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A Control Strategy for Islanded Operation of a Distributed Resource (DR) Unit Mohammad B. Delghavi, Student Member, IEEE, Amirnaser Yazdani, Member, IEEE

Abstract—This paper proposes a mathematical model and a voltage/frequency regulation strategy for an islanded, electronically-coupled, Distributed Resource (DR) unit. The DR unit can either represent a Distributed Storage (DS) unit or a dispatchable Distributed Generation (DG) unit. The proposed control strategy benefits from the power circuit configuration, dq-frame current-control scheme, and the Phase-Locked Loop (PLL) mechanism that exist and are optimized in modern gridconnected DR units. Therefore, the proposed control strategy requires minimal software modifications to enable the operation of the DR unit in the islanded mode, with black-start capability, for example, for a remote microgrid application. In addition, the proposed control strategy employs feed-forward techniques to mitigate the impacts of (i) load dynamics on the system stability and performance, and (ii) inherent inter-couplings and nonlinearities of the control system. This, in turn, remarkably facilitates the controller design procedure. The principles supporting the proposed control strategy are discussed and analyzed, and the effectiveness of the control is demonstrated through digital timedomain simulations conducted on a detailed switched model of a 5.0 M V A DR unit. Index Terms—Distributed Resources (DR), Distributed Generation (DG), microgrid, islanded-mode control, dynamics, model, control, feed-forward.

I. I NTRODUCTION ECENTLY, the concept of islanded operation of Distributed Generation/Storage (DG/DS) systems (collectively referred to as Distributed Resource (DR) systems) has attracted interests under the umbrella of microgrids [1]. While islanded operation is mainly to enhance the system reliability, it can be effectively utilized for electrification of remote offgrid communities. Each year, substantial amounts of Diesel fuel need to be transported to remote communities that are isolated from national grids. Islanded operation of DR systems provides opportunities for supplying electricity, and perhaps heat, to such communities from renewable energy resources and with a reduced reliance on Diesel fuel. Most modern DR units generate DC power, or AC power with frequencies different than 50 or 60 Hz. They are, therefore, electronically interfaced with the distribution networks and require control techniques other than those employed for conventional synchronous-machine-based generators. Moreover, presently, DR units are almost exclusively designed and optimized for operation in the grid-connected mode where their output voltage and frequency are dictated by the utility grid. Such DR units commonly employ a Phase-Locked Loop

R

The authors are with the University of Western Ontario, London, ON, Canada (e-mails: [email protected], [email protected]). This work is supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

978-1-4244-4241-6/09/$25.00 ©2009 IEEE

(PLL) mechanism for synchronization to the grid voltage, and utilize a current-mode strategy for real- and reactive-power control with the advantages of intrinsic short-circuit protection and superior dynamic response. It is therefore desirable, at least from the manufacturing viewpoint, to design DR systems in such a way that they can also operate in the islanded mode of operation with the same hardware structure and modest (or ideally no) modifications in the software. In this paper, a control strategy is proposed for the islanded-mode control of a DR unit that attempts to fulfill the aforementioned objective and also to present a convenient method for the controller design. In the islanded mode, the impact of loads frequent switching incidents on the control is highly pronounced due to the absence of a connection to the grid. This adversely affects the performance and may even jeopardize the stability of the voltage/frequency regulation scheme of the microgrid due to the loads nonlinearities, time-variance, and dynamic order variations. In [2] the problem has been addressed by a robust control technique, where the load configuration is assumed to be known while its parameters are considered uncertain. Moreover, the method of [2] employs a voltage-mode control approach which calls for additional short-circuit protection measures. In [3] a voltage-mode control strategy has been proposed for an electronically-interfaced DR unit. The method is intended for a pre-specified load configuration, but does not take into account the load topological variations. In an earlier published work, [4], a current-mode control approach has been employed. However, a parallel RL load has been assumed. Moreover, the control plant nonlinearities, inherent inter-couplings, and load dynamics are not compensated. Consequently, the controller design task must rely on linearization and is laborious, and the system performance depends on the operating point. In this paper, a voltage/frequency regulation strategy is proposed for an electronically-interfaced DR unit supplying an isolated low-voltage network. Based on the proposed control strategy, the DR unit can preserve its construction that is designed and optimized for the grid-connected operation, and benefits from the circuit and control building blocks that are commonly built in. These include a six-pulse, Pulse-Width Modulated (PWM), Voltage-Sourced Converter (VSC), and a three-phase AC filter, in conjunction with a current-mode control scheme, a synchronous dq reference frame, and a PLL. The control strategy presented in this paper employs a feedforward strategy to mitigate the impact of nonlinearities, to eliminate the inter-couplings, and to compensate for the load dynamics. Therefore, the load dynamics are masked and the

