1

Abstract--The dynamic behaviour of a PWM voltage source

inverter based voltage generator with an output LC filter is analyzed in this paper. This converter is able to participate to frequency regulation either in connected mode or in an islanded mode with minor modifications in the control algorithm. Thanks to a droop control, it is possible to achieve power sharing between this converter and a classical synchronous machine with a good dynamic behavior. In islanded mode, the converter generates a good voltage source. A strategy of islanding detection depending on the rate of Change of Frequency (ROCOF) was also developed. An original experimentation using Power Hardware in the Loop and real-time simulation was realized to verify the theoretical analysis.

Index Terms--Distributed generation, Droop control, LC filter, Voltage source Inverter (VSI), Primary frequency control.

I. INTRODUCTION he electricity market has recently seen a rapid growth of distributed generation due to environmental

considerations and the availability of, new, cheaper and efficient small size generators based. This leads to an integration of more and more distributed sources in electrical power systems which mainly use power electronic inverter as connection interface.

Microgrids can be a way to integrate distributed generation. They can be defined as an aggregation of several distributed energy sources which can feed their local loads even if the main grid is missing. Microgrids have two operation modes; it can operate either in parallel with the utility grid or in a stand-alone mode creating an islanded grid. Basically, in grid connected operation mode, inverter based generators usually work as a current injector [1], [2], since the main grid fixes the voltage to microgrid generators. On the other hand, in stand-

The author acknowledge MEDEE program and Nord Pas de Calais

Regional Council for their financial support. X. Guillaud, F. Salha are with University of Lille- Nord de France, L2EP,

Ecole Centrale de Lille, Cité Scientifique BP 48 59651 Villeneuve d’Ascq Cedex France (email : xavier.guillaud@ec-lille.fr).

F. Colas is with University of Lille- Nord de France, L2EP, Arts et Métiers ParisTech, 8, bd Louis XIV 59046 Lille cedex France (email : Frederic.COLAS@ENSAM.eu ).

alone mode, the loads in a microgrid can only receive power from the local sources, depending on the customer’s situation [3][4]. Then, a microgrid must have at least one voltage generator which is in charge of regulating voltage and frequency during stand alone operation mode [5].

The distributed generators must switch from a current injector to a voltage source behavior which needs a LC filter output. As a consequence, voltage generator control system has to adopt a power control strategy which let the microgrid generators sharing the power requested by the loads or the main grid. In such a system, every unit has to operate independently without communication due the distance between the distribution generators units [6]. In fact, control methods solely based on local measurements exhibit a superior redundancy, as they do not rely on communication [5]. These kinds of methods have a proportional controller for frequency and voltage and are denoted as droop methods [7], [8]. In [5], the control used a scheme based on droop control to operate inverters in both grid-connected and islanded operation mode. The line impedance was considered inductive which is often justified by the large inductor value or by the long distances between the units [9]. [10] has introduced a transformation matrix which can be used for any kind of output impedance and has proposed as in [11] the concept of virtual impedance for power sharing between generators. Most of these papers are dealing with the interaction between power electronic connected generators. In this paper, we are interesting in the interaction between power electronic connected generator and classical generator connected to the grid via synchronous machine.

LC current and voltage control is achieved using resonant controller. In grid connected mode, an active and reactive power control based on droop method is proposed. However, it is based on grid synchronization signal which can be lost when islanding. A ROCOF detection algorithm is then proposed to detect islanding. The power control algorithm is afterward switched to a suitable control for islanding mode.

This paper is divided into four sections; the first deals with PWM voltage source inverter based generator, its elements and control system. Whereas, the second part study the dynamic behavior of the PWM voltage source inverter based generator. This was realized by studying the power sharing between this inverter based generator and a classical voltage source represented by a synchronous machine. In this part primary frequency control will be presented. The third part deals with disconnection of the inverter based generator from

Dynamic Behavior Analysis of a Voltage Source Inverter for MicroGrid Applications

Fouad SALHA, Frédéric COLAS, Xavier GUILLAUD

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978-1-4244-6551-4/10/$26.00 ©2010 IEEE

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main grid represented by the synchronous machine. In the last part, the application of the control and islanding detecting strategies will be illustrated by using Power Hardware in the Loop principle and real time simulation.

