ADVANCED CONTROL STRATEGIES FOR THREE-PHASE GRID INVERTERS WITH UNBALANCED LOADS FOR PV/HYBRID POWER SYSTEMS Egon Ortjohann1, Alaa Mohd1, Nedzad Hamsic1, Danny Morton2, Osama Omari3 University of Applied Sciences South Westphalia/Division Soest, Lübecker Ring 2, 59494 Soest, Germany Email addresses: [email protected] , [email protected] , [email protected] 2 Bolton University, Deane Road, Bolton, U.K., Email address: [email protected] 3 The Arab American University, Jenin, Palestine, Email address: [email protected]

1

ABSTRACT: The application of renewable energy in power generation is steadily increasing. This rapid growth is supported by the recognition of these systems as an effective generation source with positive environmental and economical effects. A key element at the grid side of an isolated system is the inverter. This paper is concerned with the control strategies for three-phase voltage source inverters in PV/Hybrid power systems. The paper will first introduce the power system architecture of the system under study together with the different feeding modes. Further, the three-phase inverter topologies will be shortly discussed. Next, the paper attends to illustrate the control possibilities. The development of a four-leg inverter topology with a new advanced control approach based on symmetrical components is described briefly. Using this power electronics topology in combination with the developed control algorithms, the inverter performance can be improved. Simulation results obtained with the proposed control schemes are also presented. Keywords: Control strategies, Inverter, Hybrid. 1

INTRODUCTION

Traditional sources of energy are supplying the vast majority of the energy demand in most countries. The rapid growth of global climate change along with the fear of an energy supply shortage and limited fossil fuel is making the global energy situation tends to become more complex. The increasing demand for electric power than the offer along with many developing countries lacking the resources to build power plants and distribution networks and the industrialized countries that face insufficient power generation and greenhouse gas emission problem forces us to consider a better economical and environmental friendly alternative. Hybrid power systems (HPS) that use renewable energy sources (RESs) could be part of the solution [1,2,3]. A HPS is an electric power system that includes more than one type of energy conversion systems (ECSs). Different combinations of RESs, conventional energy systems, and storage systems may be used to construct HPSs. To specify the ECSs for a HPS, an optimisation process that takes into consideration the particular loads and meteorological conditions of the target area may be used [4,5]. In HPSs, Photovoltaic (PV) generators are often connected with other generators (e.g. wind turbine). Such systems include normally battery banks for storage, see figure 1. PV-HPSs are one of the solutions to the increasing energy demand as well as to the lack of electricity in non-electrified regions. They are safe, quite, reliable, expandable and need minimum maintenance. In addition, they are becoming more and more attractive financially as their cost continues to drop. An essential component at the grid side of such systems is the inverter due to the wide range of functions it has to perform. This includes, converting the DC voltage to sinusoidal current for use by the grid as well as the electricity flow management between the energy converting systems (ECSs), loads and power grid. Load condition has deep impacts on the design and performance of the power inverters used. In three-phase AC grids the inverter is required to feed unbalanced

loads as a symmetrical three-phase voltage source. This should also be possible under extreme unsymmetrical load conditions [6]. This paper introduces advanced control strategies based on symmetrical components in combination with power electronic inverters topologies that can supply unbalanced loads. This will be described briefly for gridforming, grid-supporting and grid-parallel feedingmodes, defined in [4].

Figure 1: PV-HPS with an inverter for unbalanced load conditions. 2

BACKGROUND

2.1 Feeding Modes A general philosophy to supply electric energy in isolated power systems through power electronic inverters is introduced in [4], see figure 2. The power produced by the ECS is fed through the DC-to-DC converter and after that this DC power is fed to the grid through the inverter. The inverter produces an AC output of a specific voltage magnitude and frequency. The intermediate capacitance is used to decouple the DC current flowing to the input terminal of the grid-inverter from the DC current flowing from the DC-to-DC converters of the ECS side.

