WO2019129729A1

WO2019129729A1 - Unbalance compensation by optimally redistributing current

Info

Publication number: WO2019129729A1
Application number: PCT/EP2018/086691
Authority: WO
Inventors: Jeroen STUYTS; Jeroen TANT; Fjo De Ridder; Sven De Breucker
Original assignee: Vito Nv; Katholieke Universiteit Leuven
Priority date: 2017-12-31
Filing date: 2018-12-21
Publication date: 2019-07-04

Abstract

A method and system is described to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution. First load- current is decomposed to outputs of at least negative- and zero-sequence components (I neg and I ze r), followed by determining a positive-sequence component (l pos,inv,i ) as a function of active power (P), reactive power (Q) and positive-sequence voltage (U), and determining a phase current, to be injected per phase and a neutral current.

Description

Unbalance Compensation by Optimally Redistributing Current

The present invention relates to converters and method of operating them and to provide Unbalance Compensation by Optimally Redistributing Currents.

Background

More and more power electronic (PE) converters are connected to the low-voltage grid (LV grid). They are used to interface distributed generation (DG), like solar and small- scale wind and they allow you to connect a battery or to charge a plug-in electric vehicle (PEV). These converters have in common that they convert the grid’s AC to DC for the consumer or the other way around. More applications exist for these AC-DC converters on the LV grid, like controlling motors (e.g. compressors and heat pumps) and generators (e.g. small wind turbines and micro water turbines) for all sorts of applications. In addition, future applications, like DC microgrids, will have an AC-DC converter as a crucial component.

All these AC-DC converters use essentially the same topology and the same controllers, as they all need to adhere to the grid code in the respective country where they are installed. The topology is composed of a number of half bridges (two switches in series), which together can compose a full bridge (two half bridge in parallel, i.e. a single-phase converter). Three half bridges are required for a three phase converter without neutral connection (i.e. one half bridge per phase). Adding a fourth connection is required for a neutral connection (e.g. a fourth leg as in Figure 1). Furthermore, each half bridge, except the one for the neutral connection, uses an LCL-filter. This topology is the most common for low voltage converters, the actual technology behind the components can vary, but the overlaying architecture is the same.

Interphase unbalance problems in the LV grid

Local interphase unbalances are a consequence of the construction of the national grids. The typical European residential LV grid has three phases at 400V line-to-line and a neutral (230V phase voltage). For example in parts of Belgium 43% of the connections are single phase grid connections (typically 40 A) to this three-phase four- wire grid. 23% has a three- phase grid connection (typically 25 A). The other 34% is connected to the old 3x230V topology (no neutral, 230V line-to-line) [1]

Most loads are single -phase, automatically leading to unbalance, as these can only be balanced out by other loads. Hence, unbalance is an old problem, even for converters [2] However, DG has made this problem only worse, as now currents can flow from the customer to the grid, instead of the other way around. Therefore, while consumption and generation can be balanced from a system perspective, they can be locally unbalanced. E.g. a PV installation producing power on phase 1 and an equal but opposite consumption on another phase. This is a cause for neutral-point-shifting and major unbalanced grids. [3].

A converter can be used to respond to an unbalanced grid in many different ways. It can inject balanced currents, it can inject balanced powers (e.g. active or reactive), it can inject only the positive sequence ... [4] . The injection of currents independent of unbalance has been achieved in [5]. A converter could also actively compensate unbalance [6], which can e.g. decrease grid losses [7], [8] . Also different unbalance compensation techniques are available [9], but some are dependent on the available hardware [10] (i.e. a neutral connection or not). The connection to the neutral is required to be able to compensate not only the negative sequence, but also the zero sequence [10] .

[7] proposes a centralized solution and a local solution. The local solution uses a fixed droop relationship for the active power output, based on the voltage in the phase(s). The solution is however voltage based and considers active power only.

[6], [11]— [14], CN103219908B, compensates only the negative sequence.

[15] compensates only the negative sequence and depends on communication.

[9] is capable of compensating negative or zero sequence, but not both at the same time.

US20160248342A1 does not take into account how much current can be injected in the phases and does not work with a neutral connection.

A lot of methodologies are available to compensate negative and zero sequences using a converter e.g. with one or more transformers. The simplest way to achieve current balance is to connect single-phase or line-connected loads manually from the phase/line with the greatest burden to a different phase/line with less burden. Distribution systems’ operators sometimes perform this action when the PV generation on a single-phase is much higher than the other phases. However, this operation is cumbersome and expensive. An automated version of this solution is proposed in [16] . Using a matrix-converter-like solution, the connected load or generation can be reconnected to another phase, based on the measured phase currents. This solution relies on the presence of a sufficient number of single-phase loads to improve the unbalance. However, complete unbalance compensation can never be guaranteed and large single-phase loads remain uncompensated if too few other loads are available for connection to the other phases. This is a crude solution, which requires an additional matrix-converter in series with any (number of) loads available for unbalance compensation. Hence, this requires extra hardware, which increases the losses (in the switches of the matrix-converter) and decreases the reliability (series connection).

A more refined form of the previous solution, is the central control of a group of single phase inverters where the combined output of the controlled inverters is adjusted until e.g. current balance is improved beyond a certain target [17] . However, this directly affects the positive sequence active and reactive power of the controlled inverters. For example, if the controlled group are PV inverters, adjustment of the combined output causes unwanted curtailment of the solar energy.

Load balancing can also be achieved by using a UPS in parallel to the load and power source. The phase imbalance of the load is compensated by the UPS, although it is not stated how the UPS manages to compensate the imbalance and is able to transfer power between phases [18]. A three phase inverter without neutral connection is used in [18], so the transfer capacity between phases is limited, but this is not addressed in the description.

The main disadvantage of the current state of the art is that the focus lies on conventional inverters which are connected to the phases, but not to the neutral. These inverters can only inject positive and negative sequence components [14] As the positive sequence components have priority, the remaining ampacity of the inverter can be used for the negative sequence injection. Hence, no optimisation between negative and zero sequence components is required and the zero sequence components remain uncompensated. The solution proposed in [9] does try to influence the negative and zero sequence current to address the problems associated with voltage unbalances in the grid. This solution uses a three-leg inverter with split dc-bus. This topology has some inherent drawbacks. The current harmonics present in the dc-bus can flow unimpeded to the neutral conductor, increasing the already present harmonic current in this conductor. As the neutral current is drawn from the middle of the dc-bus, the balance of the dc-bus is disturbed and depending of the neutral current direction, the voltage of the lower part of the dc-bus will increase or decrease compared to the upper part. Moreover, Space Vector Modulation is no longer applicable, forcing the dc-bus voltage to increase. These three drawbacks result in the adaptation of oversized dc-bus capacitors [19].

The inherent drawback of three-leg inverters with split dc-bus is their inability to actively control the current in the neutral wire as only passive elements are present in the neutral wire connection. Due to the lack of full control of all injected currents, unintentional injection of negative currents can occur in the presence of grids with zero sequence voltages, although it is indicated that this effect could be eliminated after further research

[9].

The biggest impediment towards actual implementation of the solution presented in [9] is the lack of restrictions on the negative and zero sequence currents. This will either cause excessive currents and possible damage to the converter if the converters current rating is not taken into account or will result in a sub-optimal implementation where the applied currents are abruptly limited if one of the currents in either phase or neutral reaches its maximal value, possibly resulting in unintended curtailment of the connected load or generation.