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system performance is made, to a great extent, independent of the load type. Thus, the closed-loop system possesses very similar dynamic properties under no-load and loaded conditions. In addition, the control plant turns out to be linear, in turn, permitting utilization of classical control design methods and optimization of the control loops for a stable operation and satisfactory performance over a wide range of operating points. The proposed control strategy takes advantage of the builtin PLL of the DR unit, and avoids the use of an external frequency synthesizer. Furthermore, under the proposed control strategy, the islanded DR unit has black-start capability and is robust against load switching incidents. The paper details the mathematical modeling and control design methodology, and demonstrates the effectiveness of the proposed method through simulation studies conducted on a detailed switched model of the overall system, in the PSCAD/EMTDC environment. The rest of this paper is organized as follows. Section II describes the structure of the islanded DR unit. Section III presents a mathematical model of the DR unit for the islanded mode of operation. In Section IV, the proposed voltage/frequency control strategy is introduced. Section V presents the simulation results to demonstrate the performance and effectiveness of the proposed control strategy. Section VI concludes the paper.

II. S TRUCTURE OF THE I SLANDED DR U NIT Fig. 1 illustrates a simplified schematic diagram of a DR unit, consisting of a current-controlled VSC and a three-phase LC filter, that supplies an isolated distribution network; an aggregate of the network loads as viewed from the DR unit terminals is labeled as the “effective load” and is referred to as the “load” throughout this paper. L and Cf represent the inductance and capacitance of the filter. R models the ohmic loss of the filter inductor and also includes the effect of the on-state resistance of the VSC valves. The VSC DC side is parallelled with the DC-link capacitor C and a controlled voltage source. The voltage source models the effect of a dispatchable generator-rectifier set or a storage device which is coupled with the VSC from the DC side. Fig. 1 illustrates that the DR unit is controlled in a rotating dq reference frame whose d axis makes an angle ρ against the stationary α axis. ρ is obtained from a PLL which constitutes an essential part of a modern electronically-coupled DR unit. The PLL also provides ω, i.e. the frequency of vsabc . In the grid-connected mode of operation, vsabc is dictated by the grid in which case ρ and ω represent the phase-angle of the PCC voltage and power system frequency, respectively. In the islanded mode, however, the switch S is open and the DR unit of Fig. 1 solely supplies the load. Thus, the control objective is to regulate the amplitude and frequency of the PCC/load voltage, i.e. vsabc . Ideally, this should be accomplished in a stable manner and irrespective of the load dynamic characteristics.

III. M ATHEMATICAL M ODEL OF I SLANDED DR U NIT With reference to Fig. 1, dynamics of the PCC/load voltage are described by the space-phasor equation d− → − − → → vs = i − io , (1) dt where each space phasor is defined by the generic equation → − f (t) = (2/3)(fa (t)ej0 + fb (t)ej2π/3 + fc (t)ej4π/3 ) in which fa (t), fb (t), and fc (t) constitute a three-phase signal or → − (current/voltage) waveform. Substituting for f (t) = (fd (t) + jfq (t))ejρ(t) in (1), one derives the dq-frame equivalent of (1) as d Cf [(vsd + jvsq )ejρ ] dt = (id + jiq )ejρ − (iod + jioq )ejρ , (2) Cf

where ρ(t) is the dq-frame angle. Equation (2) can be simplified and split into dvsd = (Cf ω)vsq + id − iod dt dvsq = −(Cf ω)vsd + iq − ioq , Cf dt Cf

