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M E T H O D O L O G Y Open Access

Control principles of micro-source inverters

used in microgrid

Wenming Guo

*

and Longhua Mu

Abstract

Since micro-sources are mostly interfaced to microgrid by power inverters, this paper gives an insight of the control

methods of the micro-source inverters by reviewing some recent documents. Firstly, the basic principles of different

inverter control methods are illustrated by analyzing the electrical circuits and control loops. Then, the main

problems and some typical improved schemes of the ωU-droop grid-supporting inverter are presented. In results

and discussion part, the comparison of different kinds of inverters is presented and some notable research points is

discussed. It is concluded that the most promising control method should be the ωU-droop control, and it is

meaningful to study the performance improvement methods under realistic operation conditions in the future work.

Keywords: Mirogrid, Micro-source inverter, Droop control, Control principle

Introduction

Recently, with the increased concern on environment and

intensified global energy crisis, the traditional centralized

power supply has shown many disadvantages.Meanwhile,

the high-efficiency, less-polluting distributed generation

(DG) has received increasing attentions [1, 2]. Microgrids

[3–5], which comprise micro-sources, energy storage

devices, loads, and control and protection system, are the

most effective carrier of DGs. When a microgrid is con-

nects to the utility grid, it behaves like a controlled load or

generator, which removes the power quality and safety

problems caused by DGs’direct connection. Microgrids

can also operate in islanded mode, thus increase system

reliability and availability of the power supply.

Proper control is a precondition for microgrids’stable

and efficient operation. The detailed control requirements

come from different aspects, such as voltage and fre-

quency regulation, power flow optimization etc. Since

these requirements are of different importance and time

scale, a three-level microgrid control structure is proposed

in [6]. As the foundation of microgrid control system, the

primary control is aimed at maintaining the basic oper-

ation of the microgrid without communication, which has

become a hot research topic recently. Since most micro-

sources utilize inverters to convert electrical energy, the

primary control is essentially the management of power

inverters. Micro-source inverters are required to work in a

coordinated manner based only on local measurements

and the control strategies decide the roles of each micro-

source. According to the principle of master–slave con-

trol, the micro-source inverters can be divided into grid-

feeding, grid-forming, and PQ-droop grid-supporting

inverters. From the perspective of peer control, the ωU-

droop grid-supporting invertershelp to realize microgrids’

plug and play function. Although being widely discussed

in the technical literatures, it still lacks a sufficient prac-

tical control method andexisting control technologies

need to be further studied and improved. This paper

describes the control principles of several typical micro-

source inverters and compares their characteristics so as

to provide a fundamental understanding of microgrids’

primary control.

Method

Grid-feeding inverter

The control objective of grid-feeding (GFD) [11] inverter

is to track the specified power references. Figure 1 illus-

trates the control block diagram of the most common

current controlled GFD inverter. For dispatchable micro-

sources, such as micro-turbine and fuel-cells, the inverter

power references can be set directly according to practical

requirements. For non-dispatchable micro-sources, such

as photovoltaic cells, the active power reference is usually

decided by the voltage controller of the inverter’s DC bus.

* Correspondence: gwmsch@163.com

Department of Electrical Engineering, Tongji University, Shanghai, China

Protection and Control o

f

Modern Power S

y

stem

s

© 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0

International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and

reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to

the Creative Commons license, and indicate if changes were made.

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5

DOI 10.1186/s41601-016-0019-8

In addition, this type of sources can also export reactive

power without affecting maximum power point tracking.

The GFD inverter’s power referencetrackingis realized by

adjusting the output currents. The control system calculates

the output current references based on the relationships

among the inverter’s output power, output current and the

voltage at the point of connection (PC). The three-phase

voltages at the PC are represented by vector v,andthe

inverter’s output currents are represented by vector ias

v¼vavbvc

½

T

i¼iaibic

½

T

Neglecting the power consumed on the filter inductor,

the output power of GFD inverter is calculated accord-

ing to instantaneous power theory [7]as:

P¼v:i

Q¼−vi

jj

nð1Þ

If the current controller in Fig. 1 is properly designed,

the output currents of the GFDinverter will follow their

references. Thus the current reference vector, i

ref

, can be

obtained by solving the following equation:

