6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 37 Optiization of Control Paraeters in AGC of Microgrid using Gradient Descent Method G. Mallesha, Meber, IEEE, S. Mishra, Senior Meber,IEEE, and A. N. Jha, Senior Meber,IEEE Abstract Microgrid is a sall scale independent power syste consisting of renewable energy sources- solar and wind power generation and backup by controllable sources- diesel generator, and fuel cell. In the icrogrid, the rap rate liit in power change has been ipleented by eans of Generation Rate Constraint (GRC) and power-frequency (P-f) droop characteristics (R) is also included for the parallel operation of generating sources participating in Autoatic Generation Control (AGC). These GRC and P-f droop ake the syste non linear and we have proposed a gradient descent based optiization to tune iportant paraeters siultaneously in AGC of icrogrid. The proposed ethod iproves dynaic and steady state response of the icrogrid and aintains the syste frequency at desired level. Index Ters Microgrid, Tuning of paraeters, P-f droop, GRC, Optiization and siulation analysis. P G P L P w P s P fc NOMENCLATURE Power generation Load power Power fro wind source Solar power of PV panels Diesel generator power Fuel Cell power ΔP Power deviation Δf Frequency deviation (Hz) f Syste frequency sys Bi Frequency bias (MW/Hz) R i P-f Droop in (MW/Hz) KPi Proportional gains for icrogrid eleents KIi Integral Gains for icrogrid eleents KDi Derivative Gains for icrogrid eleents i Stands for different controllable sources (i=, 2) Tsi Siulation Tie (Sec.) J Perforance Criteria: ITSE S. Mishra, G. Mallesha are with Electrical Engineering Departent, Indian Institute of Technology Delhi, India.(e-ail: sukuar@ee.iitd.ac.in, alleshag@yahoo.co). A.N. Jha is with Departent of Electrical, Electronics and Counications Engineering, ITM University, Gurgaon, Haryana. I. INTRODUCTION T HE rise in population, urbanization and rapid industrialization has lead to a coprehensive increase in the electrical power deand. The various sources of power includes fossil fuels, hydro, theral, geo-theral, solar and wind. The reduction in fossil fuels reserves has lead to an increase in the price of the existing resources. Moreover, the green house gases released because of burning the fossil fuels create environental hazards. This led to the developent of alternate energy sources and thrust on efficient utilization of existing renewable energy sources [, 2]. These sources are sall in nature and are connected at the distribution level reduce transission and distribution losses. A distribution syste having sall scale power generating sources is tered as icrogrid. This icrogrid consists of renewable energy sources such as solar and wind energy syste and controllable sources such as diesel generator, fuel cell and battery. Due to the variation in power fro renewable sources and load deand there are frequency and power fluctuations in the icrogrid. To overcoe this, controllable sources are used to supply power to balance out the increase in load deand or the reduction in power generation. However due to the delay in the output characteristics of controllable sources, the frequency oscillations are still present in the icrogrid [3]. Hence there is a necessity of designing proper controller paraeters to controllable sources for optial utilization of energy and to aintain iniu frequency deviations. It is also iportant to consider all the characteristics of power generating sources in icrogrid such as frequency bias (B), droop characteristics (R) and Generation Rate Constraints (GRC). In order to achieve proper operation of a icrogrid, an electric energy syste ust be aintained at a desired operating level characterized by noinal frequency and voltage profile. This is achieved by close control of real and reactive powers generated through the controllable sources of the syste. This AGC of icrogrid plays a significant role in aintaining scheduled syste frequency and voltage during noral operating condition. But for the sall changes in the load deand, the cross coupling between the load frequency control and autoatic voltage regulation loop is negligible and hence in this paper the load frequency control is independently analyzed. In our past work, ZN ethod [4] is used to find controller paraeters and presented the effectiveness of different controllers. But, the study of icrogrid with P-f droop, frequency bias and GRC are reains unexplored [5, 6]. The coplexity of the syste increases due to nuber of controllers, droop, frequency bias,
