coordinated control of distributed generation

7/27/2019 Coordinated Control of Distributed Generation

1/8

Coordinated Control of Distributed Generation

Karina Munoz and Kevin WedewardDepartment of Electrical Engineering

New Mexico Institute of Mining and Technology

Socorro, New Mexico 87801Email: [email protected], [email protected]

AbstractThis paper presents an approach to coordinate Dis-tributed Generation (DG) such that quantities in an unbalanceddistribution system are balanced and power factor corrected.Models for the DG and three-phase distribution network arecombined to form a set of Differential Algebraic Equations(DAE) that represent the behavior of the distribution system. Twostate-feedback controllers with reference inputs are presented forcoordinated control of DG. Both are designed via linearizationof the DAE model. The first uses an additional matrix selected sothat the outputs match the reference values in steady-state whilethe second uses an internal model design with integral to drive the

outputs to the reference values. The approach is demonstrated onmodels of 5-bus and 10-bus test systems with inverter-connectedDG. The control objective for the 5-bus test system is to balanceactive line powers across the three phases as supplied from thetransmission system. The control objective for the 10-bus systemis to correct power factor on each phase as supplied from thetransmission system. Robustness of the internal model controlleris investigated for uncertainties (up to 25%) in line parametersand unknown step changes (up to 25%) in loads, and resultsshow that control objectives are achieved in the presence of theseuncertainties.

I. INTRODUCTION

As demand for power and concern about the environment

increase, Distributed Generation (DG) is becoming more at-tractive. Installing DG at the distribution level is often less

burdensome than expanding the transmission system, which

can be difficult and expensive due to the cost of system

components and fluctuating environmental regulations [1].

Additional benefits associated with DG include reduction in

power demand from the transmission system, greater control

over costs and sources and less transmission losses. DG is

also associated with improved power reliability and higher

voltages, convenient for critical and sensitive loads. Finally,

DG such as photovoltaics, wind turbines and fuel cells reduce

green house emissions by producing cleaner energy.

While the commonly recognized benefits associated with

DG discussed above are numerous, DG can also be utilized

to perform ancillary services to the main grid for applications

such as voltage regulation, power factor correction, load bal-

ancing and load shaping [2][5]. There have been numerous

applications researched for using DG to perform functions

other than providing power in place of the transmission

network. In [6], both active and reactive power are controlled

to enhance the stability of the system and improve the quality

of the power being delivered by compensating for any load

increase or disturbances at the local level. A parameter es-

timation and feedforward method is used to reduce transient

coupling and overshoot when tracking the reference values.

The controller is tested under grid-connected and island mode.

In [3] and [7], DG is used for voltage regulation and the idea of

balancing voltages at each phase using independent controllers

is presented in [3]. In [8], fuel cells, a common type of DG,

are used to reduce oscillations caused by incidents such as

sudden load increase. The controller model takes advantage

of the fast response of the fuel cell. Frequency control for

system stability is discussed in [9]. In [1] and [10] control ofDG connected in parallel is used for island mode systems in

order to provide an optimal load sharing technique. Finally, in

[11], DG is used for microgrids to aid in the transition between

grid-connected and islanded mode.

This paper presents an approach to coordinate DG to

balance characteristics among an unbalanced distribution sys-

tem and to correct power factor via state-feedback control.

Assuming quasi-steady state, an unbalanced three-phase dis-

tribution network will be modeled with algebraic equations,

while dynamic behavior of DG will be modeled with ordinary

differential equations. The controller takes measurements from

the network (e.g., voltages or powers) as control objectives and

uses these to adjust setpoints for all DG. Linearization of theDAE model, including the algebraic equations for the network

and the differential equations for the DG, is used to design

two different controllers which are applied to the nonlinear

system. Robustness of one of the controllers is tested against

model uncertainties such as network parameters and outside

disturbances such as a change in load. Both controllers are

simulated on two different distribution systems and results are

presented.

I I . BACKGROUND

In this section, a model for the distribution system consisting

of the three-phase network and DG is presented. Loads are

assumed to be functions of time.