(3) (4)

where dρ = ω(t) (5) dt is the output of the PLL. As shown in Fig. 1, the PLL processes vsq through the filter H(s) and determines ω in such a way that vsq is forced to zero [5]. In the grid-connected mode of operation where vsabc is dictated by the grid (i.e. (1) does not apply), this ensures that the real and reactive power that the DR unit delivers to the distribution network are controlled by id and iq , respectively. In the grid-connected mode, in a steady state, ω becomes equal to ω0 , i.e. the power system angular frequency, while vsq settles at zero. In order for that to happen, H(s) must possess at least one pole at s = 0. The PLL is described by Ω(s) = H(s)Vsq (s),

(6)

which holds also for the islanded mode where vsabc is not imposed by the grid, but is a variable based on (1). As mentioned in the previous section, the electronic interface of the DR unit employs a current-controlled VSC. Thus, the current components id and iq are independently controlled through their respective reference commands, based on [6] 1 Idref (s) τi s + 1 1 Iqref (s), Iq (s) = Gi (s)Iqref (s) = τi s + 1 Id (s) = Gi (s)Idref (s) =

(7) (8)

where the time-constant τi is a design choice. The current control is implemented based on the block diagram of Fig. 2 in which the compensators kd (s) and kq (s) are ProportionalIntegral (PI) filters. Fig. 2 shows that ω is included in the current-control process as a feed-forward term to decouple the control of id and iq . In the islanded mode of operation, the DR unit output current is equal to the load current, i.e. ioabc = iLabc . The load

3

DR Unit

+

Time-Varying DC Voltage

+

v tabc R L

v dc VSC

C

ω vsdref Fig. 1.

ρ

idref

mdq

idq

ρ

vsd vsq

dq

Q

o

abc ρ

VCO

PCC

S

Grid

i Labc Effective

iodq



load

ρ

ω

ω

Current Control Scheme

iqref

d -axis compensator

kd(s)

-

md

-

Decoupling feed-forward

id

ω

iq

X

L

X

L

vdc 2

q -axis compensator

iqref -

iq

-

m

kq (s)

q

v sq

Block diagram of the current-control scheme

current components iLd and iLq are regarded as the outputs of the following nonlinear, time-variant, dynamic system whose inputs are vsd and vsq :   iod = ioq     g1 (x1 , x2 , ..., xn , vsd , vsq , t, ω) iLd , (9) = iLq g2 (x1 , x2 , ..., xn , vsd , vsq , t, ω) ⎢ ⎢ d ⎢ ⎢ dt ⎢ ⎢ ⎣

PLL

H(s)

vsd

-

idref



dq

abc

ioabc

Schematic diagram of an electronically-interfaced Distributed Resource (DR) unit in the islanded mode

id

Fig. 2.

abc ρ

Gate Drive

Voltage/Frequency Control Scheme

ωref

dq

PWM and

iodq

v sabc

Cf

6

vsdq

iabc

Po

x1 x2 . . . xn





⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣

f1 (x1 , x2 , ..., xn , vsd , vsq , t, ω) f2 (x1 , x2 , ..., xn , vsd , vsq , t, ω) . . . fn (x1 , x2 , ..., xn , vsd , vsq , t, ω)

⎤ ⎥ ⎥ ⎥ ⎥, ⎥ ⎥ ⎦

(10)

where x1 (t), ..., xn (t) signify the state variables of the load;

f1 (.), ..., fn (.), g1 (.), and g2 (.) are nonlinear functions of their corresponding arguments. Equations (3) through (10) constitute a mathematical model for the islanded system of Fig. 1. IV. C ONTROL OF I SLANDED DR U NIT In the islanded mode, the control of the DR unit involves regulation of the PCC line-to-neutral voltage magnitude, i.e. 2 + v 2 , and the frequency ω. As explained in vsd v s = sq Section III, vsq settles at zero in a steady state. Therefore, the regulation of the voltage magnitude boils down to that of vsd . On the other hand, based on (6), the frequency can be controlled by vsq . However, control of vsd and vsq is not a straightforward task. The reasons are (i) based on (3) through (10), the open-loop control plant (with idref and iqref as the inputs, and vsd and vsq as the outputs) is nonlinear; (ii) based on (3) and (4), dynamics of vsd and vsq are coupled; (iii) as (9) and (10) indicate, iod and ioq are functions of both vsd and vsq , most likely, with uncertain and time-varying parameters; and (iv) dynamics of the load are, in general, highly intercoupled, of a high dynamic order, and nonlinear, even for a fairly simple linear load; an example of this is presented in Appendix A. Fig. 3 illustrates a control scheme, capable of largely overcoming the foregoing issues, in which the filters k(s) are the compensators for the d- and q-axis control loops. Fig. 3 shows that feed-forward signals are utilized to eliminate the coupling between vsd and vsq . The decoupling mechanism employed here is similar to that used to decouple id and iq in the current-control scheme of Fig. 2. The control scheme of Fig. 3 enables independent control of vsd and vsq , respectively, by idref and iqref . Fig. 3 also shows that measures of iod and ioq are included in the control process as two other feedforward signals, to mitigate the impact of the load dynamics on vsd and vsq . Hence, the compensated system behaves under all load conditions in, approximately, the same way as the uncompensated system would behave under a no-load condition. The reason for the effectiveness of the control