6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 38 GRC and ultiple power generating sources. Surprisingly, till date no work has been reported to address the above coplexity and to optiize all paraeters siultaneously for AGC of icrogrid. In the view of the above the present work applies a gradient descent based optiization ethod for siultaneous optiization of all paraeters K Pi, K Ii, K Di, R i, and B i paraeters with and without GRC i and variations in power fro renewable sources, load deand. This paper is described as follows. Section II illustrates the icrogrid odel and its ain coponents. Section III explains the gradient descent optiization and its algorith. In Section IV, siulation results are analyzed under various conditions. The conclusions are presented in Section V. II. MODELING OF MICROGRID The proposed icrogrid consists of wind power source (2 kw), solar power source (3 kw), diesel generator (4 kw) and fuel cell ( kw) [7-]. The net power available to the load is the su of the powers fro the renewable and controllable sources. In this paper siplified odels with their first order approxiations are used as transfer functions for all the icrogrid coponents, and the power syste are taken fro [4-6] as shown in Fig.. All the icrogrid eleents are provided with controllers, frequency bias, P-f droop and realistic GRC and explained in the following sections. The noinal values of the syste are presented in the Appendix. Fig.. The block diagra of the icrogrid with diesel generator, fuelcell, wind, solar power supply and power syste. a. Frequency bias (B) In the icrogrid there are ultiple controllable sources and each can have a control signal, to regulate output power, proportional to frequency deviation tered as frequency bias (B) [, 2]. Generally the frequency bias is easured annually. The closure the frequency bias setting atches the actual control frequency characteristic, the better AGC will perfor. Hence, the proper selection of frequency bias is iportant in AGC of icrogrid which is addressed in this paper. b. Power frequency (P-f) droop characteristics (R) The power frequency (P-f) droop characteristics are iportant to ipleent in the syste when the ultiple power sources are connected in parallel like icrogrid [3, 4]. The individual power generators are responsible for aintaining frequency by appropriate sharing of the load. The load sharing without counication between the converters is the ost desirable option. A coon approach is to achieve this by use of frequency P-f droop characteristics so that parallel power sources are connected to aintain the frequency at the desired level. Conventionally, it is ipleented based on the inverse relationship with the rating of the source as in () w P p w P i P p MG pi p P Where P is turbine output, p is R/w, w is change in frequency and P is total load deand. However, it is not a strict rule to be followed and this has disadvantages in ters of technical and econoical content in the ppi=constant based scheduling. Neither the capability of providing sufficient level of reserves nor the econoies are considered in the droop coefficient assignation. Only a scheduling based on the rated power is proposed. Further, it is well known that with only priary control (i.e. PID controller absent) the saller the droop the lesser the steady state error in frequency. However, in the presence of secondary control (PID controller) there is no necessity to use a saller droop as any large but credible value of R can also guarantee zero steady state error in frequency. Hence there is a possibility of optiizing this paraeter to obtain better perforance and is ipleented in this paper by an intelligent based droop calculation. c. Generation Rate Constraint (GRC) The icrogrid considered so far does not considered the affect of the restrictions on the rate of change of power generation. In icrogrid, there are different power sources with different rate of power generation. Any power source when instructed to increase/ decrease its power fro a specified value need to follow a rap rate [5, 6]. To be ore specific, we need to ephasize here that the power output cannot be changed fro one value to another suddenly. This rap rate liit is tered as Generation Rate Constraint (GRC) and is depends on the type of the power source. So, in icrogrid there are different sources such as diesel generator, fuelcell, battery etc., need to have different GRCs. The GRC is realized by differentiating outputs fro the power sources and further a saturation liiter is used to decide the upper and lower liit of the rate. Further the signal is integrated to get back to the original signal. A typical value of GRC for theral liits is considered as i.e. GRC for the i th eleent in the icrogrid is P gk ( t) p. u. Mw / s (2) Two liits bounded ( by ±.σ are the axiu rate of power generation by the controllable sources in the icrogrid. ()
6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 39 PID Controller Power Deviation Wind and Solar Power PID du/dt /s Td.s+ Tdg.s+ M.s+D GRC_dg Droop du/dt GRC_fc Droop Frequency Bias PID PID Controller /s Diesel generator Tfc.s+ Fuelcell Load Power Power Syste Frequency Bias Frequency Deviation Fig. 2. The siulink block diagra of icrogrid in MATLAB d. Power and Frequency deviation In a power syste consisting of synchronous generator, if the balance between the generation and load deand is not aintained, the frequency deviates depending on the doination of generation or load. Power deviation is the difference between the power generation P G and the power deand P L [7, 8]. Fro the swing equation of a synchronous achine, the generator atheatical odel can be written as fsys f ( s) [ P ( s) P ( s)] (3) Where 2Hs G e P e (s)= P G (s)-p L (s) (4) P G = P W + P s + + P fc (5) Generally, the loads are of ixed type like frequency