GRID-CONNECTED PHOTOVOLTAIC POWER SYSTEMS: MODELING AND TOPOLOGY STUDIES

MIT/MIST Collaborative Research Progress Report for Period September-2011 to February-2012

Principle Investigator at MIT: Prof. J. Kirtley and Prof. D. Perreault

Principle Investigator at Masdar Institute: Prof. V. Khadkikar and Prof. W. Xiao

Research Project Start Date: September 1, 2010

INTRODUCTION

BackgroundThis research project focuses on the integration of PV solar power to the existing electric grid and addresses issues and possible solutions related with such interconnection. In this research work following aspects will primarily be considered:

To increase the performance of photovoltaic systems through the use of innovative system structures, advanced control and optimal power converter interfaces.

To develop an accurate computer simulation model of a grid connected PV plant with necessary controllers to perform maximum power extraction.

To study the potential issues as well as benefits if one or more renewable systems (combination of solar and/or wind plants) are connected on the same distribution feeder and/or nearby feeders.

It is our intention that this project will help (i) to better understand the influence of solar plant local distribution network, (ii) improve the overall performance of solar plants.

Objective and ApproachIn the third quarter of this research project (September-2011 to February-2012), following research objectives are being undertaken:

Construction of a DAB converter prototype with the modulation strategies and test the benchmark prototype under different load case including rated load, heavy and light load cases. (PI: Dr. Xiao, MI and Dr. Perreault, MIT)

Analysis of distributed power loss in DAB converter and elimination the reactive power. Analysis of the dc bus surge voltage and comparative evaluation of DC-Link Capacitors in DAB converter. (PI: Dr. Xiao, MI and Dr. Perreault, MIT)

An LCL filter design to enhance the performance of PV system with an active damping controller. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)

New control scheme to coordinate proposed interline-photovoltaic (I-PV) system. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)

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EXECUTIVE SUMMARY

This research project is based on the grid connected photovoltaic (PV) solar power plant. Two teams are involved out of which one team (Dr. Perreault, MIT and Dr. Xiao, MI) is focusing on the device level. The other team (Dr. Kirtley, MIT and Dr. Khadkikar, MI) is studying the integration aspects of PV solar plant to the main grid. During the third quarter of the joint research work, the following aspects are accomplished or under progress:

Regarding to the subproject “Design and prototyping of Dual Active Bridge Converter”, Two prototypes of DAB converter have been constructed. One prototype is used to evaluate the distributed power loss for the student thesis. The benchmark system has been tested under different load case including rated load, light load cases. Another prototype is used by Dr.Wen for loss reduction study. The modulation strategies have been implemented and the power loss analysis has been finished both for aspects of the hardware and software. The reactive power calculation has been analyzed and the way to eliminate reactive power in DAB converter is also investigated. The team has been working with several subtasks, such as reducing DC surge voltage/current, maximum power point tracking for PV systems, and high frequency AC power supply systems. This work results in several publications shown in the Publication section.

Dr. Perreault, please add here

PV system modeling and control: An LCL filter is designed to enhance the performance of PV system. Furthermore, in order to overcome the problem of possible resonance condition between L-C-L a new active damping technique is proposed. (Dr. Khadkikar and Dr. Kirtley)

Multifunction PV solar power plant operation: In the previous report, we have proposed a new system configuration for a large-scale PV solar plant, called as Interline-PV (I-PV) system. A new droop control method, given a name P-Q-V droop controller, to regulate the grid voltage using the I-PV system is developed. (Dr. Khadkikar and Dr. Kirtley)

A theoretical study of network reconfiguration of power distribution system is underway. The goal of this research is to propose a reliable and efficient topology of distribution network. Benefits, such as deferring the investment, reducing operation costs and improving energy efficiency of distribution systems, can be attained from the work. This work is carried out by Ms. Jiankang Wang under the supervision of Dr. Kirtley.

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RESEARCH TASKS

Task-1: Benchmark System Test and Power Loss Distribution Analysis (PI: Dr. Xiao, MI)

An experimental prototype is implemented using DSP 2808 control board. Main parameters are shown as following: the input voltage Vin = 32V, the input voltage range 28V – 36V, the nominal output voltage Vo = 320V, the maximum deliver power Pmax = 250W and the switching frequency 200 kHz. This work is delayed by approximately by 2 to 3 months due to the procurement process and budget freezing in summer. The research and prototyping is accordingly delayed due to the order of key components such as magnetic core and many experimental apparatus including adjustable DC power supply, adjustable load and impedance analyzer. Different load case including rated load, heavy and light load cases will be tested for this prototype and some experimental results will be presented to compare with the theoretical analysis. During the waiting time, the MI team was working with other related study including the effect of parasitic inductance, PV system modeling, Maximum power point tracking for PV systems. DC link capacitor optimization, and high frequency AC power supply systems. The PV modeling work was published by IEEE. Trans. On Sustainable energy. The voltage surge reduction work is accepted for publication on the IET journal. Another two journal submissions are waiting for review results.

Task-2: An LCL filter design to enhance the performance of PV system with an active damping controller. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)

This task is part of Objective-1 as mentioned in the original proposal. In this work we are developing an active damping method for an LCL filter based PV system to annul the effect of resonance on the system performance. This work has been delayed from the beginning of the project. However, the work has been progressing since from the hiring of Post-doc (Dr. Moin Hanif) for this project.

Task-3: Multifunction PV System: study potential benefits of one or more renewable energy systems connected two different feeders. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)

In the last two reports, we have provided initial results on a new system configuration that we have proposed for a large-scale PV system. Here idea is to connect a large-scale PV system to two different feeders/networks. The newly proposed system thus can enable to manage power flow on the two different feeders through PV solar power plant inverters. The inverter modules in a PV power plant are configured such that the system is represented as a back-to-back inverter connected multi-line system,

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called as Interline-PV (I-PV) system. In this report, newly developed P-Q-V droop control method for I-PV system is presented. This task is mentioned as “Part A: Objective-2” in the original proposal.

CURRENT REPORTING PERIOD SUMMARY (MARCH 2011 TO AUGUST 2011)

Task 1: Weidong, please add here (Dr. Perreault and Dr. Xiao)Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr.Wen, and Yosief Abraham (graduate student)

The high circulating current in the transformer is the drawback of the DAB converter. At light load, this circulating current increases the conduction losses and causes the converter to lose the natural zero-voltage switching feature. Thus, the test of the benchmark prototype under different load case including rated load, heavy and light load cases is necessary to comprehensively assess the performance of the prototype.

The simulation model based on PSIM and simulink has been created and compared with the experiment tests. Calculation and analysis of the DAB converter overall power losses will be performed. The mathematical model of the reactive power will be defined corresponding to different modulation strategies. Traditional phase-shift control strategies introduce large reactive power and contribute to large peak current and large system loss. Thus, the proposed control strategy will eliminate reactive power in DAB converter.

For DAB converter, the DC bus can experience large surge voltages due to the presence of parasitic inductance in addition to the hard-switching operations of voltage source inverters. The unexpected transient overvoltage can result in switching device failures. A surge voltage model need to be developed that takes into account the commutation loop inductances and the switching dynamics. An optimal design approach to lower the stray inductance will be presented. In DAB converter, sizing and selection of DC link capacitors involve tradeoffs among system performance including lifetime, reliability, cost, and power density. A comprehensive and comparative study on the DC-link capacitor applications and evaluations to meet the above requirements is investigated. The analysis should consider the facts of capacitor power loss, core temperature, lifetime, and the battery ripple current limit, which are critical for PV applications.

Please see Appendix-1 for more details.

Task 2: Development of PV Solar Plant Model (Dr. Kirtley and Dr. Khadkikar)Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate students: Deema Al Baik and Ammar Elnosh; Post-doc: Dr. Moin Hanif

This work is intended to develop a generic PV solar power plant simulation model. The develop model will serve as a benchmark simulation model for future research work at MI and MIT.

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Two MI graduate students, Ms. Deema Al Baik and Mr. Ammar Elnosh, are working on the PV solar plant model development. Ammar is focusing on developing an improved maximum power point tracking (MPPT) algorithm including PV solar array modeling. The MPPT work is ongoing and we expect to complete it in next 2-3 months. The details on MPPT will be provided in the next report.

Deema is also working on PV solar plant model development. However, her goal is on the AC side of the network. Part of her work was reported in the last report. Currently she is working on LCL filter design with an improved active damping method.

Dr. Moin Hanif has joined the MI research group in the month October-2011. He is also working on developing an active damping controller for LCL filter. Summary of ongoing work is given in Appendix-2.

Task 3: Multifunction PV System (Dr. Kirtley and Dr. Khadkikar)Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate student: Ahmed Moawwad

At the beginning of this project, we (Dr. Khadkikar and Dr. Kirtley) have proposed a new system configuration for a large-scale PV plants, given a name as “Interline PV (I-PV)” system. One of the graduate students at Masdar Institute (Ahmed Moawwad under supervision of Dr. Khadkikar) is working on detailed study on the proposed I-PV system. We have accomplished significant advancement in this research work and a journal paper has been submitted. A new droop controlled method, called as P-Q-V droop method is proposed to regulate the grid voltage at point of common coupling. The research findings are submitted for the possible publication in IEEE Transactions on Power Delivery. The submitted paper details are given in Appendix-3.

Task 4: High Efficiency DC-DC Converters

To connect photovoltaic panels to the grid, interface circuitry is needed. In the architecture pursued in this project, DC/DC converters are used to boost voltage of individual photovoltaic panels to a high dc-link voltage, and one or more inverters are used to convert DC to AC. These DC/DC converters have to be designed with very high efficiency. In Fig. 1, the block diagram of a grid connected PV system is shown. The focus of this project is on the DC/DC power converter. In conventional, hard switched power converters the overlap of current and voltage is large during switching resulting in significant power loss. Soft switching is achieved by resonant topologies which decrease switching losses by Zero Voltage Switching (ZVS) or Zero Current Switching (ZCS). However, the magnetic loss increases with the additional magnetics needed for soft switching and a tradeoff of these two losses is necessary to achieve minimum overall loss.

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Figure 1: Block diagram of a grid-connected PV system

Details of this work are in Appendix-4.

Unscheduled Task: Distribution System Reconfiguration

A strong motivation of the research topic is generated by the critical role of distribution network in the whole power system and the challenges it has been facing during the recent several decades. As the final stage of electricity delivery to end users, it is consist of over 65% of US power network [32]-[34]. Renewable energies installed in the form of Distributed Generation (DG) and demand response show their influence on the whole power system through the distribution system. The aging infrastructure, yearly increasing demand, and upcoming new technologies of distribution systems raise the question of how to operate and reinforce the distribution network in a reliable and economic way to fulfill all the requirements.

The problem is traditionally addressing by reinforcing distribution network based on the so-called “fit-and-forgot” policy [35]. The “fit and forget” approach implies the design of the distribution system so as to meet technical constraints in the most onerous conditions (e.g. full generation/minimum load or no generation/full load) even if such situations have a small probability of occurrence. One advantage of this approach is that control problems were solved at the planning stage. However, under rapidly growing demand and targets of integrating DG, this practice of passive operation can be very costly or it will limit the capacity of distributed generation that can be connected to an existing system [36].

In contrast, network reconfiguration, which alters the network topological structure by changing the open/close status of the sectionalizer and tie switches, actively maximizes the use of existing circuits [37].With reconfiguration, distribution systems can keep the redundancies of extra feeders for contingent cases in long-term and operate in optimal radial structure. In addition to existing control on generation and demand, reconfiguration adds another control dimension by making network structure a dispatchable resource.

In spite of many studies on operation strategies of reconfiguration, there are few of them considering reconfiguration in the planning stage [38], [39]. However, since reconfiguration can be resource of improving operation, considering its role in planning has a great potential to save capital investment in generators, transformers and etc. In addition, the reconfiguration flexibility of a distribution system is

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determined at its planning stage. Planning reconfiguration capability together with other power distribution components may save cost and improve efficiency of operation.

During this reporting period, my study mainly includes using reconfiguration to (1) guarantee the required reliability while reducing the capital investment in distribution system planning; (2) mitigating the deterioration of voltage profile caused by DG insertion. Comprehensive literature review about reconfiguration algorithms and distribution system automation was conducted. Methodologies and results of the studied two problems are summarized in the following sections. Simulations have been conducted to verify the results.

2 OBJECTIVES AND METHODOLOGIES

2.1 Objectives The overall objectives of this research can be summarized in the following points:

Proposing and demonstrating a planning scheme that fulfills the long-term and short-term requirements of distribution system.

Proposing a closed-loop planning scheme that consider and optimize the operation flexibility induced by reconfigurable network structure.

Investigating into the controllability of distribution system induced by reconfiguration.

These objectives will be addressed at the close of this research. The challenges to modern distribution networks can be interpreted as the conflicts of its short- and long-term requirements. In short-term, we want distribution networks to operate efficiently with fewer redundancies planned as possible. In long-term, however, the redundancies are needed to ensure reliable performance of networks with uncertainties induced from DG and time-varying loads. Deploying reconfiguration can exploit the existing circuits and mitigate many operation problems of distribution systems; meanwhile, it retains multiple configurations that can satisfy various system conditions. Due to these benefits, some investment may be unnecessary given reconfigurable networks. And these benefits are expected to be maximized in both short- and long-term if networks’ reconfiguration ability is well planned. Therefore, exploring reconfiguration’s effects on distribution system operation and optimizing it at the planning stage will close the loop.

2.2 Methodologies During this reporting period, my study mainly includes using reconfiguration to (1) guarantee the required reliability while reducing the capital investment in distribution system planning; (2) mitigating

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the deterioration of voltage profile caused by DG insertion. Their methodologies are discussed separately in the following subsections.

2.2.1 Optimizing Reconfiguration’s Impacts on Distribution System Planning This section briefly states the methodology of the first problem, using reconfiguration to ensure required reliability while reducing distribution system planning cost.

In last reporting period, I have shown that reconfiguration can provide larger contingency support neighborhood and thus save huge investment on transformers’ capacity and reduce the no-load loss of substations. A paper was published under the topic [40].

Following the study, customer service quality indicated by reliability of distribution systems planned is taken into account in the reporting period. Reconfiguration generates a larger contingency support neighborhood that in turn pushes upward the utilization rates of equipments. However, the probability that an outage will occur among the designated support units is increased at the same time [41].

