HEN INVERTERS IN VOLTAGE-

control mode are paired with synchro-

nous generators (SGs), they exhibit poor

transient load sharing in islanded opera-

tion. It is well known that power electronics respond

more quickly where the inverter initially picks up the

majority of every load step, and the generator’s output

slowly increases until they reach their steady-state load

sharing given by droop settings. This excessive tran-

sient power output from the inverter constrains its rat-

ing relative to the largest load step and could negatively

impact the battery life in battery energy-storage invert-

ers. This article provides a detailed examination of the

differences between the frequency-regulation character-

istics of inverters and generators to explain, in a novel

way, the cause of the poor transient power sharing.

Causes of unequal

transient load sharing

in islanded microgrid operation

W

SHARING TRANSIENT LOADS

ANDREW D. PAQUETTE , MATTHEW J . RENO, RONALD G. HARLEY , & DEEPAK M. D IVAN

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Digital Object Identifier 10.1109/MIAS.2013.2288408

Date of publication: 19 December 201323

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1077-2618/14/$31.00©2014IEEE

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The tradeoff between an improved transient load sharing and increased voltage and frequency transients is high-lighted, and it is demonstrated that equal transient load sharing can be achieved by emulating an SG using a power hardware-in-the-loop (HIL) approach. Validation is provided by simulation and experimental results.

Inverter Controls for Microgrids Microgrids have attracted attention for their role in the integration of renewables and distributed generation [1], [2]. Many types of renewables and distributed generation, such as photovoltaics, wind, microturbines, fuel cells, and energy storage, interface to the grid through dc/ac inverters. The most common strategy for providing stable real and reactive power sharing between sources in the microgrid without communication is voltage and frequency droop,

and several modifications to droop have been proposed to  address problems such as unequal l ine impedance between sources, resistive line impedance, and harmonic cur-rent sharing [3]–[5]. In cases of highly resistive line imped-ance, P V- and Q-~ droop may be used [3], [4]; however, this  article considers the tradi-tional P-~ and Q V- droop since, in the authors’ experience, the X/R ratios are  typically high enough that the P Q- coupling is acceptably low. Since internal-combustion-engine-driven SGs are the most common distributed-genera-tion  source with a combined installed capacity exceeding 100,000 MW [2], it is expected that SGs will play a major role

in microgrid installations. Therefore, it is important to care-fully consider the interaction between inverters and genera-tors, such as in the lab microgrid shown in Figure 1.

For stable islanded operation, a microgrid requires at least one source that is able to regulate voltage and fre-quency and respond quickly to changes in load. For microgrids, the practical choices are generators, invert-ers with energy storage, or a fast-responding energy source. When inverters in voltage-control mode operate in parallel with generators, the inverters will tran-siently supply the majority of any load step. This lack of transient load sharing constrains the inverters to be rated to handle the entirety of the largest possible load step, which may be problematic with high inrush loads, and it negatively impacts battery life by increasing the size of transients seen by the inverter. While inverters have short-duration overload capabilities, these over-loads may not be acceptable for the energy source, with the absorption of large negative load steps being espe-cially problematic.

To understand the power-sharing characteristics between inverters and generators, it is necessary to review the four basic types of inverter control [6], [7], as shown in Figure 2. Grid-forming control acts as a fixed-voltage source, and grid-feeding acts as a fixed-current source. Grid-supporting-grid-forming (GSGFm) control acts as a droop-controlled-voltage source, where voltage and fre-quency references are adjusted based on measured real and reactive power. Grid-supporting-grid-feeding (GSGFd) control acts as a droop-controlled-current source, where real and reactive power references are adjusted based on measured voltage and frequency. Grid-forming control is not suitable for paralleling with other voltage sources, and both grid-feeding and GSGFd controls are typically phase-locked loop (PLL) driven, thus requiring a voltage source to also be online [6], [7]. Using GSGFm control elimi-nates the need for rapid mode switching between GSGFd and GSGFm control when the generators transition on

A single bus experimental microgrid setup with an inverter and an SG.

NotConnected

208-V,Three-Phase Utility

480-V,Three-Phase

Utility

480-V,Three-Phase

Utility

Diesel Engine Emulator

IM

25 hp, 460 V

1.4 mH

SG

12.5 kW208 VL–L

Default Controller

20-hp, 480-V Drive

20-hp, 480-V Drive(11.1 kVA at 208 V)20 X,15 nF 5 nF

0–32 kW0–16 kvar

Inverter with Rectifier Input to Emulate EnergyStorage or Fast-Responding Energy Source

3.33X 12.33 mH

1.66 X

NI cRIO Controller

Speed Encoder

1

The four basic types of inverter control: (a) grid forming, (b) grid feeding, (c) GSGFm, and (d) GSGFd.

