An Accurate Power Control Strategy for
Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-V oltage Multibus Microgrid
Yun Wei Li ,Member,IEEE ,and Ching-Nan Kao
Abstract —In this paper,a power control strategy is proposed for a low-voltage microgrid,where the mainly resistive line impedance,the unequal impedance among distributed generation (DG)units,and the microgrid load locations make the conventional frequency and voltage droop method unpractical.The proposed power con-trol strategy contains a virtual inductor at the interfacing inverter output and an accurate power control and sharing algorithm with consideration of both impedance voltage drop effect
and DG lo-cal load effect.Specifically,the virtual inductance can effectively
prevent
the coupling between the real and reactive powers by in-troducing a predominantly inductive impedance even in a low-voltage network with resistive line impedances.On the other hand,
based on the predominantly inductive impedance,the proposed
accurate reactive power sharing algorithm functions by estimating the impedance voltage drops and significantly improves the reac-tive power control and sharing accuracy.Finally,considering the
different locations of loads in a multibus microgrid,the reactive
power control accuracy is further improved by employing an on-line estimated reactive power offset to compensate the effects of DG
local load power demands.The proposed power control strategy has been tested in simulation and experimentally on a low-voltage microgrid prototype.
Index Terms —Distributed generation (DG),droop control method,microgrid,parallel inverter,power control,power sharing,renewable energy resource (RES).
I.I NTRODUCTION
W
ITH the increased concerns on environment and cost of
energy,the power industry is experiencing fundamental
changes with more renewable energy sources (RESs)or mi-crosources such as photovoltaic cells,small wind turbines,and
microturbines being integrated into the power grid in the form
of distributed generation (DG).These RES-based DG systems
are normally interfaced to the grid through power electronics
and energy storage systems [1].
A systematic organization of these DG systems forms a mi-crogrid [2]–[7].Compared to a single DG,the microgrid has
more capacity and control flexibilities to fulfill system reliabil-ity and power quality requirements.The mi
crogrid also offers opportunities for optimizing DG through the combined heat and Manuscript received February 25,2009;revised April 1,2009.Current
version published December 28,2009.This paper will be presented in part
at the 1st IEEE Energy Conversion Congress and Exposition (ECCE),San Jose,CA,September 20–24,2009.Recommended for publication by Associate Editor R.Teodorescu.
The authors are with the Department of Electrical and Computer Engi-neering,University of Alberta,Edmonton,AB T6G 2V4,Canada (e-mail:
yunwei.li@ece.ualberta.ca).Color versions of one or more of the figures in this paper are available online
at
Digital Object Identifier 10.1109/TPEL.2009.2022828
power (CHP)generation,which is currently the most important means of improving energy efficiency.By presenting itself to the utility as a dispatchable load,the microgrid could “behave”well and avoid proble
ms caused by single DG units [2].Fur-thermore,the microgrid can operate in grid-connected mode or autonomous islanding mode and benefits both the utility and customers.Depending on the locations and capacities of DG units,a microgrid could operate at a medium-voltage or low-voltage distribution level.Since most microsources are of rela-tively low-power capacities at around several hundred kilowatts,a low-voltage microgrid is considered in this paper.
With a nonradial system configuration due to the presence of DG units,the power control complexity for a microgrid is substantially increased,and the “plug and play”feature is the
key to ensure that the installation of additional DG units will not change the control strategies of DG units already in the microgrid.A popular approach to realize this “plug and play”characteristic is to employ the frequency and voltage droop
control for real and reactive power regulation by mimicking
the parallel operation characteristics of synchronous generators,
which is initially proposed in [8]for parallel uninterruptible power supply (UPS)operations.While the stability analysis of this droop control is an important aspect as discussed recently in [9],[10],when implemented in a low-voltage microgrid system,
this method is subject to a few particular problems,which are
as follows.
1)The method is developed based on the predominantly in-ductive line impedance.In a low-voltage microgrid,as the
distribution feeder is mainly resistive,this droop method
is subject to poor transient (or even poor stability)due
to the real and reactive power coupling among DG units
when no additional inductance is present.
2)The unequal line impedances and DG output impedances
significantly affect the accuracy of reactive power control
during grid-connected operation mode and the reactive
power sharing during islanding mode due to the unequal
voltage drops.