Suppose that the area of the power system being considered has 88.5% loadings on all transformers, instead of 66%. In that case, when any transformer fails, and if the utility is to keep within a 133% overload limit, a failed unit's load has to be spread over two neighboring transformers, not just one. The size of the "contingency support neighborhood" for each unit in the system has increased by a factor of fifty percent. In a system loaded to 66%, there is only one major target. In a system or area of a system loaded to 88.5%, it occurs if a unit and either one of two neighbors is out. In an area of a system loaded to over 100% (as some aging areas are) it occurs whenever the unit and any one of three designated neighbors is out. But there are still Single Contingency Policy (SCP) (i.e. N-1) neighborhoods: each can tolerate only one equipment outage and still fully meet their required ability to serve demand. A second outage will very likely lead to interruption of service to some customers. In these larger neighborhoods, there are more targets for that second outage to hit. 'Trouble" that leads to an inability to serve customer demand is more likely to occur.

For this reason, reliability measured by System Average Interruption Duration Index (SAIDI) is used to constrained the distribution system plan proposed in study of last period [9]. LP models are developed to find the optimal decisions for the above problems.

The main implications of this study are: (1) enabling reconfigurable feeders can increase reliability with lower capital investment and operational cost when comparing to reinforcing transformer capacity; (2) the reliability of a set of well interconnected substations depends on the max-shortage of one of its substations, failure rates of units in the support neighborhood and size of the support neighborhood. The two implications disprove the statements in previous works [42], [43]. The approach used and the results obtained are currently being drafted in a paper.

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2.2.2 Optimizing Reconfiguration’s Impacts on Distribution System Integrated with Distributed Generation This section summarizes the methodology and results of the second problem, using reconfiguration to improve voltage profiles of distribution systems integrated with Distributed Generation (DG).

This study was initiated in July, 2011 and falls into two sub-problems: (1) quantifying the dependency of voltage profiles on DG’s insertion in terms of system voltage level, location, power capacity and dispersion level, and (2) demonstrating reconfiguration’s improvement on systems’ voltage profiles in theory and practice/ simulation.

When generators are connected to a feeder, voltage profile is likely to increase. According to ANSI, voltage of distribution systems are limited to in normal operation. Overvoltage of the standard

will decrease lifetime and even cause failure of equipments [44] The generator voltage can be

approximately given by , where is the substation bus voltage, and

are the active and reactive power injected in the generator bus, and and are the

feeder resistance and reactance. To mitigate the voltage rise, traditional methods include to [14]:

Reduce the primary substation voltage Allow DG to import reactive power Install auto transformers, or voltage regulators Increase the conductor size of feeders Constrain the generator at times of low demand

Compared the aforementioned methods, our study employs reconfiguration to changes the topology of distribution network, and thus to change and to affect the voltage profile. This method is verified with high implementation easiness, two to ten times low cost and 10-30% high effectiveness.

Until the reporting period, a DC circuit model, which may be extended to balanced 3-phase model easily, is built to for sub-problem (1), and simulations are conducted for sub-problem (2). The main implications of the study are:

1. Voltage profile of a feeder can be calculated with area criteria [46].2. DG has greater impact on voltage profile of a feeder when inserted at farther end of the feeder.

Therefore, to mitigate overvoltage induced:a) Curtailment of output of DG’s at farther end of a feeder should be firstly considered.b) A demand response program should be designed to give stronger incentive on customers at

farther end of a feeder.3. The maximum value of voltage on a feeder can be calculated with the proposed analytical

expression, and is determined at the position where current changes direction and supplement current density is negative.

4. Dispersion level of DG can have either positive or negative impact on voltage profiles, depending on DG’s location on a feeder.

A paper is drafted to include the results. Theoretic part of sub-problem (2) is under development.

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This study is a part of reconfiguration’s impacts on distribution system operation, which aims at investigating the relation of system topological flexibility and reconfiguration benefits. Results of the study are the basis of proposing a closed-loop planning scheme, which is the final purpose of my thesis.

3 CONCLUSIONDeploying reconfiguration can exploit the existing circuits and mitigate many operation problems of

distribution systems; meanwhile, it retains multiple configurations that can satisfy various system conditions. Due to these benefits, some investment may be unnecessary given reconfigurable networks. And these benefits are expected to be maximized in both short- and long-term if networks’ reconfiguration ability is well planned.

FUTURE WORK (MARCH 2012 TO AUGUST 2012)

Task 1: Comprehensive evaluation of the Benchmark prototype and analysis of the power loss and reactive powerResearch team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Imran Syed (graduate student)

This part of the project involves three main areas which include:

Testing Power loss analysis Reactive power analysis

• Testing: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI). The study will focus on the DC microgrid applications to adopt on-site PV generation and battery backup systems. The pilot project will be located in the field station of Masdar Institute. Detailed work can be found in Apendix 1-1.

• Power loss analysis: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI).The Masdar team will focus on the embedded software implementation

• Reactive power analysis: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI).

Task 2 : Novel modulation strategy investigation for DAB converter Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Imran Syed (graduate student)

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This work focuses a simplified dual-phase-shift (SDPS) control strategy for DAB converter in whole operation range is analysis. The work includes analysis the analytical expression of the average output power, the reactive power, the rms and peak current based on the switching strategy. The soft-switching conditions will be analyzed and compared with the traditional PS control. The DAB converter power loss will be calculated and the algorithm to minimize the total power loss will be discussed. Simulations and experiments are expected to be carried out to verify the analysis. Details can be found in appendix 1-2.

Task 3 : Development of PV Solar Plant Model (Dr. Kirtley and Dr. Khadkikar) Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate students: Ammar Elnosh and Deema Al Baik, Post-doc: Dr. Moin Hanif

This work is delayed by 4 to 6 months. However, there is a steady progress since the hiring of Dr. Moin Hanif. The project objective-3 in the original proposal is to validate some of the research findings using a hardware PV system. We expect the installation of a 5kW PV system at Masdar Institute (using actual PV panels) will be done in the month of March/April – 2012.

In the next stage of the project we plan to finalize the following research aspects:

Development of improved MPPT technique (student involved: Ammar)

Active damping controller to improve the harmonics generated by the PV solar plant (student involved: Deema and Dr. Moin)

Perform the initial experimental studies to validate some of the research objectives. (Dr. Moin and Dr. Khadkikar)

Task 4 : Multifunction PV System (Dr. Kirtley and Dr. Khadkikar) Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate student: Ahmed Moawwad

This task is almost completed. So far, two conference papers are resulted from this research work. A journal paper is in under review. Furthermore, we will be concluding this task by providing an additional functionality where an unbalance in the grid voltages will be compensated using I-PV system. An additional conference is expected from this last piece of the research work.

PUBLICATIONS/PRESENTATIONS

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1. V. Khadkikar and J. Kirtley, “Interline Photovoltaic (I-PV) Power System – A Novel Concept of Power Flow Control and Management”. In the conference proceedings of IEEE PES General Meeting, 24-28 July, 2011, pages 1-6. (Included in Report-I)

2. A. Moawwad, V. Khadkikar, and J. Kirtley, “Photovoltaic Power Plant as FACTS Devices in Multi-Feeder Systems”. In the conference proceedings of Industrial Electronics conference (IECON-2011), 7-10 Nov. 2011, pages 1-6. (Included in Report-II)

3. D. Al-Baik and V. Khadkikar, "Effect of variable PV power on the grid power factor under different load conditions". In the conference proceedings of IEEE Electric Power and Energy Conversion Systems (EPECS), 15-17 Nov. 2011, pages 1-5. (Included in Report-II)

PUBLICATIONS/PRESENTATIONS

[1] Y. Mahmoud, W. Xiao, and H. H. Zeineldin, "A Simple Approach to Modeling and Simulation of Photovoltaic Modules," IEEE Trans. Sustainable Energy, vol. 3, pp. 185-186, 2012. (Published).

[2] H.Wen, W. Xiao, H. Li, and X. Wen, "Analysis and Minimization of DC Bus Surge Voltage for Electric Vehicle Applications," Electrical Systems in Transportation, IET, 2011. (Accepted)

[3] H. Wen, W. Xiao, X. Wen, and P.R. Armstrong, "Analysis and Minimization of DC-Link Capacitance for Electric Vehicle Application," IEEE TRANSACTION ON VEHICULAR TECHNOLOGY, 2011. (The Second Review)

[4] H.Wen, W. Xiao, and Z. LU, "Current-Fed High-Frequency AC Distributed Power System for Medium-High Voltage Gate Driving Applications," IEEE Transactions on Industrial Electronics, 2011. (Under Review)

[5] Y. Mahmoud, W. Xiao, and H. H. Zeineldin, “A New Parameterization Method for Single Diode photovoltaic Models”, submitted to IEEE Trans. Sustainable Energy in Jan 2012, (Under Review).

[6] H. Wen, W. Xiao, Xuhui Wen, “Comparative Evaluation of DC-Link Capacitors for Electric Vehicle Application," accepted for the presentation in the 21th IEEE International Symposium on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012.

[7] Huiqing Wen, Weidong Xiao, Han Li, and Xuhui Wen, “Analysis and Minimization of DC Bus Surge Voltage for Electric Vehicle Applications," accepted for the presentation in the 21th IEEE International Symposium on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012.

[8] W. Xiao, H. Wen, and H.H. Zeineldin, “Affine Parameterization and Anti-Windup Approaches for Controlling DC-DC Converters”, accepted for the presentation in the 21th IEEE International Symposium on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012.

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[9] Y. H. Abraham, X. Weidong, W. Huiqing, and V. Khadkikar, "Estimating power losses in Dual Active Bridge DC-DC converter," in Electric Power and Energy Conversion Systems (EPECS), 2011 2nd International Conference on, 2011, pp. 1-5 (Published).

[10] W. Xiao, A. Elnosh, V. Khadkikar, and H. Zeineldin, "Overview of maximum power point tracking technologies for photovoltaic power systems," in 37th Annual Conference on IEEE Industrial Electronics Society, 2011, pp. 3900 (Published).

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APPENDICES (IF ABSOLUTELY NECESSARY)

Appendix-1: Benchmark System Test and Power Loss Distribution Analysis (PI: Dr. W Xiao)The first prototype of DAB converter has been constructed in the Laboratory of MIST. Tests have been done for different phase shift angle and load. An experimental prototype was implemented using DSP 2808 control board. Main parameters are shown in table I and figure 1 shows the schematic of a single phase DAB converter.

Table I

Circuit Parameters of the Dual Active Bridge DC-DC Converter

Rated Power 300Rated Input Voltage 32V

Rated output Voltage 320VInput Capacitor 100uF

OutputCapacitor 22uFTransformer turn ratio 1:6

Inductor 2.5uHFrequancy 200KHz

conversion ratio 1

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A simulation model for a microgrid has been created using PSIM/Simulink. Ideal voltage and current waveforms using the Phase-Shifted modulation for the boost and buck mode of operation have been simulated and analyzed. Different load case including rated load, heavy and light load cases are test for this prototype and some experimental results are presented to compare with the theoretical analysis. Figure 2 and figure 3 show the ideal voltages and current waveforms using the PS-M for the hard switching mode and the soft switching mode of operation.

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TDDD

16 | P a g e

Fig.5 Ideal voltages and current waveforms using the PSPM for

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1TV

2TV

Li

2d

1d

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

12

13

22

23

DDDD

12

13

22

23

TTTT

12

13

21

23

TTDT

11

13

21

23

DTDT

2d 2xt

9 10

11

13

21

24

DTDD

11

14

21

24

DDDD

11

14

21

24

TTTT

11

14

21

23

TTTD

11

13

21

23

TDTD

11

13

22

23

TDDD

1d

Fig.6 Ideal voltages and current waveforms using the PSPM for .

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1TV

2TV

Li

2d

1d

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

12

13

21

23

DDTD

12

13

21

23

TTDT

12

13

21

24

TTDD

11

13

21

24

DTDD

2d 2

2 1d d

xt9 10

11

13

21

23

DTDT

11

14

21

23

DDDT

11

14

21

23

TTDT

11

14

22

23

TTDD

11

13

22

23

TDDD

11

13

21

23

TDTD

17 | P a g e

Fig.7 Ideal voltages and current waveforms using the PSPM for .

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1TV

2TV

Li

2d

1d

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

12

13

21

23

DDTD

12

13

21

23

TTDT

11

13

21

23

DTDT

11

13

21

24

DTDD

2d 2

2 1d d

xt9 10

11

13

21

23

DTDT

11

14

21

23

DDDT

11

14

21

23

TTDT

11

13

21

23

TDDT

11

13

22

23

TDDD

11

13

21

23

TDTD

Fig.8 Ideal voltages and current waveforms using the PSPM for .

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1TV

2TV

Li

2d

1d

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

12

13

22

23

DDDD

12

13

22

23

TTTT

12

13

21

23

TTDT

11

13

21

23

DTDT

2d 2

2 1d d

xt9 10

11

13

21

24

DTDD

11

14

21

24

DDDD

11

14

21

24

TTTT

11

14

21

23

TTTD

11

13

21

23

TDTD

11

13

22

23

TDDD

Fig.9 Ideal voltages and current waveforms using the PSPM for .

18 | P a g e

The high circulating current in the transformer is the drawback of the DAB converter. At light load this circulating current will increase the conduction losses and causes the converter to lose the natural zero-voltage switching feature. Thus the test of the benchmark prototype under different load case including rated load, heavy and light load cases is necessary to comprehensively assess the performance of the prototype. The simulated waveform is shown in the following Figures including traditional PS-M and other modulation strategies.