(a) (b)

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~*VoltageControl

(c)

(d)

QP

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~*

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Q-V DroopP-~ Droop

~

V Z

P* i*

Q*

CurrentControl

~-P DroopV-Q Droop

P*Z

i*Q*

CurrentControl

2

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and off (or when switching from grid-connected to islanded operation). This article focuses on the power-sharing characteristics between SGs and invert-ers operating in GSGFm control, but it also demonstrates that poor transient load sharing can be problematic for the GSGFd control.

The lack of transient power sharing with inverters in GSGFm control can be observed in [8] and [9] but is not addressed in those papers. Reference [10] studies this topic in simulation and states that the reason for the lack of transient power sharing is that the generator is slower than the inverter. In [10], an angle-droop control is pro-posed to improve the transient power sharing. However, this is a GSGFd control and requires a generator to be online. The explanation that the generator is slower than the inverter is common in the literature, but it is an oversimplification. This article describes how the poor transient power sharing is caused by significant differ-ences in how the two sources regulate voltage and fre-quency.

A novel method for understanding the basic transient power-sharing characteristics between voltage-controlled inverters and generators is investigated in this article, and

an equivalent circuit is proposed to describe the initial power sharing. While the lack of transient power shar-ing between inverters and SGs is known, a better understanding of the cause, methods for quickly analyzing the expected difference in power-shar-ing magnitude, and mitigation strate-gies for improving the power sharing are important for designing future microgrids. The effects of an increased inverter droop slope and an increased governor integral gain on the power sharing are also investigated. An inverter control strategy of emulating an SG is demonstrated to assure equal transient power sharing. This method directly impacts the transient power sharing and can be used with any steady-state power sharing such as

droop or isochronous control. It is shown that any method improving the transient power sharing with generators does so at the expense of increased voltage and frequency transients. Thus, if the intent of the inverter is to provide improved power quality, it may be advantageous to use voltage control and simply use current limiting when nec-essary. However, this article focuses on characterizing the power-sharing issue and proposing methods to improve it instead of taking the current-limiting approach.

The GSGFm inverter control, where the voltage droop biases the voltage controller reference and the frequency droop directly biases the frequency output.

~0

Vabc

iabc

P, Q, VCalculation

andFiltering

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V0

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+ +

+

+

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dq 6 L

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The control diagram for a generator where the droop terms bias the AVR and governor references.

V I

PQ Q VBiasV0

AVRVRMS

VFieldPID

PowerAmp

Throttle*

(Torque)EnginePID SG

fBias

f0

fShaft

PCalc

GovGenset

Controller

-mQ

-mP+ +

+

+

-

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4

THIs ARTICLE ExAMINEs THE

trAnsIEnt powEr-sHARING

CHARACTERIsTICs bETWEEN

INVERTERs AND sYNCHRONOUs GENERATORs.

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Power Sharing Between Inverters and SGs

Basic CharacteristicsThe lack of transient power sharing between generators and inverters in the voltage-control mode is understood by considering the differences between the generator’s and the inverter’s voltage- and frequency-control loops. The control diagram for an inverter operating with voltage and frequency droop is shown in Figure 3, where the voltage and frequency references are obtained from droop, and the resulting voltage is directly synthesized. This single-loop voltage control method is the same as the approach taken by the Consortium for Electric Reliability Technology Solutions (CERTS) inverter control [11], [12] and is simi-lar to the dual-loop voltage control in [6] and [7], except without a current control loop. However, both the control in Figure 3 and the control in [6] and [7] are GSGFm con-trol strategies and thus interact similarly with generators. The real power, reactive power, and voltage magnitude

calculation block in Figure 3 is given by (1)–(3), where the instantaneous dq calculations [6] are filtered by a single-order low-pass filter with cutoff frequency c~

( ) / ( )P v i v i sd d q q c c$ ~ ~= + + (1) ( ) / ( )Q v i v i sd q q d c c$ ~ ~= - + (2)

/ ( ) .V v v sd q c c2 2 $ ~ ~= + + (3)

The control diagram of a generator operating with volt-age and frequency droop is shown in Figure 4, where the droop is implemented by biasing the automatic voltage reg-ulator (AVR) voltage reference and the governor frequency reference in proportion to the measured real and reactive power, respectively. The AVR uses a proportional-integral-derivative (PID) controller to regulate the terminal voltage, the output of which goes to a power amplifier that provides the field voltage excitation. The governor uses a PID con-troller to regulate mechanical speed, the output of which sets the throttle command.

The inverter and generator regulate frequency in funda-mentally different ways. The inverter output frequency is directly proportional to the measured power, as given by (4), where 0~ is the nominal frequency and m p is the fre-quency droop slope

.m PP0~ ~= -) (4)

The generator, however, regulates frequency by control-ling the mechanical torque in response to the measured speed error. This is shown by (5), where Tm is the mechani-cal torque, m~ is the mechanical speed, Te is the electrical load torque, B is the friction constant, and J is the inertia

.s J

T T B1m

m e m$~

~=

- -c m (5)

Therefore, the inverter operates on a dynamic frequency droop, whereas the generator operates in a frequency droop only in a steady state, once the speed error term is driven to zero by the governor’s integral action. The inverter and gen-erator have similar methods for voltage regulation, but the inverter’s voltage regulator is much faster than the genera-tor’s AVR. So again, the inverter operates on a dynamic voltage droop, whereas the generator only operates in a volt-age droop once the voltage reference error has been driven to zero by the AVR integral action. These significant differ-ences between the methods of voltage and frequency regula-tion are the cause of the unequal transient load sharing.