3)The reactive power sharing accuracy is further deteriorated
if there are local loads at DG output.To avoid the power control coupling,the virtual real and re-active power frame transformation was recently proposed [11].However,this method cannot directly share the actual real and
reactive powers.Another way to avoid the power coupling is to properly control the interfacing inverter with virtual output impedance [12]–[14].While effective in preventing the power coupling,this approach may increase the reactive power control 0885-8993/$26.00©2009IEEE
实现P Q 解耦及功率分配的正确性采用在线预测无功偏移来补偿本地负载需求不平衡的线阻以及DG 的输出阻抗影响系统控制精度
一种方法丗虚拟有功及无功另一种方法丗虚拟输出阻抗。可有效避免功率耦合丆但会因阻抗压降的增加导致无功功率控制和分配的偏差增加丠丠丠热电联产技术(CHP)
即插即用
实现即插即用特点的一种主流方式是频率和电压下垂控制非纯感性输出阻抗导致慢响应及差稳定性孤网时的分配精度
并网时无功功率的控制精度
Fig.1.Example microgrid with power electronics interfaced DG systems.
and sharing error due to the increased impedance voltage drops.To improve the reactive power sharing accuracy,a method has been proposed based on additional control signal injection [15].However,this method has a few disadvantages such as increased control complexity and possible line current distortions.
In this paper,a power control strategy is developed for the
nents at the DG output.On the other hand,based on the pre-dominantly inductive impedance,the proposed accurate reactive power sharing algorithm functions by estimating the impedance voltage drop to reactive power ratio and significantly improves the reactive power control and sharing accuracy.Finally,con-sidering the complex locations of loads in a multibus microgrid,the reactive power control accuracy is further improved by em-ploying an online estimated reactive power offset to compen-sate the effects of DG local load power demands.The proposed power control strategy has been tested in MATLAB/Simulink simulation and experimentally on a low-voltage experimental microgrid system.
II.M ICROGRID S TRUCTURE
An example structure of a microgrid is shown in Fig.1.The
microgrid is connected to the utility system through a static transfer switch (STS)at the point of commo
n coupling (PCC).
The STS ensures that the microgrid can be disconnected from the main grid promptly (typically half a line frequency cycle)
in the event of a utility interruption.As shown in Fig.1,three DG systems are employed in the microgrid.Each DG system
comprises an energy source,an energy storage system,and a grid-interfacing inverter.In Fig.1,DG1is connected near a heat load for CHP application,DG3is connected with a local critical load,and DG2is connected to the feeder directly for voltage and power support.This microgrid structure allows the line loss reduction,local voltage and power support,and waste heat usage.The microgrid can operate in grid-connected mode or is-landing mode.In grid-connected operation,the microgrid is connected to the utility,and the DG systems in the microgrid provide heat and power support for the nearby loads.When there is a fault in the utility system,the STS at PCC opens and the microgrid is disconnected from the utility as fast as possible and picks up the loads and operate in islanding mode.The STS is preferably controlled independently with a central control or power management unit,which constantly monitors the utility voltage condition and opens the switch in the case of a utility fault.Once transferred to islandi
ng operation,the DG systems must immediately share the changed power demand and continue sup-plying power to all critical loads within the microgrid.Also,the least important loads can be shed if the power capacity of the microgrid is insufficient to support all the loads in it.Note that
This multibus microgrid structure increases the complexity of power and voltage control along the feeder.Therefore,the “plug
and play”concept or “wireless communication”is the key to this arrangement.To realize this “plug and play”characteristic,con-ventional power and frequency droop power control methods have been implemented in [4].However,as mentioned previ-ously,the conventional droop method is subject to a number of
issues such as a coupling between real and reactive powers at a low-voltage microgrid with resistive line impedances and degra-dation of reactive power control accuracy in both grid-connected
and islanding operations.
III.T RADITIONAL F REQUENCY AND V OLTAGE D ROOP M ETHOD A.Frequency and Voltage Droop Control
A well-known method to realize the “plug and play”feature for each DG unit is to control the DG terminal voltage by em-ploying the “real power versus frequency (P–ω)”and “reactive power versus voltage (Q–E )”droop control [8].Put simply,this method is based on the flow of real power and reactive power (per phase)between two nodes separated by a line impedance
制结构的描述作用
本地负载
无功补偿
半个基波周期内可脱离电网STS 描述
STS DG 4为了实现热插拔微电网可工作在并网模式和孤网模式并网时按下垂曲线工作在电网频率及相应设定的输出功率丆切换至孤网时丆重新调整输出功率来提供孤网所需全部功率
LI AND KAO:ACCURATE POWER CONTROL STRATEGY FOR POWER-ELECTRONICS-INTERFACED DG UNITS OPERATING
2979
Fig.2.
Real power sharing through frequency droop control.
