for the current through the inductor as q-axis or d-axis, and the transformed measured current through the inductor to a controller transfer function, and transforming a value that is based on the output of the controller transfer function to an abc- frame using the reference value for the phase value.

In an implementation form of the third aspect, the method comprises computing the reference value for the output voltage of the three phase DC-to-AC converter by transforming the voltage across the capacitor to a dq-frame using the reference value for the phase angle, inputting the output of the controller transfer function and the transformed voltage across the capacitor to a state-feedback active damping unit, and transforming an output of the state-feedback active damping unit to the abc-frame using the reference value for the phase value.

In an implementation form of the third aspect, the method comprises computing the reference value for the current through the inductor by computing a difference between the amplitude of the measured voltage across the capacitor and the reference value for the amplitude of the voltage across the capacitor, and inputting the computed difference to a controller transfer function configured to compute, using the inputted difference, the reference value for the current through the inductor.

In an implementation form of the third aspect, the method comprises computing the reference value for the amplitude of the voltage across the capacitor by an equalization that corrects, using the measured or estimated output current, a main reference value for the voltage across the capacitor.

In an implementation form of the third aspect, the method comprises correcting the main reference value for the voltage across the capacitor by inputting an amplitude of the measured or estimated output current to a low pass filter transfer function configured to emulate an equalizing resistor, and subtracting an output of the low pass filter transfer function from the main reference value. In an implementation form of the third aspect, the method comprises estimating a value of an amplitude of the estimated output current at a current point in time by computing a difference between a value of an amplitude of the measured current through the inductor at the current point in time and a value of the amplitude of the estimated output current at a point in time directly before the current point in time, inputting the computed difference to an estimator model that models charging and discharging of a capacitor, computing a difference between a reference value for the voltage across the capacitor at the current point in time and an output of the estimator model, and inputting the computed difference to a controller transfer function configured to compute, using the inputted difference, the value of the amplitude of the estimated output current at the current point in time.

In an implementation form of the third aspect, the method comprises computing the reference value for the phase angle by inputting a reference value for the frequency of an AC grid to an integration unit, wherein the output of the integration unit is the reference value for the phase angle.

In an implementation form of the third aspect, the method comprises computing the reference value for the frequency of the AC grid by an equalization that corrects, using the measured or estimated output current, a main reference value for the frequency of the AC grid.

In an implementation form of the third aspect, the method comprises correcting the main reference value for the frequency of the AC grid by inputting an amplitude of the measured or estimated output current to a low pass filter transfer function configured to emulate an equalizing resistor, and subtracting an output of the low pass filter transfer function from the main reference value.

The above description of the control entity according to the first aspect is correspondingly valid for the method according to the third aspect.

The method according to the third aspect and its implementation forms and optional features achieve the same advantages as the control entity of the first aspect and its respective implementation forms and respective optional features. In order to achieve the method according to the third aspect of this disclosure, some or all of the implementation forms and optional features of the third aspect, as described above, may be combined with each other.

A fourth aspect of this disclosure provides computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to the third aspect, as described above.

A fifth aspect of this disclosure provides a storage medium storing executable program code which, when executed by a processor, causes the method according to the third aspect, as described above, to be performed.

An sixth aspect of the disclosure provides a computer comprising a memory and a processor, which are configured to store and execute program code to perform the method according to the third aspect, as described above.

A seventh aspect of the disclosure provides a non-transitory storage medium storing executable program code which, when executed by a processor, causes the method according to the third aspect, as described above, to be performed.

The computer program according to the fourth aspect, the storage medium according to the fifth aspect, the computer according to the sixth aspect and the non-transitory storage medium according to the seventh aspect each achieve the same advantages as the control entity of the first aspect and its respective implementation forms and respective optional features.

All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof. BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

Figure 1 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure;

Figure 2 shows an example of a method according to an embodiment of this disclosure;

Figure 3 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure;

Figure 4 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure;

Figures 5 to 8 each show an example of a function of a control entity according to an embodiment of this disclosure;

Figure 9 shows an example of a converter circuit controllable by a control entity according to an embodiment of this disclosure; and

Figure 10 shows an example of a synchronous machine of which an electrical output characteristic may be imitated by a control performed by a control entity according to an embodiment of this disclosure.