The system in Figure 1 is simulated with the generator and inverter operating with the controls in Figures 3 and 4. The control parameters used are shown in Table 1. Figure 5 shows the results of a simulation in which a 100%, 0.8-power-factor linear load was applied to the generator and inverter, resulting in inverter overload. The inverter initially picks up almost the entire load step, and the generator increases its output power slowly until they reach steady state, in which they share load relative to their droop set-tings. In this case, the droop settings are such that they share the load proportional to their ratings. When the load is removed, the inverter absorbs most of the load step, and the real power reaches -0.75 per unit (p.u.). This simulation

TABle 1. The CONTROlleR PARAMeTeRS.Parameter ValueRated voltage, line neutral 120 V

Inverter rated apparent power 11.1 kVA

Generator rated apparent power

15.625 kVA

Inverter switching frequency 10 kHz

P, Q, V calculation filter cutoff frequency, c~

2r·15 rad/s

Frequency droop gain, mP 2r (rad/s)/Pp.u.

Voltage droop gain, mQ 0.05 /V Qp.u. p.u.

AVR proportional gain, kp 0.92 /V Vp.u. p.u.

AVR integral gain, k i 23.1 / /V V s. . . .p u p u^ hAVR derivative gain, kd 0.05

/V V sp.u. p.u. -^ hGovernor kp 12 /p.u. p.u.~ ~

Governor k i 100 ( / )/sp.u. p.u.~ ~

Governor kd 0 ( / ) sp.u. p.u.~ ~ -

Voltage controller kp (Figure 3) 0.5 /V Vp.u. p.u.

Voltage controller k i (Figure 3) 44 ( / )/V sVp.u. p.u.

P, Q control kp (Figure 13) 0.5 /I Pp.u. p.u.

P, Q control k i (Figure 13) 50 ( / )/I P sp.u. p.u.

Current control kp (Figures 13 and 15)

0.5 /V Ip.u. p.u.

Current control k i (Figures 13 and 15)

150 ( / )/V I sp.u. p.u.

PLL kp (Figure 13) 22.2 /Vp.u. p.u.~

PLL k i (Figure 13) 246.7 ( / )/V sp.u. p.u.~

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demonstrates how an inverter may need to be oversized to handle more than its share of the load during a large load step, possibly having a negative impact on the battery life in battery storage inverters. The lack of power sharing may be especially problematic for negative load steps, where a bat-tery inverter that is charging prior to a negative load step would likely trip due to the excessive reverse power.

Experimental ResultsThe experimental setup shown in Figure 1 using the param-eters from Table 1 is used to demonstrate the transient power sharing between an inverter and a generator. The generator is a 12.5-  kW Marathon Electric Magnaplus 282PSL1704 with a DVR2000E digital voltage regulator and permanent magnet excitation. The generator is coupled to a 25-hp induction motor powered by a 20-hp variable-frequency drive. The drive runs closed-loop speed control to emulate a diesel engine. The induction motor and variable-speed drive were chosen to allow flexibility in emulating various types of prime movers and due to the difficulties of installing a diesel

engine in a lab environment. The inverter’s rated current is 31 A or 11.1 kVA at 208 VL L- . The inverter control and data acquisition have been implemented in a National Instruments CompactRIO field-programmable gate array (FPGA) and real-time controller. The experimental setup is shown in Figure 6.

The inverter and generator are operating with the droop control shown in Figures 3 and 4, respectively. The same settings are used as in the simulation, except for slight differences in the tuning of the simulated versus actual governor and AVR. The experimental results for the application and rejection of a three-phase, 16-kW, 8-kvar linear load are shown in Figures 7 and 8. The experimen-tal results closely match the simulation results. From Fig-ure 8, it can be seen that the current reverses when the load is turned off, and the inverter absorbs power from the generator. In the experimental setup, any reverse power is dissipated in a dynamic brake resistor.

The generator’s real and reactive power plots are per-unitized with Sb = 12.5 kVA, which is the real power base, and the inverter plots with Sb = 0.8 # 11.1 kVA. The inverter frequency shown is the internal output fre-quency, and the generator frequency is the motor speed from the variable-frequency drive. The power and volt-age measurements are instantaneous dq calculations, and all measured power, voltage, and frequency traces are fil-tered through a first-order low-pass filter with a 60-Hz cutoff frequency to facilitate visual comparison, unless otherwise stated.

