Ziegler-Nichols Based Controller Parameters Tuning for Load Frequency Control in a Microgrid

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Ziegler-Nichols based Controller Parameters Tuningfor Load Frequency Control in a Microgrid

G. Mallesham, Member, IEEE, S. Mishra, Senior Member, IEEE and A. N. Jha, Senior Member, IEEE

Abstract—This paper deals with the load frequency control ofa small scale microgrid consisting of wind, solar, diesel generatorand fuel cell as power generating sources and battery, flywheeland aqua electrolyzer as energy storage elements. To improvethe load frequency control, the controllers are properly tuned soas to reduce the mismatch between the real power generationand the load demand leading to minimum power and frequencydeviations. A systematic approach to obtain frequency biasparameter followed by tuning the gains of Proportional, Integraland Derivative controller (PID) using Integral Square TimeError evaluation criterion (ITSE)and Ziegler Nichols methodrespectively is proposed. The simulation studies are carried outfor different cases and it is found that the dynamic responses ofthe frequency and power of the microgrid is quite acceptable.

Index Terms—Automatic generation control, frequency andpower deviations,proportional, integral and derivative Control(PID), integral square time error evaluation criterion (ITSE),simulation analysis, Ziegler-Nichols method.

I. INTRODUCTION

THE rise in population, urbanization and rapid industri-alization has lead to a comprehensive increase in the

electrical power demand. The various sources of power in-clude fossil fuels, hydro, thermal, geothermal, solar and windenergies. The reduction in fossil fuels reserve has lead to anincrease in the price of the existing resources. Moreover, thegreen house gases released because of burning the fossil fuelscreate environmental hazards. This led to the development ofalternate energy sources and thrust on efficient utilization ofexisting renewable energy sources[1].

Microgrid serve as a perfect alternative in some regionsand can be combined with fossil fuel based megagrid andis progressively being used to meet the energy needs. Ituses small electric power generation systems comprising ofrenewable energy sources as well as small capacity fossil fuelsources located near consumers and load centers providingthem reliable source of electric power with less transmissionand distribution losses[2]. In addition, microgrid if integratedwith the megagrid will allow bulk consumers to save on elec-tricity costs by using their generators during high peak demandperiods when power from the megagrid becomes expensive

This research work is supported by DST Govt. of India under theproject ”Voltage and Frequency control of microgrid” having file no:SR/S3/EECE/0040/2010.

G. Mallesham (email: [email protected]) and S. Mishra (email:[email protected]) are with the Department of Electrical Engineering,Indian Institute of Technology Delhi, NewDelhi, INDIA.

A.N. Jha (e-mail: [email protected]) is with the Department of Electrical,Electronics and Communications Engineering, ITM University, Gurgaon,Haryana.

978-1-4673-0136-7/11/$26.00 c©2011 IEEE

thereby enhancing the efficiency, reliability and security oflarge and centralized plants. This technology offer new marketopportunities and enhances the industrial competitiveness.

The various types of small scale generation systems usedin a microgrid can be categorized into two groups namelyprimary sources consisting of solar and wind energy systemsand secondary sources such as diesel generator, fuel cell,aqua electrolyzer , battery and flywheel [3]-[5]. The solar andwind fall into the category of not correctly predictable energysources in which the power varies with time i.e., not a constantpower source. This results in power and frequency fluctuationsin the microgrid. To overcome this problem secondary sourcesare used to supply power to balance out the increase inload demand or the reduction in power generation. Howeverdue to the delay in the output characteristics of secondarysources, the frequency oscillations are still present in themicrogrid [6], [7]. Hence there is a need of designing propercontrollers for secondary sources for optimal utilization ofenergy and to maintain minimum frequency deviations. Inthe conventional Automatic Generation Control (AGC), it iswell established that smaller the droop characteristics, lesserwill be the frequency deviations. However, if the droop islarger, then there is a requirement for frequency bias termto be included in AGC as a secondary controller. In thepast, the modelings of microgrid in the context of AGC hasalready been explained with controller gains and frequencybias decided through trial and error approach [8]. Therefore,in this paper, a systematic method is proposed for the selectionof the controller parameters such as frequency bias Kf basedon Integral of Time Squared Error (ITSE) [9], [10] and Kp, Ki

and Kd of the PID controller through Zeigler Nichols method[11].