0 5 10 15-40

-20

0

20

40

Time (us)

v r1 (V

)

0 5 10 15

-20

0

20

Time (us)

v r2 (V

)

0 5 10 15

-20

-10

0

10

20

Time (us)

i Llk (A

)

Fig. 10 Waveforms using the conventional control strategy for phase angle 90°

0 5 10 15-40

-20

0

20

40

Time (us)

v r1 (V

)

0 5 10 15

-20

0

20

Time (us)

v r2 (V

)

0 5 10 15

-10

0

10

Time (us)

i Llk (A

)

Fig.11 Waveforms using the conventional control strategy for phase angle 45°

19 | P a g e

0 5 10 15-40

-20

0

20

40

Time (us)

v r1 (V

)

0 5 10 15

-20

0

20

Time (us)

v r2 (V

)

0 5 10 15

-10

0

10

Time (us)

i Llk (A

)

Fig.12 Waveforms using the conventional control strategy for phase angle 30°

0 5 10 15-40

-20

0

20

40

Time (us)

v r1 (V

)

0 5 10 15

-20

0

20

Time (us)

v r2 (V

)

0 5 10 15

-10

0

10

Time (us)

i Llk (A

)

Fig.13 Waveforms using the conventional control strategy for phase angle 15°

0

-5

-10

5

10

Ir-8.0676929e+000

0.19998 0.199985 0.19999 0.199995 0.2Time (s)

0

-20

-40

20

40

Vr1 Vr2/6

(a)

20 | P a g e

0

-5

-10

-15

5

10

15

Ir-2.6541422e+000

0.19998 0.199985 0.19999 0.199995 0.2Time (s)

0

-20

-40

20

40Vr1 Vr2/6

(b) Fig.14 Waveforms using the novel modulation strategy

Test Setup is shown as following:

(a) Dab prototype (b) DSP control board

(c) Power supply (d) Load

Fig.15 Experiment Test Setup

21 | P a g e

The efficiency of the DAB depends on power transfer , the input and output voltages and the difference between them for example if the voltage drops along with discharge of the energy storage device , power loss increases at a given power transfer . Experimental Waveforms are shown as following: The power transferred at the given value and phase shift angle of 45o for input

voltage and output voltage , is found as 135.5 W theoretically .

Fig.16 Experiment Result1(Vout=106.7W,d=0.8182)

22 | P a g e

Fig.17 Experiment Result2(Vout=91.8W,d=0.8734)

Appendeix 1- 2: Analysis the distribution of power loss in DAB converter and elimination the reactive power. Analysis of the dc bus surge voltage and comparative evaluation of DC-Link Capacitors in DAB converter. (Dr. Perreault and Dr. Xiao)Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Yosief Abraham (graduate student)

The expression of leakage inductor current for each time interval has also obtained. Soft-switching constraints for both bridges are also derived. Power losses in MOSFETs, diodes and transformer are calculated. The power losses in DAB can be classified as the switching and conduction losses. The switching losses in semiconductor devices are due to continuous switching (on and off) transitions during which a device is simultaneously exposed to high voltage and current. Although the DAB naturally operates in zero voltage switching (ZVS), it operates in ZVS only during “ON” switching transition. The conduction losses in DAB can further be classified as the conduction losses that occur in the semiconductor devices (MOSFETs) and the transformer and inductor losses. The switching losses in MOSFETs can be calculated from the following formula:

Where fsw is the switching frequency, VDS and IDS are the voltage and current at the time of switching, respectively, and ton and toff are time intervals during switching ON and OFF, respectively. Note that the power loss Psw represents the amount of power loss for one switch per leg during the ON switching transition. Similarly, the losses for the OFF transition can be calculated. Hence to calculate the total switching losses for bridge 1, for example, we can multiply Psw by 4 assuming the bridge has either on state or off state losses. The switching transition time can be calculated with the help of the device data sheet. To calculate the conduction losses, the losses due to the R_DS(on) and the voltage drop across the anti-parallel diode are based on the data sheet. For example, for bridge 1, on resistance of the MOSFET, R_DS(on) =8.2mΩ and the anti-parallel diode forward voltage drop, V_f=1.2V. Hence the conduction losses can be calculated in as:

The RMS current values for both the body diodes and the MOSFETs are calculated from the inductor current waveform depicted through the respective components. Fig.4 shows the different conduction time intervals for the switch .The dead time has a life time D1 hence the body diode conducts during

23 | P a g e

this time interval contributing to the power losses , in the remaining segments(D 2, D3, D4) the MOSFET conducts. The RMS currents for both the body- diode and MOSFET are estimated using (4) and (5).

𝐷3 𝐷1 𝐷2 𝐷4

𝜔𝑡

𝑖𝐿

𝐼1

Fig.18. The different conduction time intervals of the inductor current through the bridges

The reactive power is defined corresponding to different modulation strategies and the corresponding equations are derived. Traditional phase-shift control will induce large reactive power and contribute to large peak current and large system loss. The control strategy to eliminate reactive power in DAB converter is investigated.

Considerably minimized converter power loss can be achieved with the use of alternative modulation strategies, which are basically originated from the variation the duty ratio of the H-bridge output voltage and the phase shift angle. A phase-shift plus pulse width modulation (PSPWM) control strategy is presented in [3] and one more degree of control freedom is added to extend the ZVS range. A optimal selection of phase shift angle and modulation duty ratio, useful to minimize overall converter loss, is analyzed in [4]. But the duty ratio of the gate signals is variable and calculated online, besides, the calculation of duty ratio is dependent on the plow flow direction and buck/boost operation modes. All these factors result in the complexity of the PSPWM control. A double-phase-shift (DPS) control is proposed to reduce the reactive converter power [5]. This control includes two phase-shift angles, which are phase-shift between the primary and secondary side of the transformer and phase-shift between the gate signals of the diagonal devices of the same side. But it doesn’t full consider the efficiency improvement, besides, the analysis of reactive power is not completed due to the complexity. The experimental comparison of PS and DPS control is presented in [6]. The efficiency improvement is not good as expectation in [5] due to the lack of systematic analysis of power loss distribution. In [7], the phase-shift trajectories for the minimal reactive power, the minimal rms and peak current are analyzed. But due to more control parameters and complex operation modes, the expression of reactive power is extreme complicated and the optimal design is not easy to implement. Thus, a simplified dual-phase-

24 | P a g e

shift (SDPS) control strategy for DAB converter in whole operation range is analysis. The analytical expression of the average output power, the reactive power, the rms and peak current are derived based on the switching strategy. The soft-switching conditions are analyzed and compared with the traditional PS control. The DAB converter power loss is calculated and the algorithm to minimize the total power loss is proposed. Simulations and experiments are carried out to verify the analysis.

In Fig.16 the experimental inductor current wave form, , output Voltage Vo and output current Io are shown .The experimental results have shown quite a big gap from theoretical calculations mainly due to the exclusion of the inductor and transformer losses .As it is shown in Fig. 5 the efficiency for the experimental converter at 45o is 91% , the theoretical efficiency at this particular operating point is calculated to be 95.19%.. The conduction losses and the switching losses .The power transfer at the mentioned phase shift angle is . In this analysis the switching loss is seen to be a slightly higher than the conduction losses.

Fig. 19 and Fig. 20 shows the SDPS control strategy for the case of the phase-shift ratio D<0.5 and D0.5, separately, where, β corresponding to the inductor current iL zero crossing, vT1 and vT2 represent the primary and secondary voltage of transformer, τ is the pulse width and is expressed by (6), the phase-shift ratio D is defined as

25 | P a g e

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1Tv

2Tv

Li

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

2

t

Lv

11

14

23

21

DDDS

11

14

23

21

SSSD

11

14

21

24

SSDD

13

11

21

24

DSDD

12

13

23

21

DDSD

12

13

21

23

SSSD

12

13

22

23

SSDD

11

13

22

23

DSDD

Fig. 19 Ideal voltages and current waveforms using the SDPS for D<0.5

26 | P a g e

11Q

14Q12Q

13Q21Q

24Q22Q

23Q

1Tv

2Tv

Li

Particularangles

Intervals 1 2 3 4 5 6 7 8

0

Conductingswitches

2

t

Lv

11

14

23

21

DDDS

11

14

23

21

SSSD

11

13

21

23

SDDS

13

11

21

24

DSDD

12

13

23

21

DDSD

12

13

21

23

SSSD

11

13

21

23

DSSD

11

13

22

23

DSDD

Fig. 20 Ideal voltages and current waveforms using the SDPS for D0.5

The expression of the inductor current iL can be obtained based on the voltage difference between primary and secondary side of transformer vT1 and vT2.

Solving (3) for the inductor current iL considering each interval defined in Fig. 5 and Fig. 6 yields the current expression shown in Table I and Table II , where respectively, where θ=ωt, ω=2πfs, fs is the switching frequency, for the case D<0.5, α1=, α2=τ, and for the case D0.5, α1= τ, α2. n is the voltage conversion ratio defined as

27 | P a g e

TABLE IExpression of inductor current for each time interval

Zone Interval 1 and 2 Interval 3 Interval 4

SDPS, D<0.5

SDPS, D0.5

PS

TABLE IICURRENT AT THE SWITCHING ANGLES

Zone

SDPS, D<0.5

SDPS, D0.5

PS

TABLE IIIAVERAGE OUTPUT POWER, TRANSFORMER RMS CURRENT AND PEAK CURRENT

Zone P Irms Ipeak

SDPS, D<0.5

SDPS, D0.5

PS

Based on these relationships, the average output power, the inductor current RMS and peak current

of DAB converter will be expressed in Table III for both PS and SDPS control strategies. From Table III, it

28 | P a g e

can be concluded that the average output power of DAB converter can be controlled by the duty ratio D,

which is used as the manipulated variable. Other variables such as V1, fs, and Ls determine the

magnitude. Assuming the same average output power, the relationship of duty ratio for zone1 (D<0.5)

and zone2 (D0.5) using SDPS strategy with respect to the duty ratio D using PS strategy are given by

(10) and (11), respectively.

Solving (10) and (11) yields the corresponding expressions and application ranges given in table IV.TABLE IV

The corresponding expressions and application ranges for two operation zones

Zone Symbol Expression Range

SDPS, D<0.5D

z1_1

Dz1_2

SDPS, D0.5 D

z2

Comparison of PS and SDPS are shown as following.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Di

D

Dz1-1

Dz1-2

Dz2

Fig. 21 Comparison of PS and SDPS for duty ratio

29 | P a g e

0 2 4 6 8 10422

422.2

422.4

422.6

422.8

423

Time (s)

v out (V

)

PSSDPS

Fig.22 Comparison of PS and SDPS for output voltage ripple

0 2 4 6 8 10-40

-20

0

20

40

Time (s)

i L (A)

PSSDPS

Fig. 23 Comparison of PS and SDPS for the inductor current

For DAB converter, the DC bus can experience large surge voltages due to the presence of parasitic inductance in addition to the hard-switching operations of voltage source inverters. The unexpected transient overvoltage can result in switching device failures. A surge voltage model is developed that takes into account the commutation loop inductances and the switching dynamics. An optimal design approach to lower the stray inductance is presented. In DAB converter, sizing and selection of DC link capacitors involve tradeoffs among system performance including lifetime, reliability, cost, and power density. A comprehensive and comparative study on the DC-link capacitor applications and evaluations to meet the above requirements are investigated. The analysis considers the facts of capacitor power

30 | P a g e

loss, core temperature, lifetime, and the battery ripple current limit, which are critical for PV applications.

Two papers on the dc bus surge voltage and comparative evaluation of DC-Link Capacitors have been accepted for the presentation in the 21th IEEE International Symposium on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012. Another paper on the power loss analysis has been accepted for 2011 2nd International Conference on the Electric Power and Energy Conversion Systems (EPECS).

31 | P a g e

Appendix-2: An Active Damping Technique for an LCL Filter Based System (Dr. Khadkikar, Dr. Hanif and Dr. Kirtley)We expect to submit a journal paper based on this research work soon. The initial draft of the paper is given below.

An Active Damping Technique for Filtering the Resonance of an LCL Filter Based PV System

Moin Hanif, Vinod Khadkikar and James L. Kirtley

Abstract—This paper focuses on LCL-filter based three-phase voltage source inverter control for grid connected DG systems. Voltage –oriented PI control of grid current is normally adopted in the dq synchronous reference frame for such inverters. Even though a LCL filter is more effective at attenuating the switching harmonics compared to simple L-filter, it causes stability problems due to the LCL resonance. In order to stabilize the PI controller, either a damping resistor within the filter or an active damping method within the inverter control has to be incorporated. Due to the additional losses caused by the damping resistors, they are seldom used. Active damping techniques are preferred, but require extra sensors to feed back measured signals. To avoid these disadvantages, a simple active damping technique that uses the existing grid side current sensors is provided as an active damping solution suitable for industry applications. Stability of the technique is proven using simulation results and bode plots of the system transfer function. Impact of dc link voltage and resonance frequency on stability is analyzed.

Index Terms—Photovoltaic power generation, interline power system, active power control, reactive power control, voltage regulation, power management.

I. INTRODUCTIONDG systems come as pulse width modulated (PWM) voltage source inverters (VSI) that inject controlled active and reactive power as required. Output of such an inverter needs to be filtered in order prevent the current harmonics around the switching frequency from entering the utility grid [1]. A filter of higher order, such as a third order LCL filter is preferred over a simple L filter. This is not only because of the 60 dB/decade attenuation of the frequencies above the resonance frequency, but also due to the reduction of physical size of the L [2]. A small inductance in a LCL filter is effective because the capacitor impedance is inversely proportional to the frequency of the current. The LCL filter exhibits first order inductive behavior to allow proper current control and high frequency rejection to guarantee proper filtering. Nevertheless, a LCL filter can cause stability problems due to the undesired resonance caused by the zero impedance at certain frequencies. To avoid this resonance from dominating the system, the

32 | P a g e

LCL structure is modified by incorporating passive elements, usually a resistor in series with the filter capacitor that solves the issue, but causes energy loss that brings down the efficiency of the inverter system. This kind of damping is referred to as passive damping [3]. Active damping that replaces passive damping is preferred as it stabilizes the system without any energy losses. This is done by modifying the current controller loop based on a feedback parameter. The main idea of the active damping algorithm is that, it introduces a negative peak that compensates the positive peak caused by the presence of LCL filter.