In the Figures, corresponding elements are labeled with the same reference sign.

DETAILED DESCRIPTION OF EMBODIMENTS

Figure 1 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure. The control entity 1 of Figure 1 is an example of the control entity according to the first aspect of this disclosure. Thus, the description of the control entity according to the first aspect is correspondingly valid for the control entity 1 of Figure 1. The system 5 is an example of the system according to the second aspect of this disclosure. Thus, the description of the system according to the second aspect is correspondingly valid for the system 5 of Figure 1.

The control entity 1 of Figure 1 is a control entity for controlling a converter circuit 2 to imitate an electrical output characteristic of a synchronous machine. The converter circuit 1 comprises a three phase DC-to-AC converter 3, and a filter 4 comprising for each phase an inductor Lin and a capacitor C _n , which together are electrically connected in parallel to an output of the three phase DC-to-AC converter 3. A buffer of energy (e.g. an ideal voltage source, such as an ideal DC voltage source) at the DC side of the three phase DC-to-AC converter 3 may be assumed to be available for absorbing or injecting a power into the AC system (i.e. into the AC side of the converter circuit 2 at which the AC side of the three phase DC-to-AC converter 3 is present), as may be requested by the control entity 1. Examples of such a buffer of energy are indicated in Figure 4, where one or more batteries may provide a DC power p _st and/or receive a DC power p _s t, and/or one or more renewable energy sources (e.g. photo voltaic (PV) plant(s) and/or wind power plant(s)) may provide a DC power p _gen . In Figure 1 the inductor Lin and capacitor C _n for only one phase of the three phases are shown. Nevertheless, a current 104 through the inductor Lin is shown in the form of a vector i(n comprising for each phase the current 104 through the respective inductor Li _n for each phase of the three phases. This is also the case for the other Figures. Accordingly, the other electrical parameters are indicated in the Figures in the form of vectors comprising the values for each phase of the three phases (e.g. the vector u^ for an output voltage 101 of the three phase DC-to-AC converter 3; the vector for a voltage 102 across the capacitor C _n ; the vector for an output voltage 103 at an output of the converter circuit 2; the vector for an output current 105 flowing from a node N1 between the inductor Lin and the capacitor C _n to the output of the converter circuit 2 etc.). That is, in the Figures vectors (vector signals) are used for referring to three phase electrical parameters/variables. The description with regard to the measurement and control of electrical parameters/variables is correspondingly valid for each phase of the three phases. The converter circuit 2 is configured to provide, using the voltage 102 across the capacitor C _n , the output voltage 103 at the output of the converter circuit 2. The control entity 1 is configured to measure the current 104 through the inductor Li _n and the voltage 102 across the capacitor C _n , control the voltage 102 across the capacitor C _n by controlling the current 104 through the inductor Lin, and control the current 104 through the inductor Lin by controlling, using the measured current and the measured voltage, the output voltage 101 of the three phase DC-to-AC converter 3.

As shown in Figure 1, the node N1 between the inductor Lin and the capacitor C _n is electrically connected to the output of the converter circuit 2. The control entity 1 may be configured to measure or estimate the output current 105 flowing from the node N1 to the output of the converter circuit 2, and use, in addition to the measured current and the measured voltage, the measured or estimated output current 105 for controlling the output voltage 101 of the three phase DC-to- AC converter 3.

The control entity 1 may be implemented by hardware and/or software. Optionally, the control entity 1 may be a device comprising a processor or processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the control entity described herein. The processing circuitry may comprise hardware and/or the processing circuitry may be controlled by software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as applicationspecific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. The device (control entity 1) may further comprise memory circuitry, which stores one or more instruction(s) that can be executed by the processor or by the processing circuitry, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the processor or the processing circuitry, causes the various operations of the device to be performed. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device (control entity 1) to perform, conduct or initiate the operations or methods described herein.