4

vsd

v sdref

-

overall voltage control plant, effectively, into two independent Single-Input-Single-Output (SISO) plants of Fig. 4.

iod d-axis compensator

ed

k(s)

ud -

idref

vsdref

ed -

k(s)

ud

Gi(s)

Cf s

uq

Gi(s)

Cf s

1

vsd

1

vsq

Decoupling feed-forward

*

ω

*

Cf Cf

Fig. 4.

q-axis compensator

eq

v sqref -

k(s)

uq

vsq Fig. 3.

vsqref

iqref

ioq

Block diagram of the voltage control scheme

scheme of Fig. 3 can be understood based on the following discussions. As Fig. 3 shows, one has idref = ud − (Cf ω)vsq + iod iqref = uq + (Cf ω)vsd + ioq ,

(11) (12)

where ud and uq are two dummy control inputs. Substituting for idref and iqref , from (11) and (12), in (7) and (8), one obtains Id = Gi (s)Ud − Cf Gi (s)£{ωvsq } + Gi (s)Iod Iq = Gi (s)Uq + Cf Gi (s)£{ωvsd } + Gi (s)Ioq ,

(13) (14)

where £{.} denote the Laplace transform operator. It then follows from applying Laplace transform to both sides of (3) and (4), and substituting for Id (s) and Iq (s) from (13) and (14), in the resultants, that Cf sVsd = Gi (s)Ud +Cf [1 − Gi (s)]£{ωvsq } − [1 − Gi (s)]Iod (15)

  Cf sVsq =

transient terms

Gi (s)Uq −Cf [1 − Gi (s)]£{ωvsd } − [1 − Gi (s)]Ioq .(16)

  transient terms

It is then noted that the transfer function Gi (s) = 1/(τi s + 1) has a unity DC gain, and therefore [1 − Gi (s)] = τi s/(τi s+ 1) has a zero DC gain. Hence, if τi is adequately small, those terms of (15) and (16) which are labeled as “transient terms” assume negligible values, and (15) and (16) can be approximated as Vsd (s) 1 ≈ Gi (s) (17) Ud (s) Cf s Vsq (s) 1 ≈ Gi (s) . (18) Uq (s) Cf s Equations (17) and (18) indicate that vsd and vsq can be independently controlled by, respectively, ud and uq . This alternatively means that the control scheme of Fig. 3 divides the

eq -

k(s)

Equivalent block diagrams for the closed-loop voltage control scheme

To design k(s), one notes that each loop in Fig. 4 includes an integral term, i.e. a pole at s = 0, and a real pole at s = −p = −1/τi . For such a plant, a PI compensator can ensure a stable fast response and zero steady-state error, if the following procedure is exercised [7]. Let s+z , (19) k(s) = k s where k and z are the compensator gain and zero, respectively. Then, the open-loop gain is (s) =

k s+z 1 ) . ( τi Cf s + p s2

(20)

At very low frequencies, the open-loop phase  (jω) is approximately equal to −180◦ . If z < p, then  (jω) first increases until reaches its maximum, δm , at ω = ωm . For ω > ωm ,  (jω) drops and approaches −180◦ at very high frequencies. Therefore, to achieve the maximum phase-margin, one should pick the gain crossover frequency as ωc = ωm , and δm becomes the phase-margin. Knowing δm , z can be calculated from sin δm =

(p/z) − 1 . (p/z) + 1

The gain crossover frequency is determined based on √ ωc = p × z .