The solution proposed in [20] recognizes that the injection of positive and negative sequence components should be limited to prevent excessive currents in the converter. The proposed solution in [20] only takes the positive and negative sequence into account, as it assumes a three-phase converter without neutral connection, and neglects the zero sequence current.

The solution proposed in [20] can give priority to the positive sequence current. The positive and negative sequence currents have a sinusoidal representation in [20], which means that the maximum negative sequence current needs to be calculated at every phase angle as the rotation of the positive and negative sequence current is opposite, resulting in a different maximum allowable negative sequence current at each phase angle for a given maximum phase current and positive sequence current. The limit value of the negative sequence current thus changes constantly, even within a single grid-period, and forces the negative phase current controller to track this limit value. This produces an erratic negative sequence current.

It is known to control three-phase inverters in the positive and negative sequence components of the voltage and current, and occasionally the zero sequence component is also taken into account.

A control architecture for the control of the positive and negative sequence components is described in [21]. The zero sequence component is omitted, as the neutral wire is not connected, and hence, no optimization of the set points for the negative and zero sequence components is performed.

[22] describes a method to control the positive, negative and zero sequence output voltage of three-phase inverters. This approach has the merit of describing a control architecture for positive, negative and zero sequence voltages or currents, but assumes that either the set points take the hardware restrictions of the converter into account or that output is equipped with a saturation function that imposes a hard limit. Neither strategies result in an optimal solution of the applied negative and zero sequence currents.

A further control architecture for multi-level inverters is known from [23] . [23] proposes a control method for minimizing the common mode voltage with the aim of reducing the zero sequence current component of the current between the LCL-filter and the neutral point of the dc-bus (neutral point divides the dc-bus in 2 halves). [23] focuses on the control and related minimization of the zero sequence current,.

[24] describes a Steinmetz circuit with adjustable L and C components in delta or star connection can also achieve current balancing. This is usually optimised for a single known load- scenario where the unbalance is caused by a single-phase load with a known power level. This solution is used for balancing of large industrial single phase ac-loads in the MW range, such as high-speed trains and arc furnaces. This solution lacks the flexibility to adapt to the changing environment of distribution grids e.g. having a different phase with maximum current, different current amplitudes, etc. and is too expensive for use in distribution grids.

Summary of the invention

A method and system is disclosed according to embodiments of the present invention to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution. First load-current is decomposed to outputs of at least negative- and zero-sequence components (I_neg and I_zer), followed by determining a positive-sequence component l_pos,inv_,i) ^{as a} function of active power (P), reactive power ( Q ) and positive-sequence voltage (U), and determining a phase current, to be injected per phase and a optionally a neutral current.

An advantage of embodiments of the present invention is the ability to compensate negative and zero sequence, both at the same time. An advantage of embodiments of the present invention is the ability take into account how much current can be injected in the phases and to work with a neutral connection. Embodiments of the present invention are flexible, not expensive and can be used at low and medium voltage at any power level.

An advantage of embodiments of the present invention is that a transformer is not required to inject the currents calculated by method or system embodiments of the present invention.

An advantage of embodiments of the present invention is that they consider currents and also reactive power. An advantage of embodiments of the present invention is that unbalance compensation can be optimised continuously and is not based on a fixed amount (or per voltage).

An advantage of embodiments of the present invention is the ability to compensate for the negative sequence and the zero sequence. An advantage of embodiments of the present invention is the ability to operate on local measurements alone and also to compensate the zero sequence.

An advantage of embodiments of the present invention is to provide a good or to improve or to maximize the unbalance-compensating current injected by an inverter under all grid circumstances at all times. The unbalance-compensating current consists of or comprises a negative and a zero sequence current which is injected by the inverter with the purpose to reduce the negative and zero sequence current present in the grid or the property it is installed in.

In a first aspect a method to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution is disclosed, the method comprising the steps:

decomposing load-current to outputs of at least negative- and zero-sequence components

determining a positive-sequence component l_pos,inv,i) ^{as a} function of active power (P), reactive power ( Q ) and positive-sequence voltage (U), and

determining a phase current, to be injected per phase and optionally a neutral current. A transformer is not required to inject the currents.

The method can comprise evaluating:

These methods can be subject to:

,max

and

determining the phase current, to be injected for phase i according to:

and the neutral current according to:

wherein

I_neg = the negative sequence current

Ine_g,i = the negative sequence current of phase i in complex notation

Izer = the zero sequence current

I_Zer,i = the zero sequence current of phase i in complex notation

Iί,ίhn = the current through the converter leg connected to phase i

Io,ίhn = the current through the converter leg connected to the neutral

I<Dmax= the maximal phase current through the converter

Io,max = the maximal neutral current through the converter

a_n = variable for optimisation

a_z = variable for optimization

Ipos,inv,i = the positive sequence current of phase i

Ip = positive sequence component flowing through a grid, injected or consumed by the inverter or a combination of these

I_n = the negative sequence to be compensated

Iz = the zero sequence to be compensated.

This evaluation can be made subject to a_n £ 1

a_z £ 1

a_n ³ 0

&Z > 0 . Optimization aspects of the present invention can be formulated as a second order cone problem.

The three-phase converter can be a series or parallel converter.

The load current can be measured or estimated by calculation.

At least negative- and zero- sequence components can be provided in vector format. In another aspect a computer based system to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution, the system comprising:

means for decomposing load-current to outputs of at least negative- and zero-sequence components (I_neg and I_zer ),

means for determining a positive-sequence component l_pos,inv,i) ^{as a} function of active power (P), reactive power (Q) and positive-sequence voltage (£/), and

means determining a phase current, to be injected per phase and optionally a neutral current. A transformer is not required to inject the currents. The system can also comprise means for evaluating:

This can be subject to:

and

means for determining a phase current, to be injected for phase i according to: i,ihn pos,mv,i n^lneg,i z^lzer,i

and a neutral current according to:

wherein

e_g = the negative sequence current

Leg,i = the negative sequence current of phase i in complex notation

Ler = the zero sequence current

I_Zer,i = the zero sequence current of phase i in complex notation

Li_nv I = the current through the converter leg connected to phase i

Io,ίhn = the current through the converter leg connected to the neutral

Ic_Dmax = the maximal phase current through the converter

Io,max = the maximal neutral current through the converter

a_n = variable for optimisation

a_z = variable for optimization

Ipos,inv,i = the positive sequence current of phase i

L = the negative sequence to be compensated

Iz = the zero sequence to be compensated.

The means for evaluating can be subject to

a_z £ 1 a_n ³ 0

a_z > 0 .

The three-phase converter can be a series or parallel converter.

Means for measuring the load current or means for estimating the load current by calculation can be provided.

The at least negative- and zero- sequence components can be provided in vector format.

In another aspect a converter controller system can be provided comprising:

means for receiving values of 3 phase voltages of an electric grid,

a grid estimator which takes the 3 phase voltages as an input and outputs positive, negative and zero sequence voltages, grid frequency, and grid-angle, and a

a computer based system to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution, and

a current controller receiving output from the computer based for controlling switching elements of the three-phase converter.

In another aspect a computer based method of converter control is provided comprising the steps:

receiving values of 3 phase voltages of an electric grid,

grid estimating which takes the 3 phase voltages as an input and outputs positive, negative and zero sequence voltages, grid frequency, and grid-angle,

determining unbalance compensating currents to be injected or consumed by a three-phase converter and

controlling switching elements of the three-phase converter.