The control entity 1 may be configured to control the three phase DC-to-AC converter 3 (as indicated by the arrow in Figure 1). For example, the control entity 1 may be configured to control the three phase DC-to-AC converter 3 such that the three phase DC-to-AC converter 3 implements an AC voltage control over the capacitor C _n for each phase of the filter 4.

The control entity 1 and the converter circuit 2 may form a system 5, as indicated in Figure 1.

Examples of the control performable by the control entity 1 for controlling the converter circuit 2 (or multiple of the converter circuit 2, not shown in Figure 1) are described with regard to Figures 5 to 8.

Figure 2 shows an example of a method according to an embodiment of this disclosure. The method of Figure 2 is an example of the method according to the third aspect of this disclosure. Thus, the description of the method according to the third aspect is correspondingly valid for the method of Figure 2. The control entity 1 of Figure 1 may be configured to perform the method of Figure 2.

The method of Figure 2 is a method for controlling a converter circuit (e.g. the converter circuit of any one of Figures 1, 3 and 4) to imitate an electrical output characteristic of a synchronous machine. The converter circuit comprises a three phase DC-to-AC converter, and a filter comprising for each phase an inductor and a capacitor, which together are electrically connected in parallel to an output of the three phase DC-to-AC converter. The converter circuit is configured to provide, using a voltage across the capacitor, an output voltage at an output of the converter circuit. As shown in Figure 2, as a first step SI, the method comprises measuring a current through the inductor and the voltage across the capacitor. In a second step S2 following the first step SI, the method comprises controlling the voltage across the capacitor by controlling the current through the inductor. In a third step S3 following the second step S2, the method comprises controlling the current through the inductor by controlling, using the measured current and the measured voltage, an output voltage of the three phase DC-to-AC converter.

Figure 3 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure. The control entity 1 and system 5 (e.g. converter circuit 2) of Figure 3 is an example of the control entity 1 and system 5 (e.g. converter circuit 2) of Figure 1, respectively. Thus, the description of Figure 1 is correspondingly valid for the control entity 1 and system 5 (e.g. converter circuit 2) of Figure 3 and in the following mainly additional features of the system 5 (e.g. converter circuit 2) of Figure 3 are described.

As shown in Figure 3, the node N1 between the inductor Lin and the capacitor C _n is electrically connected via a second inductor Lon to the output of the converter circuit 2; and the output current 105 is the current through the second inductor Lon. That is, the filter 4 comprises for each phase the inductor Li _n , the capacitor C _n and the second inductor Lon.

Figure 4 shows an example of a control entity according to an embodiment of this disclosure and an example of a system according to an embodiment of this disclosure. The control entity 1 and system 5 (e.g. converter circuit 2) of Figure 4 is an example of the control entity 1 and system 5 (e.g. converter circuit 2) of Figure 3, respectively. Thus, the description of Figures 1 and 3 is correspondingly valid for the control entity 1 and system 5 (e.g. converter circuit 2) of Figure 4 and in the following mainly additional features of the system 5 (e.g. control entity 1 and converter circuit 2) of Figure 4 are described.

Optionally, the second inductor Lon for each phase of the filter 4 may be omitted. That is, the additional features of the system 5 of Figure 4 compared to Figure 3 may be implemented in the system 5 of Figure 1.

As shown in Figure 4, the converter circuit 2 may comprise a DC-to-DC converter 6 and a capacitor C2n. An output of the three phase DC-to-DC converter 6, the capacitor C2n and a DC- side (e.g. input) of the three phase DC-to-AC converter 3 may be electrically connected to each other in parallel. An input of the DC-to-DC converter may be configured to be electrically connected to one or more electrical energy sources, e.g. renewable energy source(s), such as photo voltaic (PV) plant(s) and/or wind power plant(s), and/or one or more batteries, optionally one or more rechargeable batteries. The renewable energy source(s) may provide a DC power p _g en to the DC-to-DC converter 6. The one or more batteries may provide a DC power p _st to the DC-to-DC converter 6 and/or receive a DC power p _st from the DC-to-DC converter 6. The DC- to-DC converter 6 may provide a DC power pin and the DC-to-AC converter may receive a DC power pout