A. Distribution Network Model

General equations for three-phase network devices such as

transmission lines, transformers and voltage regulators can

be found in [12]. These equations that describe three-phase,

voltage-current relationships for individual components can

be combined and converted to complex power equations that

represent power balance on every phase at every bus in

the network. The average power balance and reactive power

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


2/8

balance equations for every phase at every bus can be written

as follows:

Pk = |Vk|3Nn=1

|Ykn||Vn|cos( Vk Vn Ykn) (1)

Qk = |Vk|3N

n=1

|Ykn||Vn|sin( Vk Vn Ykn) (2)

where N is the total number of busses in the distribution

system; k = 1, 2, . . . , 3N, is the index used to represent everyphase at every bus; Pk, Qk are the average and reactive power,

respectively, injected into a phase at a bus; Vk is the phasor

representation of the sinusoidal voltage on a phase at a bus;

Ykn is the admittance between one phase and another phase

at the same or a different bus; | | denotes the magnitude of acomplex quantity; and denotes the phase angle of a complexquantity.

B. Models of Inverter Connected Sources

DG such as fuel cells and photovoltaic systems generate

electricity at Direct Current (DC), thus requiring an inverter

to convert DC to to Alternating Current (AC) for connection to

the grid. Several models for inverters have been proposed [10],

[11], [13], and two representative examples are considered in

this paper and briefly described below.

1) Inverter Model 1: The first inverter model is presented in

[11]. The main objective of this inverter and its controller are

to control the active power delivered to the network as well as

the voltage at the terminal bus. The terminal bus is defined as

the single-phase, AC bus on the distribution network to which

the DG is connected. The inverter bus, where DC is converted

to AC, is connected to the terminal bus via a transformer with

series branch impedance jX . Equations that describe the

inverter, controller and network are as follows:

m = K1(Vset |Vt|) (3)

= K2(P0 R(v + K4) Pgen) (4)

v = K3( Vt p) (5)

p = v + K4 (6)

Vi = + p (7)

|Vi| =mVdc

Vbase(8)

Pgen =|Vi||Vt|

Xsin( Vi Vt) (9)

Qgen =|Vi||Vt|

Xcos( Vt Vi)

|Vt|2

X(10)

where Pgen, Qgen are the real and reactive power, respectively,

injected by the generator into the network. Equations (9) and

(10) are the only tie between the generator and the distribution

network.

Vi, Vt are the phasors representing the sinusoidal voltages

at the inverter and terminal buses, respectively. m is the

modulation index of the inverter and essentially establishes

the voltage magnitude at the AC side. = Vi p is the

difference between the phase angle at the inverter bus and

reference phase angle p from a phase-locked loop. The phase-

locked loop is used to help the inverter synchronize with the

AC side. v is an intermediate variable associated with damping

in the controller, Vset is the setpoint for the desired magnitude

of the voltage at the terminal bus, P0 is the nominal real

power output of the generator, R is the droop constant, Vbaseis the base voltage for the inverter, Vdc is the DC voltage

on the DC side of the inverter, p is the estimated frequency

deviation, and K1, K2, K3 and K4 are gains. Equations (3)-(5)

make use of integral control in order to match up the voltage

magnitude |Vt|, the power Pgen and the angle p with Vset,Pset = P

0 R(v + K4) and Vt, respectively.2) Inverter Model 2: The second inverter model is pre-

sented in [10]. The time-domain version is considered in this

paper with an adaptation of the governing equations as follows

= f(kpP + ( o)) (11)

|

E| = f(kvQ + (|E| Eo)) (12)

E =E = ref (13)

where , E are the output frequency and voltage (as a phasor)

from the inverter, respectively; f is the cutoff frequency

of a low-pass filter; kp, kv are frequency and voltage droop

coefficients, respectively; P, Q are average and reactive power

injected by the inverter; o, Eo are the frequency and voltage

setpoints, respectively; and ref is the reference frequency of

the transmission network. The inverter can be considered as

an ideal voltage source where amplitude, phase and frequency

can be controlled.