There are many proposed techniques in literature, most of which require an additional sensor in order to measure the feedback variable that is used for damping the undesired resonance. A method introduced by [4] requires feedback of the filter capacitor voltage that is based on lead-lag element. Slight modifications made to [4] that use the filter capacitor voltage as feedback parameter for active damping purposes are presented in [5] - [12]. Filter capacitor current has been used to form a so called ‘virtual resistor’ and several similar active damping techniques based on capacitor currents are mentioned in [13]-[18]. In [1], [19] and [20] capacitor voltage has been estimated in order to avoid the sensors, and the estimated capacitor voltage is filtered using a high pass filter (HPF) to add the compensating peak within the current loop. In [21] to implement a virtual resistor, the capacitor current is estimated instead of using an extra sensor to measure it. Estimation of the filter capacitor current or voltage depends on the accuracy of plant parameters, which may be sometimes unknown or even vary in a wide range for a complex power system. Therefore, active damping techniques based on high order digital filters without the use of sensors is proposed in [22], [23]. [24]-[27] have made analysis based on such techniques that use digital filters within the forward path of the main current control loop, i.e. either after the PI controller or just before the PWM reference generator as described in [22]. Either genetic algorithm based tuning or different complex offline tuning methods are considered to tune such high order digital filters. Also, in [28] a design algorithm is proposed for optimizing LCL filters based on which the system can be made stable at certain switching frequencies without any kind of damping. In [29], the inherent damping characteristic of the LCL filters that may help damp the resonance is given. This is when converter side inductor current is used instead of the grid side inductor current as the main control parameter in the current loop. Further, [3] and [31] provide a review on couple of the techniques discussed above. Paper [30] preserves the meaning of ‘filtering the resonance’ by using the grid side inductor current as feedback, and also has the advantage of using the existing grid side current inductor sensors but uses an analogue filter. The analogue filter, typically a notch filter is used and then analogue to discrete transformation is applied based on a given set of specifications called the bilinear transformation.

All the techniques above either use additional sensors to retrieve the filter capacitor voltage/current or adopt a sensor-less approach based on some parameter estimation. Else higher order filters are used without sensors, whose tuning complicates the final control algorithm. Therefore a simple active damping technique that uses the existing grid side inductor current information in order control the injected power and also to damp the LCL resonance is introduced. The LCL based inverter system is simulated and the simulation results with and without active damping are analyzed. The system model and the system open loop transfer function is derived. Open loop transfer function of the system model is modified to accommodate the new active damping feedback loop, whose stability is proven using bode plots. Finally the stability of the proposed controller with respect to dc link voltage and resonance frequency is analyzed.

33 | P a g e

II. SYSTEM CONTROL, MODELING AND DESIGNFig. 1 shows the typical circuit diagram of a three-phase VSI connected to the grid via a LCL filter and Table 1 gives the parameters of the system under study. Voltage oriented control is adopted as it is one of the most commonly used control method. It is based on inverter current vector orientation with respect to the grid voltage vector. The controller typically consists of an outer dc link voltage control loop with an inner current loop that guarantees a good dynamic and static performance. The dc link controller keeps the dc link maintained at the desired constant voltage level (800V in this study) and the

grid side inductor current , is expected to be sinusoidal and in phase with the grid voltage to achieve

unity power factor. A phase locked loop (PLL) is used to determine the frequency and angle reference of the grid voltage at the point of common coupling (PCC). The three grid side inductor currents are

transformed using dq synchronous reference frame to and . and are then

compared to the which adjusts the active power and the for zero reactive power,

respectively. The generated errors are then passed through the current controller (PI controller) to generate the voltage references for the inverter. To get a good dynamic response and also to have a

voltage output during no load, and are both fed forward. The generated reference voltages

in dq axis are transformed back into a stationary frame that can be used as command voltages to generate high frequency PWM voltages. In order to better understand and analyze the system stability, the system has to be modeled so that the system transfer function can be derived. All the equivalent

series resistances of the passive components including the inverter side inductor , grid side inductor

and filter capacitor C are neglected as they provide a certain degree of resonance damping and thus

would elevate the overall system stability. Therefore the system without passive resistances represents the ‘worst case’ during design.

34 | P a g e

Vdc

AC

AC

AC

LCL Filter

BreakerSwitch 3-Phase

AC Grid3-Phase

Load

Vg PCCLinv Lg

C

Ig a

bc

Vg P

CC

PWM

Ig abcIinv abc

Sin_Cos

dq

abc

Id_CC

Iq_CC

Id_ref=1

Iq_ref=0+-

PICurrent Controller

Vd_CC

Vq_CC

++PWM

Vg_abc PLLSin_Cos

Sin_Cos

abc

dq

Vg_a

bc

Vd_CC

Vq_CC

abc

dqIg_abc

Id_CC

Iq_CC

DSP

DSP Controller

Fig.1 LCL filter based grid connected VSI (hardware and control scheme)

35 | P a g e

Table 1: System parameters used for simulation and modeling

Parameter Value Nominal Power 10 kW

Switching frequency

DC link voltage

10 kHz

800 V

Grid voltage (L-N)

Line frequency 𝐿𝑖𝑛𝑣 (filter) 𝐿𝑔 (filter)

C (filter) 𝜔𝑟𝑒𝑠

PI current controller

Damping gain

p.u attenuation factor (p.u af)

PI current controller*

Damping gain* 𝑡𝑑 (time constant of HPF) 𝑇𝑆 (controller time delay)

240 V

50 Hz

4 mH

2 mH

5 µF

1949 Hz 𝑘𝑝 = 0.031 ,𝑘𝑖 = 9.16 𝑘𝑑 = 0.051 ξ2× 10000/(3× 240) 𝑘𝑝∗= 0.6 ,𝑘𝑖∗= 180 𝑘𝑑∗= 1 1/2𝜋(1135𝐻𝑧)

50µs

*Gains when current is considered as per unit (p.u) value

Fig.2 (a) whose open loop transfer function , can be written as (1) in the frequency domain,

represents the block diagram of the undamped LCL filter with the inverter bridge. The average model for

the inverter bridge is represented by a gain of that is applied to the PWM signal reference.

(1)

where is the dc link voltage, is the normalized modulating signal, is the grid side indcutor

current.

Using the parameters listed in Table 1, the bode plot of the transfer function in (1) can be seen in Fig.2(b). It shows a sharp peak at the resonance frequency that needs to be compensated in order to have a flattened low pass response. Applying unity feed back to (1) results in a characteristic equation of

whose denominator has a polynomial without the term. Therefore, the overall closed loop

system is unstable according to Routh’s stability criterion which is also confirmed by the bode plot analysis and would require additional damping to stabilize the system. Passive damping is avoided due to the additional losses and a new improved active damping method needs to be introduced.

In Fig.1 the grid side inductor current , is already being sensed and fed to the current controller for

control purposes. Therefore, to minimize the number of additional sensors, the very same controlled

36 | P a g e

current shown in Fig.1 can now be used to damp the LCL resonance actively. This is done by modifying the block diagram in Fig.2 (a) to look like the block diagram in Fig.3(a).

As discussed, in order to stabilize the overall closed loop system, a finite term needs to be introduced

into the denominator. This can be done by calculating the second derivative of the controlled current

which passes through a damping gain , and adding it to the modulating signal . This then leads to a

transfer function that can be written as

(2)

(3)

Due to the noise in any measured signal, especially when using digital controllers such as digital signal processor (DSP), the calculation of derivatives does not lead to a reasonable result. Therefore the proposed feedback loop is introduced within the current controller with no additional sensors.

The controlled current passes through a damping gain which is then filtered using a first order HPF.

The HPF can be realized as a subtraction of and their low pass filtered signals using a LPF,

which guarantees delay less higher harmonics. The transfer function of the HPF is the transfer function of 1-LPF which can be written as

, where is the time constant.

37 | P a g e

2dcV

sL g

1sLinv

1

Cs1 -+ -+

VinvVm Iinv Ic Vc Ig

(a) Block diagram

(b) Bode plot

0

50

100

150

200

Mag

nitu

de (d

B)

101

102

103

104

-450

-405

-360

-315

-270

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Fig. 2 Undamped LCL system

The higher harmonics signal is then added to the modulating signal as shown in Fig.3 (a). The new

transfer function now can be written as

(4)

The new damped LCL transfer function constitutes, a fourth order polynomial which

contains all orders of the term and can be derived as

(5)

The modified bode plot of the open loop transfer function in (5) can be seen in Fig.3(b). Parameters

listed in Table 1 are used to retrieve the bode plot. The positive peak at the resonance frequency ,

in the undamped LCL system has now been damped and the gain in the low frequency range (below

) is un-altered, while the phase in the low frequency range (below ) has been altered. This

altered phase for frequencies below stabilizes the closed loop system controller. It can be further

38 | P a g e

noticed that there is no change in gain or phase at higher frequencies above guaranteeing

attenuation of higher order harmonics required by the inverter.

An important phenomenon of the proposed damping technique is observed before proceeding with the

design procedure. From (5) it can be seen that the can have an impact on the stability besides the

damping parameters and if the other design parameters are fixed. It is understood that a good

link controller can avoid any impact, but in order to analyze the effect of on the damped LCL system,

bode plots with different levels have been plotted in Fig.4. It is noted that a decrease in level

stabilizes the controller while an increase in the level will make the system unstable. A of up to

1200V can be tolerated to damp the LCL oscillations according to Fig.4 for this specific design.

Further, it can be noted that the control bandwidth cannot exceed or even approach close to resonance

frequency , as it will create a phase lag, which results in and inadequate phase margin for

closed loop control. Non negligible delays caused by digital sampling and pulse width modulation would

also further constrict the system’s gain cross over frequency .

Table 2: Different

C[µF] 𝝎𝒓𝒆𝒔[kHz] 5 1.949 10 1.378 15 1.125 20 0.974

Therefore, as suggested in Fig.4, is chosen such that it is . Value of will only be required

if the proportional and integral gains are derived using mathematical calculations. Since ideally, line

frequency currents are expected to be injected into the grid. This chosen is fairly a conservative value

to avoid interference between the ‘maximum harmonics of current that needs to be controlled’ and

‘resonance damping’. The choice of is such that it is below half the switching frequency, i.e. to give

sufficient harmonic attenuation of the current around switching frequency and it should be high enough to give a larger controller bandwidth. The latter can be confirmed by plotting the bode plots of (5) with

different ,by changing only the filter capacitor values according to Table 2. Fig.5 shows that the

bandwidth of the system reduces with , while the attenuation of high order harmonics increases as

expected.

39 | P a g e

2dcV

sL g

1sLinv

1

Cs1 -+ -+

VinvVmIinv Ic Vc Ig

++

dk1st

st

d

dHPF

(a) Block diagram

(b) Block diagram

-40

-20

0

20

40

60

80

Mag

nitu

de (

dB)

101

102

103

104

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Fig. 3 Damped LCL system

-50

0

50

100

150

Mag

nitu

de (

dB)

100

101

102

103

104

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

800V400V1200V1500V

Controller bandwidthregion forstable operation

Fig.4 Bode plots of damped LCL with different Vdc link levels

40 | P a g e

-40

-20

0

20

40

60

80

Mag

nitu

de (d

B)

101

102

103

104

-270

-225

-180

-135

-90Ph

ase

(deg

)

Bode Diagram

Frequency (Hz)

C=5uFC=10uFC=15uFC=20uF

Fig.5 Bode plots of damped LCL with different

Finally the systems open loop transfer function (block diagram shown in Fig.6 (a)), can be

derived using the PI current controller , a 1.5 times sampling and transport delay that is modeled

as in the forward path and as

(6)

(7)

The gains and shown in Table 1 are for model with real current values. If per unit (p.u) values

are used within the controller with a base power of and a base voltage of , then the gains

, and are calculated using the p.u attenuation

factor (puaf). Values of the gains , and the puaf are all given in Table 1. The gains and are initially found out by manual trial and error tuning for the current controller with passive resistances

41 | P a g e

in series with the capacitor filter (passive damping). Values of the gains and can also be

calculated using (8) and (9) [14].

2dcV

sL g

1sLinv

1

Cs1 -+ -+

VinvVm Iinv Ic Vc Ig

++

dk1st

st

d

dHPF

++

Vg

skk i

p +-Iref

1.5TsDelay

(a) Block diagram

(b) Bode plot

(a) Block diagram

-100

-50

0

50

100

Mag

nitu

de (d

B)

100

101

102

103

104

-540

-450

-360

-270

-180

-90

Phas

e (d

eg)

Bode Diagram Gm = 3.38 dB (at 1.53e+003 Hz) , Pm = 50.1 deg (at 573 Hz)

Frequency (Hz)

(b) Bode plot

Fig. 6 Actively damped LCL system with current controller loop model (PI +1.5Ts + damped LCL)

(8)

(9)

42 | P a g e

The calculated values for the gains and ( and ) are comparable with the

manually tuned values ( and ). The finally chosen values for the gains are the

manually tuned ones as they provide a faster current tracking response with slightly increased integral

gain. Once the gains and are finalized, then the passive damping is removed and the new active

damping loop is added to the current controller. Then is set to 1 and of the HPF is simply tuned

such that the phase margin of the transfer function is at least . A stable bode plot of (7) can

be confirmed in Fig.6 (b).

III. SIMULATION RESULTSSimulation was carried out in the Matlab/Simulink environment, based on the system shown in Fig.1 and the parameters given in Table 1. The aim was to examine the performance of the proposed active

damping method with p.u current information and to validate the gains and in simulation

against the designed model. The damping gain and the time constant of the HPF were derived for

the system whose specifications are given in Table 1 and needs further validation on simulation. The

10kW inverter supplies 5kW of power required by the parallel RLC load resonating at 50Hz ( )

and the rest is injected into the grid. Therefore, 0.5 p.u current is injected into the grid. Fig.7 shows the results of the undamped LCL system which shows oscillations in the grid side inductor current and the injected grid current with high amplitude as expected. The oscillations can also be observed at the filter capacitor voltage and current. For simplicity, results of only phase A in per unit (p.u) values are shown in Fig.7 and Fig.8. Fig.8 shows the results of proposed actively damped LCL system which shows the oscillations have been well damped by the modified current controller. The THD of the grid side inductor current is 2.6% at 1p.u. i.e. when the system is operated at full load. The system is again operated with 50% load (0.5 p.u) and the THD is 4.5%. It can be seen that THD of the injected grid current (difference between the grid side inductor current and the load current) is slightly higher due to the resonating load. In order to achieve better current THD of the grid side inductor current, the switching frequency can be increased or analogue PWM generation is suggested.