Embodiments of methods of the present invention can be run on an inverter with a parallel connection to a grid and to a property it is installed in, but can also be used in series connected converters, i.e. converters that are connected to the grid at one side and connected to a device or building at the other side. Embodiments of the present invention will be described with reference to the parallel case, but the present invention is not limited to this case but can be implemented successfully in the case of a series connected converter. Thus, embodiments of the present invention are suited for both parallel and series connected converters.

A determination of a current unbalance can be based both on direct measurement of the current in the grid or property and/or on the derivation of the grid/property current based on other parameters. The direct measurement of the current and its unbalance can, for example either be a current measurement directly connected to the current compensating converter of embodiments of the present invention or a measurement performed in a e.g. in a smart grid where the current present in the grid is transmitted to the current compensating converters of that smart grid. Several techniques exists for the derivation of the grid/property current and its unbalance, all of which can be used with the present invention, e.g. an estimation of the current per phase can be based on a voltage measurement as the current imbalance will cause different voltage drops across the phases of the cable. Embodiments of the present invention can assume that the current unbalance is measured or estimated and uses either measurement or estimation as an input.

Embodiments of the present invention comprise injection of negative and zero sequence currents, the underlying inverter technology is presumed to have a neutral connection next to the phase connections. Embodiments of the present invention can function with different neutral point connections, e.g. a split-cap implementation or a fourth half-bridge in a conventional three-legged three-phase inverter. It is anticipated that embodiments of the present invention are not limited by the chosen technology as long as the technology allows the injection of negative and zero sequence currents.

A first optional limitation of some embodiments of the present invention is that the primary function of the inverter preferably remains unaffected, being the injection or absorption of positive sequence current, which consists of or comprises the active and reactive current. The set-points of the active and reactive current can depend on the underlying application and grid requirements, such as active power of a PV inverter, (dis)charge power of a battery-inverter, mechanical drive power and reactive power compensation of a motor drive, and should not be impeded by the unbalance-compensating current settings.

A second optional limitation of some embodiments of the present invention is that the hardware limits of the inverter should preferably be respected. In embodiments of the present invention it is envisaged that an inverter is configured where all phases have the same current rating, and allows the neutral connection to have a current rating which differs from the phases. The current rating of the neutral connection depends on the functional requirements of the inverter. For example if the emphasis lies on active/reactive power injection and unbalance compensation is only allowed at one third of the power rating, then the current rating of the neutral connection might be as low as 1/4^ώ of the current rating of the phases. On the other hand, if the emphasis lies on unbalance compensation and the level of the active/reactive power injection is much lower, than the current rating of the neutral connection can be 2-3 times as high as those of the phases. Therefore, an identical maximum current per phase can be defined as well as a separate maximum current for the neutral connection. Specific current ratings of the inverter connections are not considered a limitation of the present invention, any configuration will be taken into account.

Embodiments of the present invention can take the above limitations into account and can for example determine the optimal set-point of the negative and zero sequence current. In case none of the limitations are met, the inverter will fully compensate the negative and zero sequence currents of the targeted grid or the property it is installed in. If the limitations do occur, embodiments of the present invention can make an optimization between the injected negative and zero sequence currents while the positive sequence active and reactive currents remain unaltered. Embodiments of the present invention are able to recalculate the negative and zero sequence currents settings very quickly (ms range), such that any alteration in the positive sequence current can immediately be taken into account. In any case, the positive sequence remains unaltered at all times and will always be injected/consumed or passed through.

For use in embodiments of the present invention a converter is preferably fully programmable. If this is not the case or if the controller for the converter is not suitable for upgrading to the present invention then a new controller can be added. Embodiments of the present invention can provide the converter with the possibility to compensate unbalance. Embodiments of the present invention can be used to calculate the currents that need to be injected by a PE (power electronic) converter to compensate unbalance. The present invention avoids unwanted curtailment of generation units or undesired load shaving as the positive sequence active and reactive power remains unaffected and current unbalance issues are solved by the injection of negative and zero sequence currents.

The present invention ensures that the positive sequence current required by the load or generation is not adversely affected by the negative and zero sequence currents and optimizes the applied negative and zero sequence currents within the limits of the converter hardware.

Embodiments of the present invention can give priority to the positive sequence current, for example. Embodiments of the present invention do not need to have positive and negative sequence currents having a sinusoidal representation. This avoids that the maximum negative sequence current needs to be calculated at every phase angle as the rotation of the positive and negative sequence current is opposite, resulting in a different maximum allowable negative sequence current at each phase angle for a given maximum phase current and positive sequence current. Embodiments of the present invention avoid that the limit value of the negative sequence current thus changes constantly, even within a single grid-period, and forces the negative phase current controller to track this limit value. Embodiments of the present invention avoid that an erratic negative sequence current is produced. Also the zero sequence current is not omitted in embodiments of the present invention.

Preferably, in embodiments of the present invention the positive, negative and zero sequence current have a vector representation, which means that the amplitude and phase angle are available separately. The available current limit for the negative and zero sequence current can thus be calculated directly by the algebraic difference between the current limit of the converter-phases and the positive sequence current. This fixes the available negative and zero sequence current and avoids the erratic behaviour of [20] . Secondly, the ratio between the injection of the negative and zero sequence current is optimized such that the current unbalance is minimized, this optimization is not performed in [20] as only the negative sequence current is taken into account.

The present invention preferably can be used with a controller for the positive, negative and zero sequence components of the current.. Embodiments of the present invention provide a determination of the optimal set points of the negative and zero sequence components such that the current unbalance (e.g. negative and zero sequence current components) present in the grid or the installation of the property are either minimized or eliminated.

Embodiments of the present invention provide a determination of the optimal set-points for the negative and zero sequence currents with the aim to minimize the current unbalance in the grid or property.

Brief description of the drawings

Figure 1 shows some of the connections of a converter with which embodiments of the present invention can be used such that it becomes a compensator. Figure la) shows a series connected compensator. Figure lb) shows a parallel connected compensator Figure lc) shows a parallel connected compensator in a separate grid (e.g. that of a consumer) Note that the connection to the neutral line is optional but preferred.

Figure 2 shows an embodiment of the present invention.

Figure 3 shows a decomposer which can be used in accordance with embodiments of the present invention.

Figure 4 shows a solver, running asynchronously, communicating over a buffer with the real-time synchronous converter or inverter controller according to an embodiment of the present invention.

Figure 5 shows further embodiment of the present invention.

Figure 6 shows a prior art converter without current redistribution.

Figure 7 shows a converter in accordance with an embodiment of the present invention with current redistribution.

Figure 8 shows results from application of embodiments of the present invention being complete compensation, no limits, enabled at 0.1 s

Figure 9 shows results from application of embodiments of the present invention with limits of phase and neutral currents to lApp, enabled at 0.1 s.

Figure 10 shows results from application of embodiments of the present invention with limit of currents to 2A, while injecting 500VAr with the inverter, enabled at O.ls.

Figure 11 shows of an inverter that can be used with embodiments of the present invention. Figure 12 shows an embodiment of the present invention implemented on an engineering PC communicating with a control computer over a TCP/IP LAN.