Impact of Generator Governor on Settling TimeThe governor integral action primarily determines the rate at which steady state is reached. As described previously, the generator operates in a droop only when the speed error is driven to zero by the governor integral action. Once the speed error is zero, the generator operates along its droop curve, and the inverter and generator share power according to their relative droop settings. Therefore, the rate at which the power sharing reaches steady state depends on the gover-nor time constant. Figure 9 compares the measured real power from Figure 7 and a second experiment where the generator governor integral gain is doubled. When the

The experimental setup.

LoadBank

IMInverter

SG

6

The simulation of the generator and inverter response to a 100% load step, showing poor transient load sharing resulting in inverter overload: generator and inverter (a) voltage, (b) real power, (c) reactive power, and (d) frequency.

1.1

1

0.9

(a)

1 2 3 4

(b)

1 2 3 4

(c)

1 2 3 4

(d)

Time (s)

1 2 3 4

Vol

tage

(p.

u.)

1

-1

0

1

-1

0

61

59

60

Rea

lP

ower

(p.

u.)

Rea

ctiv

eP

ower

(p.

u.)

Fre

quen

cy (

Hz)

GeneratorInverter

Time (s)

Time (s)

Time (s)

5

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integral gain is doubled, the system reaches steady state in roughly half the time, indicating that the settling time is dominated by the governor’s integral gain.

The impact of the governor on the settling time also means that for a generator with a slow prime mover, such as a large turbo-charged engine, the generator will pick up the load more slowly, and the inverter will be overloaded for a longer time. Therefore, the lack of transient power sharing becomes a more serious issue in a larger system with slower generator prime movers or when the inverter is significantly smaller than the generator, which may be the case in multimegawatt microgrids [13].

Equivalent Circuit for Initial Power SharingWhile most of the transient load-sharing characteristics are dominated by the differences between the inverter and the generator frequency-regulation controls, the initial few power cycles after the transient are dominated by the output impedance characteristics of each source. In the inverter con-trol, the voltage and frequency references are drooped in pro-portion to the filtered power measurement. Therefore, the

inverter control inputs do not change significantly during the first half-cycle or more, depending on the filtering time constants. With the generator, the AVR and governor have

The experimental results for a load step with the inverter in a voltage-control mode: generator and inverter (a) voltage, (b) real power, (c) reactive power, and (d) frequency.

1.1

1

0.9

(a)

1 2 3 54

(b)

1 2 3 54

(c)

1 2 3 54

(d)

Time (s)

Time (s)

1 2 3 54

Vol

tage

(p.

u.)

1

-1

0

1

-1

0

61

59

60

Rea

lP

ower

(p.

u.)

Rea

ctiv

eP

ower

(p.

u.)

Fre

quen

cy (

Hz)

GeneratorInverter

Time (s)

Time (s)

7

The measured current with the inverter in a voltage-control mode during the load step changes shown in Figure 7: (a) load turn-on and (b) load turn-off.

(a)

1 1.05 1.151.1

Time (s)

Time (s)

(b)

4.05 4.1 4.15 4.2

50

25

0

-50

-25

50

25

0

-50

-25

Cur

rent

(A

)C

urre

nt (

A)

Generator Inverter

8

The impact of the governor integral gain on the settling time: (a) default and (b) doubled.

(a)

0.5 1 1.5 32.52

0.5 1 1.5 32.52

(b)

Time (s)

Time (s)

Rea

lP

ower

(p.

u.)

Rea

lP

ower

(p.

u.)

GeneratorInverter

1.5

1

0.5

0

1.5

1

0.5

0

9

An equivalent circuit to describe the initial power sharing.

E'q

X'd

PGEN PlNV

EINV

Xfilt

ZLoad

10

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almost no impact during the first few power cycles, as can be seen in Figure 9, where the increased governor integral gain does not change the first few cycles. To obtain an estimate of the initial power sharing, the generator can be modeled as a simple voltage behind tran-sient reactance and the inverter as a volt-age behind filter reactance. This is shown in Figure 10, where E '

q is the generator voltage behind transient reac-tance, X '

d is the generator d-axis tran-sient reactance, EINV is the inverter voltage, and X filt is the inverter filter reactance. The voltage behind the tran-sient reactance model is the simplest model of a generator and is commonly used for transient stability studies [14]. Assuming both sources are initially at no load, it can be shown that the power sharing becomes a ratio of the output impedances given by

P P

PQ Q

QX X

XINV GEN

INV

INV GEN

INV'

filt

'

d

d $+

=+

=+^ ^ ^h h h (6)

Note that, in (6), X 'd and X filt are in X, and P and Q

are in kilowatts and kilovar. Two important points can be seen from (6). First, for a given inverter rating, a smaller filter reactance leads to the inverter producing a larger percentage of a load step. Second, as the ratio of inverter to generator rating decreases, the inverter overloading will become more severe.

A close-up of Figure 5 is shown in Figure 11, except the power is in kilowatts and kilovar instead of p.u. Using the initial power values from Figure 11, (7)–(9) compare the

expected (7) versus simulated power sharing (8), (9) to show that the equiva-lent circuit is useful for estimating the initial power-sharing ratio

/

. / . .