43 | P a g e

-1

0

1

(a) Grid voltage

-100

0

100

(b) Injected grid current

-200

0

200

(c) Capacitor voltage

-200

0

200

(d) Capacitor current

0 0.02 0.04 0.06 0.08 0.1-100

0

100

(e) Grid side inductor currentTime(s)

Fig. 5 Simulation results of the undamped LCL system

-1

0

1

(a) Grid voltage

-0.5

0

0.5

(b) Injected grid current

-1

0

1

(c) Capacitor voltage

-0.2

0

0.2

(d) Capacitor current

0 0.02 0.04 0.06 0.08 0.1-1

0

1

(e) Grid side inductor currentTime(s)

44 | P a g e

Fig.6 Simulation results of the actively damped LCL system

IV. CONCLUSIONThis paper discusses the active damping techniques in the literature that either use extra sensors to feed back certain parameters or use high order filters if no sensors are used. An active damping technique that uses the existing grid side inductor current information along with a simple 1 st order high pass filter, which is realized using a low pass filter is introduced. This can act as a plug and play feature within the existing voltage oriented current controllers in order to damp the LCL oscillations without any losses. The stability of the LCL system with and without the damping technique is discussed, i.e. using the plant and controller model transfer functions in s domain along with their respective bode plots. A simple design procedure to tune the parameters of the controller and the damping loop that ensures proper damping of LCL oscillations is given. Simulations carried out, validate the current controller parameters

against the designed model. Also the impact of different link levels and on the stability of the

damped LCL system is analyzed using bode plots and discussed.

V. REFERENCES[1] Malinowski, M.; Bernet, S.; , "A Simple Voltage Sensorless Active Damping Scheme for Three-Phase

PWM Converters With an LCL Filter," Industrial Electronics, IEEE Transactions on , vol.55, no.4, pp.1876-1880, April 2008

[2] Dannehl, J.; Liserre, M.; Fuchs, F.W.; , "Filter-Based Active Damping of Voltage Source Converters With LCL Filter," Industrial Electronics, IEEE Transactions on , vol.58, no.8, pp.3623-3633, Aug. 2011

[3] Liserre, M.; Dell'Aquila, A.; Blaabjerg, F.; , "An overview of three-phase voltage source active rectifiers interfacing the utility," Power Tech Conference Proceedings, 2003 IEEE Bologna , vol.3, no., pp. 8 pp. Vol.3, 23-26 June 2003

[4] Blasko, V.; Kaura, V.; , "A novel control to actively damp resonance in input LC filter of a three phase voltage source converter," Applied Power Electronics Conference and Exposition, 1996. APEC '96. Conference Proceedings 1996., Eleventh Annual , vol.2, no., pp.545-551 vol.2, 3-7 Mar 1996

[5] Nuilers, S.; Neammanee, B.; , "Control performance of active damp LCL filter of three phase PWM boost rectifier," Electrical Engineering/Electronics Computer Telecommunications and Information Technology (ECTI-CON), 2010 International Conference on , vol., no., pp.259-263, 19-21 May 2010

[6] Jalili, K.; Bernet, S.; , "Design of LCL Filters of Active-Front-End Two-Level Voltage-Source Converters," Industrial Electronics, IEEE Transactions on , vol.56, no.5, pp.1674-1689, May 2009

[7] Dannehl, J.; Fuchs, F.W.; Hansen, S.; Thøgersen, P.B.; , "Investigation of Active Damping Approaches for PI-Based Current Control of Grid-Connected Pulse Width Modulation Converters With LCL Filters," Industry Applications, IEEE Transactions on , vol.46, no.4, pp.1509-1517, July-Aug. 2010

[8] Agorreta, J.L.; Borrega, M.; Lopez, J.; Marroyo, L.; , "Modeling and Control of N-Paralleled Grid-Connected Inverters With LCL Filter Coupled Due to Grid Impedance in PV Plants," Power Electronics, IEEE Transactions on , vol.26, no.3, pp.770-785, March 2011

[9] Serpa, L.A.; Ponnaluri, S.; Barbosa, P.M.; Kolar, J.W.; , "A Modified Direct Power Control Strategy Allowing the Connection of Three-Phase Inverters to the Grid Through LCL Filters," Industry Applications, IEEE Transactions on , vol.43, no.5, pp.1388-1400, Sept.-oct. 2007

[10]Suul, J.A.; Ljokelsoy, K.; Midtsund, T.; Undeland, T.; , "Synchronous Reference Frame Hysteresis Current Control for Grid Converter Applications," Industry Applications, IEEE Transactions on , vol.47, no.5, pp.2183-2194, Sept.-Oct. 2011

45 | P a g e

[11]Bierhoff, M.H.; Fuchs, F.W.; , "Active Damping for Three-Phase PWM Rectifiers With High-Order Line-Side Filters," Industrial Electronics, IEEE Transactions on , vol.56, no.2, pp.371-379, Feb. 2009

[12]Dannehl, J.; Fuchs, F.W.; Thøgersen, P.B.; , "PI State Space Current Control of Grid-Connected PWM Converters With LCL Filters," Power Electronics, IEEE Transactions on , vol.25, no.9, pp.2320-2330, Sept. 2010

[13]Yi Lei; Zhengming Zhao; Fanbo He; Sizhao Lu; Lu Yin; , "An improved virtual resistance damping method for grid-connected inverters with LCL filters," Energy Conversion Congress and Exposition (ECCE), 2011 IEEE , vol., no., pp.3816-3822, 17-22 Sept. 2011

[14]Yi Tang; Poh Chiang Loh; Peng Wang; Fook Hoong Choo; Feng Gao; Blaabjerg, F.; , "Generalized Design of High Performance Shunt Active Power Filter With Output LCL Filter," Industrial Electronics, IEEE Transactions on , vol.59, no.3, pp.1443-1452, March 2012

[15]Tang, Y.; Loh, P.C.; Wang, P.; Choo, F.H.; Tan, K.K.; , "Improved one-cycle-control scheme for three-phase active rectifiers with input inductor-capacitor-inductor filters," Power Electronics, IET , vol.4, no.5, pp.603-614, May 2011

[16]Mohamed , Y. A.-R. I.; A.-Rahman, M.; Seethapathy, R.; , "Robust Line-Voltage Sensorless Control and Synchronization of LCL -Filtered Distributed Generation Inverters for High Power Quality Grid Connection," Power Electronics, IEEE Transactions on , vol.27, no.1, pp.87-98, Jan. 2012

[17]He, J.; Li, Y.; , "Generalized Closed-Loop Control (GCC) Schemes with Embedded Virtual Impedances for Voltage Source Converters with LC or LCL Filters," Power Electronics, IEEE Transactions on , vol.PP, no.99, pp.1, 2011

[18]Mohamed , Y.-R. I.; , "Suppression of Low- and High-Frequency Instabilities and Grid-Induced Disturbances in Distributed Generation Inverters," Power Electronics, IEEE Transactions on , vol.26, no.12, pp.3790-3803, Dec. 2011

[19]Malinowski, M.; Kazmierkowski, M.P.; Bernet, S.; , "New simple active damping of resonance in three-phase PWM converter with LCL filter," Industrial Technology, 2005. ICIT 2005. IEEE International Conference on , vol., no., pp.861-865, 14-17 Dec. 2005

[20]Malinowski, M.; Stynski, S.; Kolomyjski, W.; Kazmierkowski, M.P.; , "Control of Three-Level PWM Converter Applied to Variable-Speed-Type Turbines," Industrial Electronics, IEEE Transactions on , vol.56, no.1, pp.69-77, Jan. 2009

[21]Gullvik, W.; Norum, L.; Nilsen, R.; , "Active damping of resonance oscillations in LCL-filters based on virtual flux and virtual resistor," Power Electronics and Applications, 2007 European Conference on , vol., no., pp.1-10, 2-5 Sept. 2007

[22]Liserre, M.; Dell'Aquila, A.; Blaabjerg, F.; , "Genetic algorithm based design of the active damping for a LCL-filter three-phase active rectifier," Applied Power Electronics Conference and Exposition, 2003. APEC '03. Eighteenth Annual IEEE , vol.1, no., pp. 234- 240 vol.1, 9-13 Feb. 2003

[23]Liserre, M.; Dell'Aquila, A.; Blaabjerg, F.; , "Genetic algorithm-based design of the active damping for an LCL-filter three-phase active rectifier," Power Electronics, IEEE Transactions on , vol.19, no.1, pp. 76- 86, Jan. 2004

[24]Dannehl, J.; Wessels, C.; Fuchs, F.W.; , "Limitations of Voltage-Oriented PI Current Control of Grid-Connected PWM Rectifiers With LCL Filters," Industrial Electronics, IEEE Transactions on , vol.56, no.2, pp.380-388, Feb. 2009

[25]Liserre, M.; Teodorescu, R.; Blaabjerg, F.; , "Stability of photovoltaic and wind turbine grid-connected inverters for a large set of grid impedance values," Power Electronics, IEEE Transactions on , vol.21, no.1, pp. 263- 272, Jan. 2006

46 | P a g e

[26]Liserre, M.; Teodorescu, R.; Blaabjerg, F.; , "Stability of grid-connected PV inverters with large grid impedance variation," Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual , vol.6, no., pp. 4773- 4779 Vol.6, 20-25 June 2004

[27]Eric Wu; Lehn, P.W.; , "Digital Current Control of a Voltage Source Converter With Active Damping of LCL Resonance," Power Electronics, IEEE Transactions on , vol.21, no.5, pp.1364-1373, Sept. 2006

[28]Teodorescu, R.; Blaabjerg, F.; Liserre, M.; Dell'Aquila, A.; , "A stable three-phase LCL-filter based active rectifier without damping," Industry Applications Conference, 2003. 38th IAS Annual Meeting. Conference Record of the , vol.3, no., pp. 1552- 1557 vol.3, 12-16 Oct. 2003

[29]Tang, Y.; Loh, P.; Wang, P.; Choo, F.; Gao, F.; , "Exploring Inherent Damping Characteristic of LCL-Filters for Three-Phase Grid-Connected Voltage Source Inverters," Power Electronics, IEEE Transactions on , vol.PP, no.99, pp.1, 2011

[30]Dick, C.P.; Richter, S.; Rosekeit, M.; Rolink, J.; De Doncker, R.W.; , "Active damping of LCL resonance with minimum sensor effort by means of a digital infinite impulse response filter," Power Electronics and Applications, 2007 European Conference on , vol., no., pp.1-8, 2-5 Sept. 2007

[31]Sun Wei; Wu Xiaojie; Dai Peng; Zhou Juan; , "An over view of damping methods for three-phase PWM rectifier," Industrial Technology, 2008. ICIT 2008. IEEE International Conference on , vol., no., pp.1-5, 21-24 April 2008

[32]J. Northcote-Green, R. Wilson, Control and Automation of Electrical Power Distribution Systems, CRC Press, 2006, p. 27

[33]R. Brown, “Impact of Smart Grid on Distribution System Deisgn,” 2008 IEEE PES General Meeting, Pittsburge, PA, July 20-24

[34] J. Kueck, B. Kirby, “the Distribution System of the Future,” the Electricity Journal, Vol. 16, No. 5, Jun. 2003

[35] Lopes, J.A.P., et al., Integrating distributed generation into electric power systems: A review of drivers, challenges and opportunities. Electric Power Systems Research, 2007. 77(9): p. 1189-1203.

[36] Celli, G., M. Loddo, and F. Pilo, Distribution Network Planning with Active Management, in 6th World Energy System Conf. 2006: Torino, Italy.

[37] S. Venkata, A. Pahwa, R. Brown, R. Christe, “What Future Distribution Engineers Need to Learn,” IEEE Trans. on Power System, Vol. 19, No. 1, Feb. 2004

[38] R. Brown, Electric Power Distribution Reliability, 2nd Edition, Vol. 31 of Power Engineering, CRC Press, 2008

[39] L.C. Leung, S.K. Khator, and J. Pence, “Planning substation capacity under the single-contingency scenario,” IEEE Trans. on Power Systems, vol. 3, pp 1442-1447, Oct. 1995.

[40] J. Wang, P. Calvarho, and J. Kirtley, “Emergency Reconfiguration and Distribution System Planning under Single Contingency Policy,” 2012 Smart Grid Innovative Technology Conference, Washington, D.C., Jan 16-20.

[41] H. Lee Wills, “Distribution System Planning Reference Book,” published by Marcel Dekker, Inc., 2004

[42] L.C. Leung, S.K. Khator, and J. Ponce, “Optimal transformer allocation under single-contingency,” IEEE Trans. on Power Systems, vol. 11, pp. 1046-1051, May 1996.

[43] R. Sarfi, M. Salama, A. Chikhani, “A survey of the state of the art in distribution system reconfiguration for system loss,” Electric Power System Research, Vol. 31, 1994

[44] S. Conti alt., “Integration of multiple PV units in urban power distribution systems,” Solar Energy 75 (2003) 87-94.

47 | P a g e

[45] C. L. Masters, “Voltage rise the big issue when connecting embedded generation to 11kV overhead lines,” Power Engineering Journal, Feb. 2002

[46] Y. Baghzouz, “Some general rules for distribution generation- feeder interaction,” 1-4244-0493-2 IEEE

48 | P a g e

Appendix-3: Interline-PV System (PIs: Dr. V Khadkikar and Dr. J Kirtley; MI Graduate Student: Ahmed Mowwad)This research work has been submitted for the possible publication in IEEE Transactions on Power Delivery. The submitted paper work is attached for the further reading.

A New P-Q-V Droop Control Method for Interline Photovoltaic (I-PV) Power System

Ahmed Moawwad, Vinod Khadkikar and James L. Kirtley

Abstract—This paper proposes a new droop control method for an interline photovoltaic (I-PV) system. In an I-PV system, the inverters in PV plant are reconfigured in such a way that two or more distribution networks/feeders are interconnected. The I-PV system is operated as a FACTS (flexible AC transmission system) device to regulate the point of common coupling (PCC) voltage on either feeder. One of the key features of I-PV system is that the real power can be exchanged between two feeders via PV plant inverters. A P-Q-V droop control method is thus proposed, especially for system with low X/R ratio, to facilitate simultaneous active and reactive power control to regulate the PCC voltage. A lookup table based approach is developed and implemented to determine the P and Q droop coefficients. The MATLAB/ Simulink based simulation model is developed to evaluate performance of the system with the proposed controller.