(Z
(1)(2)
where E 1and E 2are the magnitudes of the two voltages,and δis the phase angle difference between the two voltages.For a
mainly inductive line impedance,the line resistance (R )may be
neglected.Further,considering that the phase angle difference δis typically small,it is reasonable to ass
ume sin(δ)=δand cos(δ)=1.Therefore,the flow of real power is proportional to the phase angle difference (δ)and the flow of reactive power is proportional to the voltage magnitude difference (E 1−E 2).For this reason,the real power from each DG unit can be controlled by varying the DG output frequency,and hence,the phase angle and the DG reactive power can be regulated by changing the DG in both the grid-connected and islanding operation modes.Fig.2shows the P–ωdroop characteristics for two DG sys-tems (note that the control strategy is equally applicable to a microgrid with more DG units).Preferably,these droop char-acteristics should be coordinated to make each DG system sup-plying real power in proportion to its power capacity,and can mathematically be expressed as
ωi =ω∗−SP P i (P ∗
i −P i )
(3)SP P i =ω∗−ωmin
P ∗
i −P i max
(4)where P i is the actual real power output of DG system i (i =1,2,...,n ),{P i max ,ωmin }are the maximum real power output of DG system i and the minimum allowable operating frequency,{P ∗i ,ω∗}are the dispatched real power and operating frequency of DG system i in grid-connected mode,and SP P i (<0)is the slope of the droop characteristics.As shown in Fig.2,each DG system is initially designed to generate the dispatched real power output of P ∗i at the com-mon base frequency of ω∗when operating in the grid-connected mode (ω∗is fixed solely by the stiff utility grid).Once islanded,the power outputs of both DG systems must immediately be changed in accordance with their droop characteristics to sup-ply power to all critical loads in the microgrid at a new steady-state frequency of ω.This arrangement obviously allows both DG systems to share the total load demand in a predetermined manner according to their respective power ratings.
In a similar manner,the magnitude set point of each DG out-put voltage can be tuned according to a specified Q–E droop scheme to control the flow of reactive power within the micro-grid.Mathematically,the Q–E characteristics can be expressed as
E i =E ∗−SP Q i (Q ∗i −Q i )(5)SP Q i
=E ∗−E min
Q ∗
i −Q i max
(6)
where Q i is the actual reactive power output of DG system i ,{Q i max ,E min }are the maximum reactive power output
and minimum allowable voltage magnitude of the microgrid,{Q ∗i ,E ∗}are the dispatched reactive power of DG system i and PCC voltage magnitude when in grid-connected mode,and SP Q i is the slope of the droop characteristics.Conceptually similar to the P–ωoperation,the accuracy of reactive power control and sharing is,however,subject to the voltage drop on line impedances,as discussed later.B.Power Coupling at Low-Voltage Microgrid
While working well in a power grid with mainly inductive line impedances,the traditional real and reactive power con-trol (where the line resistance is neglected)leads to a concern when implemented on a low-voltage microgrid,where the feeder
impedance is not inductive and the line resistance (R )should
never be neglected.This is especially true for DG units without
a grid-side inductor or transformer,where the output inductance
is very small.In this case,the change of phase angle or voltage
magnitude will influence both the real power and reactive power
flows,as can be noticed from (1)and (2).As a result,controlling the power flow using conventional P–ωand Q–E droop meth-ods will introduce a significant coupling between the real and reactive power flows especially during transients.reactive to
To avoid this P –Q coupling,virtual real and reactive powers can be used,which are decoupled through frame transformations
with the line impedance angle information [11].While effective for power control in grid-connected mode,this method cannot directly share the actual real and reactive powers between the DG units in microgrid islanding operation mode.Another way to decouple the powers with direct power control is to employ
the virtual voltage and frequency control frame [17].Unfortu-nately,these frame transformation methods are still subject to the accuracy of the power control due to unequal impedance voltage drops.In order to control the decoupled real and reac-tive power flows in a similar manner as the conventional power system with a high X/R ratio,a method employed in this paper is to control the DG interfacing inverter with a virtual output inductor that introduces a predominantly inductive impedance without the need of line impedance information.The virtual in-ductance can effectively decouple the real and reactive power flows and requires no physical connection of any passive com-ponents at the DG output.With a virtual inductor at each DG’s output,the conventional P–ωand Q–E methods can be used,
两个假设需考虑每个模块的输出能力是不是有网侧电感和变压器可以直接应用丠前面是功率环流的结论丆怎么推出后面单机控制的结论丠丠
无功功率控制和分配受线阻压降影响有功也受阻抗压降影响丠丠应该是给
逆变器设定的最低点
2980IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.24,NO.12,DECEMBER
2009
Fig.3.