C. DAE Modeling

Once algebraic equations for the network and the differential

equations for the inverters have been identified, they canbe combined with load models (here functions of time) to

form a system of Differential Algebraic Equations (DAE) that

represent the complete distribution system. If equations that

represent outputs yout to be controlled are also included, the

following system of equations is obtained:

x = f(x,y,uf) (14)

0 = g(x,y,ug) (15)

yout = h(x, y) (16)

where the vector function f(x,y,uf) represents the differen-tial equations of all inverters given by equations (3)-(6) for

Inverter Model 1 and by (11)-(13) for Inverter Model 2; the

vector function g(x,y,ug) represents the algebraic networkequations (1) and (2) for all phases and buses; vector function

h(x, y) represents the equations of outputs to be controlledand will be seen in later examples; x are the states of the

model; y are the algebraic variables; yout are the outputs

to be controlled; and uf and ug are the inputs with respect

to f and g, respectively. It is important to note that quasi

steady-state is assumed for the network; therefore, although

variables such as V , Y ,P, Q in equations (1) and (2) vary, the


3/8

frequency is assumed to be fixed. The DAE model comprised

of equations (14)-(16) will serve as the system for which

coordinated controllers are designed in the next section.

III. STATE-FEEDBACK CONTROL DESIGN

This section presents approaches to design two state-

feedback controllers. The process begins by linearizing the

nonlinear DAE model consisting of the differential equations(14) describing the DG, the algebraic equations (15) describing

the network and the equations (16) describing the outputs to

be controlled. Once the system is linearized, a controller can

be designed for the linear system and applied to the nonlinear

system.

When there are several DG within a distribution system,

all DG aid in the process of meeting the control objective

and the term coordinated control of DG may be applied.

A conceptual diagram of coordinated control of DG within

a distribution system is shown in Figure 1. The controller

takes measurements of quantities (e.g., line powers, power

factor, bus voltages, etc.) from the distribution system. These

measurements are used by the controller to specify setpoints(e.g., voltage and power) for the DG to meet control objectives.

Fig. 1. Conceptual diagram of coordinated control of DG

A. Initial Conditions

Linearization begins by finding an operating point about

which to linearize. The operating point is selected here by

finding a load flow solution to the distribution systems power

balance equations and then computing the corresponding

initial conditions for the DG such that the system is at

equilibrium. Initial conditions for the algebraic variables, yo,

come from a load flow solution, or equivalently, finding a

solution to the nonlinear equations for the network given by

(1) and (2).

1) Inverter Model 1 Initial Conditions: Initial conditions

for the algebraic variables, yo, can be used to find initial

conditions for the states, xo, and setpoints of the inverter.

Differential equations describing Inverter Model 1 are given

by equations (3)-(6) which can be set to zero for equilibrium

and solved for the initial conditions. Here it is assumed that a

load flow solution has been computed from which the complex

power Sgen = Pgen + jQgen injected by the generator andterminal voltage Vt are specified. Following some algebra, the

complex generator power and terminal voltage can be used to

find the magnitude and phase angle of the phasor representing

the voltage at the inverter bus. Equations (9) and (10) are

manipulated to find

|Vi| =

X2

P2gen + Q

2gen

+ 2|Vt|2XQgen + |Vt|4

|Vt|2

Vi = Vt tan1

PgenX

XQgen + |Vt|

With |Vi|, Vi known, equations (3)-(6) are set to zeroand combined with (7) and (8) to find the following initial

conditions for the states and setpoints.

mo =|Vi|Vbase

Vdc(17)

po = Vt (18)o = Vi po = Vi Vt (19)

vo = K4o = K4( Vi Vt) (20)

Vset = |Vt| (21)

P0o = R(vo + K4o) + Pgen = Pgen (22)

Initial conditions for the outputs to be controlled, youto , can

be found by substituting in the initial conditions for yo and

xo into their particular equation (16).2) Inverter Model 2 Initial Conditions: Initial conditions

for the states, xo, for Inverter Model 2 described by equations

(11)-(13) can also be found using yo given by the load

flow solution. Since the load flow solution gives the terminal

voltage (here denoted E), initial conditions for |E| and Eare simply

|Eo| = |E| (23)

Eo = E = E (24)

where E is the complex voltage at the bus where the dis-

tributed generator is connected. Initial conditions for the

setpoints o and Eo can be found by setting equations (11)

and (12) equal to zero and are given by:

o = n + kpPgen (25)

Eo = |E| + kvQgen (26)

The initial condition for , o

, is simply the nominal fre-

quency ref.