Figure 2: System overview of the intermediate DC stage. The mismatches between these two currents result in variations in the voltage across the intermediate capacitance caused by changes in the capacitor’s current. This can be expressed using the following equation:

VC =

1 1 IC dt + VC ,0 = C C

∫

∫ (I

DC

− I INV )dt + VC, 0

(1)

These voltage variations can be utilised to control the power flow. The size of the capacitor is determined depending on the maximum possible mismatches between power production and power consumption. The voltage variations across the capacitor should be kept within the allowable ranges. This has two important characteristics. Firstly, it provides a decoupling between the voltages across the terminals of the ECSs from one side and the grid voltage from the other side. Secondly, it provides a decoupling between the frequency of the ECSs (in the case of AC energy conversion systems) from one side and the grid frequency from the other side. In this philosophy the power flow from an energy conversion source (ECS) into the grid may be driven by the grid or by the ECS itself [4,7] as summarised in Figure. 3. In a grid-driven feeding mode the flow of power from the ECS to the grid is controlled according to the requirements of the grid while in an ECS-driven feeding mode, the flow of power is controlled according to the requirements of the ECS itself. In the second case, ECSs are normally controlled to maximise their power production despite the requirements of the grid [7].

Figure 3: Feeding modes. The grid-driven feeding mode represents the active integration case while the ECSs-driven feeding mode represents the passive one. A grid-driven feeding mode may be realised through two different cases: Gridforming case and grid-supporting case, while an ECSdriven feeding mode may be realised through a gridparallel case [7]. An ECS in a grid-forming case is responsible for establishing the voltage and the frequency of the grid and maintaining them [8]. This is done by increasing or decreasing its power production in order to keep the power balance in the electrical system [7].

An ECS in a grid-supporting case produces predefined amounts of power which are normally specified by a management unit. Therefore, the power production in such a case is not a function of the power imbalances in the grid. Nevertheless, the predefined amounts of power for these units may be adjusted. The management system may change the reference values according to the system’s requirements and the units’ own qualifications [6]. The control strategy of the intermediate DC circuit is driven from the feeding modes definition. Therefore, in the grid-driven feeding mode the voltage across the capacitor is kept within the allowable ranges through controlling IDC current while keeping IINV free to change, see figure 4.

Figure 4: General control of a system operating in a grid-driven feeding mode (Forming, Supporting). An ECS in a grid-parallel case is a power production unit that is not controlled according to the requirements of the electrical system. RES’s such as wind energy converters and photovoltaic systems may be used to feed their maximum power into the grid (standard applications in conventional grids). In such a case, these systems are considered as grid parallel units [7]. For the ECSs-driven feeding mode control strategy the vice versa applies, IINV is controlled and IDC is free to change, see figure 5.

Figure 5: General control of a system operating in ECSsdriven feeding mode (parallel). 2.2 Three-Phase Inverter Topologies To bring the control strategies in relation to power electronic devices a short introduction of the different three-phase topologies is given. Three half-bridge single-phase arrangements can be extended to the three phase arrangement, one leg for each phase, see figure 6. In this case it requires that the three currents are a balanced three-phase set. However, this topology can be used to feed balanced loads only.

Figure 6: Three leg inverter without a neutral point (balanced output). Two configurations able to generate three-phase asymmetrical signals will be discussed. These are the three-leg neutral point build by capacitors and the fourleg inverter with a controlled neutral point by the fourth leg. Three-phase inverters with neutral point are an evolution from the single-phase ones. Three half-bridge single-phase inverters joined together can be seen as a three-phase neutral point inverter, see Fig. 7, where each output feeds one phase. This topology can be used to feed balanced or unbalanced loads. In case of unbalanced loads, the sum of the output currents ia, ib, and ic will not be zero and the neutral current will flow in the connection between the neutral point and the mid-point of the capacitive divider [4,9,10]. To maintain a symmetrical voltage across the two capacitors an adequate power electronic and a voltage stage management are needed, this will not be taken further into discussion.