II. DROOP CONTROL OF PWM VOLTAGE SOURCE INVERTER The overall diagram of the voltage source inverter based

generator is summarized in Fig. 1. Generally, these primary power sources are variable speed driven. So power electronics has to be used for connecting this source to the network. A rectifier is used to transfer the power delivered by the source into a DC voltage link. Then, the inverter connects this DC bus to the grid. The three-phase modulated voltages (vm) has to be filtered. Usually, a simple R, L inductance is used. Since a voltage source is required, a LC filter is chosen. The capacitor voltage control will give a voltage source behavior.

DC link voltage is controlled by the primary source thanks to the rectifier. On the grid side, currents and voltages are controlled by the inverter. Considering that the power demand is always within the capability of the device and the primary generator is able to maintain the DC-bus voltage in a narrow band, therefore this voltage us is assumed to be constant. Thus, the analysis can be limited to the control of the inverter.

The control system of the voltage generator is composed of three levels:

• LC filter voltage and current control. • Active Power control. • Primary frequency control.

A. LC filter voltage and current control Fig. 1 depicts the overall control system proposed for the

inverter and its output LC filter. This control strategy aims to generate a quasi sinusoidal three-phase voltages (vc1, vc2, vc3), [3], [12]. For this aim, we define a set of three voltage references (vc1REF, vc2REF, vc3REF). The control of the instantaneous voltage value is achieved by the mean of a resonant algorithm.

The control strategy is based on a state feedback for state variables. Pole placement technique is used to design the controller parameters. The whole method has been explained in [3].

This three-phase voltage source has to be synchronized to the network voltage. A classical Phase Lock Loop (PLL) is implemented and applied on the grid voltage (vG1, vG2, vG3). It generated the instantaneous grid angle θ.

B. Active power controller In a classical current source connection, the power

delivered to the grid is controlled by the magnitude and the phase of the current. In this application, the controlled quantities are the voltages. We have to implement another way for controlling the power flow to the grid. This is based on the classical power transfer method between two voltage sources in the lines. (Fig. 2 a-b) [10], [13].

(a)

(b)

Fig. 2 Power through a line (a) phase diagram (b)

In a three-phase non resistive line, the active and reactive power depends on the transmission angleδ between both voltage sources.

Fig. 1 Three Phase LC filter-connection to the grid

3

XVVP GC

cδsin

3= (1)

( ) CGCc

C LXVVXVQ ωδ =−= cos3 (2)

If the power angle δ is small, then δδ sin≈ and 1cos ≈δ

Equation (2) becomes: ( )GCc

C VVXVQ −= 3

Moreover if, we suppose: VVV GC =≈

Equation (1) becomes

XVPc

δ23= (3)

Since there is a close relation between the power flow and the angle, we use the algorithm presented in Fig. 3 to control the active power.

Fig. 3 Principle of calculating of the reference angle

The presence of a low pass filter is justified to reduce the 2ω components due to a possible imbalance in three-phase currents.

The coefficient Kp is calculated to obtain a 0.7 damping for the closed loop system. The chosen time response is 1.3s.

The value of δ is then introduced in the calculation of vc reference:

( )( )( )3/4sin.2.

3/2sin.2.

sin.2.

3

2

1

πδθ

πδθ

δθ

−+=

−+=

+=

REFREFc

REFREFc

REFREFc

Vv

Vv

Vv (4)

Where: θ is the grid angle delivered by the PLL. It achieves the synchronization of 321 ,, ccc vvv three-phase sources to the grid.

C. Primary frequency control The primary frequency control is similar to that usually

used in synchronous generators. A frequency decrease means an unbalance power between production and consumption. The rotational speed of the synchronous machine is proportional to the frequency, so it decreases also. A simple proportional speed regulator is used to adjust the generated power to the frequency. It is well known that this type of control leads to a good sharing of the load between generators.

Equation (5) describes the classical linear relation between the frequency and the active power in per unit which is proportional with a KVS droop value:

( ) 01 Pff

KP pumespuref

VSpuref +−= (5)

Fig. 4 presents the droop control for the active power.

Fig. 4 Frequency-power characteristic

Fig. 5 represents the primary frequency regulator applied in this study. The per unit value of the active power is converted into an actual value by multiplication with a base value of the converter power Pbase. We choose this base value equal to the nominal value of the converter active power.

Fig. 5 Primary frequency regulator Fig. 6 depicts the general organization of the studied

system. The power is delivered to the load by two sources: the studied voltage source inverter and a synchronous machine. A droop (KMS) is applied on the control of synchronous machine power to achieve the primary frequency control. We will afterward present what occurs when the synchronous machine is tripping.