Pref ¼v⋅iref

Qref ¼−viref

jj

ð2Þ

The output currents of the GFD inverter are the same

as the currents flownthrough the filter inductor. In nat-

ural reference frame, there exists the following relation:

sLi¼uinv −uð3Þ

The voltages at the PC, u, are measured using voltage

transducers, the output voltages of the inverter, u

inv

, can

then be adjusted based on u(see the voltage feedforward

in Fig. 1) to control the voltage drop on the filter in-

ductor. This implies that the filter inductor’s currents

can be controlled indirectly. If the potential at the mid-

dle point of the inverter’s DC bus equal zero and ignore

the delay of PWM process, the inverter is equivalent to

a proportional element with gain k

PWM

. Thus, the

closed-loop transfer function of the inverter’s current

control can be written as:

GcsðÞ¼ kpwmTcsðÞ

sL þkpwmTcs

ðÞ ð4Þ

T

c

(s) needs be designed in a way to ensure G

c

(s) have

sufficient bandwidth. Meanwhile, the gain and phase

shift of G

c

(s) around fundamental frequency should be

close to 0 dB and 0 degree respectively. Therefore, the

output current of the GFD inverter can track their refer-

ences quickly and accurately.

For three-phase balanced operation cases, the control

system of the GFD inverter is usually designed in dq refer-

ence frame, where the voltages and currents are DC signals.

In this case, using PI controller can realize the output

current tracking without steady-state error. In dq reference

frame, the Park transformation will result in coupling

between the dand qaxis inductor currentcomponents, as

shown in Eq. (5). Therefore, the control system must com-

prise dq decoupling modules. The detailed control block

diagram in dq reference frame is illustrated in Fig. 2.

sLIdq ¼Uinv;dq−Udq −0−ωL

ωL0

Idq

ð5Þ

For unbalanced operation cases, the GFD inverters

need simultaneously controlthe positive and negative se-

quence currents [8, 9]. Under such condition, using PR

controller [10] in αβ reference frame might be a better

choice as a single PR controller can regulate both the

positive and negative sequence currents, and the control

effect is similar to that of using two PI controllers in

double positive/negative dq reference frames.

Fig. 1 Control block diagram of grid-feeding inverter

Fig. 2 Current control loop of GFD inverters in dq reference frame

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5 Page 2 of 7

Grid-forming inverter

The control objective of the grid-forming (GFM) [11] in-

verters is to maintain stable voltage and frequency in a

microgrid. GFM inverters are characterized by their low

output impedance, and therefore they need a highly accur-

ate synchronization system to operate in parallel with other

GFM inverters [11]. GFM inverters usually equips with

energy storage on their DC sides, therefore they can

respond to the change of load in a short time. The control

block diagram of a GFM inverter is shown in Fig. 3, includ-

ing an inner inductor current loop, which is identical to

that of the GFD inverter, and an outer capacitor voltage

loop. GFM inverters achieve their control objective by regu-

lating the filter capacitor’svoltage,u. In natural reference

frame, there exists the following relation:

sCu¼i−ioð6Þ

where iandi

o

are the inductor and grid currents,

respectively.

According to the above analysis, the GFM inverters can

also precisely control their inductor current by a properly

designed inner current loop. The impact of the grid current

on capacitor voltage is removed by current feedforward

and thus, uis fully controlled by adjusting i.

As shown in Eq. (7), in thedq reference frame, the dand

qaxis component of the filter capacitor voltage are also

coupled. Similarly, it is necessary to introduce dq decoup-

ling modules in the voltage control loop as illustrated in

Fig. 4.

sCUdq ¼Idq −Io;dq−0−ωC

ωC0

Udq

ð7Þ

Grid-supporting inverter

There exists an approximate linear droop relation between

the P-ωand Q-U of traditional synchronous generators. By

emulating this output characteristics, grid-supporting (GS)

[11] inverters, aimed at sharing load proportional to their

power capacities, can deploy two different droop control

structures, namely “PQ-droop”and “ωU-droop”. The PQ-

droop GS inverter adjusts its output power as a function

of the variation of the microgrid’s voltage and frequency.