The control entity 1 may be configured to control the three phase DC-to-DC converter 6 (not indicated in Figure 4). For example, the control entity 1 may be configured to control the three phase DC-to-DC converter 6 such that the three phase DC-to-DC converter 6 controls, optionally regulates, a power flow from one or more electrical energy sources (e.g. renewable energy source(s), such as photo voltaic (PV) plant(s) and/or wind power plant(s)) and optionally a voltage Vdc (DC link voltage) across the capacitor C2n.

The control entity 1, the converter circuit 2 and optionally one or more electrical energy sources (e.g. renewable energy source(s), such as photo voltaic (PV) plant(s) and/or wind power plant(s), and/or one or more batteries, optionally one or more rechargeable batteries) may optionally form a system 5, as indicated in Figure 4. Figures 5 to 8 each show an example of a function of a control entity according to an embodiment of this disclosure. The functions of any one of Figures 5 to 8 may be performed by the control entity 1 of any one of Figures 1, 3 and 4.

In the following, the Figures 5 to 8 are described with respect to the control entity 1 and system 5 of Figure 4. Further it is assumed, that an input of the converter circuit 2 is electrically connected to a photo voltaic (PV) plant. This is only by way of example and, thus, the following description is correspondingly valid for different implementation forms of the converter circuit 2 and/or different electrical energy sources. Optionally, the control entity 1 may control a multiple of the converter circuit 1, wherein the output of each of the multiple of the converter circuit 1 is electrically connected with a primary winding of a step up transformer and a secondary winding of the step up transformer is electrically connected to an AC grid (as exemplarily shown in Figure 9). That is, multiple converter circuits may be present, wherein each of the multiple converter circuits is implemented as the converter circuit 1. The control entity 1 may control each of the multiple converter circuits and the output of each of the multiple converter circuits is electrically connected with the primary winding of the step up transformer. The control entity 1 may be configured to perform a distributed control (at converter circuit level) of the one converter circuit 1 (as shown in any one of Figures 1, 3 and 4) or each of multiple of the converter circuit 1 (i.e. of multiple converter circuits, exemplarily shown in Figure 9).

Distributed control may be understood that local currents and voltages at the converter circuit point of connection are employed with a high-bandwidth control, i.e. actions performed at a sampling frequency equal or higher than the switching frequency of the power electronics converter (e.g. the three phase DC-to-AC converter(s) 3). System level commands may be sent at a much slower speed by communication means: For example power plant control (i.e. control of the PV plant) may change a reference value for the amplitude of the voltage 102 across the capacitor C _n to multiple of the converter circuit (in case each of the multiple of the converter circuit are connected with a primary winding of a step up transformer) for a given objective at the power plant level (low bandwidth communication does not impair the distributed control feature that relies on control of the converter circuit(s), e.g. real-time control of the converter circuit(s)). Furthermore, it is assumed that the control entity 1 performs control of the converter circuit(s) using transformation(s) to dq-frame(s). The following description is correspondingly valid in case of not using transformation(s) to dq-frame(s). Following a common criterion for a control of synchronous machine, it can be assumed that flux is aligned with d-axis. Thus, it is assumed that back emf (counter emf) is aligned with q-axis and torque/power flow may be controlled, optionally regulated, by acting on the q-axis current. Meanwhile when working in the dq-frame domain, several trivial dq-axis definitions may be followed given similar performance. In other words, the present disclosure is not limited to the dq-axis definition described herein. The description of the Figures, such as Figures 5 to 8, is correspondingly valid in case of different dq-axis definitions.

Figure 5 shows an example of controlling, optionally regulating, the current 104 flowing from the three phase DC-to-AC converter 3 through the inductor Li _n . The control loop exemplarily shown in Figure 5 may be referred to as an innermost current control loop.