Index Terms—Droop control, interline power system, active and reactive power control, voltage regulation, photovoltaic power generation and control.

INTRODUCTIONPhotovoltaic (PV) and wind power plants are considered as promising solutions to produce clean electric energy. Their penetration in the electric network is increasing because of government policies and due to continuous improvements in the solar cells and wind turbines technologies (Yoshino, Amboh et al. 4-7 July 2010; Reed, Grainger et al. 19-22 April 2010; Sheng, Liu et al. 2010; Borgstrom, Wallentin et al. 2011). The impact of such plants should be assessed because large-scale penetration of these renewable power plants may affect the normal operation of the power distribution systems (Enslin and Heskes 2004; Zavadil, Miller et al. 2007; Walling, Saint et al. 2008; Barbosa, Rolim et al. Sep 1998 ).

When connected to the grid, large-scale PV/ wind power plants mainly inject active power. While in islanding mode these power plants should inject both active and reactive power to support load requirements. Most recent research works assign different tasks for grid-connected power plants to do more than injecting active power. These plants can generate reactive power, either capacitive or

49 | P a g e

inductive, to regulate the point of common coupling (PCC) voltage, and/or harmonic filtering (Wu, Nien et al. 2007; Flores, Dixon et al. 2009; Varma, Khadkikar et al. 2009; Patel and Agarwal 2010). Therefore, it is more beneficial to control active and reactive power injected from these large-scale power plants. Several control techniques have been developed to achieve active and/or reactive powers, such as, master-slave control method (Chandorkar, Divan et al. 1993), power deviation control method (Chen and Chu 1995), and frequency - voltage droop methods (Yao, Chen et al. 17-21 June 2007 ; Chandrokar, Divan et al. 20-25 Jun 1994 ; Hanaoka, Nagai et al. 23-23 Oct. 2003 ; Arias, Lamar et al. 24-28 Feb. 2008 ; Guerrero, Matas et al. 2006).

Flexible AC Transmission Systems (FACTS) devices are widely used to enhance the quality of power system networks. Among useful FACTS devices are the Static Synchronous Compensator (STATCOM), Unified Power Flow Controller (UPFC), and Interline Power Flow Controller (IPFC) (Aminifar, Fotuhi-Firuzabad et al. 1-3 Dec. 2008; Gyugyi, Sen et al. 1999; Hingorani, Gyugyi et al. 2000) . The IPFC connects more than one electric network together using back-to-back inverters. These back-to-back connected inverters can control the power flow (both active and reactive) through series connected transformers. Such a system configuration gives an opportunity to improve overall system performance (Hingorani, Gyugyi et al. 2000).

In (Khadkikar and Kirtley 24-29 July 2011 ), we have introduced a new concept and system configuration, called ‘Interline-PV’ (I-PV) system. An I-PV system interconnects multi-line transmission or distribution networks using PV plant inverters. Unlike IPFC, in I-PV system two or more feeders or networks are interconnected through shunt-connected inverters. The I-PV system can have various applications, for example, feeder voltage regulation, load reactive power support, real power management between two feeders and overall system performance improvement against dynamic disturbances.

The droop method is a very effective technique to control inverter based PV and wind power plants. It tends to enforce automatic load sharing between plants and extends the operating range of inverter active and reactive power with given ratings [13]. It was first introduced and used to control voltages of conventional generating units over the transmission system network (Bergen 1986). Transmission networks are generally characterized by high X/R ratio. To the extent that resistance values of these networks can be neglected compared to their inductance values, conventional droop controllers used for these systems rely more on the inductive nature of the lines. For such systems, the Q-V droop is very popular technique to control the PCC voltage magnitude (De Brabandere, Bolsens et al. 2007). A second droop method is the P-ω droop that can be used to control the frequency of the system in isolated mode.

For distribution networks equipped with underground cables, the resistance cannot be neglected with respect to the reactance of feeder. This yields to low X/R ratio, which causes a coupling effect between active and reactive power. Therefore, for low X/R ratio systems, the Q-V droop method cannot achieve the required voltage regulation. In (Yao, Chen et al. 2011), the authors suggest the use of active and reactive power to overcome the aforementioned coupling effect for low X/R ratio system. However, it

50 | P a g e

takes into consideration the same droop coefficients for active and reactive power. This approach thus may not be sufficient for voltage regulation for I-PV systems.

This paper proposes a new droop control method called as “P-Q-V droop controller” for I-PV system where both active and reactive powers are used to control the PCC voltage. The necessary active power for the compensation is drawn from the interconnected feeder via the PV solar plant inverters. The controller is designed to circulate the minimum active power between the two feeders. The active and reactive power droop coefficients are adjusted online through a lookup table based on the PCC voltage level.

SYSTEM CONFIGURATIONFig.1 shows a two-feeder distribution system in which feeder-1 and feeder-2 are considered to be located close to each other. A large-scale PV solar power plant is connected at feeder-1. The PV plant inverters are reconfigured in such a way that the two feeders could be interconnected with each other. This configuration is addressed as Interline-PV (I-PV) system (Khadkikar and Kirtley 24-29 July 2011 ). The two inverters are connected back to back through switch SD3. To operate the PV plant as I-PV system, switches SA, SB1, SA1, SD1, SA2, SB, SD2 and SD3 are closed, while switch SB2 is kept open. During night-time when the PV solar plant does not produce real power, switches SD1 and SD2 can be opened.

Feeder-2Feeder-1PV Solar PlantInv-1

Inv-2

1eqZ

1SV

L11

1Si

CS

1pccV

-1T

2BS2AS

1AS1BS

-2T

AS

BS

PCC-1 PCC-2

2SV

L21

2Si

2pccV

2DS

3DS

1DS

Fig. 1 Interline-PV (I-PV) power plant system configuration.

For distribution systems, the resistive values of the feeders are taken into account with respect to the reactance values of the feeders, and considered as low X/R ratio feeders. Fig.2 shows Thévenin equivalent of feeder-2 (Vth 0, Zth = Rth+ jωLth) connected to inverter-2 (Inv-2) of the I-PV power system,

51 | P a g e

represented as power source (EPV ). The Zth represents the feeder as well as inverter coupling

impedance. In Fig. 2, represents the phase angle difference between PCC and grid voltages, whereas,

and represents impedance angle due to Zth. The active and reactive power flow (S = P +jQ) from

inverter-2 (the power source) to feeder-2 (the grid) are controlled through the below equations:

(1)

(2)

Zth

S = P+jQ

Vth

jωLth Rth

0

EPVφ

ϴ

Fig. 2 Thévenin equivalent circuit considering feeder-2 and inverter-2.

Usually the phase difference between the PCC and grid voltages is very small, that is, cos ≈ 1, and sin

≈ . Hence, (1) and (2) become:

(3)

(4)

Equations (3) and (4), show the dependency of delivered active and reactive power on the impedance

angle and the phase difference angle .

52 | P a g e

DIFFERENT DROOP CONTROLSTwo conventional droop methods to regulate the PCC voltage are P-V and Q-V methods.

A]. P-V droop control method

This method is convenient for the feeder with predominant resistive value where the reactance of the

line can be neglected with respect to the resistance of the line. This makes the impedance angle equals to zero. Hence, (3) yields that the active power delivered by the inverter is proportional to the voltage difference (EPV – Vth), i.e. proportional to the inverter EPV. The reactive power of inverter-2 is

proportional to the phase difference , i.e. proportional to the frequency ω of the system.

Fig. 3 shows the polar plot for (3) and (4) with pure resistive impedance for different values of the

voltage magnitude EPV and phase difference angle . The polar radii denote the values of active and

reactive power, whereas, the polar angles denote the values of the phase difference angle . It should

be noticed that is varying within small range as stated before.

Effect of changing on P and Q:

(i) P remains constant irrespective of any change in (represented by an arc which has the same

radius).

(ii) Q significantly changes with different polar angles .

Effect of changing EPV on P and Q:(i) P significantly increases with increase in EPV (represented by arcs with different radii for different

values of EPV).(ii) There is hardly any change in Q due to the changes in EPV as shown in the zoomed part of Fig. 3.

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Fig.3 Polar plot for the inverter P and Q injected to the system with pure resistive impedance. Real power is red. Reactive power is blue.

Fig. 4 shows the P-V droop characteristics of an inverter with different loading. The load lines: Load 1, Load 2, and Load 3 represent different operating points with corresponding PCC voltages V 1, V2, and V3, respectively. The droop characteristic intersects the load characteristics to get the new operating points of PCC voltages V’

2 and V’3 with corresponding active power injected or absorbed by the inverter as P ’

2

and P’3, respectively. It should be noticed that the active power injected or absorbed by any inverter is

circulated between the two feeders (feeder-1 and 2). In I-PV system, this active power will be taken from or injected to the other feeder.

Injected

V

Absorbed

Load 2Load 1Load 3

V1

V2

V3

V’2

V’3

Droop characteristics

PP’2P’

3

Fig.4 P-V droop characteristics for the system with pure resistive impedance.

B]. Q-V droop control method

For high X/R ratio systems, where the reactance of the line is predominant over the resistance, impedance angle θ goes to 90o. The reactive power of the inverter is proportional to the inverter voltage EPV and the active power is proportional to the frequency ω. The polar plot for (3) and (4) for pure inductive impedance is shown in Fig. 5.

Effect of changing on P and Q:

(i) P significantly changes with different polar angles .

(ii) Q remains constant regardless of any change in angle (represented by an arc which has the

same radius). Effect of changing EPV on P and Q:

(i) There are hardly any changes in P due to the changes of EPV as shown in the zoomed part of Fig. 5.

(ii) Q significantly changes when EPV increases (represented by arcs with different radii for different values of EPV).

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The Q-V droop control method is one of the widely used methods for voltage regulation. Unlike the P-Q droop method where additional provision for real power is required; Q-V droop method does not need such a source of real power for generating the necessary Q for compensation.

Fig. 5 Polar plot for the inverter P and Q injected to the system with pure inductive impedance. Real power is red. Reactive power is blue.

PROPOSED P-Q-V DROOP CONTROLLER FOR I-PV SYSTEMThe power distribution networks may contain feeders with complex impedances, where neither reactance of the line nor the resistance can be neglected with respect to each other. In some cases, the resistance of the line may equal or even more than the reactance of line, giving a low X/R ratio feeder system. Such a kind of situation where X/R ratio is small (close to 1), neither the P-V nor the Q-V droop method may be sufficient to regulate the PCC voltage. Fig. 6 shows the polar plots for active and reactive power with a complex impedance system. It is shown that active and reactive power is affected by the

changes in voltage magnitude EPV and the phase difference angle simultaneously.

The I-PV system has the advantage of circulating active power between two adjacent feeders through back-to-back connected inverters. Furthermore, these inverters, with proper control, can also inject reactive power while circulating the active power. Thus, the I-PV system configuration may be considered as one of the possible solutions for voltage regulation in low X/R ratio feeder systems. In order to achieve the desired PCC voltage regulation, a new droop control method is proposed in this paper in which both active and reactive powers are used. Since both active and reactive powers are utilized for voltage regulation, the proposed droop method is called as “P-Q-V droop control”. Two different droop coefficients, namely, nd for active power and md for reactive power, are thus estimated according to PCC voltage levels to achieve the P-Q-V droop controller objectives. However, in this approach, the desired performance should be achieved with the least possible active power circulation to insure minimum voltage variation on the other feeder. In the proposed method, a lookup table approach is developed to circulate the minimum active power between two feeders.

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Fig. 6 Polar plot for the inverter P and Q injected to the system with complex impedance. Real power is red. Reactive power is blue.

For electric systems with complex impedance, both active and reactive power (P, Q) affect the voltage magnitude (V). Such systems can be represented by the following equation:

(5)

Where Vpcc is the voltage before compensation, while nL and mL are the electric load droop coefficients.

Fig. 7 P-Q-V droop characteristics for the system with complex impedance.

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The droop characteristics for the proposed P-Q-V droop method are represented by:

(6)

Where, Vref is the desired reference value of the PCC voltage, in this case 1 pu. nd and md are the active and reactive power coefficients for the proposed P-Q-V droop method. Equations 5 and 6 are plane functions and they are plotted as shown in Fig. 7. The droop characteristic intersects the load characteristics in Line1 as shown in Fig. 8. Line1 contains the new operating point of the PCC voltage after regulation.

Line1 can be obtained as follows.

Step-1: The normal vectors of the two planes (i.e. Eq.5 and Eq.6) are determined as given below:

(7)

(8)

Step-2: The cross product of both N1 and N2 yields a vector, named as U and is perpendicular to both N1 and N2. This vector represents the direction vector of Line1 as shown in Fig. 8.

(9)

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Fig. 8 Graphical comparison between the three droop methods.

Step-3: The direction vector has to stem from a point called as position vector and is referred to A o (Fig. 8). This point can be obtained by putting P = 0 in (5) and (6), then solving for V and Q:

(10)

(11)

Step-4: Knowing both position and direction vectors, Line1 can be fully determined as follows:

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(12)

Where s is an arbitrary constant.

Similar steps can be applied to express Line2 shown in Fig. 8 as follows:

(13)

Where Bo is the position vector, L is the direction vector of Line2 and t is the arbitrary constant.

Step-5: The new operating point after compensation lies on a line that is perpendicular to both Line1 and Line2. Such a line represents the shortest distance. This shortest distance between Line1 and Line2 can be calculated by Eberly (Eberly 2004) as follows:

(14)

Where |d1| is the shortest distance between line1 and Line2, sS and tS are the values of the arbitrary constants at the shortest distance.

Step-6: d1 is perpendicular to both; U and L (Fig. 8). Thus, sS and tS can be calculated using the following relations:

(15)

Substituting (14) into the above relations:

(16)

(17)

Considering,

8)

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Solving for sS and tS:

; (19)

Step-7: The new operating points Z3 and shown in Fig. 8, can be expressed by:

(19)

(20)

Fig. 8 also shows a 3-dimension comparison between the three different droop control methods mentioned above. For simplified discussion, the X/R ratio of the system is considered as 1. Inverter capacity is defined as 1 pu on 1 MVA base. The point Vpcc is the PCC voltage before compensation. Points Z1 and Z2 are the new operating points after compensation using P-V and Q-V methods, respectively. Since the X/R ratio of the system under discussion is 1, both PV and Q-V droop methods will inject equal amount P and Q to compensate the PCC voltage, in this case full inverter rating of 1 pu for example. The

new operating voltage point after compensation is depicted as point . For this same system, to

regulate the PCC voltage from Vpcc to the proposed P-Q-V droop control will utilize 0.707 pu active

as well as 0.707 pu reactive power. The point Z3 in Fig. 8 represents the new operating point using the proposed P-Q-V droop controller. In other words, almost 30% of inverter rating can be utilized to

regulate the PCC voltage below operating point. Thus, the proposed P-Q-V droop control method

may give better system voltage regulation in low X/R system.