III. DYNAMIC PERFORMANCE WHEN ISLANDING OCCURRENCE Microgrid islanding or Loss Of Grid (as named in [14])

process occurs in case of a an incident or preplanned switching. The disconnected system part remains energized due to the PWM voltage source inverter existing in the islanded system.

This generator has to meet the corresponding load requirements and stay operational in an autonomous mode after islanding [15].

The control of the LC filter has to be modified to take into account this new situation. The main modification is the calculation of voltage reference angle.

Indeed, in case of a grid connected mode, the PLL is calculating the grid angle. In case of islanded mode, the grid angle is imposed by the source and generated by integration of the microgrid frequency reference.

4

∫=t

ref dtf0

2πθ (6)

The instantaneous frequency f may be slightly modified by the “P control”.

IV. SWITCHING BETWEEN CONNECTED AND ISLANDED MODE The distributed generator needs a specific system to detect

the switching between connected and islanded mode. Several islanding detection methods are discussed on [13], [16], [17]. In this paper, relay ROCOF (Rate Of Change Of Frequency) is used to detect the islanding mode. When the grid is tripped, all the load power has to be instantaneously delivered by the voltage source inverter. Due to “P control algorithm”, the instantaneous frequency fΔ increases quickly. The level of rate of change of frequency increases. This level is used to detect the islanded operation. A model of the ROCOF relay was established taking into account the natural frequency variation resulting from measures noise. Fig. 7 shows the implemented model of the rate of change of frequency measurement.

Fig. 7 ROCOF relay implemented model

Two parameters have to be chosen: • T: the time constant of the filter : 0.12 s

• limdt

df : the rate of change of frequency limit : 0.5 Hz/s

The ROCOF relay output signal validates the switching

event. This signal is called the Switching Validation (SV).

V. REALIZATION AND EXPERIMENTAL STUDY An experimental setup based on a real-time simulator is

developed to validate the theoretical dynamic study of the whole system.

We use a Power Hardware In the Loop (PHIL) simulation technique to validate the control strategy. HIL is still commonly used to test the actual control system in interaction with real-time simulation [18].

In case of PHIL, a power device is tested, so it needs the use of a high bandwidth power amplifier between the real-time simulator and the device itself (See Fig. 8).

This power amplifier generates a three phase voltage source whose magnitudes are delivered by the simulator. The sensors placed on the device under test are giving some data (current, voltage) which are introduced in the simulator thanks to Analog Digital Converters.

Fig. 8 Illustration for the Power Hardware In the Loop (PHIL) scheme simulation

A. Experimental facility The structure under study (Fig. 9) is composed of two main

parts: The first one is the virtual environment implemented in RT-LAB real time simulator [19]-[21]. It contains the model of a voltage source inverter with LC filter controlled by the

Fig. 6 Scheme for studied case implementation

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proposed explained strategy. The second part is the actual system which represents the

physical elements of the studied power system. The classical voltage source connected to the voltage source inverter is the synchronous machine, whose power is controlled by a DC current motor. The speed control of the DC motor was achieved by a proportional controller which emulates a droop control. The voltage magnitude delivered by the synchronous machine is controlled by action on the excitation system.

B. Results and discussion 1. Connected Operation Mode (Power sharing tests):

The studied system parameters were presented on TABLE 1

TABLE 1 STUDIED SYSTEM PARAMETERS

Fig. 10 describes the behavior of the whole system when the voltage source inverter and the synchronous machine are connected on the same grid.

• t = 22.9 s, a 8.8 kW load is applied. The inverter does not generate any active power because of a fixed zero active power reference value. We notice, because of the frequency primary controller, the frequency decreases to 46.55 Hz (Fig. 10 a-b).

• t = 46.85 s, 1 kW active power reference value was added to inverter active power control system. We can check on Fig. 11 that the time response is 1.4 s which corresponds to the theoretical time response (1.3 s).

The synchronous machine decreased its generated power of 1 kW value which induces an increase on the frequency (47.1 Hz) (Fig. 10-b). This signifies that the injected inverter active power reduces the generation of the synchronous generator.

• t= 61 s: the voltage source inverter primary frequency control is validated leading the two voltage sources to a load sharing. The power is shared between both sources in proportion with the droop value. Due to the inverter primary frequency regulation the power reference values increased to 3.8 kW and the frequency to 48.1 Hz.

