MODELING AND CONTROL OF A DISTRIBUTED GENERATION SYSTEM

G. Shridhar Reddy, R.K.Singh

IET-UK International Conference of Information and Communication Technology in Electrical

Sciences (ICTES 2007)

Report Prepared By:

Rabindra Maharjan

In Partial fulfillment of Linear System Theory (EE615) course

Department of electrical Engineering and Computer Science

South Dakota State University

Instructor: Dr. Songxin tan

Date: 05/04/2011

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Contents 1 Introduction .................................................................................................................................... 3

1.1 Background .............................................................................................................................. 3

1.2 Motivation ............................................................................................................................... 4

1.3 Objective.................................................................................................................................. 5

2 Modeling of Distributed Generation system ..................................................................................... 6

2.1 Mathematical modeling of DG system ...................................................................................... 6

2.2 Design of Voltage and Speed Controller ................................................................................... 8

3 Matlab/ Simulink Simulation ......................................................................................................... 10

3.1 Voltage and Speed Controller ................................................................................................. 10

3.2 Simulation of DG system ........................................................................................................ 11

4 Simulation Results and Analysis ..................................................................................................... 13

4.1 Results of Voltage Controller .................................................................................................. 13

4.2 Results of Speed Controller .................................................................................................... 15

4.3 Result of DG system control ................................................................................................... 17

5 Conclusion ..................................................................................................................................... 20

6 Limitation ...................................................................................................................................... 21

References ............................................................................................................................................ 22

Appendix: .............................................................................................................................................. 23

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Table of figures:

Figure 1: Power System with synchronous generator machine based Distributed Generation (DG) ........... 4

Figure 2: Distributed Generator-Rectifier System for mathematical modeling .......................................... 6

Figure 3 Functional block diagram of DG with Speed and Voltage Controller .......................................... 8

Figure 4: Block Diagram of voltage controller ....................................................................................... 10

Figure 5: Block Diagram of speed controller .......................................................................................... 10

Figure 6: Matlab/simulink realization of voltage controller .................................................................... 11

Figure 7: Matlab/simulink realization of speed controller ....................................................................... 11

Figure 8: Block diagram of DG system with speed and voltage controller .............................................. 11

Figure 9: Matlab/simulink diagram for DG system with voltage and speed controller ............................. 12

Figure 10: DG subsystem simulation diagram ........................................................................................ 12

Figure 11: Frequency and time response of voltage controller by the author. .......................................... 13

Figure 12: Frequency response for voltage controller in matlab/simulink ............................................... 14

Figure 13: Time response for voltage controller in matlab/simulink ....................................................... 14

Figure 14: Frequency and time response of speed controller by the author. ............................................ 15

Figure 15: Frequency response for speed controller in matlab/simulink .................................................. 16

Figure 16: Time response for speed controller in matlab/simulink .......................................................... 16

Figure 17: Response with DG system with reference voltage changed for a) load voltage and b) power

drawn by author..................................................................................................................................... 17

Figure 18: Response with DG system with reference voltage changed for a) load voltage and b) power

drawn by Simulink ................................................................................................................................ 17

Figure 19: Response with DG system with load changed for a) load voltage and b) power drawn by author

.............................................................................................................................................................. 18

Figure 20: Response with DG system with load resistance changed for a) load voltage and b) power

drawn by Simulink ................................................................................................................................ 18

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1 Introduction

1.1 Background

The demand of power is escalating in the world of electricity. This growth of demand triggers a

need of more power generation. DG uses smaller-sized generators than does the typical

central station plant. Distributed generation (DG) is defined in literature as

standalone small to medium size power generation. IEEE defines the generation of electricity by

facilities sufficiently smaller than central plants, usually 10 MW or less, so as to allow

interconnection at nearly any point in the power system, as Distributed Resources. DG is

also used for the grid-based power system, both as power generation source, and sink

(with the connected local loads). The generation in DG systems, can be broadly

classified as DC or AC generation. The prime sources of DC generation are

Solar Cells or Photovoltaic cells, whereas AC generation for DG system are

wind turbine , micro turbines , small hydro turbines, diesel generator or natural gas

engines etc. DC based DG sources, are interconnected to the grid or local loads

through Voltage Source Converters (VSCs). Whereas AC based DG sources may or may

not use VSCs.