In this case, the inverter behaves like a power source and

its control system is designed based on that of the GFD

inverter, as shown in Fig. 5(a). On the contrary, the voltage

and frequency at the PC of the ωU-droop GS inverter are

adjusted according to the variations of its output power.

The ωU-droop GS inverter behaves as a controlled voltage

source and its control system is based on that of the GFM

inverter, as shown in Fig. 5(b).

In Fig. 5, ω

0

and U

0

represent the no-load frequency

and no-load voltage, k

P

and k

Q

represent the active and

reactive power droop coefficients, respectively. In steady

state, the frequency of the microgrid is a global quantity,

and the voltages at different points of the microgrid are

almost identical. If “ω

0

”and “U

0

”of each inverter are identi-

cal, then both the PQ-droop GS inverter and the ωU-

droop GS inverter can share load variations as follows:

kp1ΔP1¼kp2ΔP2¼…¼kpnΔPnð8Þ

kQ1ΔQ1¼kQ2ΔQ2¼…¼kQnΔQnð9Þ

where k

Pi

and △P

i

(i = 1,2,…,n) represent the active

power droop coefficient and output active power vari-

ation of the ith GS inverter, respectively. k

Qi

and △Q

i

represent the reactive power droop coefficient and out-

put reactive power variation of the ith GS inverter,

respectively. Although both types of GS inverters shown

in Fig. 5have a good load-sharing performance, the PQ-

droop GS inverter cannot operate by itself. In contrast,

the ωU-droop GS inverter is controlled as a voltage

source, and thus can work independently regardless of

the microgrid operation mode. The ωU-droop GS in-

verter has acquired extensive attentions for its excellent

features though some problems still exist, including:

Fig. 4 Voltage control loop of GFM inverters in dq reference frame

Fig. 3 Control block diagram of three-phase grid-forming inverter

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5 Page 3 of 7

the line impedance of a low-voltage microgrid has a

large resistive component, thus P-ωand Q-U droop

control is no longer suitable.

the voltages at the PCs of each inverter are not

completely equal, thus the GS inverters cannot

share reactive power precisely.

Many researchers have proposed various improved

methods to deal with the above problems and some typ-

ical schemes will be presented in the following sections.

A. Decoupling transformation method

As depicted in Fig. 6, the voltage at the PC of

theωU-droop GS inverter is denoted by U∠δ,and

the voltage at the microgrid bus is denoted by E∠0.

Z

L

is the line impedance between the inverter’s filter

capacitor and the microgrid bus with an impedance

angle of θ.

Due to the small power angle δ, it is assumed that:

sinδ¼δ;cosδ¼1ð10Þ

Thus, the output power of the GS inverter can be

expressed as:

P¼EU cosθ−E2cosθþEUδsinθ

ZL

Q¼EU sinθ−E2sinθ−EUδcosθ

ZL

ð11Þ

If both the resistive and reactive components of the

line impedance cannot be ignored, the output active and

reactive power of the inverter will be dependent on both

δand U. In this case, the P-ω(δ) and Q-U decoupling

relation will no longer valid. To solve this problem, the

virtual power P’,Q’and the transformer matrix T

PQ

are

introduced in [12, 13]:

P0

Q0

hi

¼TPQ P

Q

hi¼sinθ−cosθ

cosθsinθ

P

Q

hi ð12Þ

According to Eq. (11) and (12), it can be derived that:

P0¼EU

Zδ

Q0EU−E2

Z

ð13Þ

The ωU-droop control based on the virtual power is

given as:

ω¼ω0−kPP0

U¼U0−kQQ0

nð14Þ

Similarly, transforming ω(δ) and Uwith the matrix

T

ωU

[14] gives the virtual frequency (phase angle) and

voltage as:

ω0δ0

ðÞ

U0

hi

¼TωE

ωδðÞ

U

hi

¼sinθcosθ

−cosθsinθ

ωδðÞ

U

hi ð15Þ

According to Eq. (11) and (15), it can be derived that:

Fig. 6 Simplified model of ωU-droop grid-supporting inverter

Fig. 5 Control block diagram of grid-supporting inverter. aControl

block diagram of PQ-droop grid-supporting inverter. bControl block

diagram of ωU-droop grid-supporting inverter

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5 Page 4 of 7

P¼EUδ0þU−U2−E2

ðÞ

Ecosθ

Z

Q¼EUU0þU−U2−E2

ðÞ

Esinθ

Z

ð16Þ

Since Eand Uare constant when the droop control

process reaches steady-state, the output active and reac-

tive power of the GS inverter will be regulated by the

virtual frequency and voltage respectively. Thus, a novel

ωU-droop can be established:

ω0¼ω0

0−kPP

U0¼U0

0−kQQ

nð17Þ

In Eq. (17), ω

0

’and U

0

’is the corresponding virtual no-

load frequency and voltage. The droop control block dia-

gram of the GS inverters applying two types of decoupling

transformation method is shown in Fig. 7.