dependant and non dependant. So speed load characteristics of coposite load is approxiated by Pe PL D w (6) Where the first part of (6) is the non frequency dependant and second part is the frequency sensitive part of the load. Cobining (3) and (6) we get (7) 2H PG PL s D f f sys Because of the tie delay between the syste frequency deviation and power deviation, the transfer function for syste frequency variation to per unit power deviation is given by f K Gsys ( s) (8) P D sm e 2H Where, K is the syste frequency character constant. M= f sys and D are the inertia constant and daping constant of power syste respectively. III. GRADIENT DESCENT OPTIMIZATION METHOD It is well known fact that the function value increases at the fastest rate, when we ove along the gradient direction fro (7) any initial point in N-diensional space. The gradient direction is called the direction of steepest ascent. The negative of the gradient vector denotes the direction of steepest descent. Thus the gradient descent ethod is expected to give iniu point faster than other non-gradient based optiization ethod. In this paper, gradient descent based optiization is adopted to iprove the dynaic and steady state response of icrogrid. The paraeters chosen for optiization are K Pi, K Ii, K Di, R i, and B i. These paraeters are initialized based on Z-N ethod. The tie doain specifications of Δf are defined in siulink response optiization tool box. IV. SIMULATION ANALYSIS AND RESULTS DISCUSSION To represent the actual syste, the coponents in the icrogrid are odeled and connected with frequency bias, P-f droop, controllers and GRC as shown in Fig. 2. and it is siulated with MATLAB s Optiization toolbox to ipleent the gradient descent based optiization [9]. The total nuber of paraeters to be optiized in the syste are (Two PID controllers i.e., total 6 gains, 2 frequency bias, 2 P-f droop) as shown in the Table-I. The analyses were carried out by running the syste for 5 sec. During this tie the syste was put under power variation in load as well as in power sources. Before creating disturbance in all the cases, a wind power supply of approxiately kw, solar power supply of 2 kw and a load deand of 5 kw are considered. It is assued that there exists sufficient hydrogen to fuelcell for the power supply. Initially, the difference power 5 kw is supplied by diesel generator (27 kw) and fuelcell (23 kw). In our previous paper [4] we have shown that the syste perforance with PID controller is better and hence we considered PID controllers and corresponding results shown in the paper. Siulation analysis with/ without Droop and GRC: The siulation results of icrogrid without GRC and Droop characteristics are shown in the Fig. 3. Fro the siulations we can observe aplitude of oscillation is very sall when there is no GRC and P-f droop. This is due to the the power rate at which diesel generator and fuelcell are supplying power to icrogrid is infinite which is not practical in realistic scenario. To represent the controllable sources in ters of their actual physical behavior, GRC, P-f droop and frequency
P fc P fc f (Hz) P 6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 4 bias are to be included. This results increase in systes coplexity and takes ore tie to eet the required deand and hence there is a large undershoot in frequency deviation. So for the representation of actual behavior of the syste, GRC and P-f droop ust be included. 2 5 5-5 (c).4.2.8.6.4.2 Fig. 3. Response of the icrogrid with and without GRC. Case: In this case wind power is increased by 5 % at sec. by keeping solar power and load deand constant. In realistic scenario this disturbance can coe into picture due to increase in wind velocity. The siulation results are shown in Fig. 4 (a)-(d). Initially the 5 kw power difference is supplied by diesel generator and fuelcell. When the wind power is increased by 5 % (2.5 kw), diesel generator and fuelcell decreases its power output to copensate the reaining power deviation. The peak frequency deviation shown in Fig. 4 (d) is between -. and.35 Hz in transient and zero in steady state which is well within the tolerance liit and reaches steady state within 44. sec. fro the point of disturbance. 3 -.2 (d) Fig. 4. Siulation results of Case : (a) Power supply for diesel generator, (b) P fc: Fuel cell power, (c) Power difference between P G and P L and (d) Δf : Frequency deviation of power syste. Case2: The load is increased by 5 % at sec. while the wind and solar power sources are kept constant. This variation in load ( kw) is et by all other icrogrid eleents and their dynaic perforance is shown in the Fig. 5 (a)-(d). In the transient period, the controllable sources, diesel generator, fuel cell are supplying the power. In the steady state period, the contributions fro diesel generator and fuel cell are responding to copensate the difference in load power. The observed frequency deviation is between -.78 and.45 Hz in transient and zero in steady state period. 45 2 4 5 35 5 (a) 2 8 6 4 3 (a) 3 29 28 2 8 6 (b) 27 26 24 23 2 2 (b)