space vector modulation to three-dimensional (3-DSVM) making the selection of the modulation vectors more complex. The 3-D-SVM of three-leg with neutral point inverter differ from that of the four leg inverter. Nevertheless, the control strategies are similar. A very efficient 3-D-SVM algorithm was developed and implemented as a part of this work but this will not be taken further into discussion here. 2.3 Sequence Decomposition For getting the actual values of current and voltage needed for the control unit of the inverters able to feed unbalanced loads, decomposition from three phase system to symmetrical components is needed. In [11] a controller based on symmetrical components for handling unbalanced conditions with a multilevel inverter was introduced. The authors described the sequence decomposition in details in [6] and it will not be repeated here. In the present work, sequence decomposition is used in the implementation of the four leg three-phaseinverter controller. Sequence Decomposition (SD) is able to represent an asymmetrical three-phase signal as a sum of positive, negative and zero sequence. Positive and negative components are three-phase symmetrical signals, while the zero sequence is a single-phase one. The relationship between the symmetrical dqcomponents corresponding to the three-phase unsymmetrical dq signals is given by the following equation:

⎡1 a ⎡V p _ dq ⎤ ⎥ 1⎢ ⎢ 2 ⎢V n _ dq ⎥ = .⎢1 a 3 ⎢1 1 ⎥ ⎢V ⎣ 0 _ dq ⎦ ⎣

(2)

where

Figure 7: Three-leg inverter with a neutral point. The general power electronic topology of the fourlegged inverter is shown in Figure. 8. The goal of the three-phase four-leg inverter is to supply a desired sinusoidal output voltage waveform to the load for all load conditions and transients. Compared with the fourleg inverter, the three leg inverter has a lower number of semiconductor switches and the control function can be built like three individual single line inverters. However the four-leg inverter still have the advantages of higher utilisation of the DC link voltage, small DC link capacitor as no zero sequence current flow across the DC link capacitor and an additional degree of freedom due to the 4th leg [10].

a 2 ⎤ ⎡V a _ dq ⎤ ⎥⎢ ⎥ a ⎥.⎢V b _ dq ⎥ 1 ⎥ ⎢V c _ dq ⎥ ⎦ ⎦⎣

a=e

j

2π 3

j

4π 3

2π 2π 1 3 + j sin =− + j 3 3 2 2

(3)

4π 4π 1 3 + j sin =− − j 3 3 2 2

(4)

= cos

and a2 = e

= cos

The phasors are defined in a complex dq-plane. The complete transformation process is represented in Figure 9.

Figure 9: Sequence decomposition [6].

Figure 8: Four-leg inverter. In general, three-leg inverter (See Figure 6) will use the two-dimensional space vector modulation (2-DSVM). On the other hand, the three-leg inverter with neutral point and the four leg inverter will extend the

3

CONTROL STRATEGIES

In the following sections, the known control strategies of symmetrical inverters will be briefly reviewed. Afterwards, the proposed control strategies for the asymmetrical inverters will be introduced.

Unfortunately, this will be done generally since the control fine points are associated to its applications. A number of detailed applications were presented by the authors in [6,7] and will not be repeated at this event. Still, more applications will be introduced in separate publications.

In the case of grid-parallel feeding mode, see figure 12, all of the produced active power by the ECS is passed to the grid through the inverter. The active power management is done in this application by the control of the voltage of the DC stage. The reactive power control is similar to the grid supporting case.

3.1 Control Strategies of Symmetrical Inverters The control strategy of a three-phase inverter in grid forming mode for balanced load is shown in Figure. 10. The inverter in this case determines the voltage and the frequency of the grid. There is one inner current control loop and a second voltage control loop. Both loops use only the d-component. The q-component of the current can not be influenced since the reactive part is depending on the load condition. Therefore, the q-component is not considered in this case. The reference angle for the dqtransformation is taken from the reference frequency.

Figure 12: Q-controlled inverter in grid parallel mode [4].

Figure 10: Inverter in grid forming mode for balanced loads [4]. The grid supporting unit for balanced loads feeds the grid with a specified amount of power, which might be active, reactive, or a combination of both, see figure 11. The control strategy for the grid supporting unit using active and reactive power has four controllers, two for the current (id and iq), and two for the power (P and Q). Active power, P, is controlled by the real part of the grid current “id“, while reactive power, Q, is controlled by the imaginary part ”iq“. Synchronization is implemented by the generation of the angle for the dq transformation from the voltage on the grid. Other control strategies for the grid supporting mode can be implemented straight forward through controlling the real and the imaginary components of the grid current or the magnitude of the voltage and the active component of the power fed into the grid.