This paper is organized as follows. Section II illustratesmicrogrid model and its main elements. Section III presentscalculation of the optimal frequency bias Kf and tuningof the PID controller by Ziegler Nichols method and theprocedure to incorporate them in microgrid. simulation resultsare demonstrated under various conditions in section IV.

II. THE MICROGRID MODEL

The proposed microgrid consists of wind power source,solar power source, diesel generator (dg), fuel cell (fc), aquaelectrolyzer (ae), battery (bat) and flywheel (fw). The varyingoutput of wind turbine generator, due to fluctuations of windspeed, can be smoothed out by using a constant powersmoothing strategy [12]. Moreover, the time frame duringwhich AGC action comes into effect in a microgrid is within500 sec. Hence it is quite reasonable to assume a constant

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power output from the wind turbine and solar system. The netpower available to the load is the sum of the powers fromthe primary and secondary sources in microgrid. In this paper,the simplified models with their first order approximations areused as transfer functions for all the microgrid components,and the power system [13]. The proposed system is shown inFig. 1. The mathematical models of each component in themicrogrid, and the power system are as follows.

Fig. 1. The block diagram of the microgrid with primary sources : solar,wind energy system and secondary sources: diesel generators, fuel cell, aquaelectrolyzer, battery, flywheel and power system.

A. Diesel generator

Diesel generator can follow the load demand variations bymeans of their speed and power control mechanisms withinshort intervals of time. When power demand fluctuates, thediesel generator varies its output via fuel regulation. On theother hand since this is a synchronous generator, its outputvoltage can be regulated by controlling the excitation. In thispaper the diesel generator is represented with a first ordertransfer function, represented in (1) as proposed in [14].

Gdg(s) =Kdg

1 + sTdg(1)

Where, Kdg is the gain and Tdg is the time constant of thediesel generator. The gain and time constant of diesel generatorare considered as 1 and 2 sec. respectively. For the dieselgenerator it is also considered the delay in the output as

Gd(s) =Kd

1 + sTd(2)

Where Kd=1 and Td =20 sec. Therefore the transfer func-tion of a diesel generator will be represented as

GdgT (s) =Kdg

1 + sTdg× Kd

1 + sTd(3)

It is assumed that the diesel generator power output will bebetween 0 to 0.8 p.u. The Fig. 2. presents the integrated blockdiagram for a diesel generator with a controller in a microgrid.

B. Aqua electrolyzer

Part of the generated power from wind and solar is sent tothe aqua electrolyzer to produce hydrogen for fuel cell if theload demand is less than the combined powers of wind andsolar system. The decomposition of water into hydrogen and

Fig. 2. The block diagram of the diesel generator with its delay characteristicsin output in power system.

oxygen can be achieved by passing electric current betweenthe two electrodes separated by aqueous electrolyte. The aquaelectrolyzer is modeled as a first order equation given by (4)and implemented in microgrid as shown in Fig. 3.

Gae(s) =Kae

1 + sTae(4)

Where Tae is the time constant and Kae is the gain of theaqua electrolyzer are considered as 0.2 sec. and 1 respectively.It is assumed that the power taken by aqua electrolyzer will

Fig. 3. The block diagram of the aqua electrolyzer in power system.

be between 0 to 0.2 p.u.

C. Fuel cell

The fuel cell operates on the same principle as that of abattery and can supply energy as long as fuel is supplied toit rather than like a battery which requires recharging for itscontinuous operation [15]. The hydrogen produced in the aquaelectrolyzer acts as a fuel which is passed over the anode of thefuel cell where inverse electrolysis takes place. In this paper wehave assumed that there is sufficient hydrogen reserve so thatit does not stop forcedly. The fuel cell is modeled as first orderequation given in (5) and implemented in microgrid throughFig. 4.

Gfc(s) =Kfc

1 + sTfc(5)

Where Tfc is the time constant and Kfc is the gain of thefuel cell. In our case Tfc and Kfc are taken as 4 sec. and 1respectively.

It is assumed that the fuel cell power output will be between0 to 0.3 p.u.