CONTROL DESIGN FOR THE P-Q-V DROOP METHODIn this section the I-PV inverter control algorithm with the proposed P-Q-V droop method is developed and is shown in Fig. 9. The algorithm uses a decoupled current control strategy utilizing both direct and quadrature components. It consists mainly of outer and inner current loops. The controller is initialized by calculating the difference between the reference voltage Vref and the measured PCC voltage. It passes the output signals through PID controllers to generate Id,ref and Iq,ref (compensating current in d-q frame). The inner current loop is used to regulate the direct and quadrature components of the inverter output current, passed through PI controller to produce the corresponding reference voltages Vd,ref and Vq,ref. A voltage loop is used to get the ABC frame of Vd,ref & Vq,ref and produce the reference signals V*

abc & Ф for PWM operation of the inverter.

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Vabc Iabc

DQ transformation & power

calculation

Voltage Loop

Vref

ΦPWM + PV

Inverter

Id,ref

Iq,ref

P

Q

Vmeas – nd*P

Vmeas – md*Q PID

+

+

-

-

Vref

PID

V*abc

Outer current loopDroop controller

Vd,ref

Vq,ref

nd from Lookup table

Current Loop

Inner current loop

PLL

Lookup table RMSSin ωt

Cos ωt

Vref

md from Lookup table

nd

md

Sin ωtCos ωt

From PLL

Fig. 9 I-PV system control schematic-using P-Q-V droop method.

The park’s d-q transformation is used to calculate the inverter active and reactive powers used in compensation as follow:

(21)

(22)

Using , , , and , the active and reactive powers are calculated as follows:

(23)

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(24)

The active and reactive powers calculated in (23) and (24) are used with the droop coefficients from lookup table, to droop the reference voltage by certain amount as shown in the outer control loop of Fig. 9.

The droop coefficients nd and md are determined by calculating the difference between the measured and reference values of PCC voltage, and comparing it with a predefined limit. Based on this comparison, the controller starts with reactive power compensation. The droop coefficient md is obtained first from the lookup table. If the reactive compensation is found to be insufficient to regulate the PCC voltage within acceptable limit, the controller shifts to use both active and reactive power by obtaining the new droop coefficients nd and md from the lookup table. In each case the controller observes the limits of the active and reactive powers (rating of the inverter) to guarantee not exceeding this limit.

SIMULATION STUDYA simulation study based on the I-PV configuration illustrates the effectiveness of P-Q-V method to regulate the PCC voltage.

A]. System under consideration

A power distribution network resembling the two-feeder network configuration and a PV solar plant of Fig. 1 is considered. The voltage levels of both the feeders are considered as 11 kV. The acceptable range of PCC voltage variation is considered as ±5%. Inverter-1 and 2 each have a rating of 2 MVA. It is considered that feeders-1 and 2 can circulate a maximum of 1 MW active power between them through the PV inverters. This limit is considered to avoid considerable voltage drop on the other feeder from which the active power is to be taken. The loads on the feeders are considered as P and Q loads, located at the ends of each feeder and have different values. The voltages V pcc1 and Vpcc2 represent the PCC voltages at feeer-1 and feeder-2, respectively. P inv1, Qinv1, Pinv2 and Qinv2 are the active and reactive powers injected or absorbed by Inverter-1 and Inverter-2, respectively. The leading reactive powers supported by Inverter-1 and Inverter-2 are shown as positive quantities, while the lagging reactive powers are shown as negative quantities.

The simulation results are expressed in per unit (pu), with base voltage of 11 kV and base power of 1 MVA. Appendix-I contains the data used for the simulated system.

B]. Simulation Results

For simplicity, only one feeder voltage, in this case feeder-2, is regulated. The change in PCC voltage beyond ±5% is achieved by simulating the following scenarios: (i) for voltage rise more than 5% limit, active power from another renewable source is injected into the system and (ii) for voltage drop below

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5%, heavy load is connected to the feeder-2 (without additional active power injection from the renewable source in the previous condition). The important simulation timelines are listed below:

t1: Inverter-2 starts operation to regulate the feeder-2 PCC voltage based on P-V, Q-V or P-Q-V droop methods, with normal loads.

t2: Feeder-2 PCC voltage is increased above 5% limit due to active power injection from another source.

t3: Feeder-2 PCC voltage is decreased below 5% limit due to increased load and with no active power injection from another source.

(i) System Performance with P-V droop method

Fig. 10 shows the performance of feeder-2 for the above mentioned three different conditions. The PCC voltage is regulated according to the P-V droop control method. Figs. 10 (a) to (d) show the PCC voltage before and after compensation, active and reactive powers injected by inverter-2, the circulated active power between feeder-1 and feeder-2, and the apparent power S circulated through inverter-2 with respect to its rated capacity of 2MVA, respectively.

For the first interval (time = t1 to t2 sec), the PCC voltage is 1.035 pu, and it is reduced to 1.015 pu using P-V droop method. This reduction is achieved by absorbing 0.6 pu active power through inverter-2 and is drawn from the feeder-1. For the second interval (time = t2 to t3 sec), the PCC voltage is increased to 1.089 pu and it is regulated to 1.06 pu. This reduction in PCC voltage is achieved by absorbing 1 pu active power. It should be noted that the inverter-2 could absorb up to 2 pu to regulate the PCC voltage. However, we have considered a maximum limit of 1 pu for active power injection in order not to overload the feeder-1 and thus to maintain its voltage within acceptable limit. During the third interval (time = t3 to 1.4 sec), the PCC voltage falls to 0.925 pu due to heavy load on the feeder-2. In this case, the inverter-2 injects maximum allowable 1 pu active power to improve the PCC voltage from 0.925 to 0.945 pu. The droop coefficient for this method is 0.02 pu/MW for all the operating conditions.

(a) Feeder-2 PCC voltage before and after compensation

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(b) Active and Reactive powers of inverter-2

(c) Active power circulated between the two feeders

(d) Apparent power S and inverter-2 limits

Fig.10 Feeder-2 performance using P-V droop control method.

(ii) System Performance with Q-V droop method

Fig. 11 shows the performance of feeder-2 with Q-V droop method. The conditions for the PCC voltage before compensation are kept identical as that of P-V droop method. During the first interval the voltage is reduced from 1.035 pu to 1.02 pu [Fig. 11 (a)] by injecting 1.0 pu inductive reactive power through inverter-2 [Fig.11 (b)]. During the second interval, the PCC voltage is regulated around 1.055 pu. This is achieved by absorbing 2 pu inductive reactive power capacity of inverter-2 as shown in Fig. 11 (b). The PCC voltage is raised from 0.925 to 0.948 pu for the third interval by injecting capacitive reactive power of 2 pu. The droop coefficient for this method is 0.01 pu/MVAR. As noticed from the results of Fig. 11,

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the Q-V droop method utilizes the full inverter rating to compensate for voltage rise and voltage drop. A low X/R ratio system would require higher capacity of inverter to regulate the PCC voltage below the set margin of ±5%.

(a) Feeder-2 PCC voltage before and after compensation

(b) Active and Reactive powers of inverter-2

(c) Apparent power S and inverter-2 limits

Fig.11 Feeder-2 performance using Q-V droop control method.

(iii) System Performance with P-Q-V droop method

Fig. 12 gives the performance of the same system with the proposed P-Q-V droop method. During the first interval, as illustrated in Fig. 12 (a), the PCC voltage is reduced to 1.025 pu by absorbing 0.5 pu inductive reactive power through inverter-2. The preceding evaluation using the Q-V droop method suggests that only reactive power compensation may not be enough to regulate the PCC voltage within the ± 5% limit during the second and third intervals. As viewed from Fig. 12 (a), the PCC voltage is regulated to 1.04 pu during the second interval. This is achieved by absorbing 1.4 pu inductive reactive power and 0.8 pu active power [Fig.12 (b)].

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(a) Feeder-2 PCC voltage before and after compensation

(b) Active and Reactive powers of inverter-2

(c) Active power circulated between the two feeders

(d) Apparent power S and inverter-2 limits

Fig. 12 Feeder-2 performance using the proposed P-Q-V droop control method.

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Furthermore, for the third interval, the PCC voltage is improved from 0.925 to 0.96 pu. This is achieved by injecting simultaneous 1.4 pu capacitive reactive power and 0.7 pu active power, as noticed from Fig.12 (b). The total amount of apparent power S handled by inverter-2 using the proposed P-Q-V droop method is given in Fig.12 (d). It can be noticed that the inverter capacity is optimally utilized to achieve better voltage regulation over P-V and Q-V droop methods.

During the first interval, the active power coefficient is 0, as the controller primarily uses the reactive power for the compensation. In this case the reactive power coefficient is 0.04 pu/MVAR. For the second interval the active droop coefficient is 0.08 pu/MW, while the reactive power coefficient is 0.018 pu/MVAR. Note that the reactive power coefficient is reduced to absorb as much as possible the reactive power from the inverter. The active power and reactive power coefficients are noticed as 0.1 pu/MW and 0.024 pu/MVAR during the third interval, respectively.

CONCLUSIONIn an I-PV system, the PV solar plant inverters are reconfigured and connected back-to-back to interconnect two feeders. The I-PV system with proposed P-Q-V system is then controlled as flexible AC transmission system device to regulate the point of common coupling voltage. It is shown in the paper that the coupling effect between active and reactive powers due to complex network impedance need to be considered to achieve adequate voltage regulation. A lookup table approach is used to determine active and reactive droop coefficients. A MATLAB/Simulink based simulation study has been performed to evaluate the effectiveness of proposed P-Q-V droop method for the PCC voltage regulation.

ACKNOWLEDGMENTThis work is supported by Masdar Institute under MIT-Masdar Institute joint research project grant.

APPENDIX-IFeeders-1 and -2 system voltage level, Vs1 = Vs2 = 11 kV.

Line parameters: 0.08 + j0.04 ohm/km.

Line lengths: L11 = L21 = 20 km, L12 = L22 = 4 km.

REFERENCES

Aminifar, F., M. Fotuhi-Firuzabad, et al. (1-3 Dec. 2008). Effect of Interline Power Flow Controller (IPFC) on interconnected power systems adequacy. Proc. Power and Energy Conference (PECon), Johor Bahru

67 | P a g e

Arias, M., D. Lamar, et al. (24-28 Feb. 2008 ). Simple droop voltage control system for parallel operation of UPS. Proc. Applied Power Electronics Conference and Exposition (APEC), Austin, TX

Barbosa, P., L. Rolim, et al. (Sep 1998 ). Control strategy for grid-connected DC-AC converters with load power factor correction. IEE Proc. Generation, Transmission and Distribution.

Bergen, A. R. (1986). "Power systems analysis."

Borgstrom, M., J. Wallentin, et al. (2011). "Nanowires with promise for photovoltaics." IEEE Trans. on Selected Topics in Quantum Electronics 17(4): 1050 - 1061.

Chandorkar, M. C., D. M. Divan, et al. (1993). "Control of parallel connected inverters in standalone ac supply systems." IEEE Trans. on Industry Applications 29(1): 136-143.

Chandrokar, M., D. Divan, et al. (20-25 Jun 1994 ). Control of distributed UPS systems. Proc. Power Electronics Specialists Conference (PESC), Taipei , Taiwan

Chen, J. F. and C. L. Chu (1995). "Combination voltage-controlled and current-controlled PWM inverters for UPS parallel operation." IEEE Trans. on Power Electronics 10(5): 547-558.

De Brabandere, K., B. Bolsens, et al. (2007). "A voltage and frequency droop control method for parallel inverters." IEEE Trans. on Power Electronics 22(4): 1107-1115.

68 | P a g e

Eberly, D. H. (2004). 3D game engine architecture: engineering real-time applications with Wild Magic, Morgan Kaufmann Pub.

Enslin, J. H. R. and P. J. M. Heskes (2004). "Harmonic interaction between a large number of distributed power inverters and the distribution network." IEEE Trans. on Power Electronics 19(6): 1586-1593.

Flores, P., J. Dixon, et al. (2009). "Static var compensator and active power filter with power injection capability, using 27-level inverters and photovoltaic cells." IEEE Transactions on Industrial Electronics 56(1): 130-138.

Guerrero, J. M., J. Matas, et al. (2006). "Wireless-control strategy for parallel operation of distributed-generation inverters." IEEE Trans. on Industrial Electronics 53(5): 1461-1470.

Gyugyi, L., K. K. Sen, et al. (1999). "The interline power flow controller concept: a new approach to power flow management in transmission systems." IEEE Trans. on Power Delivery 14(3): 1115-1123.

Hanaoka, H., M. Nagai, et al. (23-23 Oct. 2003 ). Development of a novel parallel redundant UPS. Proc. Telecommunications Energy Conference (INTELEC), Yokohama, Japan

Hingorani, N. G., L. Gyugyi, et al. (2000). Understanding FACTS: concepts and technology of flexible AC transmission systems, IEEE press New York.

Khadkikar, V. and J. L. Kirtley (24-29 July 2011 ). Interline Photovoltaic (I-PV) power system—A novel concept of power flow control and

69 | P a g e

management. Proc. Power and Energy Society General Meeting, Detroit, MI, USA

Patel, H. and V. Agarwal (2010). "Investigations into the performance of photovoltaics-based active filter configurations and their control schemes under uniform and non-uniform radiation conditions." IET Trans. on Renewable Power Generation 4(1): 12-22.

Reed, G. F., B. M. Grainger, et al. (19-22 April 2010). Analysis of high capacity power electronic technologies for integration of green energy management. Proc. IEEE Transmission and Distribution (TDC), New Orleans, LA, USA.