B. Linearization

The nonlinear system given in equations (14)-(16) may be

linearized by letting x = x + x, y = y + y, yout =yout+yout, uf = uf+uf and ug = ug+ug where x,y, yout, uf and ug are the operating point and equivalently

the initial conditions found in the previous section, and x,y, yout, uf, and ug are small deviations from the


4/8

operating points x, y, yout , uf and ug, respectively.

Taking the Taylor Series Expansion about the operating point

and ignoring 2nd and higher order terms, equations (14), (15)and (16) become:

x =f

xx +

f

yy +

f

ufuf (27)

0 = gx

x + gy

y + gug

ug (28)

yout =h

xx +

h

yy (29)

where the notation ab

is the partial derivative of the vector

function a with respect to the vector of variables b evaluated

at the operating point. Solving for y in equation (28) andsubstituting into equations (27) and (29) yields a linearized

mathematical model of the system in the general state-space

form

x = Ax + B1uf + B2ug (30)

yout = Cx + Dug (31)

where A =

fx f

y

gy

1gx

, B1 =

fuf

, B2 =

fy

gy

1gug

, C =

hx h

y

gy

1gx

and

D =

hy

gy

1gug

all of which are constant matrices

that result from evaluation at the operating point.

C. Controller Design

Two state-feedback controllers, both based upon the lin-

earized system above are presented below.

1) State-Feedback Controller with Reference Input: Using

the linearized equations (30) and (31) a state-feedback con-

troller with reference input can be defined as:

uf = Kx + Nr (32)

where K is a matrix of gains with appropriate dimensions used

to select the closed-loop poles of the system and N is a scaling

matrix used to set constant yout equal to constant referenceinput r in steady-state. Substituting the controller defined byequation (32) into the system defined by equations (30) and

(31) yields the closed-loop system:

x = (A B1K)x + B1Nr + B2ug (33)


To find N, steady-state is assumed such that x = 0 in

(33) and yout = r in (34). Assuming that ug is knownand is equal to some constant l times r, N can be found tobe

N =C(A B1K)

1 B11

I + l

C(A B1K)1B2 D

(35)

It is important to note that N can only be obtained if the

disturbance ug and system matrices are known. Therefore,the state-feedback controller with reference input will not work

for a system with unknown disturbances or uncertainty in

parameters.

2) Internal Model Controller: Although the state-feedback

controller with reference input is simple, many times a dif-

ferent controller is more appropriate, especially when the

input ug is unknown or there is uncertainty in the model.An internal model controller is developed below to provide

tracking capabilities and robustness to uncertainties related to

the model and/or disturbances.

Let the tracking error, e, be defined as youtr, whereyout is the deviation in output and r is the deviation inreference value. For a step reference value, the derivative of

the tracking error becomes:

e = yout

= Cx + Dug (36)

Equation (36) can be combined with the derivative of equation

(30) to form a new augmented system also based upon the

tracking error. The new system can be described by the

following two equations:

e = Cx + Dug (37)

x = Ax + B1uf + B2ug (38)

Assigning z = x, the system above becomes:

e = Cz + Dug (39)

z = Az + B1uf + B2ug (40)

which can be written in the general form of equation (30) as:ez

=

0 C0 A

ez

+ 0

B1 uf + 0

B2 ug (41)This new system can be used to design a controller with

control law:

uf = [Ke, Kz]

ez

= Kee Kzz (42)

or equivalently (via integration)

uf = Ke

edt Kzx (43)

where Ke and Kz are gain matrices of appropriate size. If

this new augmented system is stable and ug is constant orslowly varying, e 0 as will z = x. For a higher orderreference input, additional integral terms will be necessary

[14].

IV. EXAMPLES WITH SIMULATION RESULTS

This section presents simulation and analysis of two dis-

tribution systems (a 5-bus and a 10-bus) that implement the

approaches to control described in Section III. For simplicity,

only one type of DG is used in each distribution system.

Control objectives are defined for each system and the design

process summarized.