It is worth noting that the first decoupling method is

designed to share the virtual power rather than the real

power. So there exists a complicated relation between the

variations of each inverter’s output power and their droop

coefficients when the load in the microgrid changed. The

second decoupling method avoids this problem consider-

ing that all inverters have the same ω′and U′,i.e.theR/X

of each line in the microgrid must be identical. In

addition, the variables directly controlled by Eq. (17) are

ω′and U′, and thus, it is necessary to carefully select the

droop coefficients [14] to ensure that the real frequency

and voltage are located in reasonable ranges.

B. Virtual impedance method

The coupling between the output active and

reactive power of the conventional ωU-droop

control can be mitigated by introducing virtual

impedance [15], as illustrated in Fig. 8. The voltage

at the inverter’s PC is expressed as:

U¼GusðÞ Uref −GusðÞ ZVIoð18Þ

where G

u

(s) is the voltage closed-loop transfer function

of the ωU-droop GS inverter, and Z

V

is virtual impedance.

The total impedance between the equivalent voltage

source of the inverter and the microgrid bus can be writ-

ten as:

Z¼GusðÞ ZVþZLð19Þ

where Z

L

is the line impedance.

If the magnitude of the virtual impedance is much larger

than the line impedance, the total impedance will be

largely decided by the virtual impedance. However, the

large total impedance may cause the microgrid voltage to

reduce substantially. In [16], a novel method was proposed

to solve this problem by introducing a negative resistive

component into the virtual impedance. As the virtual

negative resistor counteracts the line resistor, the total

impedance can be designed to be mainly inductive and of

small magnitude. According to Eq. (11), if the total imped-

ance is mainly inductive [17], the GS inverter should

adopt P-ωand Q-U droop control. However, if the total

impedance is mainly resistive [18], P-U and Q-ωdroop

control should be applied.

C. Reactive power sharing method based on

communication

To improve the reactive power sharing accuracy, a

common method is to revise the GS inverters’

droop control parameters, including no-load voltage

and droop coefficient. The following analysis takes

the inductive line (cosθ≈0,sinθ≈1) as examples.

According to Eq. (11), the relation between the

output reactive power and the voltage of the GS

inverter’s PC is shown as:

U¼EþZL

EQð20Þ

In the Q-U plane, the intersection of the operational

curve described by Eq. (20) and the reactive power

droop curve is the GS inverter’s stable operating point

[19].

Fig. 7 Control block diagram of ωU-droop Grid-supporting inverter

applying decoupling transformation method

Fig. 8 Control structure of virtual impedance method

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5 Page 5 of 7

As illustrated in Fig. 9, there are two inverters, namely

1# and 2#, with the same droop coefficient. The total

impedance between these two inverters’equivalent voltage

sources and the microgrid bus are Z

1

and Z

2

, respectively.

If Z

1

is not equal to Z

2

,theinverters’operating points will

be different. Increasing inverters’droop coefficient leads

to new operating points. The voltage of the microgrid bus

moves from Eto E’, and the inverters’output power

changes move from Q

1

and Q

2

to Q

1

’and Q

2

’, respectively

It can be seen that the reactive power sharing accuracy is

improved with the increase of the inverter’s droop coeffi-

cient. Decreasing the GS inverter’s no-load voltage can

also increase reactive power sharing accuracy, as shown in

Fig. 10. To adjust each inverter’s droop curve parameters

in a coordinated manner [19, 20], it is necessary to employ

a centralized control system.

Different with the method of adjusting droop parameter,

reference [21] proposed an improved control structure by

introducing integral module, as shown in Fig. 11.

