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I. NOMENCLATURE

Abstract-- In the 21st century the concept of electrical power supply is morphing gradually from centralized into decentralized system, indicated by increasing the Installation of distributed generation on the main grid. With emerging of advanced Communication and information technology, the aggregation of several small size, environmentally compatible, generators close to the loads can be developed as virtual power plant in order to provide added-value to the electric Power system. In this paper an operation optimization algorithm is proposed to integrate two DGs and a micro grid into a VPP control area, containing several loads, which will be able to generate and sell electrical energy to loads and power market. Suitable models are proposed to simulate electric production, and the energy exchange between VPP and Grid. The optimization problem is here formulated as a non-liner maximization algorithm with constraints, where the objective function is profit of the VPP with supply of electric energy for all the loads.

Solving the VPP optimization problem in two different scenarios with GAMS software will complete the paper.

Index Terms-- Distributed generation, Operational optimization, Virtual Power Plant, Profit maximization, Control Coordination Center, and Local Controller.

1LoadP Total active power provided for sensitive loads;

1Load� Active power price provided for sensitive loads;

2LoadP Total active power provided for non-sensitive loads;

2Load� Active power price provided for non-sensitiveloads;

M.Amin Salmani is with the MAPNA Co., Tehran-Iran (E-mail: amin.salmani@gmail.com).S.M.Moghaddas Tafreshi is with the Department of electrical engineering,

K.N.Toosi University of technology, Tehran-Iran(E-mail: tafreshi@eetd.kntu.ac.ir).Hosein Salmani is with the Department of electrical engineering, Shahid

Beheshti University, Tehran-Iran(E-mail:salmani@ee.kntu.ac.ir).This Paper is sponsored by MAPNA Co.

exiP Total active powers exported to ith inter connected system or imported from ith inter connected system (if exiP was negative) to the VPP area;

exi� Price of imported or exported energy from ith inters connected system;

ukC Penalty factor for un-served energy for loads;

ukP Total un-served energy for loads;

DGIP Total active power purchased from DGI;

MaxDGIP Maximum active power that DGI is offeredto provide;

DGI� Active power price purchased from DGI;

DGDCP Total active power obtained from the DGDC;

DGDCC Producing cost of DGDC;

micP Total active power purchased from micro grid;

MaxmicP Maximum active power that micro grid is Offered to provide;

mic� Active power price purchased form micro grid;

II. INTRODUCTION

The VPP uses the billing system of the Local Distribution Company (LDC) which is defined as low voltage, retaildistribution, to aggregate the electrical output of severaldistributed generators located close to the loads so that the VPP appears to investors as one unit power plant, rather thanseveral individually financed appliances [1, 2].The primary objective of operation optimization algorithm canvary. For example, economic optimization can either aim to minimization the cost of producing energy or maximizing the profit of the VPP [3, 4].In this paper operational optimization is mainly focused on providing electrical energy for loads in the VPP control areawith maximum profit achieved from selling of energy, in addition the VPP can also trade with power market to increase total profit, but in this case some limitations should be considered, e.g. capacity of distribution lines[5].Considering these facts, virtual power plants are an interesting option for the future to substitute conventional power plants.

Operation Optimization for aVirtual Power Plant

M. Amin Salmani, S.M.Moghaddas Tafreshi , and Hosein Salmani

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III. VIRTUAL POWER PLANT (VPP)In this section, a general formulation of the VPP model will bedescribed.

A. General Structure in Power MarketThe general model considers two different DGs, a micro grid and several loads inside a VPP control area.

Wholesale Energy market

Interconnectedsystem

DisCo

DG1

DG2

Micro grid

Load

VPPBuyer

Seller

Fig. 1."connections between vpp control area and power grid"

In Fig.1 the VPP has shown in dashed line as part of a more general power market structure. The definitions of a market agent are as followed [1, 6].•VPP: the aggregation of two DG units, a micro grid and loads which are connected with power grid.• DisCo: Distribution Company that operates the facilities and purchases energy from the power market or VPP. • Micro Grid: Distributed generation unit inside the VPP Control area. This unit is managed or owned independently from the VPP. • DGI: Distributed generation unit inside the VPP Controlarea. This unit is managed or owned independently from the VPP. From the market point of view DGI sends energy offers (price and quantity) to VPP controller.Note: The difference between DGI unit and micro grid is the loads which exist inside the micro grid control area. Because of this feature some times micro grid purchasing energy from VPP to provide energy for loads.

• DGDC: Distributed generation unit inside the VPP Controlarea, which are managed or owned by the VPP.• Loads: Customers which VPP has to provide them energy.In this model have two different types of loads are considered[7, 8]:

1. Sensitive loads: which is obligatory to provide them energy completely.

2. Non-sensitive loads: Also defined as Cut-able load, are those non critical loads that incase energy shortage occurs, the system can forsake their needed power, partially or completely, but financial penaltyis the consequence.

VPP is organized as a day-ahead market with daily offers from DGI, DGDC, micro grid, DisCo, and the wholesale market. In addition, VPP manages the cost of un-provided energy for all of the Loads.