Definitions

PE = Power Electronic, PEV = Plug-in Electric Vehicle, DG = Distributed Generation, UPS = Uninterrup table Power Supply, SOCP = Second-Order Cone Program

L_eg = the negative sequence current

Leg.i = the negative sequence current of phase i in complex notation

Ler = the zero sequence current

Ler.i = the zero sequence current of phase i in complex notation

Ii.inv I = the current through the converter leg connected to phase i

Io,ίhn = the current through the converter leg connected to the neutral

I< _max = the maximal phase current through the converter

Io._max = the maximal neutral current through the converter

a_n = variable for optimisation

a_z = variable for optimization

Ipos,inv,i = the positive sequence current of phase i

I_p = positive sequence component flowing through a grid, injected or consumed by the inverter or a combination of these

L = the negative sequence to be compensated

I_z = the zero sequence to be compensated.

In accordance with this invention an“inverter” is interchangeable with“converter”, e.g. in the description and claims. The name‘inverter’ is typically used for applications that transfer power from the DC side to the AC side (e.g. photovoltaic panels connected to the grid). Converters are applications that transfer power between the DC side and the AC side, independent of the direction of power. So an inverter is also a converter. Applications such as fast-charging of electric vehicles, controlling AC drives ... all use converters.

Embodiments of the present invention provide controlling of a converter, hence provide a‘converter controller”. Converter controller is to be understood as covering an“inverter controller”. Description of the preferred embodiments

The present invention is suited for both parallel and series connected converters and is only limited by its use in three-phase power systems. It can be applied to virtually any converter, as long as it is connected to at least three-phases of the power system. An additional connection to the neutral conductor is preferred but not required.

With reference to Figure 2, embodiments of the present invention can be used with a 3- phase grid (lines 1, 2, 3 and neutral) and a converter controller 2 providing current redistribution, the converter controller 2 running on a processing unit 3 of a computer and controlling an inverter 4. The inverter 4 is controlled in such a way that the unbalanced currents flowing through the grid (here to the left) become balanced with the additional currents from the inverter 4 (balanced currents go to the right). The grid can be any grid, e.g. a distribution grid or a local grid from a residence or company. For example, the converter can be connected to any of a low-voltage grid, medium-voltage grid, high- voltage grid or any other voltage level grid. It has been tested in a low- voltage grid purely as an example. Embodiments of the present invention provide a converter, which can be used, for example, for solar panels, fast-charging of cars or only compensating unbalance.

For adjustments to the electrical grid to which a compensating converter according to embodiments of the present invention is connected it is preferred that the grid is capable of being used for distributed generation, so that bidirectional power flows are not a problem (e.g. installing the correct fuses. If a neutral connection is not yet established and the converter supports this, it would be advisable to establish this connection.

Adjustments to the converter to which the present invention can be applied are for example: o Firstly, firmware of the converter can be altered/upgraded/updated, so that it includes embodiments of the present invention. In cases where the controller of the converter is not good enough a new controller can be installed.

o Secondly, considering hardware, preferably also an optional neutral connection can be available or would preferably be added to the converter, if it’s not already present. Adding this to existing converters can be quite cumbersome, so that it can be better to change this in the design phase of the converter and add an extra switching leg.

o The previous two situations imply an existing converter to which the invention is implied. However, the invention is especially suited to be implemented in new converters still in the design phase.

Embodiments of the present invention support less than perfect balancing but which is still an optimal balancing taking into account the limitations of the system. This can be caused by limitations of the system i.e. are actually due to external causes. Embodiments of the present invention are capable of injecting the best possible unbalance compensation under all situations, i.e. limited by the (re)active power injection or limited by the hardware which will determine how much current can be injected or consumed. Removal of external limitations, results in complete balancing when embodiments of the present invention are used.

For example, the converter maybe only capable of injecting 2App per phase and at the same time, that converter is also injecting 500VAr. Under these circumstances, the present invention can still compensate unbalance optimally for that converter, taking into account these limits. If the converter would be twice as big (4App), an overall better result could be achieved, yet again for that converter the optimum for that converter will be achieved.

Embodiments of the present invention use a grid/load current. The grid/load current can be calculated or measured by any suitable means. A current measurement device can be used, or a device able to estimate or measure e.g. the current based on a voltage measurement.

An advantage of embodiments of the present invention is that readily available devices can be used. For example, embodiments of the present invention can calculate the correct pulse widths for switches like IGBTs. Driving the witches with Pulse Width Modulation (PWM), for example, the switches inject, on average, the required current. But other techniques like Space Vector Modulation (SVM) can also be used.

Embodiments of the present invention generate current setpoints. When a converter applies these setpoints, current will flow from and to the converter in the different phases and optionally the neutral conductor. These compensating currents will at least partially eliminate the unbalanced currents (e.g. in the grid or from a load). This can result in phase shifted currents and voltages, as well as changes in amplitude of the currents and voltages. Embodiments of the present invention can be used with multi-phase inverters that are connected to two or more, e.g. three phases and a neutral, but the present invention can be used with other inverters and embodiments described below which are targeted towards three-phase inverters with a neutral connection, for example. Different neutral point connections can be used with embodiments of the present invention, e.g. a split-cap implementation or by using a fourth half-bridge such that a four-legged three-phase inverter is obtained. The multi-phase inverter can be used in a parallel or serial set-up, and the implementation can be performed on a parallel connected inverter.

Embodiments of the present invention can improve or optimise the set-points of the unbalance compensating current for a given unbalance situation, i.e. the improved or optimal negative and zero sequence currents are determined such that the remaining unbalance in the given grid-node can be reduced or minimized. This reduction or optimisation process can take several restrictions or limitations into account.

As a first restriction or limitation, embodiments of the present invention can ensure optionally that the positive sequence current has priority and is not affected by injection of negative and zero sequence current. Positive sequence current encompasses, for example, at least the fundamental frequency active and reactive current. Positive sequence current can, for example, be affected by e.g. a voltage or frequency droop control, such that the injected active and reactive power can still be adjusted depending on the grid situation.

A second restriction or limitation can be for example that the hardware limitations of the inverter are respected. A first hardware limitation can be the maximal phase current, which is identical in all phases and should not be exceeded. A second hardware limitation can be that the maximal neutral current is respected, which can be different from the maximal phase current.

A third restriction or limitation can be that the injected negative and zero sequence currents do not amplify or overcompensate the given current unbalance, i.e. the given current unbalance will disappear in the ideal scenario.

The obtained solution of embodiments of the present invention will preferably improve or maximize the injected negative and zero sequence currents within these restrictions. If the unbalance compensating inverter has ample ampacity in its phases and neutral, the current unbalance can be made to disappear entirely.

Embodiments of the present invention can use a vector representation of the positive, negative and zero sequence current. Hence, the limit values can be calculated economically as the amplitude and phase angle are separately available. For a given situation with a known current unbalance in the grid, a known limit value of the converter currents and a fixed positive sequence current, the injected negative and zero sequence current remain stable.

Embodiments of the present invention can be compatible with any vector representation of the grid.

Embodiments of the present invention can take the restrictions of the hardware and fundamental (re)active current pro-actively into account, such that additional limiters at the output of the current controllers of the negative and zero sequence current are not required.

Embodiments of the present invention can be augmented for example by including the harmonic compensation currents.

• If the converter or inverter control gives priority to the harmonic compensation over the unbalance compensation, the implementation is straightforward;

o If the harmonic compensation currents are balanced, the amplitude of the injected harmonic currents are simply added to the amplitude of the positive sequence currents and the present invention remains otherwise unaltered o If the harmonic compensation currents are unbalanced, the amplitudes of the injected harmonic phase and neutral currents are added to their respective boundary conditions (i.e. the first four equations of the boundary conditions, representing Ll, L2, L3 & N) and the present invention remains otherwise unaltered.