5/8

A. 5-Bus Distribution System

Fig. 2. Diagram of 5-bus distribution system

The first distribution system is shown in Figure 2. The

system consists of five buses, three loads and three distributed

generators. It is assumed that the distribution system is directlyconnected to the transmission system, and therefore bus num-

ber one is modeled as an infinite bus. Loads and DG have

been placed at buses three, four and five. All three of the

DG were of type Inverter Model 1 [11], and can be described

by equations (3)-(10). The system has unbalanced loads and

unbalanced impedances among phases. Parameters for all three

distributed generators are given in Table I. Network parameters

TABLE IDG PARAMETERS FOR 5- BUS DISTRIBUTION SYSTEM

K1 10

K2 20

K3 20

K4 10R 0.4 p.u.

X 0.2 p.u.

Vset 0.96 p.u.

Vdc 480 V

Vbase 240 V

for the distribution network are given in Table II with all values

in p.u.

TABLE II

NETWORK PARAMETERS FOR 5- BUS DISTRIBUTION SYSTEM

SLoad1 0.5 + 0.25i

SLoad2 0.6 + 0.25i

SLoad3 0.55 + 0.2i

Z23 0.0909 + 0.1818iZ24 0.1000 + 0.2000i

Z25 0.1111 + 0.2222i

Z12

0.22 + 0.31i 0.25 + 0.02i 0.25 + 0.002i

0.25 + 0.02i 0.2 + 0.3i 0.0025 + 0.002i

0.25 + 0.02i 0.0025 + 0.002i 0.2 + 0.28i

The controller used was the state-feedback controller with

reference input given by equation (32). The control objective

was to balance the active line powers as seen from the

transmission system to a desired value of 0.3 p.u. for all threephases. A load flow was performed to find initial conditions for

the algebraic variables, yo. These were then used to solve for

the initial conditions for the states of the differential equations,

xo, using equations (17)-(22).

The nonlinear equations for outputs to be controller, yout,

were defined as those needed to compute the active line powers

PLine1a , PLine1b , and PLine1c provided by the transmission

system (infinite bus). System variables for the DAE model

given in general form in equations (14)-(16) are as follows:

x = [m1, 1, v1, p1, m2, 2, v2, p2, m3, 3, v3, p3]

y = [ V2a, |V2a|, V2b, |V2b|, V2c, |V2c|,

V3, |V3|, V4, |V4|, V5, |V5|]

yout = [PLine1a , PLine1b , PLine1c ]

uf = [P0

1 , P0

2 , P0

3 ]

The assumption that there were no inputs with respect to g

(ug = 0) was made and equations (30) and (31) for thelinearized system were reduced to:

x = Ax + B1uf (44)

yout = Cx (45)

Once the controller was designed with a response time similar

to that of the uncontrolled system in mind, it was applied to

the nonlinear system. Simulation results are shown in Figure

3 where it is noted that the controller was turned on at 5

seconds. Figure 3 shows the active line powers for all three

Fig. 3. Line powers delivered from the infinite bus for 5-bus distributionsystem using state-feedback with reference input controller

phases as seen from the transmission system (between buses

one and two). Although initially they are quite different, at

about 8 seconds, 3 seconds after the controller was started,

the line powers are extremely close to the desired value of 0.3p.u. for all three phases.

B. 10-Bus Distribution System

The second distribution system studied is shown in Figure 4

and was obtained from [15]. The distribution system consists

of ten buses, nine loads and three distributed generators. The


6/8

Fig. 4. 10-bus distribution system

DG are of type Inverter Model 2 described by equations (11)-

(13). Parameters for the DG can be found in Table III and

network data are given in Tables IV and V.

TABLE IIIDE R PARAMETERS FOR 10 -BUS DISTRIBUTION SYSTEM

ref 377 rad

kp .01

kv .01

f 37.7 rad

TABLE IV

LOADS (KW AND KVAR ) FOR THE 10- BUS DISTRIBUTION SYSTEM

Phase A Phase A P hase B Phase B Phase C Phase C

Node P Q P Q P Q

2 22.5 11.25 50 25 50 12.5

3 22.5 11.25 37.5 12.5 0 0

4 22.5 11.25 25 25 25 25

5 0 0 37.5 12.5 50 12.5

6 70 58.75 0 0 0 0

7 45 33.75 0 0 25 12.5

8 45 33.75 25 12.5 0 0

9 0 0 0 0 50 37.5

10 0 0 50 37.5 0 0

TABLE V

BRANCH DATA FOR THE 10 -BUS DISTRIBUTION SYSTEM IN P.U.