B. VPP's Technical Coordination The VPP must handle the technical coordination among the DisCo, the interconnected power grid, the micro grid, DGI,DGDC and Loads. Fig. 2 summarizes these interrelations.

It should be considered that VPPs are divided into two categories according to the control topology [9]:1. The decentralized VPP: Each DG unit is locally controlled by local controller (LC). 2. The centralized VPP: The DG unites are centrally controlledby control coordination center (CCC).In this paper centralized VPP (CCC) is used.

VPPDGDC

MicroGrids

Loods

DGI

CCC

communication system

Public Grid

20KV/400v

400V/20KV Publ

ic G

rid

Power transmissionsystem

Fig. 2."Power grid in vpp's control area"

In Fig. 2, two LV substations between the public grid and the VPP control area are shown [10]. For this model following coordination requirements are identified:• DGI unit offers: DGI unit must send energy offers (price and quantity) to the CCC to inform the VPP about its energy producing schedules.• Micro grid offers: micro grid must send energy offers (price and quantity) to the CCC to inform the VPP about its energy producing or requirement schedules.It should be noted that in micro grid offers the negative amount of energy show that micro grid is willing to buy energy from VPP instead of selling energy to VPP.• DGDC unit offers: In DGDC unit offers instead of the price,the cost of producing energy is mentioned.• Load predictions: It identifies Load contracts, with detailed cost Information for un-served energy ranges, which must be submitted to the CCC.• Market predicted prices: CCC has to predict the prices in each node that VPP is connected to the main Grid.All the above information is supplied to the CCC in order to

take a decision on amount of energy that each generator can generate.

IV. VPP’S MODELING

The information described in previous section can be formulated for each time period as a mathematical optimization problem (OP).

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A. General StructureOP in previous section represents the general structure of the proposed model [1]:

Max Z=f(x)s.t. g(x)=0 (1)

h(x) �0xmin < x <xmax

This structure corresponds to a maximization problem. The objective function f(x) represents the VPP revenues for supplying its demand and trading with power market.B. Objective Function The resulting objective function for CCC is as Followed:

iexiexiexiexiLoadukiiLoadiLoadiLoadi

PPPPPxf 22112211

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1)()( ���� ����� �

�

DGDCDGDCukuk PCPC � DGIDGImicmic PP �� ��(2)

V. CONSTRAINETS

1. Power Balance: These are the nodal active power balances [1, 10]. Its general form is

BipiDGIimiciDGDCiBisiiexiexukiiLoadiLoad PPPPPPPPPP ��������� 2121 )(

(3)

2. Transmission Line Limits: These constraints represent the power flow limits on transmission lines. Two alternative models are proposed [1]:

• By using active power flow transmission limit:

ijMaxij PP � (4)

• By using current limit:

ijMaxij II 22 � (5)3. LV substations limit: This constraint represent the power flow limit on LV substations:

maxTT SS � (6)

4. Bounds: All optimization variables are subject to the following operational constraints:

iii VVV maxmin �� (7)

..05.1

..95.0

max

min

uPVuPV

��

maxmin PPP �� (8)

maxmin QQQ �� (9)5. Unserved energy limitation: Total unserved energy must be less than 10% of total loads:

)(1.0 21 LoadLoaduk PPP �� (10)

VI. PRODUCING COST OF DGDC

In this paper the features of a 90 KW fuel cell unit [10, 11] is used for the DGDC unit. Producing cost function for this unit is shown:

2DGDCDGDCDGDC PPC � ��� (11)

The parameters of this function are different for each case study, for the first case study:

0)/($ �h� , 4.30)/($ �MWh and 01.0))/(($ 2 �hMW

And for the second case study:0)/($ �h� , 4.30)/($ �MWh and 05.0))/(($ 2 �hMW

VII. SOLVING THE OPTIMIZATION PROBLEMThe General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming problems. It consists of a language compiler and a variety of integrated high-performance solvers. Solving the VPP optimization problem with the GAMS will discussed in the following part. [12, 13, 14, 15, 16]In this paper the solutions for two different case studies will be presented. The inputs of both cases are the same, only some changes in general assumptions of modeling made these two cases different.In the first case study this assumptions are considered valid:• 1Load� = 68.5 $/MW�• 2Load� = 55.5 $/MW

•� ukC = 10.566 $/MW

You can see the inputs below:TABLE I

MICRO GRID'S BID:Hour )/($ MWmic� )(kWPMaxmic

1 31.234 2402 28.475 2503 28 2404 26.5 2305 26.45 2206 29.865 2307 30.465 2108 45.861 2109 49.5 190

10 53 18011 55.741 19012 56.1 17013 56.99 13014 55.274 13015 62.5 12016 64.8 11017 64.719 -2018 60.01 -3019 56.399 -3020 48.26 15021 45.5 18022 40.1 18023 35.55 23024 33.8 230

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TABLE IITHE DGI'S BID

Hour )/($ MWDGI� )(kWPMaxDGI1 30.34 1802 26.82 1803 27.2 1804 27.652 1805 28.655 1806 29.399 1907 31.45 1908 44.3 1909 48.68 190