3.2 Control Strategies of Asymmetrical Inverters The control strategy of the three-phase asymmetrical grid forming inverter is described lengthy in [6,12]. As a grid forming unit the inverter has to provide the voltage and the frequency of the grid. This is done as following. The voltage and the current sensed values are transformed from the abc-frame to the positive-negativezero dq sequence components. The controller block comprises current and voltage PI controllers for each component. Six controllers are needed for the voltage and the current components of the load. For the controller only the d-component of the positive sequence Vp_d_ref is considered. The other reference values are set to zero since the inverter has to supply symmetrical three phase voltage. The output reference values from the control unit are transformed to the αβγ-space and the SVM block uses them to calculate the pulse pattern for the switches. Figure 13, shows an inverter in grid forming mode for unbalanced loads. The control functions are described as vectors according to the following definition: ⎡V p _ d _ ref ⎤ ⎡V p _ d _ act ⎤ ⎢ ⎥ ⎢ ⎥ ⎢V p _ q _ ref ⎥ ⎢V p _ q _ act ⎥ ⎢V ⎥, ⎢V ⎥, n _ d _ ref ⎥ n _ d _ act ⎥ [V pn0 _ dq _ ref ] = ⎢ [V pn0 _ dq _ act ] = ⎢ ⎢Vn _ q _ ref ⎥ ⎢Vn _ q _ act ⎥ ⎢ ⎥ ⎢ ⎥ ⎢V0 _ d _ ref ⎥ ⎢V0 _ d _ act ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣V0 _ q _ act ⎥⎦ ⎢⎣V0 _ q _ ref ⎥⎦ ⎡V p _ d ⎤ ⎡ I p _ d _ act ⎤ ⎢ ⎥ ⎥ ⎢ ⎢V p _ q ⎥ ⎢ I p _ q _ act ⎥ ⎢V ⎥, ⎥ ⎢I n_d ⎥ ⎢ n _ d _ act ⎥ [V pn0 _ dq ] = ⎢ ⎢Vn _ q ⎥ [ I pn0 _ dq _ act ] = ⎢ I ⎥ n _ q _ act ⎢ ⎥ ⎥ ⎢ ⎢V0 _ d ⎥ ⎢ I 0 _ d _ act ⎥ ⎢ ⎥ ⎥ ⎢ ⎢⎣ I 0 _ q _ act ⎥⎦ ⎢⎣V0 _ q ⎥⎦

Figure 11: P, Q-controlled inverter in grid supporting mode for balanced loads [4].

In Figure 14, the controller layout is illustrated more clearly.

⎡ I p _ d _ act ⎤ ⎢ ⎥ [ I pn0 _ d _ act ] = ⎢ I n _ d _ act ⎥ , ⎢ ⎥ ⎣⎢ I 0 _ d _ act ⎦⎥ ⎡V p _ d ⎤ ⎥ ⎢ [V pn0 _ d ] = ⎢Vn _ d ⎥ , ⎥ ⎢ ⎣⎢V0 _ d ⎦⎥

Figure 13: Inverter in grid forming mode for unbalanced loads.

Figure 14: Controller layout of asymmetrical grid forming inverter. The asymmetrical grid supporting unit has to supply the grid with a specified amount of power, which might be active, reactive, or a combination of both as mentioned before. Synchronisation with the grid voltage is done by the voltage reference angle which has to be generated as in the symmetrical grid supporting mode. The desired amount of power has to be set by a management unit in positive, negative and zero sequence components. The power controller block generates a reference signal for the current controller. The current controller is delivering a reference voltage signal represented by positive, negative and zero sequence components. These reference values have to be transformed (composed) to the αβγ-space vector and the SVM block uses them to calculate the pulse pattern for the switches. Figure 15, shows a P, Q-controlled Inverter in grid supporting mode for unbalanced loads, where: ⎡ Pp _ ref ⎤ ⎢ ⎥ [ Ppn0 _ ref ] = ⎢ Pn _ ref ⎥ , ⎢ ⎥ ⎣⎢ P0 _ ref ⎦⎥