.

X X X

0 807 0 807 0 528

0 604

' 'filtd d+

= +

=

^^

hh

(7)

/

. / . .

.

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12 8 12 8 7 6

0 627

INV INV GEN+

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=

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(9)

Impact of Increased Inverter Droop SlopeBased on the description of the generator and inverter fre-quency-regulation characteristics, it is expected that an increased inverter frequency droop slope will cause the gen-erator to pick up load more quickly by allowing the gover-nor to see a larger speed error. However, the droop slope is not expected to have any impact on the initial power shar-ing. The experimental results for the impact of doubling and quadrupling the inverter’s frequency droop slope are shown in Figure 12. The power traces are the unfiltered, instanta-neous power calculation, and it can be observed that the power output during the first cycle is independent of the inverter droop slope. This supports the previous analysis that

The impact of the varied inverter frequency droop slope on the transient power sharing: (a) 1x, (b) 2x, and (c) 4x.

0

1

Rea

lP

ower

(p.

u.)

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(b)

Time (s)

0

1

Rea

lP

ower

(p.

u.)

Time (s)

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(a)

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

0

1

Rea

lP

ower

(p.

u.)

Time (s)

(c)

GeneratorInverter

12The simulation of the initial power sharing: (a) real and (b) reactive power.

0

5

10

15

Rea

lP

ower

(kW

)

0.95 1 1.05 1.1 1.150

5

10

Rea

ctiv

eP

ower

(kv

ar)

Time (s)

0.95 1 1.05 1.1 1.15

Time (s)

(b)

(a)

PINV

QINV

GeneratorInverter

PGEN

QGEN

11

THIs ARTICLE FOCUsEs ON THE powEr-sHArIng CHARACTERIsTICs

bETWEEN sGs AND INVERTERs OPERATING IN

GsGFm CONTROL.

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the initial power sharing is given by the output impedance characteristics of the inverter. Note that if an increased droop slope is used in a practical system, it should be a transient droop to avoid impacting the steady-state power sharing.

This brings up the important discussion of the tradeoff between improved transient load sharing and increased volt-age and frequency transients. By increasing the droop slope, the generator picks up load more quickly by allowing a larger frequency deviation. This is intuitive for real power output: the generator only increases its mechanical torque in response to an error between its measured speed and speed reference, and if the inverter tightly regulates the frequency, the governor will see a small speed error and will increase its output power slowly. Thus, any control that causes the gen-erator to pick up more of the load will do so by allowing larger voltage and frequency deviations. However, this may be warranted if it reduces necessary overrating of the inverter, reduces strain on the inverter, and increases battery life.

Inverter-Generator Power Sharing with GSGFd ControlPoor transient load sharing is also problematic for GSGFd inverter controls. Although the generator initially picks up the load, for large load steps, the inverter ends up sup-porting most of the load during the transient. With the GSGFd control, the inverter begins injecting power once the voltage and frequency begin to sag. During a load step, the voltage and frequency sag because of the genera-tor transient response to picking up load. Therefore, for a small load step, the generator will initially pick up the load step and then the inverters will pick up their share of the load. However, for a large load step, where the genera-tor frequency would otherwise transiently drop below the rated droop frequency, the inverter will end up picking up the majority of the load step to maintain the frequency. For example, if the generator frequency would sag to 57 Hz without the help of the inverter, but the inverter oper-ates on a 1-Hz frequency droop, the inverter will inject 1-p.u. power once the frequency drops to 59 Hz, thereby partially unloading the generator. Once the inverter is car-rying more than its p.u. share, the generator will see a speed-reference error and will increase its output power similar to the GSGFm inverter case. Therefore, the prob-lem of overloading is still present, although the beginning portion of the transient occurs differently.

The transient load sharing between a generator and a GSGFd inverter is simulated with the inverter control shown in Figure 13 [15]–[17] and the network in Figure 1.

The GSGFd inverter control.

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1/mQ

13

A simulation of a 100% load step shows the same poor tran-sient load sharing, resulting in the overload of the inverter with the GSGFd control mode: generator and inverter (a) voltage, (b) real power, (c) reactive power, and (d) frequency.

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1 2 3 4

59

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Fre

quen

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Hz)

Time (s)

Time (s)

Time (s)

Time (s)

(d)

1 2 3 4

(a)

1 2 3 4

(b)

1 2 3 4

(c)

GeneratorInverter

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The simulation results are shown in Figure 14, where the generator initially picks up the load step. Then the inverter picks up most of the load as the frequency sags, and finally the generator increases its output power until the system reaches steady state. In the simulation, the current control-ler, power controller, and PLL [18] bandwidths are set at 260, 17, and 5 Hz, respectively, with the gains in Table 1. The voltage and frequency feedback are filtered with the same low-pass filter as in (1)–(3). This simulation shows that the tradeoff between power sharing and voltage and fre-quency regulation is also pres-ent with the GSGFd control. With this method, the inverter could be made to respond more slowly such that it does not immediately take up the load from the generator; but this would be at the expense of allowing a larger voltage and frequency transient.