Branch Zself Zmutual1-2 1 + 2i 0.5i

2-3 1 + 1i 0.25i

2-4 1 + 2i 0.5i

2-5 1 + 1i 0.25i

3-6 4 + 2.25i 04-7 1 + 1i 0.25i

4-8 1 + 1i 0.25i

7-9 5 + 5i 0

8-10 6 + 4.5i 0

The controller used for this system was the internal model

controller described by equation (43). A load flow was per-

formed to provide initial conditions for algebraic variables yofrom which the initial conditions for the states xo and setpoints

were found through equations (23)-(26). yo and xo were used

to find initial conditions for yout variables taken here to be

reactive power delivered by the transmission system.

1) Power Factor Correction: The control objective for the

10-bus system was power factor correction to be achieved by

reactive power control. The nonlinear equations for the outputs

yout were those used to compute reactive powers QLine1a ,

QLine1b , and QLine1c delivered by the transmission system

(infinite buses). System variables for the DAE model are as

follows:

x = [1, |E1|, E1, 2, |E2|, E2, 3, |E3|, E3]

y = [ V2a, |V2a|, V2b, |V2b|, V2c, |V2c|, V3a, |V3a|,

V3b, |V3b|, V4a, |V4a|, V4b, |V4b|, V4c, |V4c|,

V5b, |V5b|, V5c, |V5c|, V7a, |V7a|, V7c, |V7c|,

V8b, |V8b|, V8c, |V8c|]

yout = [QLine1a , QLine1b , QLine1c ]

u = [Eo1 , Eo2 , E

o3 ]

Again the assumption that there were no inputs with respectto g was made and the general equations (30) and (31) for the

linearized system were reduced to:

x = Ax + Buf (46)

yout = Cx (47)

The linear control system (43), (46), (47) was used find gains

such that responses similar to that of the original, uncontrolled

system were achieved. The controller was then applied to the

nonlinear system at 10 seconds, and simulation results are

shown in Figure 5. Reactive power for all three phases, shown

in Figure 5, has gone down to the desired value of 0 p.u. in

about 50 seconds. This corresponds to dramatic improvement

in power factor on all three phases that become extremelyclose to the desired value of one.

Fig. 5. Reactive line powers delivered from the infinite bus for 10-busdistribution system with power factor correction and internal model controller

2) Step Change in Loads: It was shown above that the in-

ternal model controller works even when there is an unknown

step change in load, or equivalently there exists an input with

respect to g, which was denoted ug. Because the loads are


7/8

not necessarily known, they are considered here as unknown

inputs with respect to the algebraic equations, and the linear

system used for design of the internal model controller (43)

has the form

x = Ax + B1uf + B2ug (48)


To simulate a step change in load both active and reactive

power for the loads at the buses with DG were increased

by 25% at 60 seconds. Figure 6 shows reactive power as

transferred from the transmission line in the case of the

unknown step change in load. At 60 seconds, the reactive

power immediately responds to the load increase, but still

achieves the ultimate desired value of zero.

Fig. 6. Reactive line powers delivered from the infinite bus for 10-busdistribution system with 25 percent increase in load at 60 seconds

3) Uncertainty in Parameters: The internal model con-

troller was also tested against uncertainty in network pa-

rameters. Assuming all DG are tested before installation,only network parameter uncertainty will be considered. The

linearized model with errors in the network parameters was

used to design the internal model controller for the nonlinear

system. Assuming there are no inputs with respect to g (i.e.,

ug = 0), the linear system used for design of the controllerwill have the form

x = (A + A)x + B1uf (50)

yout = (C + C)x (51)

where the deviation matrices A, C are the due to the errorin the network parameters. Because B1 is not dependent on the

algebraic variables, y, it is unaffected by changes in network

parameters. Although eigenvalues for the closed-loop system

(A B1K) vs. ((A + A) B1K) will vary, the systemgiven by equations (50) and (51) can still be controlled using

the internal model controller given by equation (43).

To test the effect of uncertainty in network parameters they

were randomly changed by up to 25% of their actual value

taken from a uniform distribution. Several cases were ran and

results overlaid as shown in Figure 7. Figure 7 shows the

Reactive Power with up to 25% uncertainty in the network

parameters. The control objective of reducing reactive powers

to zero for all phases is met even though the uncertainty is

present. This is due to the fact that the actual system states

and outputs are fed back to the controller and the integral term

eventually helps meet the control objective.