D. Battery

A battery is a combination of one or more electrochemicalgalvanic cells which converts the chemical energy stored init into electrical energy. Due to its feasibility and simplicity,the battery has become a common power source for many

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Fig. 4. The block diagram of the fuel cell in power system.

household and industrial applications, and a big economicindustry. The battery is modeled as first order equation as (6)and implemented in microgrid as shown in Fig. 5.

Gbat(s) =Kbat

1 + sTbat(6)

Where Tbat is the time constant and Kbat is the gain of thebattery as 0.1 sec. and 1 respectively. The amount of chargingand discharging powers vary between -0.5 to +0.5 p.u.

Fig. 5. The block diagram of the battery in power system.

E. Flywheel

A flywheel, in essence is a mechanical battery, simply amass rotating about an axis. This may still prove to serveus as an important component on tomorrow’s vehicles andfuture energy needs. Flywheels are one of the most promisingtechnologies for replacing conventional lead acid batteriesas energy storage systems for a variety of applications, in-cluding automobiles, economical rural electrification systems,and stand-alone, remote power units commonly used in thetelecommunications industry. With recent advances, the me-chanical property of composites has rekindled interest in usingthe inertia of a spinning wheel to store energy. The flywheelis modeled as a first order equation (7) and implemented inmicrogrid as shown in Fig. 6.

Gfw(s) =Kfw

1 + sTfw(7)

Where Tfw is the time constant and Kfw is the gain of theflywheel as 0.1 sec. and 1 respectively.

F. Power and frequency deviation

In a power system, if the balance between the generationand load demand is not maintained, the frequency deviatesdepending on the domination of generation or load. The powerdeviation is the difference between the power generation PS

and the power demand PL.

Pe = PS − PL (8)

Fig. 6. The block diagram of the flywheel in power system.

Where

PS = PW + Psol + Pdg + Pfc − Pae ± Pbat ± Pfw (9)

Due to the time delay between the system frequency de-viation and power deviation, the transfer function for systemfrequency variation to per unit power deviation is given by

Gsys(s) =∆f∆Pe

=K

Ms+D(10)

Where, K is the system frequency character constant. Mand D are the inertia constant and damping constant of powersystem respectively. In this study D and M are chosen as 0.012and 0.2 respectively.

III. TUNING OF FREQUENCY BIAS AND PID CONTROLLERGAINS

The objective of the controllers is to regulate the poweroutput of secondary sources, to minimize the frequency devi-ation by generating appropriate control signals and hence toenhance the performance of the microgrid. In the presence ofmany secondary sources there is a chance of adverse interac-tion between their regulators which leads to deterioration offrequency stability of the microgrid. So far there is no singledefinition for best tuning that applies to all loops. Therefore,to avoid the adverse interaction there is a need of appropriatetuning of the individual PID controller [16]. The control outputfrom the PID controller subjected to frequency error is givenas

u(t) = Kp[∆f +1τI

∫ t

0

∆fdt+ τDd∆fdt

] (11)

Where u(t) is the control input to the microgrid elements and∆f is the change in frequency. In this paper the Ziegler-Nichols method, a heuristic method of tuning PID controlleris used to decide about the magnitudes of the controllerparameters. Initially the range of Kf is considered and itlies between minimum value: 0.1 to maximum value: 10.For each bias setting Kf , the system is made to oscillateby increasing the proportional gain Kp and keeping othercontroller gains Ki, Kd to zero until it reaches the ultimategain Ku at which the output frequency of the system begins tooscillate with ultimate period Tu . The disturbance to initiatethe oscillation is considered as a sudden increase in loaddemand from 0.9 p.u. to 0.95 p.u. For each set of Kf , Ku

and Tu the controller gains: Kp,Ki and Kd are calculated andthe frequency deviations against time for the above mentioned

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disturbance is obtained and the performance criterion J givenby (12) is calculated.

J = ITSE =∫ t

0

t|∆f |2dt (12)

TABLE ITUNING OF THE PID CONTROLLER GAINS ACCORDING TO ZIEGLER

NICHOLS METHOD

Controller Kp Ki Kd

P 0.5 Ku - -PI 0.45 Ku 1.2 Kp / Tu -

PID 0.6 Ku 2 / Tu Tu /8

The controller gains corresponding to the least valued ITSEis taken as the optimized one. In this case, there are fivesecondary sources and are tuned by calculating gains Ku andKf in a sequential manner considering one source after theother in the system. The controller parameters so obtainedbased on the proposed approach are shown in the Table II.