emulating SGOverrating inverters and reduced battery life are two of the main consequences of poor transient load sharing between inverters and genera-tors, and these consequences could have a significant impact on the microgrid cost. While it may often be desir-able for the inverter to improve the power quality by supplying transient loads, cost constraints may prevent sizing the inverter to supply the largest possible load step. One method to alleviate the overrating and reduced bat-tery life is to ensure equal transient power sharing. A method to guarantee equal transient power sharing is to emulate a generator via a

power HIL approach. Using inverters to emulate machines has been done before in various power HIL applications, including the testing of motor drives [19], [20]. This method is expanded here to demonstrate equal transient power sharing.

Control StrategyAn inverter can be made to exactly emulate a generator by simulating the equations governing a generator inside the inverter’s controller and using the simulated stator currents

The structure of the generator emulation algorithm.

Simulate AVR, GOV,Droop, Ts = 3 ms NI cRIO-9022

(DSP)

iabc

Vabc

Vdc

NI cRIO-9114 (FPGA)

A/D

PWMGate

Signals

PWMCenter

10 kHz

CurrentControl

Integrate DynamicEquations with

Euler IntegrationTs = 2.5 ns

(Mechanical Equations Not Shown)

Formulate Equations into Derivative of State Variables

eq = -riq + ~md + pmq h

mq = -Lqiq + Laq i1q

ed = -rid - ~mq + pmd h

md = -Ldid + Lad(ifd + i1q)

i

id, iq

id, iq

Van, VbnTm, efd

~

Dabc

Vdc

idifdi1dff f

f

-Ld-Lad-Lad

LadLfdfdLad

LadLadL1d1d

ff f

f ff f

f

iqi1q

ddtbb b

b -Lq-Laq

LaqL1q1q

-1bb b

b eq + riq - ~md- r1qi1q

-1 ed + rid + ~mqefd - rfd ifd- r1d i1d

bb b

b= ~base

ddt

= ~base

16

An inverter control for the emulation of a generator.

SimulateMachine

EquationsVd

Vq

iq

i*q

iq iabc

Vabc

iqSim

idSim

i

i

i

-

+

id

i*d

idVq

Vd

-

+

PI dqSVM

6

C

L

ab

i

dqabc

dq

abc

PI

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as a current reference for the inverter operating in current control, as shown in Figure  15. References [21]–[23] describe methods for emulating SGs, but [21] and [22] only approximate the machine dynamics and [23] does not close the loop by simulating both a gov-ernor and an AVR. This article describes the full emulation of a generator, including the governor and the AVR, to demonstrate equal transient power shar-ing between an inverter and a generator.

The math and control structure for emulating a generator are shown in Figure 16. The electrical and mechan-ical dynamic equations [14] are for-mulated into the derivatives of the state variables [24], and the state vari-ables are integrated in real time on the FPGA, as shown in Figure 16. The simulated stator currents and rotor angle are used in the inverter current control, as shown

in Figure 15. Note that, when inte-grating the state variables in real time, the derivatives are with respect to time in seconds as opposed to time in p.u., thus all derivatives should be multiplied by .base~ The algorithm has been implemented in fixed point on a National Instruments Compac-tRIO FPGA and real-time processor.

Experimental ResultsIn the second set of experimental results, the inverter is controlled to emulate a generator using the control shown in Figures 15 and 16 and is programmed with the data sheet parameters of the 12.5-kW generator. The current control gains in Table 1

were chosen heuristically and provide a closed-loop cur-rent control bandwidth of 260 Hz. This is a relatively low bandwidth, but it provides sufficient performance for emulating a generator in a stand-alone mode or in parallel with an actual generator.

The experimental results with the same 16-kW and 8-kvar load step are shown in Figures 17 and 18. The inverter and generator share power proportionally, both transiently and in steady state. There are some minor differences in the output power due to a small error in the data sheet parameters, which impacts the first few cycles after the transient and slight differences between the tuning of the simulated and actual AVR and gover-nor. The errors in real power sharing are similar during load application and rejection, although the reactive power-sharing error is significantly larger during turn-off. However, some error is not surprising and would be present even in two identical generators due to manu-facturing and tuning variations. These experimental results show that emulating a generator is effective for providing transient power sharing between inverters and generators.

It is interesting to note that the generator emulation method reaches steady state more quickly than the GSGFm control, as shown in Figure 17 versus Figure 7, respectively. The main reason for the faster settling time is that a power-sharing error creates a relatively small ref-erence error for the generator AVR and the governor, and thus the generator responds slowly to a power-sharing error. For the generator emulation method, the power-sharing error stays close to zero, and the system reaches steady state quickly. Figure 19 shows the power-sharing error ( )P PINV, p.u. GEN, p.u.- and the generator frequency reference error ( )f fref- from the GSGFm control and generator emulation control experimental results in Fig-ures 7 and 17, respectively. In the GSGFm, the generator frequency reference error decreases slowly and roughly in proportion to the power-sharing error. Another factor causing the emulation method to settle more quickly is that a larger voltage and frequency dip causes the AVR and governor to make larger control actions. However, if a power-sharing error was present in the emulation case, it would also take longer to settle.