The control entity 1 may be configured to compute a reference value 106 for the current 104 through the inductor Li _n using a reference value for an amplitude of the voltage 102 across the capacitor C _n and an amplitude of the measured voltage 102 across the capacitor C _n . An example of a control loop for the aforementioned computation is shown in Figure 6. As shown in Figure 5, the control entity 1 may be configured to compute a reference value 108 for the output voltage 101 of the three phase DC-to-AC converter 3 using the computed reference value 106 for the current 104 through the inductor Li _n . In Figure 5, a vector is shown for the reference value 108 for the output voltage 101 of the three phase DC-to-AC converter 3 comprising for each phase of the three phases a respective reference value Ug _n , u(, _n , or Uc _n . As shown in Figure 5, the control entity 1 may be configured to compute the reference value 108 for the output voltage 101 of the three phase DC-to-AC converter 3 using a reference value 107 for the phase angle of the voltage 102 across the capacitor C _n . In Figure 5, the reference value 107 for the phase angle of the voltage 102 across the capacitor C _n is labelled as “0 _M ”.

As shown in Figure 5, the control entity 1 may be configured to compute the reference value 108 for the output voltage lOlof the three phase DC-to-AC converter 3 by transforming the measured current 104 through the inductor Lin to a dq-frame using the reference value 107 for the phase angle, inputting the dq-frame of the reference value for the current 104 through the inductor Lin which comprises the computed reference value 106 for the current through 104 the inductor Li _n as q-axis (e.g. [0 li*Q _n ]) or d-axis (e.g. [Ii* _Dn 0]), and the transformed measured currentl09 through the inductor Lin to a controller transfer function 8 (e.g. K _cc (z)), and transforming a value that is based on the output of the controller transfer function 8 to an abc- frame using the reference value 107 for the phase value. In Figure 5, a vector is shown for the measured current 104 through the inductor Lin comprising for each phase of the three phases a current i _Ian , i _Ibn , or i _Icn through the respective inductor Li _n . The transformation to the dq- firame is indicated in Figure 5 by an abc-frame to dq-frame transformation block 6. The dq- frame of the measured current 104 through the inductor Lin (provided by the transformation block 6) is indicated as a vector comprising a value of the d-axis “iron” and a value of the q-axis “iiQn”. The terms “value of the d-axis” and “value of the x-axis” may be referred to as “d-value” and “q-value”, respectively. The transformation to the abc-frame is indicated in Figure 5 by a dq-frame to abc-frame transformation block 7.

Optionally, as indicated in Figure 5, the control entity 1 may be configured to compute the reference value 108 for the output voltage 101 of the three phase DC-to-AC converter 3 by transforming the voltage 102 across the capacitor C _n to a dq-frame using the reference value 107 for the phase angle, inputting the output of the controller transfer function 8 and the transformed voltage across the capacitor C _n to a state-feedback active damping unit 9, and transforming an output of the state-feedback active damping unit 9 to the abc-frame using the reference value 107 for the phase value. In Figure 5, a vector is shown for the voltage 102 across the capacitor C _n comprising for each phase of the three phases a voltage e _an , ebn, or e _cn across the respective capacitor C _n . The controller transfer function 8 may be or may comprise a transfer matrix K _cc (z) with non-zero decoupling terms. The transfer matrix K _cc (z) may be a 2 by 2 matrix (2x2 matrix).

Figure 6 shows an example of controlling, optionally regulating, the amplitude of the voltage 102 across the capacitor C _n . The control loop exemplarily shown in Figure 6 may be referred to as back emf (counter emf) control loop.