(21)

(22)

The compensator gain, k, is obtained from the solution to | (jωc ) |= 1, that is k = Cf ωc .

(23)

Based on the above-mentioned design procedure, the resultant closed-loop voltage control system is of the third order. It can be shown that the closed-loop system always has a real pole at s = −ωc , while the two other complex-conjugate poles are located on a circle whose radius is ωc . The exact locations of the two poles depend on the phase margin which is typically chosen in the range of 30◦ to 75◦ . For the particular choice of δm = 53◦ , the two poles are s = −ωc and thus the closed-loop system has a triple pole at s = −ωc . In Fig. 3, vsdref is set to v sn , that is the nominal peak value of the PCC line-to-neutral voltage. However, vsqref is issued by another control loop to regulate ω, as shown in Fig. 5. For this loop, the compensator kω (s) can be as simple as a pure

5

k(s)

Gi (s)

1

Cs

v sq

f

H(s) ω

Block diagram of the frequency control loop

gain. This however results in no steady-state error since H(s) includes an integral term. It should be pointed out that for the grid-connected mode of operation, idref and iqref are not obtained from the voltage control scheme of Fig. 3; rather, they are determined based on the real and reactive power that the DR unit is expected to exchange with the grid as idref = Poref /(1.5

vsn ) vsn ) + Cf ω0

vsn . iqref = −Qoref /(1.5

DR system to the aforementioned sequence of events, for the no-load condition (i.e. when both Switch #1 and Switch #2 are open), the partially-loaded condition (i.e. when Switch #1 is closed but Switch #2 is open), and the full-load condition (when both Switch #1 and Switch #2 are closed), respectively.

500

vsdq

eq

vsqref

i2a i2b i2c

Switch #2

Fig. 6.

i1a R1 L1 i1b i1c

iLd iLq

4000 0 −4000

ω

400 377 350 0

0.05

0.1

0.15

time(s)

Fig. 7.

Start-up transient and voltage step responses of the islanded DR unit under the no-load condition

vsdq

500 250

vsd vsq

vsabc

0

500 250 0 −250 −500 8000

iLd iLq

4000

iLdq

#1

500 250 0 −250 −500

0 −4000 400

ω

vsa iLa vsb iLb vsc iLc

Switch

vsd vsq

8000

V. C ASE S TUDIES AND S IMULATION R ESULTS In this section, the performance of the DR unit of Fig.1, with a capacity of 5.0 M V A, is evaluated under the proposed control strategy. Thus, a detailed switched model of the overall system is simulated using the PSCAD/EMTDC software package [8]. Two types of loads are considered, being (i) the configurable passive load of Fig. 6, and (ii) an induction machine. For the DR unit, vsdref = 500 V and ωref = 377 rad/s, unless otherwise mentioned. In the graphs, voltages are expressed in V , currents in A, frequency and rotational speeds in rad/s, real powers in M W , and reactive powers in M V Ar. The parameters of the system and the loads are given in Appendix B.

250 0

vsabc

Fig. 5.

kω (s)

iLdq

ωref

377 350 0

R2 L2 C2

Schematic diagram of the configurable passive load

A. Configurable Passive Load The first case study demonstrates the response of the DR system to the start-up transient and stepwise changes in vsdref , when the configurable load of Fig. 6 is supplied. To ensure a soft start-up process, vsdref is ramped up from zero to 500 V , and is kept constant from t = 0.02 s onwards. Then, vsdref is subjected to two step changes, one from 500 to 550 V , and the other one from 550 to 500 V , respectively, at t = 0.05 and 0.1 s. Figs. 7 through 9 illustrate the responses of the islanded

0.05

0.1

0.15

time(s)

Fig. 8.