TABLE IITUNING OF THE PID CONTROLLER GAINS ACCORDING TO ZIEGLER

NICHOLS METHOD

Microgrid Compo-nents

Frequency biasKf

Kp Ki Kd

Diesel generator 4 0.0397 0.0756 3.3084Fuel cell 2 0.1220 0.2154 3.1608Aqua electrolyzer 0.2 0.35 0.03 0.07Battery 0.1 0.4188 0.01666 0.01Fly wheel 0.1 0.3654 0.01666 0.01

IV. SIMULATION ANALYSIS

The components in the microgrid are modeled and areconnected with PID controllers as shown in the Fig. 7. andit is simulated using MATLAB. The analysis were carried out

Fig. 7. The Simulink block diagram of the microgrid in MATLAB

by running the system for 500 sec. During this time the system

was put under power variation in load as well as in sources.Before creating disturbance in all the cases, constant windpower supply of approximately 0.6 p.u., solar power supplyof 0.3 p.u. and a load demand of 0.9 p.u. are considered.The time period shown in some plots is the different fromthe simulation time since in those cases the system is settlingbefore the simulation time.

Case1: The wind power is varied from 0.6 p.u. to 0.4p.u. at 50 sec. by keeping solar power and load demandconstant at 0.3 p.u. and 0.9 p.u. respectively.

In realistic scenario this disturbance can come into pictureowing to a sudden change in wind velocity. The simulationresults are shown in Fig. 8. In the transient period, all thesecondary sources except aqua electrolyzer are supplying thepower to compensate the disturbance. In the steady stateperiod, the diesel generator and fuel cell taken together aresupplying which is equal to the reduction in wind power of 0.2p.u. while the power fluctuations both in transient and steadystate period in the system are absorbed by aqua electrolyzer.In steady state the power absorbed by the aqua electrolyzer is0.0015 p.u. which is quite small. So, under steady state con-dition, battery, flywheel and aqua electrolyzer are supplyingzero power. Besides, the peak frequency deviation is between-0.6464 and 0.1718 Hz which is well within the tolerancelimits and reaches steady state within 100 sec. from the pointof disturbance.

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Fig. 8. Simulation results of Case 1: (a) Supply power PS (b) Power supplyform diesel generator Pdg (c) Fuel cell Pfc (d) Aqua electrolyzer Pae (e)Battery Pbat (f) Flywheel Pfw (g) Error in power supply ∆P (h) Frequencydeviation of power systems ∆f .

Case2: A sudden decrease of solar power from 0.3 p.u.to 0.2 p.u. is undertaken at 50 sec.

The dynamic response of the microgrid for this disturbanceis depicted in Fig. 9. In the transient period, the secondarysources, diesel generator, fuel cell are supplying the powerand aqua electrolyzer is absorbing the power. Similarly bothbattery and flywheel are undergoing charging and dischargingcycle resulting in minimum oscillations in the frequency.In the steady state period, the contributions from the dieselgenerator , fuel cell are 0.0416 p.u., 0.0592 p.u. respectivelyto compensate the reduction in the solar power by 0.1 p.u.and a very small part 0.0018 p.u. is in turn absorbed byaqua electrolyzer. The frequency deviation is observed to bebetween -0.2445 and 0.0518 Hz in transient and zero in steadystate period. The frequency deviation in the system subsideswithin 100 sec. of the occurrence of disturbance.

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Case3: The load is increased from 0.9 p.u. to 0.95 p.u.at 50 sec. while the wind and solar power sources are keptconstant at 0.6 p.u. and 0.3 p.u. respectively.

This variation in load is met by all other microgrid elementsand their dynamic performance is shown in the Fig. 10. Inthe transient period, the secondary sources, diesel generator ,fuel cell are supplying the power whereas aqua electrolyzeris absorbing the power. Besides both battery and flywheel areundergoing charging and discharging resulting in a minimumoscillations in the frequency. In the steady state period, thecontributions from diesel generator and fuel cell are 0.0208p.u. and 0.0296 p.u. respectively to compensate the differencein load power of 0.05 p.u. and part of which 0.0003 p.u. isin turn absorbed by aqua electrolyzer which is negligible. Thefrequency deviation is observed to be between -0.0781 and0.0145 Hz in transient and zero in steady state period.