As shown in Figure 6, the control entity is configured to compute the reference value 106 for the current 104 through the inductor Lj _n by computing a difference between the amplitude 110 of the measured voltage 102 across the capacitor C _n and a reference value 112 for the amplitude of the voltage 102 across the capacitor C _n , and inputting the computed difference to a controller transfer function 13 (e.g. Kbemf( ^z )) configured to compute, using the inputted difference, the reference value 106 for the current 104 through the inductor Li _n . According to Figure 6, the reference value 106 for the current 104 through the inductor Li _n is exemplarily shown as a q- value of a dq-frame (li*Q _n ). Alternatively, as indicated in Figure 5, the reference value 106 for the current 104 through the inductor Lin may be a d-value of the dq-frame (not show in Figure 6). In Figure 6, a vector is shown for the voltage 102 across the capacitor C _n comprising for each phase of the three phases a voltage across the respective capacitor C _n . The amplitude 110 of the measured voltage 102, which may be a q-value Eq _n of a dq-frame (or alternatively a d- value of a dq-frame), may be computed by the magnitude (norm) of the vector (i.e. |e^|).The reference value 112 for the amplitude of the voltage 102 across the capacitor C _n may be a q- value EQ _n = | e^| * of a dq-frame (or alternatively a d-value of a dq-frame). In Figure 6, the computation of the aforementioned difference is indicate by a subtraction block 12.

As indicated in Figure 6, the control entity 1 may be configured to compute the reference value 112 for the amplitude of the voltage 102 across the capacitor C _n by an equalization that corrects, using the measured or estimated output current 105, a main reference value 111 for the voltage 102 across the capacitor C _n . The control entity 1 may be configured to correct the main reference value 111 for the voltage 102 across the capacitor C _n by inputting an amplitude of the measured or estimated output current 105 to a low pass filter transfer function 10 (e.g. H _eq (z)) configured to emulate an equalizing resistor, and subtracting an output of the low pass filter transfer function 10 from the main reference value 111. In Figure 6, the computation of the aforementioned difference is indicate by a subtraction block 11. The main reference value 111 for the voltage 102 across the capacitor C _n is labelled in Figure 6 as “|e ₀ 1*”. In Figure 6, a vectorl^ is shown for the measured or estimated output current 105 comprising for each phase of the three phases a measured or estimated output current. The amplitude of the measured or estimated output current 105, which may be a q-value ! ₀ Q _n of a dq-frame (or alternatively a d- value of a dq-frame), may be computed by the magnitude (norm) of the vector (i.e. |l^|).

The control loop of Figure 6 allows controlling, optionally regulating, the amplitude of the voltage 102 across the capacitor C _n itself (i.e. perform a voltage control) and regulating a buffer of energy that may play a similar role as kinetic energy in a synchronous machine rotation (i.e. inertia for frequency control action). The main reference 111 for the voltage 102 across the capacitor C _n may be be set at the park control level (e.g. PV plant control level). The main reference 111 may be a constant or slowly changing parameter. The main reference 111 may be corrected with an equalization action: the equalization may use a measurement or estimation of the output current 105 and pass it through a low pass filter transfer function 10 (e.g. H _eq (z)) that emulates a equalizing resistor (e.g. DC gain of H _eq (z)). The low pass filter transfer function 10 may be defined as transfer function in order to consider bandwidth limitation (usually below 5 Hz to avoid further interaction with other control loops). Once the reference value 112 for the amplitude of the voltage 102 across the capacitors C _n is set or computed, the controller transfer function 13 (e.g. Kbemf( ^z )) ^ma Y compute the reference value 106 for the current 104 through the inductor Li _n . The computed reference value 106 for the current 104 through the inductor Lin may be fed or provided as an input to the control loop of Figure 5. The controller transfer function 13 may comprise a proportional controller (e.g. proportional gain).

Figure 7 shows an example of estimating a value of an amplitude of the estimated output current 105.

As shown in Figure 7, the control entity 1 may be configured to estimate the value of the amplitude of the estimated output current 105 (|TcTn I = loQn) ^{at a} current point in time by computing a difference between a value of an amplitude of the measured current 104 through the inductor Li _n at the current point in time and a value of the amplitude of the estimated output current 105 at a point in time directly before the current point in time (e.g. indicated by a subtraction block 16), inputting the computed difference to an estimator model 17 (e.g.

T z ^-1

— — — ) that models charging and discharging of a capacitor (e.g. the capacitor C _n ), computing a difference between the reference value 110 for the voltage 102 across the capacitor C _n at the current point in time and an output 113 (e.g. Eq _n ) of the estimator model 17 (e.g. indicated by a subtraction block 14), and inputting the computed difference to a controller transfer function 15 (e.g. K _est (z)) configured to compute, using the inputted difference, the value of the amplitude of the estimated output current 105 at the current point in time.