Fig. 7. Reactive line powers delivered from the infinite bus for 10-bus

distribution system with up to 25 percent uncertainty in network parameters

with internal model controller

V. CONCLUSION

This paper examined the use of coordinated control of DG

for balancing characteristics among phases and for power

factor correction. Two state-feedback controllers with refer-

ence inputs were presented. Both controllers were designed

based upon linearization of the DAE model that consisted of

dynamic equations for the DG and algebraic equations for the

three-phase network. The first controller used an additional

matrix selected so that the outputs match the reference in

steady-state. The second controller used an internal model

design with integral to drive the outputs to the references.

5-bus and 10-bus distribution systems were simulated andanalyzed to demonstrate the effectiveness of the controllers.

Active line powers were controlled and balanced on the 5-

bus distribution system using the state-feedback with reference

input controller. Power factor correction was performed on the

10-bus distribution system using the internal model controller

which performed well even in the presence of uncertainty in

network parameters and loads.

ACKNOWLEDGMENT

The research described in this paper was supported through

a contract with the Department of Energy.

REFERENCES

[1] J.-W. J. Mohammad N. Marwali and A. Keyhani, Control of distributedgeneration systems-part II: Load sharing control, IEEE Transactions onPower Electronics, vol. 19, no. 6, pp. 15511561, November 2004.

[2] R. H. Lasseter and P. Piagi, Extended microgrid using (DER) dis-tributed energy resources, in 2007 IEEE Power Engineering Society

General Meeting, PES, June 2007.[3] Y. Xu, F. Li, J. D. Kueck, and D. Tom Rizy, Experiment and sim-

ulation of dynamic voltage regulation with multiple distributed energyresources, in 2007 iREP Symposium- Bulk Power System Dynamics andControl - VII, Revitalizing Operational Reliability, August 2007.

[4] J. C. et. all, Ancillary services provided from DER, Oak RidgeNational Laboratory, Tech. Rep., 2005.


8/8

[5] S. R. Oliver Gehrke and P. Venne, Distributed energy resourcesand control: A power system point of view, Internal Report Ris-R-1608(EN).

[6] J.-W. J. Min Dai, Mohammad Nanda Marwali and A. Keyhani, Powerflow control of a single DG unit, IEEE Transactions on Power Elec-tronics, vol. 23, no. 1, pp. 343351, January 2008.

[7] M. A. Kashem and G. Ledwich, Distributed generation as voltage

support for single wire earth return systems, IEEE Transactions onPower Delivery, vol. 19, no. 3, pp. 10021011, July 2004.

[8] K. Ro and S. Rahman, Control of grid-connected fuel cell plants forenhancement of power system stability, Renewable Energy, pp. 397

407, 2003.[9] Y.-J. S. Xiangjun Li and S.-B. Han, Frequency control in micro-grid

power system cobined with electrolyzer system and fuzzy pi controller,

Journal of Power Sources, vol. 180, pp. 468475, February 2008.[10] P. C. C. Ernane Antonio Alves Coelho and P. F. D. Garcia, Small-

signal stability for parallel-connected inverters in stand-alone AC supplysystems, IEEE Transactions on Industry Applications, vol. 38, no. 2,

pp. 533542, March 2002.[11] I. A. Hiskens and E. M. Fleming, Control of inverter-connected sources

in autonomous microgrids, in Proceedings of the American ControlConference, Seattle, WA, United States, June 2008.

[12] W. H. Kersting, Distribution System Modeling and Analysis, 2nd ed.CRC Press, 2006.

[13] T. Green and M. Prodanovic, Control of inverter-based micro-grids,

Electric Power Systems Research, vol. 77, no. 2, pp. 12041213,

Sepetember 2007.[14] R. C. Dorf and R. H. Bishop, Modern Control Systems, 9th ed. Prentice

Hall, 2001.[15] A. G. E. Esther Romero Ramos and G. A. Cordero, Quasi-coupled

three-phase radial load flow, IEEE Transactions on Power Systems, June2004.

coordinated control of distributed generation

Documents