• If the harmonic current compensation has no priority over the unbalance compensation, the harmonic currents need to be included in the optimisation problem. Theoretical background

Pan [24] calculated, based on the theory of Steinmetz, the properties of an ideal compensator that can be realized with inductors and capacitors. For a three-phase four- wire network, two compensators are required. One connected in Delta (D) and one in Star (Y). Concluding that:

In essence, compensation thus requires:

· compensating the negative sequence of the load,

• compensating the zero sequence of the load,

• and compensating the balanced three-phase reactive power.

The latter is actually not related to compensating unbalance as such, as the reactive power is balanced (and can thus be represented in the positive sequence). The methodology proposed by [24] however, is made by passive components and therefore requires two filters that partially compensate each other. Embodiments of the present invention can compensate unbalance by means of a power electronic converter with, for example, full control over the positive, negative and zero sequence. However, it is enough to only compensate the negative and zero sequence of the load to fully compensate unbalance. When this requires more current than is available, special actions are preferably taken.

Reference [24] also discusses the three-phase three-wire grid, which in this context can be seen as compensating unbalance in a three-phase four- wire grid when the converter has no neutral connection (or I₀,max ⁼ 0)· The result is that only the negative sequence component can be or has to be compensated, as no zero sequence can be injected due to the absence of a neutral connection.

This conclusion was also summarized in [25]:

“Any three-phase current can be decomposed in positive, negative and zero sequence components. In any scenario, the positive sequence can come from the grid, as this is a balanced current, which transports the active power. Either one of the two other components will lead to an unbalanced current. Therefore, the ideal current response from a 4-leg converter is the sum of the negative and zero sequence current. A 3-leg converter cannot deliver the zero sequence as it has no neutral connection. To maximally limit ( unbalanced ) current in the grid, the ideal current response of this converter is therefore the negative sequence current. As a consequence, the grid delivers the sum of the positive and zero sequence.”

Achieving perfect unbalance compensation is therefore relying on measuring or calculating the currents, decomposing them in negative and zero sequence and injecting the opposite currents. An important aspect is the determination of the current(s). In addition, hardware constraints will preferably need to be taken into account.

Constraints to unbalance compensation

An important feature of a converter is that it can inject or consume balanced power e.g. active and/or reactive power. It is important that a converter which is used for current redistribution is still able to do its primary job: inject or consume power. However, in many instances the converter will not be injecting or consuming the designed or maximal amount of power (e.g. solar in the night, morning or at noon at which time power generation is high but consumption is lower). Furthermore, the unbalance that needs to be compensated will be very situation and time dependent as well. The amount of unbalance to be compensated as well as the balanced power that needs to be consumed or injected is thus time and case dependent.

Furthermore, injecting both a positive sequence and the compensation term, i.e. negative and zero sequence of the load, could lead to a phase or neutral current that is higher than allowed or achievable. This adds an additional constraint, as the allowed current through a connection is always limited.

Unbalance compensation and balanced power injection or consumption can be unbound. At each given moment, for each specific situation, also in hardware, an inverter preferably should be capable of compensating as much unbalance as possible ; given its constraints. This triggers the use of an optimization, for example.

Enabling unbalance compensation in any inverter

Without being limited by theory, it is clear that unbalance compensation comprises injecting negative and zero sequence components. Injecting or consuming balanced power is injecting or consuming positive sequence currents. Any actively controlled three-phase converter is therefore theoretically capable of compensating some sort of unbalance, if controlled correctly. Injecting negative and zero sequence currents does not necessarily conflict with injecting positive sequence. This can be enabled by a hardware constraint optimization.

This is important, as implementing a method in accordance with embodiments of the present invention which makes use of an algorithm, should preferably enable all three- phase converters connected to the grid today to compensate unbalance. Obviously, it will depend on how much power it is injecting and consuming and whether or not a neutral leg is available, which, however, is often not the case.

The actual optimization problem

Defining the objective

An objective of embodiments of the present invention is to reduce or minimize (preferably well or optimally) unbalanced currents in the grid which cause unwanted losses in the grid. An optimization according to embodiments of the present invention is to minimize or maximize an objective function. A suitable objective function to calculate how much unbalance can be compensated is then the losses in the grid, caused by the currents. This also means that the amount of unbalanced current is decreased or is decreased to a minimum. As was made clear earlier, in the best-case scenario, only positive sequence remains in the grid. One could thus represent the objective function as:

where I_t are the grid currents of the 1-3 respective phases, which are squared to calculate a representation of the losses. This assumes an equal resistance of the phases.

With respect to whether or not to include the current through the neutral in this equation, this is a current which actually flows through the cable and therefore contributes to losses, although it could be reduced to zero under perfect compensation. One could argue that the neutral current is actually already included in the three phase currents, as it is their sum (cfr. the zero sequence). Including it, would double the impact of the zero sequence, compared to the negative sequence. Furthermore, assuming an equal resistance for the phases will be acceptable for many situations. Also an assumption can be made that this resistance for the neutral current is less acceptable, as it can be significantly different. A higher neutral resistance would further increase the impact of the zero sequence. It is an option of embodiments of the present invention not to distinguish between the importance of negative and zero sequence, e.g. as it is preferred if few assumptions on environmental variables are to be made. The neutral current can for example not be taken into account for the optimization in embodiments of the present invention.

In embodiments of the present invention, the formulation of the objective function can be expanded, as to clearly include the compensation terms and the positive sequence:

min ( (/_p + (1 - a_n)I_n + (1 - a_z)I_z)₁ + (/_p + (1 - a_n)I_n + (1 - a_z)/_z)₂

Where I_p is the positive sequence component which is flowing through a grid, injected or consumed by the inverter or a combination of these, I_n is the negative sequence that needs to be compensated i.e. (either the grid, a (sum of) load(s) or both), I_z is the zero sequence that needs to be compensated (i.e. either the grid, a (sum of) load(s) or both). This is split up per phase (e.g. 1, 2 and 3). a_n and a_z are now the variables for optimization, as these indicate how much negative and zero sequence is compensated. It is clear that when both are 1, the compensation is perfect, as only the positive sequence remains, and that when it is 0, there is no compensation.

Formulating the problem like this, clearly shows that the positive sequence component of the inverter is not limited, i.e. injecting or consuming balanced power can have absolute priority over unbalance compensation. Obviously, one cannot inject more current than the phases allow, but that is not subject to the optimization problem.

As the variables in this problem are only related to the negative and zero sequence components, the positive sequence can be omitted from the minimization. It has no influence, as it is a constant and balanced over the three phases. This further changes the objective function to:

where i_neg is the negative sequence current of phase 1 in complex notation, i_zer is the zero sequence current (of phase 1) in complex notation and the modulus | | operation is to determine the absolute value.

Using complex notations and thus the vector format of the decomposed currents is important, as their lengths (i.e. absolute values) are (e.g. in a steady-state) not time dependent, which means that in steady- state the outcome of the optimization is at any time always the same. It should be noted that using sinusoidal currents would or could yield incorrect results as the maxima of the waveforms should be taken into account.