Figure 8 shows an example of a computation of the reference value 107 for the phase angle. The control loop exemplarily shown in Figure 8 may be referred to as frequency control loop (e.g. distributed frequency control loop).

As shown in Figure 8, the control entity 1 may be configured to compute the reference value 107 for the phase angle by inputting a reference value 115 for the frequency of an AC grid (e.g. co _M ) to an integration unit 20 (e.g. wherein the output of the integration unit is the reference value 107 for the phase angle. The reference value 107 for the phase angle may be a discrete time integral of the frequency. As indicated in Figure 8, the control entity 1 may be configured to compute the reference value 107 for the frequency of the AC grid by an equalization that corrects, using the measured or estimated output current 105, a main reference value 114 (e.g. co^) for the frequency of the AC grid. The control entity 1 may be configured to correct the main reference value 114 for the frequency of the AC grid by inputting an amplitude of the measured or estimated output current 105 to a low pass filter transfer function 18 (e.g. Hdr(z)) configured to emulate an equalizing resistor, and subtracting (indicated in Figure 8 by the subtraction block 19) an output of the low pass filter transfer function 18 from the main reference value 114. In Figure 8, a vector is shown for the measured or estimated output current 105 comprising for each phase of the three phases a measured or estimated output current. The amplitude of the measured or estimated output current 105, which may be a q- value l ₀ Qn of a dq-frame (or alternatively a d-value of a dq-frame), may be computed by the magnitude (norm) of the vector (i.e. |l^|).

For example, in case the output of each of multiple of the converter circuit 1 being electrically connected with a primary winding of a step up transformer (as exemplarily shown in Figure 9) and an equal active current sharing is achieved, in steady-state, amplitude of the measured or estimated output current 105 may be used or employed for a frequency droop control/function. A main objective of droop control is that the multiple converter circuits working in grid-forming reach the same frequency in steady-state, and this frequency is also a good information of the kinetic energy stored in each of the multiple converter circuits. Using the amplitude of the measured or estimated output current and the low pass filter transfer function allows computing the reference value for the frequency of the AC grid that coincides to all the multiple converter circuits. This allows imitating the inertia of a rotating synchronous machine.

When the power system load increases in real-time, the internal frequency of each of the converter circuits controlled by the control entity (i.e. the proposed virtual synchronous machine embodiment) may also decrease its internal frequency at the same time so that they may provide or deliver a requested increase of power demand: this behavior well resembles a fast-frequency control action (e.g., inertial response) of a rotating synchronous machine; in the case that load consumption decreases, the effect on the (either virtual or real) rotating machine is the opposite one. Figure 9 shows an example of a converter circuit controllable by a control entity according to an embodiment of this disclosure. The control entity may be the control entity 1 of any one of Figures 1, 3 and 4.

As indicated in Figure 9, the output of each of multiple of the converter circuit 2 of Figure 3 or 4 may be electrically connected with a primary winding 21a of a step up transformer 21. A secondary winding 21b of the step up transformer 21 is electrically connected to an AC grid (not shown in Figure 9). In other words, the output of each of multiple converter circuits may be connected to the primary winding 21a of the transformer 21, wherein each converter circuit may be the converter circuit 2 of Figure 3 or 4. According to Figure 9, three converter circuits are connected to the primary winding 21a of the transformer 21. This number of converter circuits is only by way of example and may be differently. In Figure 9, only the second inductor Loi, L02, or Lon of the filter 4 of the respective converter circuit and the voltage across the capacitor C _n of the respective converter circuit (in the form of a vector e^, e^, or e^) are shown. A leakage inductor L _o of the step up transformer 21 is shown in Figure 9 that is a physical parameter that well imitates an inductor of a synchronous machine of the same power. The step up transformer 21 converts a voltage at the primary winding 21a (represented in Figure 9 by a vector Vg comprising for each phase of the three phases a respective value) to a greater voltage at the secondary winding 21 (represented in Figure 9 by the vector Vg that is multiplied by the factor “k” (i.e. k v^). As indicated by the vectors e^, e^, or for the respective voltage across the capacitor C _n of the converter circuits 2, the AC side of each converter circuit 2 is a three phase system. That is, each part of the filter 4 of a respective converter circuit 2, such as the inductor Lin,, the capacitor C _n and the optional second inductor Lon is made or implemented with three components. In other words, the filter 4 of a respective converter circuit comprises for each phase of the three phases the inductor Lin,, the capacitor C _n and the optional second inductor Lon.