Sheng, X., J. Liu, et al. (2010). "Integration of Self-Assembled Porous Alumina and Distributed Bragg Reflector for Light Trapping in Si Photovoltaic Devices." IEEE Letters on Photonics Technology 22(18): 1394-1396.

Varma, R. K., V. Khadkikar, et al. (2009). "Nighttime application of PV solar farm as STATCOM to regulate grid voltage." IEEE Trans. on Energy Conversion 24(4): 983-985.

Walling, R., R. Saint, et al. (2008). "Summary of distributed resources impact on power delivery systems." IEEE Trans. on Power Delivery 23(3): 1636-1644.

Wu, T. F., H. S. Nien, et al. (2007). "PV power injection and active power filtering with amplitude-clamping and amplitude-scaling algorithms." IEEE Trans. on Industry Applications 43(3): 731-741.

Yao, W., M. Chen, et al. (17-21 June 2007 ). An improved multiple-loop controller for parallel operation of single-phase inverters with no

70 | P a g e

control interconnections. Proc. Power Electronics Specialists Conference (PESC), Orlando, FL.

Yao, W., M. Chen, et al. (2011). "Design and analysis of the droop control method for parallel inverters considering the impact of the complex impedance on the power sharing." IEEE Trans. on Industrial Electronics, 58(2): 576-588.

Yoshino, T., T. Amboh, et al. (4-7 July 2010). MW-rated power electronics for sustainable and low carbon industrial revolution. in Proc. IEEE International Symposium on Industrial Electronics (ISIE).

Zavadil, R., N. Miller, et al. (2007). "Queuing up." IEEE Power and Energy Magazine 5(6): 47-58.

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Appendix 4: High Efficiency Resonant Power Converter For Solar Power Applications

Introduction:

The goal of this project is to build a high efficiency dc/dc resonant power converter with simultaneous near zero current and zero voltage switching at all power levels for a varying input voltage and fixed output voltage.

In this project we are developing, designing, building and testing a new class of high efficiency dc/dc resonant power converter that operates with simultaneous zero voltage switching and near zero current switching across a wide range of input voltages and output power levels. A converter implementation providing galvanic isolation and enabling large voltage conversion ratios greater than 1:10 is targeted. The dc/dc converter consists of an inverter, a transformation stage and a rectifier stage. The three stages have to be designed to minimize the total power loss (Fig.2).

Figure 2: Block diagram of a dc-dc converter

The converter is designed for connection to photovoltaic panels with varying output voltage depending on the solar insolation. The input voltage of the converter (from a single solar panel) will vary from 25-40V and it will have and output voltage of 350-400V. The converter is required to operate across an output power range of 20-200W.

The topology selected for this project is shown in Fig. 3. It consists of a converter with a resistance compression network. The converter will operate at fixed frequency with on/off control to vary the power output. Resistance compression networks [1] consist of inductors and capacitors which are lossless components. The network not only makes the input look resistive but also limits the power flow to the output in a desirable manner as the voltage conversion ratio varies.

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Figure 3: The Resistance Compression Network (RCN) dc/dc Converter

2 Resistance Compression Network Converter

The proposed RCN converter topology is shown in Fig. 3. It consists of a full-bridge inverter (S1-S4) operated at fixed switching angular frequency ω. A transformer for voltage up conversion and isolation, and a Resistance Compression Network terminating in diode rectifiers (synchronous rectifier may be used instead if desired). Snubbing capacitances (not shown) enable zero voltage switching, while the resistive load provided by the RCN and rectifier networks enable near zero- current switching. At resonant frequency ω0 the resonant tank composed of Lr and Cr acts as a short. Also, the tank is sufficiently high Q to have nearly sinusoidal current waveforms. The inductor Ls and the capacitor Cs with conjugate reactance comprise the RCN. They are chosen to limit the power flow as the voltage conversion ratio varies, and to make the impedance seen by the inverter look nearly resistive. The two diode half bridges are present for rectification; these may be realized as synchronous rectifiers in some implementations.

The RCN converter has near zero current switching as the resistance compression network makes the impedance seen by the inverter look substantially resistive at the fundamental of the switching frequency. A fundamental harmonic model of the converter is shown in Fig. 4. Here V x is the fundamental of the input voltage as seen on the secondary side of the transformer. V x is a function of the input voltage V in and the transformer turns ratio N and is given by:

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Figure 4: Fundamental harmonic model of the Resistance Compression Network (RCN) dc/dc converter

(1)

The rectifier half bridges can be modeled as equivalent resistors. The effective resistance of the rectifier is proportional to the output voltage V out and inversely proportional to average power P delivered to the rectifier [2]:

(2)

Since the output voltage is fixed the effective resistance of the rectifier decreases when the power increases with increase in input voltage. In our case it varies from 324.2Ω to 3242.3Ω. The use of a resistance compression network reduces this change in resistance and also limits the output power.

The input impedance of the RCN transformation stage looks purely resistive and is given by:

(3)

where X is the reactive impedance magnitude of the RCN elements (Ls and Cs) at the switching frequency. The value of the impedance is selected in such a way so as to limit the output power to 200W at an input voltage of 25V. Since the power deliver capability of the converter increases with input voltage, this ensures that the converter can deliver at least 200W across its entire input voltage range of 25-40V.

The current in each branch is

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(4)

The effective resistance of the rectifier is

(5)

where V D is the voltage at the diode which is (2/π)V out. Using equation (4)and (5) we get an expression for RL:

(6)

The power output is thus given by

(7)

So X has been chosen to get 200W output power with 25V input.

(8)

By increasing the input voltage from 25V to 40V the output power increases from 200W to maximum power. In Fig. 5 transformer turns ratio of 10 has been selected.

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Figure 5: Plot of Power vs. Input voltage

Power can be further modulated by on-off control of the converter at a frequency well below the switching frequency. Figures 6 and 7 show simulated waveforms for the proposed converter. The transistors output capacitance was not included in the simulation. In Fig. 6 the converter has an input voltage of 25V, while in Fig. 7 the input voltage is 40V. For this analysis the output voltage is fixed at 400V.

Figure 6: Waveforms of voltage and current at 25V input. V(vt2) and Ix: Voltage and current at primary of transformer. V(n009) and I(D4): Voltage and current at the D4 diode.

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Figure 7: Waveforms of voltage and current at 40V input. V(vt2) and Ix: Voltage and current at primary of transformer. V(n009) and I(D4): Voltage and current at the D4 diode.

3 First Prototype

The converter was designed with careful selection of components to minimize all the losses to maximize efficiency. For the first converter the operating frequency was 100kHz and the experimentally- measured efficiency was 93.5%

3.1 Detailed Design

3.1.1 Transformer Design

To select the transformer turns ratio the tradeoff between the losses in the parasitics of the transformer and the parasitic resistance of the RCN have to be considered. By increasing the transformer turns ratio and accordingly increasing reactance of RCN and resonant tank we can reduce the maximum output power at 40V (8) which reduces the current through the circuit. Also, the impedance of the resonant tank has to be greater than the RCN so that it does not greatly affect the resonant frequency of each branch.

Transformer turns ratio of 10 was selected which seems a reasonable tradeoff between the two losses. Considering the power requirements three core sizes were shortlisted among which RM10 is the smallest and RM14 the largest. The loss in a transformer can be divided into mainly core loss and copper loss. A good design usually balances the two to minimize the overall loss. By increasing the number of turns wound across the transformer core (increasing copper loss) the magnetic field density can be decreased (decreasing core loss). Figure 9 shows a plot of the total power loss versus different cores. Although RM14 has the least lost but RM12 has been selected to tradeoff size and loss.

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Figure 8: Plot of Power vs. Transformer turns ratio (N)

Figure 9: Plot of Power loss vs. the core size

In Fig. 10 the cross-section of one of the core windows is shown. The blue circles represent the cross-section of litz wire which is used for secondary winding and the black rectangles are the copper foils which is used for primary winding. The black circles is the cross-section of the total number of turns of litz wire that can fit in the allocated area. By using MATLAB both designs in Fig. 10 is optimized to minimize the loss. The number of turns of the windings (which

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corresponds to the length of the wire) and diameter of litz wire (which corresponds to number of strands of wire) varies in both designs.

(a) (b)

Figure 10: Cross-sectional of core windows. RM12 and RM14

Ferrite 3F3, 3C90 and 3C94 were considered as possible options. Figure 11 is the plot of core loss versus the change in temperature. Ferrite 3F3 was selected because it has the less loss over the entire temperature range of operation and more experimental data for parameter extraction was available.

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Figure 11: Plot of Power loss vs. materials

The cores loss is given by

(9)

Cm,x,y,ct0,ct1 and ct2are parameters found by curve fitting of the measured power loss data. f is frequency, Bmax is the maximum flux density and T is the temperature [3]. The design selected has RM12 core with 8 turns of primary winding and 80 turns of secondary winding. For the primary copper foil is used which is 0.488 m in length, 254um (10 mils) in thickness and 0.01405m in width. For secondary winding, 40 AWG litz wire is used which is 4.88 m in length with 30 strands in parallel.

3.1.2 Inductor

For the design of the inductors RM8, RM10, RM12 and RM14 gapped Ferrite 3F3 cores were considered. There are three inductors in the design of which two inductors of 506uH are for the resonant tank and an inductor of 372uH is for the resistance compression network. For 506uH inductor RM12A160 is selected as seen in fig. 7. Some cores are out-right rejected because of reaching the Bsat limit or thermal limit. They are replaced by zero power dissipation. The total loss for 506uH inductor is 2.175 W with a maximum current of 2.07A at a maximum input voltage of 40V. It has 56 turns using a 40 AWG 100 strands litz wire. It is 3.146m in length.

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Although, effort is made to balance the core and copper loss but in this case the core loss is approximately 3 times more than the copper loss. The core loss can be decreased by decreasing the B which in turn requires more number of turns (tradeoff between copper and core loss). However, this also implies increase of gap size to keep the inductance constant. RM12A160 which has the largest gap size (0.058 inches) is used. There is a limit to the increase in gap size as fringing and leakage becomes dominant. The total loss for 372 uH inductor is 1.1747W with a maximum current of 1.85 A at a maximum input voltage of 40V. The core used is RM12A160 with 48 turns of wire. The wire is 40 AWG 125 strands litz wire which is 2.928m in length.

Figure 12: Plot of total power loss of 506uH inductor vs. cores of different gaps and sizes at 40V input

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Figure 13: Plot of total power loss of 372uH inductor vs. cores of different gaps and sizes at 40V input

3.1.3 Transistors

For the full-bridge inverter EPC’s enhancement mode GaN transistors are being used. These devices have a much lower RQ product (On state resistance x total charge required to turn the device on and off) compared to the state-of-the-art silicon transistors.

LM5113 has been chosen as the gate driver. It is specially designed for the EPC GaN devices. It is a 100V bridge driver with an integrated high-side bootstrap diode. It also has under-voltage lockout capability.

3.2 Experimental Results

The first prototype experimentally-measured efficiency was 93.5% with the transistors switching at 25% of the peak current.

3.2.1 Components

Components Type

Transistors GaN HEMTs (EPC 2001)

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Diodes SiC schottky Diode (C3D02060E)

Transformer RM12 core , Copper foil and litz wire

Capacitors MC and MCN Multilayer RF Capacitors

Inductors RM12A160

Drivers LM5113

Controller TMS320F28335

3.2.2 Measurement Setup

The input voltage was provided by HP 6012 A DC power supply with voltage regulation. For the output load, thick film power resistors of 800Ω of TGH series by Ohmite were used. This resulted in a power dissipation of 200W. These were mounted on a large heat sink and cooled using a fan. A power analyzer (Yokogawa WT1800) was used to measure the efficiency. The converter voltage and current waveforms were obtained using Tektronix mixed signal oscilloscope (MSO 4054B).

3.2.3 Characterization of the transformer

The transformer built according to the procedure stated above was characterized using an impedance analyzer (Agilent 4395A). It was found to have a primary side leakage inductance of 0.689uH and mutual inductance at the primary 258.218uH. It has a secondary leakage

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inductance of 78.8uH. The capacitance is 3234pF at the primary and 12.8pF at the secondary. These are shown in fig. 14

Figure 14: Transformer parameters

Ringing was observed due to Lsl, Lpl and C2 resonating. This increases the over all loss.

Figure 15: V ds,V gsand Iprimaryat 25V input is shown

3.2.4 Soft switching

In Fig.16 the schematic of an inverter leg is shown. Dds are the body diodes of the switches and Cds is the drain to source capacitance. This could also represent additional external capacitance. At turn off the current Ix should be small and postive to reduce the current voltage overlap which causes power loss. The waveforms in Fig. 17 (a) show the turn off of the bottom switch. The bottom is turned off when the current Ix is 3.75A. It takes some time for the voltage V ds to rise to 25V. This overlap causes power loss in the device.

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At turn on the capacitor discharges and the current flows through the switch and causes power loss. In this case, the capacitor should be fully discharged and V dsshould be zero before the switch is turned on. This can be seen in Fig. 17(b)

Figure 16: Schematic of inverter leg

(a)

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(b)

Figure 17: Softswitching waveforms. (a) V ds,V gsand Ixfor bottom switch at turn off .(b) V ds ,V gs and Ix

for bottom switch at turn on.

4 Second Prototype

4.1 Detailed design

An important consideration for the second prototype is the operating frequency. The loss parameters and device area were sweeped over a frequency range of 100kHz to 600kHz to find the frequency with the minimum total loss. 500kHz was then chosen.

In fig.18 the predicted breakdown of loss is given. With increase in switching frequency the hard switching loss of the devices increases shown . With the help of carefully designed magnetics we can soft switch the converter and decrease the total loss. With increase in frequency, inductor loss and transformer loss decrease as seen in fig. 19 and fig. 20, respectively.

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Figure 18: Power loss vs Frequency. Device loss (Soft switching), Magnetic loss, Total loss and Hard switched device loss respectively

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(a) (b)

Figure 19: Inductor loss vs frequency. In part a resonant inductor loss is broken down in to conductor and copper loss. In part b the compression network converter loss has is given.

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Figure 20: Transformer loss vs frequency

Two EPC GAN devices are being used in parallel to form each inverter switch, which decreases the total device loss by almost half (fig.21)

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Figure 21: Device loss for 1, 2, 3 and 4 transistors used in parallel to decrease the conduction loss

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