The experimental results for the load step with the inverter emulating generator: generator and inverter (a) voltage, (b) real power, (c) reactive power, and (d) frequency.

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Time (s)

Time (s)

Time (s)

(d)

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(c)

1 2 3 4 5

(b)

1 2 3 4 5

(a)

17

AN INVERTER CONTROL

sTRATEGY OF EMULATING AN sG Is DEMONsTRATED TO AssURE EQUAL TRANsIENT POWER

sHARING.

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While using the inverter to emu-late, a generator provides equal tran-sient power sharing with generators, there are drawbacks. The generator emulation method is sensitive to mea-surement channel dc offsets and unbalance that cause dc and negative sequence currents, respectively, in the simulated stator currents. For emulat-ing large generators, it is necessary to properly model the governor and prime mover dynamics, and extensive modeling efforts would be required to emulate large, turbo-charged engines. As noted in [22], the emulated generator model breaks down during severe transients and faults, when the inverter cannot supply the same peak currents as a gener-ator due to the inverter’s limited overcurrent capabilities.

Tradeoff Between Transient Power Sharing and Voltage and Frequency RegulationOne of the main contributions of the generator emulation method is to highlight the inherent tradeoff between improved transient power sharing and fast voltage and frequency regulation. As described previously, the only way for the generator to con-tribute more during a transient, and thus improve the transient power sharing, is by allowing the voltage and frequency to dip. If the inverter

regulates the voltage and frequency tightly, it will do so at the expense of supporting most of the load step.

The GSGFm control and generator emulation control give the endpoints of the spectrum of power-sharing error versus voltage and frequency dip. In Table 2, the power-sharing error and voltage and frequency dip are compared for the experimental results, showing maxi-mum real and react ive power-shar ing error

,P PINV,p.u. GEN,p.u.-^ ,Q QINV,p.u. GEN,p.u.- h and the mini-mum voltage Vmin^ h and frequency dip fmin^ h during the load application transient. When the inverter acts as a stiff, grid-forming source, the inverter will supply almost the entire load step and the voltage and frequency dip will be given by the transient response characteristics of the inverter. With the generator emulation method, the load sharing is equal, and the voltage and frequency dip are given by the transient response characteristics of the generator. Possible future work could develop inverter controls that would allow control over where the inverter lies on the spectrum of power-sharing error ver-sus power quality.

While inverters are capable of regulating the voltage and frequency more tightly than SGs, this is not always necessary in islanded operation. Superior power quality is often not required in islanded operation. Traditional backup generator systems use SGs, and thus have large voltage and frequency transients during load steps. In designing microgrids, it is important to recognize the tradeoffs between cost and power quality and the impact of poor transient load sharing on inverter rating require-ments. Sacrificing some of the inverter’s fast voltage and frequency-regulation capabilities for improved transient load sharing may be justified if it has a significant impact on microgrid cost. Cost constraints may also

The measured current with the inverter emulating the genera-tor during the load step changes shown in Figure 17: (a) load turn-on and (b) load turn-off.

1 1.05 1.1 1.15-50

-25

0

25

50

Cur

rent

(A

)

Time (s)(a)

(b)

GeneratorInverter

3.55 3.6 3.65 3.7

-50

-25

0

25

50

Cur

rent

(A

)

Time (s)

18

The (a) power-sharing error and (b) generator frequency ref-erence error for the GSGFm and generator emulation controls.

0

0.5

1

Pow

er-S

harin

g E

rror

(p.

u.)

0.5 1 1.5 2 2.5 3 3.5

0

1

2

Fre

quen

cy R

efer

ence

Err

or(H

z)

Time (s)

0.5 1 1.5 2 2.5 3 3.5Time (s)

(a)

(b)

GSGFmEmulation

19

TABle 2. The POWeR-ShARING eRROR VeRSUS VOlTAGe AND FReQUeNCY DIP.

Control MethodPerr (p.u.)

Qerr (p.u.)

Vmin (p.u.)

fmin (Hz)

gsgFm (Figure 7) 1.1 0.86 0.92 58.7Generator emulation (Figure 17)

0.1 0.05 0.81 57.8

bY INCREAsING THE DROOP sLOPE, THE

GENERATOR PICKs UP LOAD MORE QUICKLY.

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restrict the inverter rating, forcing a reduction in voltage and frequency regu-lation.