Reactive power sharing with traditional voltage droop control.
which makes the power sharing algorithm equally applicable even when the rotational machine based DG units (where the P–ωand Q–E characteristics are determined by the mechanical governor and excitation system,respectively)are present in a microgrid.Note that although the impedance voltage drop effect is more severe with the virtual inductance control,this effect can be estimated and properly compensated.C.Inaccuracy of Reactive Power Control Due to Line Impedance
Unlike the P–ωcontrol where the DG systems and utility grid have the same steady-state frequency in
the grid-connected mode,allowing the
same P–ωcontrol algorithm to be used for
both the grid-connected and islanding modes,a complication with
the Q–E droop control is that the DG output voltage has to be different from that of the utility grid to introduce a volt-age magnitude difference,and therefore,allows proper reactive power flow in grid-connected operation.As a result,the Q–E reactive power control,forcing the DG reactive power output to track its dispatched value with zero steady-state error.When the microgrid transfers to islanding operation,the reactive power
control scheme can be switched to the Q–E droop control for
proper reactive power sharing among the DG units (see Fig.3).For a similar reason,a second complication with the Q–E droop control is that the reactive power sharing accuracy is af-fected by the line impedance voltage drop.This phenomenon is illustrated in Fig.4,where the predominantly inductive line impedance is assumed that leads to an approximately linear rela-tionship between the DG output reactive power and the voltage magnitude difference (between DG output voltage and PCC voltage)∆E ,as can be noticed from (2).This linear relationship for DG system i can be expressed as
K Q i =
∆E Q i =X i
E i
(7)
where K Q i is the slope of DG output voltage magnitude differ-ence ∆E versus reactive power (note that K Q i should be scaled
Fig.4.Reactive power sharing diagram with line impedance (inductive)
effects.
down by a factor of 3for a three-phase system).As the DG
output voltage is limited to vary only in a small range (e.g.,±10%)and the inductance between two voltages is normally a constant,it is reasonable to assume K Q i as a constant slope.To simplify the illustration,it is first assumed that the power factor of the two DGs is unity with zero reactive power out
put in grid-connected mode,and the two DGs share the load reac-tive power demand only in islanding mode.Without considering the line voltage drop,the voltage droop slopes of the two DG systems defined by (5)and (6)are shown by the dashed lines
(SP  Q 1and SP
Q 2
)in Fig.4.It can be seen that if the dashed lines are used for reactive power sharing,when the two DG units supply the maximum total reactive power to the loads,DG2output reactive power (Q 2)will be smaller than its maxi-mum value (Q 2max ),and the DG1output reactive power (Q 1)will be larger than its maximum value (Q 1max ).This reactive power sharing inaccuracy leads to a risk of exceeding the DG system current ratings.Furthermore,it can be seen in Fig.4that with the slopes determined in (5)and (6),the final min-imum system voltage (PCC voltage)will be smaller than the minimum allowable voltage (E min ),which is unacceptable to the sensitive loads.
With the consideration of the line impedance effects and the ∆E/Q slopes defined in (7),the voltage droop slopes can be redefined to be SP Q 1and SP Q 2,as shown by the solid lines in Fig.4,where the minimum allowable DG output voltage and the Q–E droop slope of each DG system can be obtained a
s
E i
min
=E min +K Q i Q i max
(8)SP Q i
=E ∗−E i min −Q i max
.
(9)
With (8)and (9),both DG units will provide the maximum reactive power at the minimum allowable system voltage.More details on the accurate reactive power sharing are discussed in Section V .
IV .V IRTUAL I NDUCTANCE FOR P –Q D ECOUPLING
This section presents the interfacing inverter control scheme with virtual output inductance,which provides a mainly
尽管虚拟电感上压降会更严重丆
但可通过预测来补偿虚拟电感上的压降
由于电网和逆变器有相同的稳态角频率丆故P-ω控制。
孤网与
并网相同对于Q-E 控制DG 的输出
电压与丆导致Q-E 控制产生静差并网用PI 控制无功丆孤网下垂控制无功丠丠阻抗对无功分配精度的影响曲线图
孤网中或负载上的电压幅值丆当负载所需无功越大丆此点越小
理想情况下丆并联最大输出点
为实际输出幅值和无功的对应曲线和虚线交点为下垂调节后稳定点实际情况稳定输出点
LI AND KAO:ACCURATE POWER CONTROL STRATEGY FOR POWER-ELECTRONICS-INTERFACED DG UNITS OPERATING
2981
Fig.5.V oltage control scheme for the DG interfacing inverter. inductive impedance between the DG and the utility even in a low-voltage network with resistive line impedances.