Start-up transient and voltage step responses of the islanded DR unit under the partially-loaded condition

Figs. 7 to 9 indicate that, based on the proposed control strategy, the system responds similarly under all three load conditions. In other words, the dynamic properties of the closed-loop system are, to a large extent, independent of the load dynamic characteristics. It is observed that, in all three cases, the PCC/load voltage tracks its reference value in less than 6 ms, exhibiting a well-damped response. The figures also show that vsq and ω remain unaffected subsequent to the changes in vsd ; this is due to the dynamic decoupling strategy of Section IV. Figs. 10 to 12 show the performance of the DR system in response to stepwise changes in ωref , respectively, for the no-load, partially-loaded, and fully-loaded conditions. Thus, ωref is step-changed from 377 to 400 rad/s, at t = 0.05 s, and is changed back to 377 rad/s at t = 0.1 s. It is

6

500

250

vsd vsq

vsabc

500 250 0 −250 −500 8000 0

250

−4000

500 250 0 −250 −500

iLd iLq

4000 0 −4000

400

400

377

ω

ω

vsd vsq

0

8000

iLd iLq

4000

iLdq

vsabc

0

iLdq

vsdq

vsdq

500

377 350

350 0

0.05

0.1

0.15

0

0.05

time(s)

Fig. 9.

Start-up transient and voltage step responses of the islanded DR unit under the fully-loaded condition

Fig. 11.

0

vsabc

8000

Frequency step responses of the islanded DR unit under the partially-loaded condition

0

vsd vsq

0

500 250 0 −250 −500 8000

iLd iLq

4000

250

iLd iLq

4000 0

−4000

−4000

400

400

377

377

ω

iLdq

vsdq

vsd vsq

500 250 0 −250 −500

ω

0.15

500

250

iLdq

vsabc

vsdq

500

350

350 0

0.05

0.1

0.15

0

0.05

time(s)

Fig. 10.

0.1

time(s)

Frequency step responses of the islanded DR unit under the no-load condition

observed that in all three cases, the frequency rapidly tracks its reference command. Moreover, while the change in the frequency disturbs vsq , as expected, its impact on vsd and therefore on the PCC/load voltage is insignificant. It should be pointed out that the frequency is usually not changed in practice. Here, the foregoing case study is used as a test means for evaluating the control design and performance. Fig. 13 illustrates the performance of the DR system in response to sudden load switching incidents. Initially, the system is in a steady state, while both Switch #1 and Switch #2 are open and the system operates under a no-load condition. At t = 0.05 s, Switch #1 is closed and the RL branch of the load is switched on. This load, introduced earlier as the partial load, corresponds to a power rating of 3.28 M W and a lagging power-factor of 0.85. Subsequent to the load energization, the load current increases and, as Fig. 13 shows, iLd and iLq develop. It is noted that since the load is inductive, iLq settles at a negative value. At t = 0.1 s, Switch #2 is also closed and the RLC branch of the load is brought into operation. This configuration, i.e. the full-load, corresponds to the power rating of 3.9 M W and the unity power-factor. Thus, iLq approaches the steady-

0.1

0.15

time(s)

Fig. 12.

Frequency step responses of the islanded DR unit under the fully-loaded condition

state value of zero, whereas iLd exhibits a large overshoot subsequent to the switching incident. The overshoot is due to the charging current of the capacitor C2 . At t = 0.15 s, Switch #2 is opened and the RLC branch of the load is switched off. Therefore, the load configuration and the system operating condition become identical to those for the time interval between 0.05 and 0.1 s. At t = 0.2 s, Switch #1 is also opened and the remainder of the load is switched off. Thereafter, the system continues operation under the no-load condition. Fig. 13 indicate that, despite the load switching events, the PCC/load voltage and frequency are well regulated, and the disturbances are rejected rapidly. The largest excursion in the voltage is due to the inrush current of the load RLC branch which takes place at t = 0.1 s. Nonetheless, the PCC/load voltage retrieves its pre-disturbance form and quality in less then half 60-Hz cycle. B. Induction Machine Load This case study demonstrates the effectiveness of the proposed control strategy when a highly nonlinear load, being a

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and generating modes is due to the machine internal losses. A negative PL can occur when other distributed generators, for example constant-speed wind turbines, are also connected to the islanded distribution network, and their aggregate power generation surpasses the total load. As Fig. 15 shows, the DR system maintains its stability under the power-flow reversal, and vsd , vsq , and ω remain tightly regulated. At t = 1.2 s, ωref is stepped up from 377 to 385 rad/s; and it is brought back to 377 rad/s at t = 1.4 s. Consequently, the machine shaft speed increases over the foregoing period. However, the disturbances impose insignificant impacts on vsd and vsq , as Fig. 15 shows.