P fc f (Hz) f (Hz) P P 6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 4 5 2 8-5 6 4-2 -5-2 -2.2. -. -.2 -.3 -.4 -.5 -.6 -.7 (c) -.8 (d) Fig. 5. Siulation results of Case 2: (a) Power supply for diesel generator, (b) P fc: Fuel cell power, (c) Power difference between P G and P L and (d) Δf : Frequency deviation of power syste. Case3: The solar power is reduced by 5% at sec. while the wind and load deand are kept constant. -4.6.5.4.3.2. (c) -. -.2 (d) Fig. 6. Siulation results of Case 3: (a) Power supply for diesel generator, (b) P fc: Fuel cell power, (c) Power difference between P G and P L and (d) Δf : Frequency deviation of power syste. V. CONCLUSIONS The dynaic response of the icrogrid is presented in Fig. 6 (a)-(d). The reduced power fro solar is copensated by diesel generator and fuelcell. The frequency deviation is observed to lie between -.5 and.56 Hz in transient period and the frequency fluctuations in the syste die out in sec. with zero steady state error. 3 28 26 24 2 8 6 4 2 (a) 28 26 24 For the first tie, the tuning of controller gains, frequency bias in the presence of P-f, GRC in a icrogrid are presented in this paper. The difficulty in tuning ore nuber of paraeters in coplex systes can be addressed through the optiization techniques like gradient descent ethod which is better than trial and error or Z-N ethod. It is also found that when load is ore than the power generated by the renewable sources, the excess power requireent is supplied by diesel generator and fuelcell. Thus, the controllers work in coordination with the deand fro load to obtain a proper energy anageent. Further, if the power fro the renewable energy source is excess than the load deand, then the energy storage devices like battery, flywheel and aqua electrolyzer are required to store the energy for further utilization. These storage devices are fast acting and reduce the power fluctuations in controllable sources. The coplexity of the syste still increases due to storage devices in icrogrid and tuning of the paraeters with conventional ethods becoes tedious. So the tuning of the iportant paraeters in icrogrid using Artificial Intelligence Techniques (AI) will be a future research work. 2 8 6 (b)
6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 42 APPENDIX NOMINAL PARAMETERS OF THE MICROGRID INVESTIGATED f sys =5Hz, Base Power= MVA, D=.2 MW/Hz, H=5s; Kdg= Kdt=K fc =,Tdg=2s, Tdt=2s, T fc =.4s GRCdg=3%, GRCfc=%. Paraeters TABLE I PARAMETERS OF MICROGRID AFTER THE OPTIMIZATION Initialization of Microgrid paraeters using Z-N ethod Diesel generator Fuelcell K P.42.426 K I.438.9329 K D.7877.4 B (Mw/Hz) Optiized paraeters of Microgrid using gradient descent ethod. Diesel generator Fuelcell.426 3.4584.5595.62 2.327 5.395 5.7778.9524.9977.4 R % 6.3934 2. 27.78 4.264 REFERENCES [] A. Keyhani and Jin-Woo Jung, Distributed energy systes, Journal of Iranian Association of Electrical and Electronics Engineers, vol., no. 2, pp. 33-4,Suer and Fall 24. [2] Online, http: //nes. nic. In. [3] P. Kundur, Power Syste Stability and Control, Tata Mc Graw Hill, Inc., New York,994. [4] G. Mallesha, S. Mishra, and A. N. 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[9] http://www.athworks.co/products/sl-design-optiization/ BIOGRAPHIES S Mishra (M 97-SM 4) received the B.E. degree fro University College of Engineering, Burla, Orissa, India, and the M.E. and Ph.D. degrees fro Regional Engineering College, Rourkela, Orissa, India, in 99, 992, and 2, respectively. In 992, he joined the Departent of Electrical Engineering, University College of Engineering Burla as a Lecturer, and subsequently becae a Reader in 2. Presently, he is an Associate Professor with the Departent of Electrical Engineering, Indian Institute of Technology Delhi, India. Dr. Mishra has been honored with any prestigious awards such as the INSA Young Scientist Medal in, the INAE Young Engineer s Award in, and recognition as the DST Young Scientist in 2 to, etc. He is a Fellow of Indian National Acadey of Engineering and Institute of Electronics and Telecounication Engineering. His interests are in soft coputing applications to power syste control and power quality and renewable energy. A. N. Jha obtained his PhD degree in Electrical Engineering in the year 977 fro Indian Institute of Technology, Delhi. He joined I.I.T Delhi as a lecturer in Electrical Engineering Departent in the year 98. He was Professor in the sae departent fro February 994 to January 2. Currently he is with the Departent of Electrical, Electronics and Counications Engineering, ITM University, Gurgaon, Haryana. He is working in areas of Estiation, Identification and Control of Systes. He has published ore than 2 research papers in National and International journals and conferences. He is a senior eber of I.E.E.E USA, fellow of the Institution of Electronics and Telecounication Engineers, India and life eber of syste society of India. G. Mallesha received the B.E degree in Electrical and Electronics Engineering fro University College of Engineering, Osania University, Hyderabad, India in 2. He received his Masters degree in Control Engineering and Instruentation fro Indian Institute of Technology, Delhi, India in. Presently he is a PhD research scholar in the Departent of Electrical Engineering, Indian Institute of Technology, New Delhi, India.