Fig.5shows the interfacing inverter voltage control scheme. As shown,the reference voltage for the inverter comes from the real and reactive power control loops,which determine the DG output voltage magnitude and frequency.For the inverter voltage control,a multiloop control scheme is implemented, where an innerfilter inductor current(I L)feedback loop is embedded in an outerfilter capacitor voltage(V c)feedback loop. Both the voltage and current controllers are implemented on the stationary frame to avoid the complex frame transformations. For the voltage loop,the P+resonant controllers in the form of(10)are employed in theα–βframe[20]–[22]
G(s)=k P+
2k IωC s
s+2ωC s+ω20
(10)
where k P is the proportional gain,k I is the resonant gain for the resonant peak adjustment,andωC is t
he cutoff frequency for resonant bandwidth control.The controller in(10)is actu-ally a practical form of the ideal P+resonant controller that can be mathematically derived by transforming a synchronous frame PI controller to the stationary frame.It is worth noting that(10)ensures almost zero steady-state error regulation by having significant gains in the vicinity of the controller’s reso-nant frequency±ω0,which,in this case,is chosen to be the line fundamental frequency.Output of the voltage controller is then transformed to the a–b–c frame to generate the reference current I∗L for the innerfilter inductor current loop.The current error is fed to a proportional controller whose output gives the de-sired modulation signal and is fed to the pulsewidth-modulated (PWM)generator.
To emulate the effect of an inductor,the line current is fed back to calculate the virtual inductor voltage drop(V V L),which is then subtracted from the reference voltage(generated from the power loops)to produce thefinal inverter voltage reference.
A concern for the virtual inductor control scheme is the induc-tor voltage drop calculation,which involves the differentiation of line current(V V L=L0(di line/dt)=sL0i line,where L0is the virtual inductance value).Differentiation can cause high-frequency noise amplification,which in turn may destabilize the DG voltage control scheme especially during a transient.A common approach to avoid noise amplification is to add a high-passfilter toflatten the high-frequency gain of the
resulting Fig.6.Virtual inductor realization scheme.
transfer function[13],[14].However,this approach is subject
to the tradeoff between the high-frequency noise attenuation
and the fundamental component phase and gain errors(or the tradeoff between overall control scheme stability and the virtual inductor control accuracy).
As the power control in this paper is based on the funda-
mental component,a more robust approach to determine the
virtual inductor voltage drop is,therefore,proposed to avoid
the differentiation by approximating sL0as jωL0,whereωis
the system angular frequency.This jωL0representation can be realized in polar form with polar–rectangular transformations
or through direct complex number manipulations in theα–βframe.Both methods are illustrated in Fig.6.For the polar–rectangular form transformations,the measured three-phase cur-
rents arefirst transformed to theα–βframe and converted to
the polar form of|Iαβ|arg(Iαβ),where|Iαβ|=
I2α+I2
β
and arg(Iαβ)=tan−1(Iβ/Iα).Multiplying Iαβby the de-
sired virtual inductance jωL0gives the desired inductor voltage
drop(in polar form)of|Vαβ|=|Iαβ|ωL0,and arg(Vαβ)=
arg(Iαβ)+(π/2),which is subsequently transformed back to rectangular form of V V L(αβ).On the other hand,for the complex number manipulations in theα–βframe,as shown in the shaded
part of Fig.6,theα–βframe voltage drop can be directly found
from the line current with(Vα+jVβ)=jωL0(Iα+jIβ)=
ωL0(−Iβ+jIα),where the magnitude and angle calculations required in the polar–rectangular form transformations can be avoided.
V.R EACTIVE P OWER C ONTROL A LGORITHM W ITH
I MPROVED A CCURACY
As mentioned in Section III,the reactive power control and
sharing based on the traditional voltage droop method are in-accurate due to the voltage drop in the line impedances.One
method to improve the accuracy is to exaggerate the Q–E droop
effect and make the line voltage drop negligible[23].However,
with a given minimum allowable system voltage,the voltage
droop slope cannot be made arbitrarily large.As mentioned previously,a better way to improve the reactive power control
and sharing accuracy is to incorporate the line voltage drop
effect into the power control scheme.This can be realized by
adding the∆E/Q slopes into the voltage droop control.It is
如何
实现丠两相静止坐标虚拟电感实现

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