Defining the boundary conditions

Equally important to the objective function, are the boundary conditions. The optimization problem is constrained by the amount of current that can flow through each individual connection (i.e. converter leg), i.e.:

|^l,inv | — If,thac

|^2,inv | — If,thac

|^3,inv | — If,thac

where / _inv is the current through the i^th converter leg, If _hiac is the maximal phase current through the converter and /_{0 max} is the maximal neutral current through the converter. If _thac ^can be equal to /_{0 mai}, but this is not required. If _hiac can be different for each phase, but this is not a requirement.

Two additional boundary conditions can be formulated that limit the solution space. The parameters a_n and a_z should preferably, for example never get any number not within a limited range, e.g. not in the range [0,1] thus including the boundaries. Any value below 0 would result in an additional injection of negative and zero sequence, as would any value over 2. The range [1 2] would mean a sign was wrong in the definition of the equation. Adding these boundaries considerably limits the solution space, which should speed up an algorithm computing the solution.

The overall problem

The optimization problem that needs to be solved is thus:

Minimize:

Subject to:

a„ £ 1

a < 1

a„ > 0

a₇ > 0

The current through phase i can be calculated as:

i,ihn pos,mv,i n^Ineg_>i z^lzer,i Where I_pos,inv,i is the positive-sequence current of phase i that needs to be injected by the converter rather than the one of the load or grid.

The current through the neutral as:

This is a quadratic problem with quadratic constraints, as both for the objective function as for the boundary conditions, the optimization parameters are squared. This type of problem can be formulated, for example as a second-order cone program (SOCP). Here the norm of vectors is used, which is ideal for SOCP. Furthermore, SOCP is convex, which guarantees that there is one global minimum [26], [27]

Such problems can be solved by a variety of methods. In the results section, a suitable implementation is presented.

Applying the solution

The previously presented problem has two factors as a solution: a_n and a_z, that determine how much negative- and zero-sequence current should be injected. The solution proposed in embodiments of the present invention is a very good way to compensate unbalance. The currents that are required as data input can be the result of a measurement or an estimation e.g. determining the positive, negative and zero- sequence decomposition. The solution determines how much current should be injected in each inverter leg (i.e. each connection), using the formula’s for the current through a phase and the neutral. The phase current, to be injected by the converter, for phase i can be calculated as: i,ihn roe,ihn,i n^lneg,i z^lzer,i 1 where all components are now known. The neutral current is calculated as:

2

Injecting this amount of current optimally compensates unbalance while injecting/consuming positive sequence power. Furthermore, this solution is guaranteed to be feasible.

Determining the inputs for the optimization problem

The optimization problem requires that the load-current is decomposed in its positive-, negative- and zero- sequence components and preferably with as high an accuracy and as little of a delay as possible. Figure 3 shows a block diagram of an implementation of an online decomposition unit that can be used with any of the embodiments of the present invention.

The input is the three-phase current measurement 1 of the current to be compensated and the detected grid frequency w. The outputs are the positive-, negative- and zero-sequence components of the current l_pos, l_neg and I_zer.

The three-phase input current /, is sent through an adaptive band-pass filter at frequency w, which has the same structure as a SOGI (see P. Rodriguez, A. Y. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg,“Flexible Active Power Control of Distributed Power Generation Systems During Grid Faults,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2583-2592, Oct. 2007). The SOGI is made up of a gain k, and two (Laplace)

= -. The outputs of the filters stage are the filtered in-phase component / (per phase) and quadrature component I_q (per phase) of the three-phase input. The calculation is as follows:

The four-quadrant arctangent atan.2 of these gives the filtered angle Q of the current (per phase), i.e. :

Q = atan2(J_q )

The quadratic sum gives the filtered amplitude 1/1 of the current (per phase), i.e.

Writing this in the complex exponential form by applying:

and applying the Lyon transformation, gives the sequence components I_pos, I_negSLl_zer, i.e.

Accordingly the input to the online decomposition unit is the current measurement i.e. of the current / to be compensated and determined grid frequency w and the outputs are the sequence components I_pos (e.g. optionally not used), I_neg and l_zer. The three-phase input current /, is sent through an adaptive band-pass filter at frequency w, which is the same structure as a SOGI. The output of this filter stage is an in-phase component / and quadrature component I_q . (see Second Order Generalized Integrator P. Rodriguez, A. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg,“Flexible Active Power Control of Distributed Power Generation Systems During Grid Faults,” IEEE Transactions on Industrial Electronics, vol. 54, pp. 2583-2592, oct 2007. pages 27, 41). The four-quadrant arctangent atari 2 of these gives the current angle Q, while the quadratic sum gives the amplitude |/ |. Writing this in the complex exponential form and applying the Lyon transformation, gives the sequence components I_pos, I_neg and I_zer. (see W. V. Lyon, Transient analysis of alternating-current machinery: an application of the method of symmetrical components. Cambridge : New York: Technology Press of Massachusetts Institute of Technology ; Wiley, 1954. page 53.)

Additionally, the positive-sequence of the inverter l_pos,inv,i needs to be determined which is a function of active power P, reactive power Q and positive-sequence voltage U. Typically the inverter will have a setting for active power P and reactive power Q. Using the positive-sequence voltage U the calculation becomes:

The required grid frequency w for the current decomposition as well as the positive- sequence voltage U can be derived with a Frequency or Phase Locked Loop, to the likes of e.g. [5], [6]

Implementing a solver

Now that the inputs of the optimization problem can be determined, the optimization problem itself needs to be solved. This can be achieved with any solver that can tackle these kinds of problems. One can use for example ECOS [7], fmincon [8], CVX [9] ...

The exact implementation depends on the solver used. However, it can happen that a solver will require more time than the maximum time allowed in between two inverter time steps. Such a problem can be tackled by using an asynchronous process that is able to communicate with the real-time synchronous process, usually via a buffer [10]. A generic implementation is visualized in Figure 4.

How to implement communication between an asynchronous and a synchronous process in such a situation is known to those skilled in the art. For example, the problem can be solved with ECOS, whereby the real-time synchronous components where implemented in a Matlab/Simulink environment, which was compiled afterwards and embedded on the converter control computer. Such a computer has a digital processing engine such as a microprocessor and a memory. The asynchronous process was written in native C language and also running on the converter control computer having the processing engine. Communication happened over a buffer.

Referring to Figure 4, the path 19 of the software synchronous converter or inverter controller process 10 executed on a processing engine is shown. The relevant data 11 for inputting to the asynchronous optimisation process 20 are measured and/or calculated. This data is written in a step 12 to a buffer which is part of the synchronous process 10. Within the asynchronous process 20, the data is read in step 13 from the buffer. The asynchronous problem is constructed in step 14 and solved in step 15. In step 16 the solution is written to a buffer. In step 17 the solution is read into a buffer which is part of the synchronous process 10. In step 18 the asynchronous solution is adapted to the state of the synchronous process.

Overall implementation

Now that all components are determined, they can be brought together. Figure 5 shows an implementation as an embodiment of the present invention. The block‘Decompose’ 5 is as described with respect to Figure 3. The block‘Construct positive sequence’ 6 calculates Equation 3, e.g. using a digital processing engine. The gathered data is sent via a buffer to the optimization, which sends the results back to construct the solution. In this overview, only the optimization runs asynchronously. The blocks ‘Gathering data’ 7 and Optimization’ 8 depend on the actual solver being used and an example has been described with respect to Figure 4 e.g. using a digital processing engine. The construction of the solution is achieved according to Equations 1 and 2 in the“Construct Solution block” 9 e.g. using a digital processing engine.