ConclusionsThis article examines the transient power-sharing characteristics between inverters and SGs. Poor transient power sharing is undesirable in terms of strain and constraints on inverter ratings and negative impact on battery life for bat-tery storage inverters. While inverters have short-duration overload capabili-ties, these overloads may not be accept-able for the energy source, with absorbing large negative load steps being especially problematic. This arti-cle provides a novel understanding of the cause of the poor transient power sharing and high-lights the tradeoff between improved transient load sharing and increased voltage and frequency transients. This tradeoff is important to recognize as the overrating of inverters due to factors, including high inrush loads and poor transient load sharing with generators, which may significantly impact the cost of microgrid installa-tions. If allowing increased voltage and frequency tran-sients reduces necessary overrating of inverters and improves battery life, then this may be a worthwhile tradeoff in real-world applications.

AcknowledgmentThe authors would like to thank Eaton Corporation for the donation of the inverters. This work was supported by the Intelligent Power Infrastructure Consortium.

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[4] K. De Brabandere, B. Bolsens, J. van den Keybus, A. Woyte, J. Dries-en, and R. Belmans, “A voltage and frequency droop control method for parallel inverters,” IEEE Trans. Power Electron., vol. 22, no. 4, pp. 1107–1115, 2007.

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[7] K. De Brabandere, “Voltage and frequency droop control in low voltage grids by distributed generators with inverter front-end,” Ph.D. disser-tation, Faculteit Ingenieurswetenschappen, K. U. Leuven, Belgium, 2006.

[8] S. Krishnamurthy, “On the modeling and control of wound field syn-chronous machine based gensets for operation in a microgrid environ-

ment,” Ph.D. Dissertation, Dept. Elect. Eng., Univ. Wisconsin Madison, Madison, WI, 2008.[9] S. Krishnamurthy, T. M. Jahns, and R. H. Lasseter, “The operation of diesel gensets in a CERTS microgrid,” in Proc. Power Energy Soci-ety General Meeting, Pittsburgh, PA, July 20–24, 2008, pp. 1–8.[10] M. Dewadasa, A. Ghosh, and G. Ledwich, “Dynamic response of distributed generators in a hybrid microgrid,” in Proc. Power Energy Society General Meeting, Detroit, MI, July 24–29, 2011, pp. 1–8.[11] H. Nikkhajoei and R. H. Lasseter, “Dis-tributed generation interface to the CERTS microgrid,” IEEE Trans. Power Delivery, vol. 24, no. 3, pp. 1598–1608, 2009.[12] R. Lasseter and M. Erickson. (Oct. 2009). Integration of battery-based energy storage

element in the CERTS microgrid. Dept. Electr. Comput. Eng., Univ. Wisconsin-Madison, Madison, Wisconsin, Tech. Rep. [Online]. Avail-able: http://certs.lbl.gov/pdf/microgrid-battery-storage.pdf

[13] R. H. Lasseter, “Smart distribution: Coupled microgrids,” IEEE Proc., vol. 99, no. 6, pp. 1074–1082, 2011.

[14] M. S. Sarma, Electric Machines, 2nd ed. St. Paul, MN: West, 1994.[15] Z. Miao, A. Domijan, and L. Fan, “Investigation of microgrids with both

inverter interfaced and direct AC-connected distributed energy resources,” IEEE Trans. Power Delivery, vol. 26, no. 3, pp. 1634–1642, 2011.

[16] F. Katiraei and M. R. Iravani, “Power management strategies for a microgrid with multiple distributed generation units,” IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1821–1831, 2006.

[17] C. Il-Yop, L. Wenxin, D. A. Cartes, E. G. Collins, and M. Seung-Il, “Control methods of inverter-interfaced distributed generators in a microgrid system,” IEEE Trans. Ind. Applicat., vol. 46, no. 3, pp. 1078–1088, 2010.

[18] S. K. Chung, “A phase tracking system for three phase utility interface inverters,” IEEE Trans. Power Electron., vol. 15, no. 3, pp. 431–438, 2000.

[19] S. Grubic, B. Amlang, W. Schumacher, and A. Wenzel, “A highper-formance electronic hardware-in-the-loop drive-load simulation using a linear inverter (LinVerter),” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1208–1216, 2010.

[20] S. Lentijo, S. D’Arco, and A. Monti, “Comparing the dynamic perfor-mances of power hardware-in-the-loop interfaces,” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1195–1207, 2010.

[21] Q. Zhong and G. Weiss, “Synchronverters: Inverters that mimic synchro-nous generators,” IEEE Trans. Ind. Electron., vol. 58, pp. 1259–1267, 2010.

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Andrew D. Paquette (adpaquet@gatech.edu), Matthew J. Reno, Ronald G. Harley, and Deepak M. Divan are with the Georgia Institute of Technology, Atlanta. Paquette and Reno are Student Members of the IEEE. Harley and Divan are Fel-lows of the IEEE. This article first appeared as “Transient Load Sharing Between Inverters and Synchronous Generators in Islanded Microgrids” at the 2012 IEEE Energy Conversion Congress and Exposition.

IN DEsIGNING MICROGRIDs, IT Is

IMPORTANT TO RECOGNIzE THE

TRADEOFFs bETWEEN COsT AND POWER

QUALITY.