In last few years, the use of DGs has been increased due to liberalization of electricity

markets, environmental concerns, constraints on construction of new transmission line, increased

interest of consumers on reliability and quality of power supply in standalone and grid

connected modes. DG is also used for improving the power quality in a power system. DC or

inverter based DG is used for mitigation of voltage dips and compensation of harmonics.

The operation of DG can be classified into: grid connected and standalone/island

modes. In grid connected mode, DG is used to supply regulated/controlled real and reactive

power to the grid. Whereas, in standalone mode the objective is to provide power

supply, with regulated/controlled voltage, to the consumers/local-load. Power system

with, synchronous generator based, DG is shown in Fig. 1. The DG is said to be in grid

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connected mode, when the switches „S1‟ and „S2‟ are in closed position: with switch „S3‟ opened.

The DG is said to be in standalone mode, when switch „S3‟ is closed: keeping the switches S1‟

and „S2‟ open [1].

Figure 1: Power System with synchronous generator machine based Distributed

Generation (DG)

1.2 Motivation

The performance of the AC based DG system (including the behaviour of the

machine) for different types of applications mentioned above, is yet to be studied. AC based

DG system consists of a synchronous generator coupled to a diesel driven engine

(acting as a prime-mover). In developing economy, standalone synchronous generator

(powered by diesel engines) based DG, cater the industrial, commercial and residential

loads (emergency services cover 30% of the duty ratio on yearly basis), during

power cuts. It is necessary to know the electrical parameters like voltage, power, angle, speed

etc. of the generator in AC based DG system, used for power supply in standalone and grid

connected modes. Power quality of power system is to maintain the desired voltage and

frequency while providing uninterrupted supply to customer. In the system loads may be

resistive as well as reactive load so the energy vendor should supply not only the active power

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but also the reactive power. Further, the active and reactive powers are affected directly by the

frequency and voltage of the system. In the system, load is never constant but there is always

changing load. The change in load directly alters frequency and voltage of system. Further,

frequency is directly dependent on the speed of prime-mover. Therefore to maintain the quality

of power system the frequency and voltage of power system should be always maintained. A

study by Electric Power Research Institute (EPRI) in 2001 indicated that by 2010, 25% of the

new generation will be distributed generation [2]. Hence, there comes the importance of the DG

in power system to maintain the power quality and to provide required the active and reactive

power. Since the use of DG in the power system has been increased the modeling of the DG

system has been essential.

1.3 Objective

The objective of this research project was to develop a mathematical model for a standalone

synchronous machine based distributed generation (DG) system and to design a simple PI

controllers for controlling load voltage and generator speed at the desired values in the presence

of load variations and changing reference conditions[1]. The results had been obtained by

MATLAB programming and PSCAD/EMTDC simulation by the authors which has been

validated by the MATLAB/Simulink simulation results.

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2 Modeling of Distributed Generation system

2.1 Mathematical modeling of DG system

The equivalent diagram of the system, consisting a standalone DG connected to rectifier with

a load, considered for modeling and control, is shown in Fig. 2. Inverter in Fig. 1 has been

assumed as an device i.e. „K1V‟, output voltage of the inverter is equal to „V‟,

the DC link voltage[1]. Electronic power inverters: All DG technologies that generate

either dc or non–power frequency ac must use an electronic power inverter to interface with the

electrical. The early thyristor-based, line-commutated inverters quickly developed a reputation

for being undesirable on the power system. The line-commutated inverters produce harmonic

currents in similar proportion to loads with traditional thyristor-based converters. Besides

contributing to the distortion on the feeders, one fear was that this type of DG would produce a

significant amount of power at the harmonic frequencies. Such power does little more than heat

up wires. To achieve better control and to avoid harmonics problems, the inverter technology has

changed to switched, pulse-width modulated technologies [3].