Application to a converter control scheme

The implementation of Figure 6 shows a conventional converter control scheme without current redistribution: the PLL (Phase Locked Loop) uses the voltage measurement t/₁₂₃ to determine the grid-angle Q and passes this information, together with the voltage measurement, on to a current controller. Voltage measurement devices are shown as circled V’s. The current controller gets its settings from a power setpoint (P_set and Q_set)· The current controller then determines the voltage U_{123 sp} that needs to be applied by the converter, applying limits if the setpoint cannot be reached. The voltage setpoint is applied by the converter, using for example PWM (Pulse Width Modulation), thereby requiring the DC-bus voltage U_dc. The calculated switching states s₁₂₃ for the three legs are sent to and applied by hardware known to the skilled person. The neutral connection is, with this arrangement, not yet required.

Figure 7 shows an implementation of a current redistributing system according to embodiments of the present invention for compensating unbalance with a regular converter. This embodiment can be included in a converter controller having a processing engine. Voltage measurement devices are shown as circled V’s. The measurements are provided to a grid state-estimator 22 (e.g. an expanded version of a Frequency or Phase Locked Loop), whereby the positive, negative and zero-sequence of the voltages U_pnz are provided, as well as the frequency w. These can be derived with e.g. from a decomposer as shown in Figure 3 see also [5], [6].

The current /₁₂₃₀, resulting from the current redistribution provided by the current redistributor 24 according to embodiments of the present invention as described with reference to Figure 5 for example, is then sent to a conventional current controller, where the limiting action is no longer required. But now also the current from the neutral conductor needs to be controlled. From there, PWM signals are generated to control the switching elements in the converter. Figure 7 shows a parallel implementation, but other configurations are included within the scope of the present invention, for instance those in Figure 1. Note that the neutral connection is optional but preferred otherwise one cannot act on that conductor and as such, additional neutral measurements have to be included.

Results/Comparative data

Implementation

A measurement system provides the required information to the optimizer. The presented optimization is reformulated to an SOCP and is solved online with ECOS [28] as explained above. The generated set points are implemented and injected using a current controller. This control is implemented on the setup described in [9] .

In the tests presented below, the load is emulated using resistive light bulbs, resulting in a single phase load current of 4App, 2.8Arms on phase 2 and the neutral.

Explanation of the results

Results of embodiments of the present invention are described below wherein:

• Grid current [A] : The grid current is the current flowing in the (distribution) grid or after the point of common coupling. It is the sum of the load current and the inverter current. The grid current is made up of three phase currents (Ll, L2 & L3) and the neutral current (N)

• Load current [A]: The load current is the current of the load that is to be compensated. This can be any current, made up of any combination of loads and/or distributed generation and represents thus also the current flowing in a grid before any compensation. The load current is made up of three phase currents (Ll, L2 & L3) and the neutral current (N)

• Inverter current [A] : The inverter current is the current that compensates the load according to embodiments of the method of the present invention. It adheres to the boundary conditions applied and optimally compensates the load current. The inverter current is made up of three phase currents (Ll, L2 & L3) and the neutral current (N)

• Grid power [VA]: the grid power is calculated according to the method of [29] and is made up of three different orthogonal, independent components: o S: S is the apparent power and addresses the total burden on the grid. It is the‘sum’ of the different grid power components as S² =

+ P² + Q² o Du: is“a quantitative measure of the source current rms value increase due to the load asymmetry” [29] . It is thus a value that comprises the negative and zero sequence and can be used to quantify unbalance in one parameter o P: the amount of active power that is present in the grid (ideally as three- phase balanced positive sequence).

o Q: the amount of reactive power that is present in the grid (ideally as three- phase balanced positive sequence).

Results

To represent how and that the invention works, three embodiments are described. The unbalance compensation is always enabled at 0.05s, i.e. the first vertical line.

Complete compensation

In this embodiment, no limits are imposed on the inverter and it is capable of compensating the unbalance of the load completely. The results are visualized in Figure 8 showing complete compensation, no limits, enabled at O. ls. The grid current is reduced from a single-phase unbalanced load to a balanced three-phase load. This is clear from the absence of a neutral current at 0.5s and the decrease of Du to zero. It is also clear that P remains unaltered and S, the total power in the grid, decreases to P.

The converter or inverter is clearly injecting all the neutral current and the appropriate phase currents to compensate the negative sequence. Furthermore, as P and Q remain unaltered, it is also clear that unbalance compensation is achieved without injecting or consuming any (re)active power. These results demonstrate that embodiments of the present invention are able to perform unbalance compensation by current redistribution.

Compensation with limits

In this embodiment, limits are imposed on the inverter and thus its ability to compensate the unbalance of the load completely. The results are visualized in Figure 9 limit phase and neutral currents to lApp, enabled at 0.1 s. The limits on phase and neutral current are lApp and 0.7Arms. The grid current is reduced from a single-phase unbalanced load to a more balanced three-phase load, although the result is still unbalanced, due to the imposed limits. The neutral current is reduced by one amp, the maximum allowed by the limits and the current in phase 2 has decreased, while that in phase 1 and 3 has increased. The decrease of Du clearly shows that unbalance is compensated. P and Q remain unaltered and S also decreases.

The converter or inverter is clearly injecting the maximum of 1A per phase and in the neutral. Furthermore, as P and Q remain unaltered, it is also clear that unbalance compensation is achieved without injecting or consuming any (re)active power. This embodiment indicates that the imposing of limits works. The optimizer finishes in 11. lms.

Compensation with limits, while injecting current

In this embodiment, limits are imposed on the inverter and thus its ability to compensate unbalance, while the inverter is injecting balanced current itself. The results are visualized in Figure 10 enabled at O.ls. The limits on phase and neutral current are 2App, l.4Arms and the inverter is injecting 500VAr. The grid current is reduced from an unbalanced load to a more balanced load, although the result is unbalanced, due to the imposed limits. The neutral current is reduced and the current in phase 2 has decreased, while that in phase 1 and 3 has increased. The decrease of Du clearly shows that unbalance is compensated. P and Q remain unaltered and S also decreases.

The inverter is clearly injecting the maximum of 2A per phase and neutral. Furthermore, as P and Q remain unaltered, it is also clear that unbalance compensation is achieved without injecting or consuming any additional (re)active power, while still being able to inject the desired amount of reactive power. This embodiment indicates that imposing of limits function correctly, while being able to inject power. The optimizer finished in 10.8ms.

The current redistribution computer based method has been implemented on an actual 3ph+N inverter, including

• A functional and practical measurement system comparable to the measurement systems used in e.g. PV inverters, including a:

o Voltage measurement (three phases and optional neutral) at the terminals, indicated with a circled V on figure 6 and 7 o Current measurement (three phases and optional neutral) at the output of the inverter, indicated with a circuled ® on figure 6 and also on 7, which includes the additional measurement of the load).

• The hardware of a commercially available KEB inverter, which is similar to that which can be used in practical implementations, the basic configuration is shown in Figure 11. Two three-phase inverters were used: one for the three-phase currents and one for the neutral current (using all three inverter legs in parallel)

Figure 11 is a drawing of an inverter to which any of the embodiments of the present invention can be applied: on the left is the DC connection, which links to three identical half-bridges. Each halfbridge connected to an LCL-filter stage and then to the AC side.