vsdq

500 250

vsd vsq

0

vsabc

500 250 0 −250 −500 8000

iLd iLq

iLdq

4000 0 −4000

ω

400 377 350 0

0.05

0.1

0.15

0.2

0.25

Dynamic response of the islanded DR unit to sudden changes in the load configuration

vsdq

500 250 0

vsd vsq

PL , QL

iLdq

4

1 0.5 0 −0.5 −1

x 10

iLd iLq

6 3 0

PL QL

ωr

400 200 0

ω

400 377 350 0.4

0.5

0.6

0.7

0.8

time(s)

Fig. 14.

Dynamic response of the islanded DR unit to sudden switching of the induction machine load

Fig. 15 shows the system response to a power-flow reversal followed by two frequency changes. The power flow is reversed by changing the external torque of the induction machine from 0.7 to −0.7 pu, at t = 1.0 s. Thus, PL changes from about 600 kW to slightly higher than −600 kW ; the discrepancy between the absolute values of PL in the motoring

0

iLd iLq

ωr

0.6 0.3 0 −0.3 −0.6

PL QL

390 380 370

385

ω

two-pole induction machine, is energized by the DR system. Initially, the system is in a steady state while the induction machine is yet not connected to the PCC. In addition, the machine shaft speed (ωr ) and mechanical torque are both zero. At t = 0.5 s, the machine terminals are suddenly connected to the corresponding phases of the PCC, and the machine is energized; simultaneously, a mechanical torque of 0.7 pu is exerted on the machine shaft. Fig. 14 illustrates the response of the DR system and the machine. Fig. 14 shows that subsequent to the switching incident, iLd, iLq , PL , and QL exhibit large overshoots due to the machine inrush current. These overshoots, however, get damped in less than 0.17 s, as the machine speed increases. Despite the disturbance severity, vsd , vsq , and ω rapidly revert to their pre-disturbance values, and the system remains stable.

vsq vsd

250

1000 500 0 −500 −1000

PL , QL

iLdq

Fig. 13.

500

vsdq

time(s)

377 370 0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

time(s)

Fig. 15.

System behavior in response to a power flow reversal and step changes in the frequency

VI. C ONCLUSION This paper proposes a mathematical model and a voltage/frequency regulation strategy for an islanded, electronically-coupled, Distributed Resource (DR) unit. The proposed control strategy uses the circuit configuration, dq-frame current-control scheme, and the Phase-Locked Loop (PLL) mechanism that are typically employed in modern DR units. It therefore requires minimal software modifications to enable the islanded mode operation of the DR unit, for example, for a remote electrification application. The proposed control strategy takes advantage of suitable feed-forward compensation techniques to mitigate the impacts of the load dynamics, inherent inter-couplings, and nonlinearities of the control system. This facilitates the controller design process. The system performance and control robustness/effectiveness under black-start operation, load switching incidents, and bi-directional power-flow conditions are demonstrated by means of simulations conducted on a detailed switched model of the system in the PSCAD/EMTDC software environment. A PPENDIX A M ATHEMATICAL M ODEL OF THE L OAD OF F IG . 6 To derive the load mathematical equations, let us consider the load RL branch with the following equation d− → → − → vs . (24) L1 i1 = −R1 i1 + − dt

8

→ − Substituting for f = (fd + jfq )ejρ(t) in (24), performing the derivatives, and decomposing the resultant into real and imaginary parts, one obtains di1d R1 = − i1d + ωi1q + dt L1 di1q R1 = −ωi1d − i1q + dt L1

1 vsd L1 1 vsq . L1

(25)

Therefore, the RL branch of the load has two state variables, receives the inputs vsd , vsq , and ω, and provides the outputs i1d and i1q . Similarly, the RLC branch of the load is described by di2d R2 = − i2d + ωi2q + dt L2 di2q R2 = −ωi2d − i2q + dt L2

1 1 vsd − vd L2 L2 1 1 vsq − vq , L2 L2

(26)

and dvd 1 = ωvq + i2d dt C2 dvq 1 = −ωvd + i2q . dt C2

(27)