Figure 2: Distributed Generator-Rectifier System for mathematical modeling

The Fig. 2 is the system showing a synchronous generator as a DG source operating in

standalone mode connected to a controlled rectifier, with a resistive load. „E‟, is the

generator terminal voltage and „V‟, is the load bus voltage (also voltage across the

capacitor „C‟). „kV‟, is the voltage at rectifier/converter input terminal. „X‟, is the

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line reactance and „R‟, is load resistance. „Pi‟, is active power transmitted through the line and

„PL‟, is active power drawn by the load[1].

In Fig. 2, the synchronous generator equations are given by eqn. (1) and eqn. (2).

„δ‟ is the rotor angle (also the phase-angle difference between „E‟ and „kV‟) and „ω‟ is

the angular speed.

(1)

(2)

The eqn. (2) is given by the Swing equation of Synchronous generator where Pm is mechanical

power developed by prime mover.

Active power flow from the generator (DG) to rectifier is given by eqn. (3). Power

balance equation, relating the input and output power of the rectifier is given by eqn. (4)

(3)

(4)

Line arising the eqn.s (1)-(4) around an operating point, eqn.s (5)-(8) can be obtained.

(5)

(6)

(7)

(8)

Using eqn.s (5)-(8), state variable model of the generator rectifier with resistive load can be

written as eqn. (9)

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(9)

In the state-variable eqn. (9), „∆δ‟, „∆ω‟ and „∆V‟ are the state variables, with „∆Pm‟ and „∆k‟ as

inputs[1].

2.2 Design of Voltage and Speed Controller The functional block diagram of the standalone synchronous generator driven distributed

generation with voltage and speed controller for maintiang voltage at load terminal and generator

speed at the desired values is shown in Fig. 3.

Figure 3 Functional block diagram of DG with Speed and Voltage Controller

The transfer function of voltage controller from eqn. 9 is given as

(10)

From eqn. 10 assuming the effect of „∆δ‟ negligible the transfer function for voltage controller is

obtained.

(11)

From eqn. (9) the equation for the speed is obtained as follows.

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(12)

Assuming the effects of „∆δ‟, „∆k‟ and „∆V‟ negligible the transfer funct ion of speed controller

is as given by eqn. (13).

(13)

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3 Matlab/ Simulink Simulation

3.1 Voltage and Speed Controller

The closed loop block-diagram of voltage and speed controller as shown in Fig. 3 is simulated in

simulink using the transfer function given by the eqn.s (11) and (13). The controllers are

designed with simple PI controller. The block diagram of voltage controller is as in Fig. 4.

Figure 4: Block Diagram of voltage controller

In fig. 4, the block diagram of closed loop control of voltage is shown where Vref is the

reference voltage and Kpv and Kiv are the proportional and integral gains of the

controller.Similarly, the block diagram of the speed controller can be derived from the transfer

function given in the eqn. (13).

Figure 5: Block Diagram of speed controller

Here,in the fig.5, the ωref is the reference speed and Kpn and Kin are the proportional and integral

gains of the controller respectively.

The realization of the mathematical modeling of the standalone synchronous generator based

distributed generation is done in the Matlab/Simulink using its inbuilt structure in simulink

library.

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The matlab/simulink realization of voltage controller alone is given in fig. 6.

Figure 6: Matlab/simulink realization of voltage controller

The matlab/simulink realization of voltage controller alone is given in fig. 7.

Figure 7: Matlab/simulink realization of speed controller

3.2 Simulation of DG system The complete distributed generation system consists of standalone synchronous generator,

rectifier and loads. The block diagram of the complete DG system with voltage and speed

controller is shown in fig. 8[1].

Figure 8: Block diagram of DG system with speed and voltage controller

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The matlab/simulink realization of voltage controller alone is given in fig.9.

Figure 9: Matlab/simulink diagram for DG system with voltage and speed controller

The change in the reference voltage was done simply by changing the step input which is the

reference input but for variation for load change in the transfer function of subsystem was

incorporated. The fig. 9 depicts the simulation diagram of subsystem with provision of change in

load at time t=15sec.

Figure 10: DG subsystem simulation diagram

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4 Simulation Results and Analysis

4.1 Results of Voltage Controller

The voltage controller block diagram is shown in fig. 4 and matlab/simulnik realization is shown

in fig.6. In the simulation the values of different parameters was set accordingl given in the

appendix. For the voltage control different values of PI was set and response was observed.The

response obtained for voltage controller by author of paper in PSACAD/EMTDC and response

obtained in matlab/simulinnk is presented in fig.11 and fig.12 and fig. 13.