⎡Q p _ ref ⎤ ⎢ ⎥ [Q pn0 _ ref ] = ⎢Qn _ ref ⎥ , ⎢ ⎥ ⎣⎢Q0 _ ref ⎦⎥

⎡ Pp _ act ⎤ ⎢ ⎥ [ Ppn0 _ act ] = ⎢ Pn _ act ⎥ , ⎢ ⎥ ⎣⎢ P0 _ act ⎦⎥

⎡Q p _ act ⎤ ⎢ ⎥ [Q pn0 _ act ] = ⎢Qn _ act ⎥ , ⎢ ⎥ ⎣⎢Q0 _ act ⎦⎥

⎡ I p _ q _ act ⎤ ⎢ ⎥ [ I pn0 _ q _ act ] = ⎢ I n _ q _ act ⎥ , ⎢ ⎥ ⎣⎢ I 0 _ q _ act ⎦⎥ ⎡V p _ q ⎤ ⎥ ⎢ [V pn0 _ q ] = ⎢Vn _ q ⎥ ⎥ ⎢ ⎣⎢V0 _ q ⎦⎥

Other control strategies can be implemented simply through the real and the imaginary components of the grid current or the magnitude of the voltage and the active component of the power fed into the grid.

Figure 15: P, Q-controlled Inverter in grid supporting mode for unbalanced loads. Obviously, In the case of asymmetrical grid-parallel unit, shown in figure 16, the values that can be controlled are the flow of the reactive power or reactive current to the grid. In compare to the asymmetrical grid supporting notable is the active power control using Vdc and: ⎡ Pn _ ref ⎤ [ Pn0 _ ref ] = ⎢ ⎥, ⎣⎢ P0 _ ref ⎦⎥

⎡ Pn _ act ⎤ [ Pn0 _ act ] = ⎢ ⎥ ⎣⎢ P0 _ act ⎦⎥

Figure 16: Inverter in grid parallel mode for unbalanced loads. Nevertheless, the introduced controls functions can be easily extend to parallel operation mode. Several approaches have been proposed to do this. However, this is out of the scope of this study.

4

SIMULATION RESULTS AND DISCUSSION

Simulation models were implemented for the different feeding modes. The aim of the simulation work is to demonstrate the performance of the selected inverter topologies and their control strategies under different operation conditions and/or reference values. The following sections describe these results. 4.1 Symmetrical Inverters Figure 17 shows the response of a symmetrical grid forming unit to a change in the load from 15kw to 30kw at t=0.2 sec. At the moment of the load increase the peak of the voltage will experience a drop. The controller reacts against this drop and restores the voltage to it is original value within less than 0.03 sec. Furthermore, the output currents of the inverter start to increase instantly after the increase of the grid’s loads in order to satisfy the requirements resulting from this increase and to restore the grid’s voltage.

Figure 19: Asymmetrical grid forming inverter results. To test the asymmetrical grid supporting unit, a series resistive-inductive load was placed at phase “a” Ra = 10 Ω and XLa = 10 Ω (L = 32,4mH). The resistance at phase “b” has been kept constant at 10 Ω and a capacitive load was placed at phase “c” (C=1μF).When the active power requirements change from 10kw to 15kw the values of the inverter currents increase to satisfy the requirements. However, the voltages stay constant as specified by the grid. Notable is the constant neutral current which is related to the load it self and not to the change in the power requirements. See figure 20.

Figure 17: Symmetrical grid forming inverter results. Figure 18 presents a change in the active power requirements from 20kw to 40kw at t=0.35. The values of the inverter currents increase to satisfy the requirements increase unlike the voltages which are not influenced by the changes of the grid requirement. The grid itself specifies the voltages at the connection point. As long as the grid’s voltage is constant, the voltage at the connection point will stay constant.