An embodiment of the present invention has been implemented on a processing engine comprising a dual core 2.26 GHz PC with 4 GB of RAM. This is an embodiment of the present invention with controls on a rapid prototyping platform, the details of which can be found at https://triphase.com/products/overview/. The principle is shown in the Figure 12 This embodiment of the present invention can be implemented on a wide variety of microprocessors, CPU or GPU. In the setup used, the engineering PC is adapted to communicate with the control computer (having processing engine and memory) over a TCP/IP local area network. This control computer controls the inverter by calculating the setpoints and processing the measurements. The communication between the control computer and the inverter happens over a real-time fieldbus. The converter or inverter is the one shown in Figure 7.

This inverter- system was tested on the grid of an office building with realistic grid voltages and current unbalances and is able to inject current into this grid. The current redistribution on an operational inverter-system has been tested in a relevant environment, e.g. testing of a prototype in a realistic simulated operational environment.

Applications

Embodiments of the present invention can be implemented in all technical sectors which utilize three-phase inverters. These sectors include, for example

• renewable power generation sectors (PV, wind, micro-hydro-turbines),

• combined heat-and-power installations with variable speed gas turbines, • large electric loads in the residential and commercial building environment (heat pumps, air-conditioning, elevators)

• large electric loads in the industrial environment (variable speed drives in fans, compressors and pumps),

• electric vehicles (external mode 4 dc-chargers, on-board semi-fast mode 3 chargers),

• Residential and industrial electrical storage (batteries, supercapacitors, Li- capacitors, fuel cells ...), including UPS systems.

• Grid-connection inverters in PV-inverters, wind- turbines, micro-hydro-turbines and gas-turbines of CHPs: All these applications are de facto equipped with a grid- tied inverter.

• Variable speed drives in elevators, heat-pumps, air-conditioning in residential and commercial buildings: All these applications benefit from a grid-tied inverter, near 100% adaptation of grid-tied inverter.

• Variable speed drives for industrial fans, compressors and pumps with a grid- tied inverter: Currently only some 10% of these applications benefit from a grid- tied inverter, but a further reduction of throttling losses in the industry could increase the adaptation of grid-tied inverters to some 40-50%.

• Chargers for electric vehicles: Internal semi-fast chargers and external fast- chargers of electric vehicles are de facto equipped with a grid-tied inverter

• Electrochemical / Electrical storage in batteries, supercapacitors, Li-capacitors, fuel cells... These dc-devices are de facto equipped with a grid- tied inverter

Advantages of embodiments of the present invention include any, some or all of:

• Reduction of current unbalance in distribution grids: All grid- tied inverters can contribute to the reduction of current unbalance in the distribution grid. In practice a selected group of grid-tied is sufficient to reduce the current unbalance. The extra investment in the grid-tied inverter, required to transfer the current between phases and neutral, is compensated by the distribution grid-operator or other interested parties which benefit from the higher usable capacity in the distribution grid. In this scenario the maximum amplitude of the negative and zero sequence current is most likely a fraction of the positive sequence current. • Controlled current unbalance in own grid: The current unbalance in the own grid, introduced by large single-phase load/generation, is compensated by the grid-tied inverter, but the maximum amplitude of the negative and zero sequence current can be higher than the positive sequence current. For instance a single-phase 32 A EV charger is connected to the 20 A three-phase grid of a property; If the unbalance- compensating inverter can inject an additional 20 A in the EV phase and draw 10 A from the 2 other phases, the vehicle can still be charged.

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Claims

1. A method to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution, the method comprising the steps: decomposing load-current to outputs of at least negative- and zero-sequence components (I_neg and I_zer),

determining a positive-sequence component l_pos,inv,i) ^{as a} function of active power (P), reactive power (Q) and positive-sequence voltage (t/), and

determining a phase current, to be injected per phase and a neutral current, further comprising evaluating:

subject to:

and determining the phase current, to be injected for phase i according to:

and the neutral current according to:

^O,ίhn— cL_zI_zer

wherein

e_g = the negative sequence current

I_neg,i = the negative sequence current of phase i in complex notation

I_zer = the zero sequence current

I_Zer,i = the zero sequence current of phase i in complex notation I_ί,ίhn = the current through the converter leg connected to phase i

Io_,ίhn = the current through the converter leg connected to the neutral

Ic_Dmax I = the maximal phase current through the converter

Io,max = the maximal neutral current through the converter

a_n = variable for optimisation

a_z = variable for optimization

Ipos,inv,i = the positive sequence current of phase i

I_n = the negative sequence to be compensated

I_z = the zero sequence to be compensated

2. The method according to claim 1 subject to a_n £ 1

a_z £ 1

a_n ³ 0

a_z ³ 0 .

3. The method according to any previous claim, formulated as a second order cone problem.

4. The method according to any previous claim, wherein the three-phase converter is a series or parallel converter.

5. The method according any previous claim, wherein a load current is measured or estimated by calculation.

6. The method according any previous claim, wherein the at least negative- and zero- sequence components are in vector format.

7. A computer based system to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution, the system comprising: means for decomposing load-current to outputs of at least negative- and zero-sequence components ( I_neg and I_zer ),

means for determining a positive-sequence component l_pos,inv,i) ^{as a} function of active power ( P ), reactive power (Q) and positive-sequence voltage (U), and means determining a phase current, to be injected per phase and a neutral current, further comprising means for evaluating:

subject to:

I h,« — If,thac

| Io,i — IQ ,max and

means for determining a phase current, to be injected for phase i according

and a neutral current according to:

wherein

e_g = the negative sequence current

Ine_g,i = the negative sequence current of phase i in complex notation

I_zer = the zero sequence current

I_Zer,i = the zero sequence current of phase i in complex notation Iί,ίhn = the current through the converter leg connected to phase i

Io,ίhn = the current through the converter leg connected to the neutral

I< max = the maximal phase current through the converter

Io,max I = the maximal neutral current through the converter

a_n = variable for optimisation

a_z = variable for optimization

Ipos,inv,i = the positive sequence current of phase i

I_n = the negative sequence to be compensated

Iz = the zero sequence to be compensated.

8. The system according to claim 7, wherein the means for evaluating is subject to a_n £ 1

a_z £ 1

a_n ³ 0

a_z ³ 0

9. The system according to claim 7 or 8, wherein the three-phase converter is a series or parallel converter.

10. The system according to any of the claims 7 to 9, further comprising means for measuring a load current or means for estimating a load current by calculation.

11. The system according to any of the claims 7 to 10, wherein the at least negative- and zero-sequence components are in vector format.

12. The system according to any of the claims 7 to 11, wherein the means for evaluating is adapted to evaluate a second order cone problem.

13. A converter controller system comprising:

means for receiving values of 3 phase voltages of an electric grid, a grid estimator which takes the 3 phase voltages as an input and outputs positive, negative and zero sequence voltages, grid frequency, and grid-angle, a computer based system to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution according to a system of any of the claims 7 to 12, and

a current controller receiving output from the computer based system to determine unbalance compensating currents to be injected or consumed by a three-phase converter by current redistribution and for controlling switching elements of the three-phase converter.

14. A computer based method of converter control comprising the steps:

receiving values of 3 phase voltages of an electric grid,

grid estimating which takes the 3 phase voltages as an input and outputs positive, negative and zero sequence voltages, grid frequency, and grid-angle, determining unbalance compensating currents to be injected or consumed by a three- phase converter according to a method of any of the claims 1 to 6, and

controlling switching elements of the three-phase converter.