Figure 11: Frequency and time response of voltage controller by the author.

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Figure 12: Frequency response for voltage controller in matlab/simulink

Figure 13: Time response for voltage controller in matlab/simulink

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From above results of voltage controller it can be seen that without use of compensator the open-

loop gain are less than „0‟ dB and time response with unit-step settle at the values much less than

unity. The results of matlab/simulink simulation almost matches with results of the author. With

the increase in proportional constant the system has been more responsive or sensitive.

4.2 Results of Speed Controller The speed controller block diagram is shown in fig. 5 and matlab/simulink realization is shown

in fig.7. In the simulation the values of different parameters was set accordingly given in the

appendix. For the speed control different values of PI was set and response was observed.The

response obtained for speed controller by author of paper in PSACAD/EMTDC and response

obtained in matlab/simulinnk is presented in fig.14 and fig.15 and fig. 16.

Figure 14: Frequency and time response of speed controller by the author.

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Figure 15: Frequency response for speed controller in matlab/simulink

Figure 16: Time response for speed controller in matlab/simulink

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From above results of speed controller it can be seen that without use of compensator the open-

loop gain are less than „0‟ dB and time response with unit-step settle at the values much less than

unity[1]. The results of matlab/simulink simulation almost matches with results of the author.

4.3 Result of DG system control The simulation diagram of the functional block diagram is shown in fig. 9. The response of the

load voltage and power drawn by load was observed for the change in the system reference

voltage and variation in load. Keeping load constant and speed constant the reference voltage

was reduced from 1 p.u. to 0.5 p.u. at time t=15sec. The following are the responses of the author

and matlab/simulink result.

Figure 17: Response with DG system with reference voltage changed for a) load voltage

and b) power drawn by author

Time (s)

Figure 18: Response with DG system with reference voltage changed for a) load voltage

and b) power drawn by Simulink

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It can be seen that keeping the load resistance constant voltage is changed from 1 p.u. to 0.5 p.u.,

voltage „V‟ is following the „Vref‟ without any error and power drawn „PL‟ changes from 0.25

to .15 pu. The results of voltage is similar to author but difference in power may due to different

value of constant used.

When the load is changed in the system there may be unsatability in the system unless the

voltage and other parameters return to reference. In the simulation the load was changed from 5

p.u. to 2.5 p.u. and the response of voltage and power drawn was observed.

Figure 19: Response with DG system with load changed for a) load voltage and b) power

drawn by author

Figure 20: Response with DG system with load resistance changed for a) load voltage and

b) power drawn by Simulink

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It can be seen that change in load resistance from 5 p.u. to 2.5 p.u. at time t=15s but the due to

voltage controller the voltage is still following reference voltage of 1 p.u. and the power is still

constant. The result of matlab/simulink is similar to responses of author.

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5 Conclusion The mathematical model of standalone synchronous machine based distributed generation was

developed. The model for voltage and speed controller was presented and was incorporated in

model of DG. The simulation was implemented in the matlab/simulation and control of the DG

system was done for change in reference voltage and load.

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6 Limitation The reference speed has been assumed constant and the change in rotor angle has been neglected.

The study can be extended by incorporating these two factors as well in future.

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References [1] G. Shridhar Reddy,R.K.Singh, “Modeling and Control of a Distributed Generation System”,

IET-UK International Conference of Information and Communication Technology in Electrical

Sciences (ICTES 2007)

[2] Thomas Ackermann, “Distributed Generation:Definition”, Electric Power System Research

57 [2001] 195-204 Thomas Ackermann ,Royal Institute of Technology, Sweden

[3]Distributed Generation and Power QualityUmar Naseem Khan

[4] Hadi Sadat, “Power System Analysis”,Tata McGraw Hill Edition-2002

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Appendix: Synchronous generator (in p.u.)

E=1.3, δ=45, D=10, M=4

System parameters (in p.u.) and k-constants

X=0.5, R=5, C=8, k1=0.2828, K2=1.414, k3=0.2828