In Fig. 11, U

0

is the inverter no-load voltage; Eis the

voltage of microgrid bus; k

Q

is the reactive power droop

coefficient; K

u

is the integral gain. The transfer function

of the inverter’s output reactive power can be written as:

QsðÞ¼KuUo−EsðÞ½EsðÞ−sE2sðÞ

sZLþKukQEsðÞ ð21Þ

and its steady-state value can be calculated as:

limt→∞QtðÞ¼lims→0sQ sðÞ

¼lims→0

U0−EðÞKuE−sE2

sZLþKukQE¼U0−E

kQ

ð22Þ

In this method, the output reactive power of each GS

inverter is independent to the line impedance Z

L

. By de-

livering the voltage information of the microgrid bus to

each GS inverter, accurate reactive power sharing can be

realized. This method doesn’t require a central controller

to participate, avoiding the usage of complicated algo-

rithms. Besides, the additional parameter, K

u

, can be

used to adjust the dynamic response of reactive power

control.

Results and Discussion

As can be seen from the above sections, the GFD inverter

behaves as constant power source and it participates

neither in voltage regulation nor in load variations sharing.

The GFM inverter behaves as constant voltage source and

it is responsible not only for maintaining the microgrid’s

voltage and frequency, but also for keeping power balance.

Load sharing among the GFM inverters is a function of

the impedances between the inverters and microgrid bus.

The PQ-droop and ωU-droop GS inverters can be

regarded as the upgraded version of the GFD and GFM

inverters, and they behave as controlled power source and

controlled voltage source, respectively. When the micro-

grid operation conditions change, they can adaptively

adjust the output power or voltage to achieve a more flex-

ible load sharing. Currently the most promising control

method is the ωU-droop control, because it can make the

system autonomy and achieve seamless mode switching.

When the microgrid is operated in islanded mode, any

Fig. 9 Reactive power sharing with different droop coefficients

Fig. 10 Reactive power sharing with different no-load voltages

Fig. 11 Large-signal representation of the proposed reactive

power control

Guo and Mu Protection and Control of Modern Power Systems (2016) 1:5 Page 6 of 7

addition or reduction of a single ωU-droop GS inverter do

not influence the configuration of the original system.

When the microgrid operated in grid-connected mode,

the ωU-droop GS inverter can output the specified power

by modifying its no-load voltage and frequency. However,

this autonomous control method is not widely applied

among numerous experimental microgrids, because there

still exist many practical problems, such as the dynamic

response speed, the impact of control parameters on

system stability, the capability to deal with unbalanced

and non-linear loads, and control strategies under fault

conditions. In addition, it can be seen from the above ana-

lysis that the performance of the ωU-droop GS inverter

operating with no communication is inferior. In order to

enhance the accuracy of reactive load sharing, it is worth-

while to study the design of the control algorithms with

reduced communication requirements.

Conclusions

This paper illustrates the control principles of micro-

source inverters, including grid-feeding, grid-forming, and

grid-supporting inverters. The PQ-droop and ωU-droop

grid-supporting inverters can be regarded as the upgraded

version of grid-feeding and grid-forming inverters with a

more flexible load sharing capability. Since the conven-

tional ωU-droop control exists some shortages, several

improved methods of ωU-droop based grid-supporting in-

verters are presented. The comparison of various inverters

is carried out and the valuable research points are also

discussed.

Acknowledgments

This work was supported in part by Nation Natural Science Foundation of

China (51407128) and the key technologies research project on distribution

network reconfiguration of State Grid Hunan Electric Power Company

(5216A1300JV).

Competing interests

The authors declare that they have no competing interests.

Authors’contributions

WG and LM conceived and designed the study. WG wrote the paper. All

authors read and approved the final manuscript.

About the authors

W. M. Guo was born in 1989 in Hunan, China. He received his B.S. degrees in

electrical engineering from Tongji University in 2011, where he is currently

working towards a Ph.D. degree. His current research interests are microgrid

protection and control.

L. H. Mu was born in 1963 in Jiangsu, China. He is currently a full professor in

the Department of Electrical Engineering, Tongji University, Shanghai, China.

His current research interests include protective relaying of power system,

microgrid and power quality.

Received: 12 May 2016 Accepted: 16 May 2016

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