Thus, the RLC branch of the load has four state variables, receives the inputs vsd , vsq , and ω, and provides the outputs i2d and i2q . Since, iLabc = i1abc + i2abc , then and iLd = g1 (i1d , i1q , i2d , i2q , vsd , vsq , ω)

The transfer function of the PLL filter is s + 133.85 [(V s)−1 ] H(s) = 4700 s(s + 1195) The parameters of the passive load of Fig. 6 are R1 = 83 mΩ, L1 = 137 μH, R2 = 50 mΩ, L2 = 68 μH, and C2 = 13.55 mF . The parameters of the induction machine are Rr = 0.0132 pu, Rs = 0.0184 pu, Lm = 3.8 pu, Llr = 0.0223 pu, and Lls = 0.0223 pu. The machine has two poles, and its rated power, voltage, and frequency are 800 kV A, 868 V (line-toline, rms), and 377 rad/s, respectively. R EFERENCES [1] N. Hatziargyriuo, H. Assano, R. Iravani and C. Marnay, “Microgrids,” IEEE Power and Energy Magazine, vol. 5, no. 4, pp. 78-94, July-August 2007. [2] H. Karimi, H. Nikkhajoei, and R. Iravani “A Linear Quadratic Gaussian Controller for a Stand-alone Distributed Resource Unit-Simulation Case Studies,” IEEE Power Engineering Society General Meeting, PES07, June 2007. [3] H. Karimi, H. Nikkhajoei, and M. R. Iravani, “Control of an Electronically-Coupled Distributed Resource Unit Subsequent to an Islanding Event,” IEEE Transactions on Power Delivery, vol. 23, no. 1, pp. 493-501, Jan. 2008. [4] C. K. Sao and P. W. Lehn, “Intentional Islanded Operation of Converter Fed Microgrids,” IEEE Transactions on Power Delivery, vol. 20, no. 2, pp. 1009-1016, April 2005. [5] S. K. Chung, “A phase tracking system for three phase utility interface inverters,” IEEE Transactions on Power Electronics, vol. 15, no. 3, pp. 431-438, May 2000. [6] C. Schauder and H. Mehta, “Vector analysis and control of advanced static VAR compensators,” IEE Proceedings – Generation, Transmission, and Distribution, vol. 140, no. 4, pp. 299-306, July 1993. [7] W. Leonhard, Control of Electrical Drives, 3rd ed. Springer-Verlag, 2001. [8] PSCAD/EMTDC v. 4.2, Manitoba HVDC Research Centre, Winnipeg, MB, Canada.

iLq = g2 (i1d , i1q , i2d , i2q , vsd , vsq , ω) . (28) Equations (25) to (28) describe the dynamics of the load of Fig. 6 and include six state variables, the three inputs vsd , vsq , and ω, and the two outputs iLd and iLq . It is noted that the equations are nonlinear. A PPENDIX B S YSTEM DATA The DR unit parameters are L = 100 μH, Cf = 500 μF , R = 1.5 mΩ, vdc = 1600 V , and the switching frequency fs = 3420 Hz. The compensators of the current control scheme have the transfer functions s + 15 kd (s) = kq (s) = [Ω] s corresponding to τi = 0.1 ms. The compensators of the voltage and frequency control loops have the transfer functions k(s) =

1.66s + 1844 [Ω−1 ] s

kω (s) = 10.0 [V s]

Mohammad B. Delghavi (S’09) received the M.Sc. degree from Iran University of Science and Technology (IUST),Tehran, Iran, in 1996. Presently, he is a Research Assistant with the Department of Electrical and Computer Engineering, the University of Western Ontario, London, Canada, working towards the Ph.D. degree. His research interests include design, dynamic modeling, and control of switching power converters, distributed generation, and microgrids.

Amirnaser Yazdani (S’02-M’05) received the Ph.D. degree in Electrical Engineering, from the University of Toronto, Canada, in 2005. He was with Digital Predictive Systems (DPS) Inc., Mississauga, Ontario. Presently, he is an Assistant Professor with the University of Western Ontario, London, Ontario, Canada. His research interests include dynamic modeling and control strategies for switching power converters and electronically-interfaced generators, distributed generation, and microgrids.