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Therefore, from the above simulations, it is seen that thetuned PID controllers with optimal frequency bias manages tomaintain constant frequency in the microgrid following anydisturbance.

V. CONCLUSION

In this paper a systematic approach for tuning of PID con-trollers in microgrid and calculation of optimal frequency biasare presented. The frequency bias calculation is an importantaspect in the power system dynamics and plays a key rolein controller gains. This factor directly effects the individualcomponents and subsequently the overall performance of themicrogrid. So the selection of frequency bias is very crucialand is addressed in this paper. The tuning of the PID con-troller through Zeigler Nichols approach is quite robust to

tackle different types of disturbances. The simulation analysisof microgrid with PID controller shows acceptable dynamicperformance with zero steady state error. It is also found thatwhen the load is less than the power generated by the primarysources the excess power goes into the battery and flywheel.Similarly when load is more than the power generated by theprimary sources, the excess power requirement is mitigated bydiesel generator and fuel cell. Thus, the controllers work incoordination with the demand from load to obtain a properenergy management scenario.

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[6] N. Kodama, T. Matsuzaka, and N. Inomata, “The power variation controlof a wind generator by using probabilistic optimal control,” Trans. Inst.Elect. Eng. Jpn, vol. 121-B, no. 1, pp. 22-30, 2001.

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[14] S. Dokopoulos, A. C. Saramourtsis, and A. G. Bakirtzis, “PredictionAnd evaluation of the performance of wind-diesel systems ,” IEEE Trans.Energy Conversion., vol. 11, no. 2, pp. 385-393, Jun. 1996.

[15] K. Sasaki et al., “On the voltage drop of phosphoric acid fuel celldue to its on-off operation,” Trans. Inst. Elect. Eng. Jpn., vol. 118-B, no.12, pp. 1450-1456, 1998.

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G Mallesham received the B.E degree in Electrical and Electronics Engi-neering from University College of Engineering (A), Osmania University,Hyderabad, India in 2000. He received his Masters degree in Control Engi-neering and Instrumentation from Indian Institute of Technology, Delhi, Indiain 2002. Presently he is working towards PhD in the Department of ElectricalEngineering, Indian Institute of Technology, New Delhi, India

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S Mishra (M’97-SM’04) received the B.E. de-gree from University College of Engineering, Burla,Orissa, India, and the M.E. and Ph.D. degrees fromRegional Engineering College, Rourkela, Orissa, In-dia, in 1990, 1992, and 2000, respectively. In 1992,he joined the Department of Electrical Engineer-ing, University College of Engineering Burla asa Lecturer, and subsequently became a Reader in2001. Presently, he is an Associate Professor withthe Department of Electrical Engineering, IndianInstitute of Technology Delhi, India. Dr. Mishra has

been honored with many prestigious awards such as the INSA Young ScientistMedal in 2002, the INAE Young Engineer’s Award in 2002, and recognitionas the DST Young Scientist in 2001 to 2002, etc. He is a Fellow of IndianNational Academy of Engineering, Institute of Engineering and Technology(IET), London, UK and Institute of Electronics and Communication Engineer-ing (IETE), India. His interests are in soft computing applications to powersystem control and power quality and renewable energy.

A. N. Jha obtained his PhD degree in ElectricalEngineering in the year 1977 from Indian Instituteof Technology, Delhi. He joined I.I.T Delhi as alecturer in Electrical Engineering Department in theyear 1981.He is Professor in the same departmentsince February 1994.He is working in areas ofEstimation, Identification and Control of Systems.He has published more than 110 research papers inNational and International journals and conferences.He is a senior member of I.E.E.E USA, fellow ofthe Institution of Electronics and Telecommunication

Engineers, India and life member of system society of India.His interestsare in soft computing applications to power system control, power quality,distributed generation and renewable energy.

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Ziegler-Nichols Based Controller Parameters Tuning for Load Frequency Control in a Microgrid