Figure 10 shows an example of a synchronous machine of which an electrical output characteristic may be imitated by a control performed by a control entity according to an embodiment of this disclosure.

According to the example of Figure 10, a group of converter circuits, that may be implemented e.g. in line with the converter circuit 2 of any one of Figures 1, 3 and 4, may be connected to a common point with voltage (the vector indicates a three phase voltage, i.e. a voltage for each phase of the three phases). The number of converter circuits of Figure 10 is only by way of example and may be differently. The voltage represent the primary (low-voltage) terminal of a step up transformer, such as the step up transformer shown in Figure 9. In other words, the output of each of the group of converter circuits is electrically connected to a primary winding (primary side) of the step up transformer. In Figure 10, each converter circuit is represented by an AC voltage source 3 providing a three phase voltage (represented by the respective vector , u^ or u ) and an inductor Lin, Ln or Ln for each phase of the three phases of a filter of the converter circuit, wherein the inductor is connected to the AC voltage source 3. The respective AC voltage source 3 corresponds to the three phase DC-to-AC converter of the converter circuit 2 of any one of Figures 1, 3 and 4. The respective inductor Lin, Ln or Ln for each phase of the three phases corresponds to the inductor Li _n for each phase of the three phases of the filter 4 of the converter circuit 2 of any one of Figures 1, 3 and 4. A current flowing through the respective inductor Lin, Ln or Ln for each phase of the three phases is indicated in the form of the vector n, O2 ^or hi comprising for each phase the current through the respective inductor Lin, Ln or Ln for each phase of the three phases. In addition, in Figure 10, for each converter circuit a voltage across a capacitor for each phase of the three phases of the filter of the converter circuit is shown in the form of the vector e^, or e)* comprising for each phase the voltage across the respective capacitor for each phase of the three phases. The respective capacitor for each phase of the three phases corresponds to the capacitor C _n for each phase of the three phases of the filter 4 of the converter circuit 2 of any one of Figures 1, 3 and 4. A leakage inductor L _o of the step up transformer (present on the primary side/primary winding of the step up transformer) is shown in Figure 10 that is a physical parameter that well imitates an inductor of a synchronous machine of the same power. Thus, the example of Figure 10 may correspond to the example of Figure 9 and, the description of Figure 9 may be correspondingly valid for Figure 10. The secondary side of the step up transformer may be connected to an AC grid, such as a medium voltage distribution grid. A distributed control of the group of converter circuits by the control entity of any one of Figures 1, 3 and 4 may shape the back emf signal, i.e. the voltage representing the primary (low-voltage) terminal of the step up transformer. The leakage inductor L _o of the step up transformer may play the role of the machine inductor. The capacitive energy buffered by the group of converter circuits may play a role in frequency regulation of the power system. As indicated in Figure 10, each converter circuit may control, optionally regulate, the voltage (amplitude and phase-angle) at a terminal of an equivalent multi-phase machine acting as a motor 22. An electric torque may be converted to a virtual mechanical one TOM and transmitted from the motor to the generator through an ideal shaft 23 to an equivalent generator 24 that establishes the virtual synchronous machine as seen by the power system. Since an ideal shaft 23 is considered, the torque TIG received by the generator 24 matches the torque TOM of the motor 22 (i.e. TOM = TIG). The torque TIG received by the generator 24 may then be fully converted to electrical torque and power.

The present disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.