20 40 60 80 100 120 140 160-2000

0

2000

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6000

8000

10000

Time (s)

Filte

red

Pow

er R

epar

titio

n (W

)

Voltage source inverter Power

Load Power

Synchronous Machine

Power

(a) Active power sharing between generators and load

20 40 60 80 100 120 140 16046

46.5

47

47.5

48

48.5

49

49.5

50

50.5

51

Freq

uenc

y (H

z)

Time (s) (b) Frequency

Fig. 10 Description of connected operation mode

Connecting network inductance Lc 10 mH Connecting network resistance Rc 1.5 ohm LC filter resistance (Rs) 0.1 ohm LC filter inductance (Ls) 1 mH LC filter capacity C 20 µF Operation voltage magnitude 400 V ph-ph DC bus voltage us 760 V Synchronous machine rated power 15 KVA Synchronous machine rotation speed 1500 rpm Load power 9 kW SnomVS 15 KVA KMS 11.5% KVS 20%

Fig. 9 Experimental Test Bench

6

42 44 46 48 50 52 54 56

-200

0

200

400

600

800

1000

1200

Vol

tage

sou

rce

inve

rter f

ilter

ed p

ower

(W)

Time (s) Fig. 11 Transient on voltage source inverter power

2. Islanding test ROCOF principle relay is integrated on the overall control

strategy in order to detect the islanding, and consequently to switch the control to work in islanding operation mode. Before the switching event, the two generators are sharing 1.3kW load via the primary frequency control system. The synchronous machine is tripped at 94.7 s Fig. 12-a. This induces a decreasing in ( f) shown on Fig. 12-b. Fig. 12-c depicts the rate of change of frequency at the islanding moment. When this curve crosses the ROCOF level limit (0.5 Hz/s), SV signal is toggled (Fig. 12-b). In Fig. 12-b the frequency turned to a constant value as mentioned before.

94.4 94.5 94.6 94.7 94.8 94.9 95 95.1 95.2 95.3 95.4

0

500

1000

1500

Filt

ered

Pow

er re

parti

on (W

)

Time (s)

Islanding

Synchronopus Machine Power

Voltage source inverter Power

(a) Inverter based generator and alternator generated powers

94.4 94.5 94.6 94.7 94.8 94.9 95 95.1 95.2 95.3 95.449.6

49.7

49.8

49.9

50

50.1

Freq

uenc

y (H

z)

Time (s) (b) Frequency

94.4 94.5 94.6 94.7 94.8 94.9 95 95.1 95.2 95.3 95.4-1.5

-1

-0.5

0

0.5

1

1.5

2

Filte

red

df/d

t (H

z/s)

Time (s)

IslandingDetection

(c) Rate of change of frequency

94.4 94.5 94.6 94.7 94.8 94.9 95 95.1 95.2 95.3 95.4

0

0.2

0.4

0.6

0.8

1

RO

CO

F re

lay

outp

ut

Time (s) (d) ROCOF relay output signal (SV)

Fig. 12 Transient behavior on a switching event.

3. Islanded operation mode: When the system is in islanded mode, we verify its good

behavior in case of load variation by applying a 8.8 kW load. Fig. 13 depicts the power generated by the voltage source inverter in the islanded operation mode. We notice a slight frequency variation due to “P control” algorithm which is still available (Fig. 14). Fig. 15 depicts the voltage source inverter voltage during the load variations. This voltage remains controlled in the islanded operation mode when the load is varied.

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sour

ce in

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r Pow

er (W

)

Time (s) Fig. 13 Voltage source inverter power in an islanding operation mode

7

50 60 70 80 90 100 110 120

49.4

49.6

49.8

50

50.2

50.4Fr

eque

ncy

(Hz)

Time (s) Fig. 14 Voltage source inverter power in an islanding operation mode

Fig. 15 Inverter output voltage

VI. CONCLUSION In this paper, the dynamic behavior of voltage source

inverter embedded on a distribution system has been studied. A primary frequency control strategy based on droop control was proposed. ROCOf relay principle was used in this paper in order to detect the islanding. The proposed control algorithm relies on islanding detection via ROCOF and then switching the control to work with an imposed frequency. The control strategy was tested and analyzed in three operation stages; first in a grid connected operation mode, then during the islanding operation and finally in the islanded mode. Experimental implementation for the control strategy was achieved on a real time simulator. Frequency and power sharing were traced in every part of study. Experimental results show the effectiveness of the control strategy in both grid-connected and islanded operation mode. For the future work, a droop control for the reactive power will be applied and then the parallel connected operation mode of several voltage source inverters will be studied.

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