Figure 20: Asymmetrical grid supporting inverter results. 5 CONCLUSIONS

Figure 18: Symmetrical grid supporting inverter results. 4.2 Asymmetrical Inverters As a testing case for asymmetrical grid forming, a series resistive-inductive load was placed at phase “a” Ra = 10 Ω and XLa = 10 Ω (L = 32,4 mH). The resistance at phase “b” has been kept constant at 10 Ω and the resistance of phase “c” has been varied in the range between 25 and 50 Ω at different time intervals, see Figure. 19. The reference voltage for the positive d component (Vp_d_ref) is set at 315V while the other reference values are set to zero. During this test the neutral current is not zero and the output voltage is almost a constant three-phase signal in amplitude and phase shift.

A key element at the grid side of a PV/hybrid power system is the inverter. This paper introduces varied opportunities of control functions for three-phase inverters used to feed grids with balanced/unbalanced loads. The different modes of feeding a grid were outlined. Detailed simulation models have been developed for the different units. The simulation results are presented to verify the performance and effectiveness of these control schemes. These results show that the proposed control schemes in combination with the different inverter topologies can carry out the feeding requirements of an isolated three-phase electrical power supply system efficiently. Furthermore, it can be pointed out, that the control functions for unbalanced loads are producing excellent results associated to symmetrical reference values. 6 ACKNOLEDGMENT This research work is supported by the FH3 Program

of the German “Bundesministerium für Bildung und Forschung” administrated by the “Arbeitsgemeinschaft industrieller Forschungsvereinigungen "Otto von Guericke" e.V. (AiF)”. 7

REFERENCES

[1] P.C. Ghosh , B. Emonts, H. Janßen, J. Mergel, D. Stolten. “Ten years of operational experience with a hydrogen-based renewable energy supply system”, Solar Energy 75, 2003, pp. 469–478 [2] R.Teodorescu, F.Blaabjerg. “Overview of Renewable energy systems”, Aalborg University, Institute of Energy Technology. [3] A. Bilodeau, K. Agbossou. Control analysis of renewable energy system with hydrogen storage for residential applications, Journal of Power Sources, 2005. [4] Osama Omari, “Conceptual Development of a General Supply Philosophy for Isolated Electrical Power Systems”, PhD Thesis, South Westphalia University of Applied Sciences, Campus Soest, Germany, February 2005. [5] S. Veradat, “Developing a General Optimisation Strategy for Hybrid Power Systems”, a master thesis submitted to Bolton Institute of Higher Education, April 2003, Bolton, U.K. [6] E. Ortjohann, A. Arias, D. Morton, A. Mohd, N. Hamsic, O. Omari. Grid-Forming Three-Phase Inverters for Unbalanced Loads in Hybrid Power Systems, IEEE 4th World Conference on Photovoltaic Energy Conversion, Waikoloa, Hawaii, May 2006. [7] O. Omari, E. Ortjohann, D. Morton S. Mekhilef. Active Integration of decentralised PV Systems in Conventional Electrical Grids, PV in Europe from PV Technology to Energy Solutions Conference and Exhibition, Mai 2005,Spain, Barcelona. [8] A. Engler, “Control of Parallel Operating Battery Inverters”, Photovoltaic Hybrid Power Systems Conference, Sep. 2000, Aix-en-Provence, France. [9] G. Seguier, F. Labrique., “Power Electronic Converters, DC-AC Conversion”, Springer-Verlag, Heidelberg, Germany, January 1993. [10] Said El-Barbari, W. Hofmann., “Digital Control of a Four Leg Inverter for Standalone Photovoltaic Systems with Unbalanced Load”, TU Chemnitz, Chemnitz, Germany. [11] C. Hochgraf, R. Lasseter., ”StatCom for operation with unbalanced voltages”, Electrical and Computer Engineering Department, University of WisconsinMadison, July 1998. [12] A.Arias. Standardized Control Functions for Modular Inverters in Isolated Power Systems. Master Thesis, South Westphalia University of Applied Sciences, Soest, Germany, November 2005.