10 52.251 20011 54.479 20012 55.01 20013 56.978 20014 55.3 20015 63.715 20016 63.99 20017 65.267 20018 59.89 20019 49.865 19020 47.65 19021 45.348 19022 38.69 18023 36.1 18024 31.724 180

TABLE IIILOADS FORECASTING�

Hour

1 365 300 652 350 305 453 300 265 354 300 265 355 350 300 506 400 350 507 400 330 708 460 375 859 485 385 100

10 505 405 10011 511 396 11512 545 425 12013 535 415 12014 545 425 12015 550 415 13516 555 420 13517 570 405 16518 540 380 16019 510 360 15020 485 360 12521 465 365 10022 410 310 10023 385 300 8524 380 305 75

TABLE IVMARKET FORECASTED PRICES:

Hour )/($ MWexi�1 29.2552 26.3973 22.474 21.075 23.1636 30.8637 31.5568 47.399 49.7

10 52.111 55.3512 55.513 57.0114 54.4215 63.1216 65.5917 67.2418 63.8719 55.6120 52.5521 47.5522 39.6923 3724 30.51

The GAMS out puts for the first case study are shown in Fig. 3:

Fig. 3." The GAMS out puts for first case study"

We used these information for second case study’s input, In addition for the second case study, some assumptions are changed, for instance energy prices. The assumptions are considered valid [10, 11]:

• 1Load� = 77.5 $/MW

• 2Load� = 63.5 $/MW

•� ukC = 12.5 $/MW

1LoadP 2LoadPLoadP

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And the GAMS out puts for the second case study can be observed in Fig.4:

Fig. 4." The GAMS out puts for second case study"

It can be derived that the amount of power that is produced by each generator, especially amount of power produced by theDGDC unit, is totally different in case studies. This difference is occurred because of increasing energy prices and producing cost of DGDC.In addition total profit for the VPP in first case study was506.046 $ for a day and for the second one was 715.6974 $ for a day and it is an effective proof for this model.

Fig. 5." The VPP’s hourly profit for each case study”

The profit for each hour of both strategies can be compared in Fig. 5.

VIII. CONCLUSIONS

The formulation of the algorithm enables to easily deal with different forms and types of production units, eachcharacterised by its own cost function and constrains.

The proposed approach has demonstrated to be flexible and suitable to manage a VPP with more than three generating systems.The ever greater diffusion of small generating systems areexpected to affect distribution systems, since each VPP, or single producer, manages its own plant in an independentmanner. Economic optimisation should thus be subject to the

respect of the network constrains, such as allowable line loading and bus-bar voltage levels.New constraints are also taken into accounts, which are related to lines capacity and voltage level at each bus of the network. This approach involves many innovative aspects concerning the management of distribution systems, especially related to the planning strategies for active networks or micro grids.

IX. REFERENCES

[1] Rodrigo Palma-Behnke, Senior Member, IEEE, José Luis Cerda A., Luis S. Vargas, Senior Member, IEEE, and Alejandro Jofré," A Distribution Company Energy Acquisition Market Model With Integration of Distributed Generation and Load Curtailment Options", IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 4, NOVEMBER 2005

[2] Robertoo Caldon, Andera Rossi Patria and Roberto Turri,"optimization algorithm for a virtual power plant operation".

[3] K.Dielmann, Alwin van der Velden,"VIRTUAL POWER PLANTS (VPP)- A NEW PRESPECTIVE FOR ENERGY GENERATION?" 2003 IEEE.

[4] D. Pudjianto, C. Ramsay and G. Strbac," Virtual power plant and system integration of distributed energy resources", The Institution of Engineering and Technology 2007

[5] Christian Schulz, Gerold Roder, Michael Kurrat Technical University Braunschweig, Institute of High-Voltage and Electric Power Systems, Germany," Virtual Power Plants with combined heat and power micro-units".

[6] J.Oyarzabal, J.Jimeno,J.Ruela,A Engler and C.Hardt, "Agent based Micro grid management system " Digital Object Identifier: 10.1109/FPS. 2005.204230, Current Version Published: 2006-03-06

[7] Heiko Englert, "Informationstechnische Vernetzung der DEA inVirtuellen Kraftwerken", presented at the Workshop Virtual PowerPlants, Unna, Germany, 2005.

[8] T. Ackermann, G. Andersson, and L. Söder, “Electricity market regulations and their impact on distributed generation,” in Proc. Conf, Electric Utility Deregulation and Restructuring and Power Technologies 2000, London, U.K., Apr. 4–7, 2000, pp. 608–613.

[9] Eko Adhi Setiawan. "Concept and Controllability of Virtual Power

Plant."Kassel University Press GmbH, Kassel , Diss. 2007,ISBN: 978-3-

89958-309-0.

[10] D. Pudjianto, C. Ramsay and G. Strbac," Microgrids and Virtual power plants: concept to support integration of distributed energy resources", IMechE 2008.

[11] R. Caldon, A. Rossi Patria, R. Tum. “Optimal Control of a Distribution System with a Virtual Power Plant”, Bulk Power System Dynamics andControl - VI, Cortina d’Ampezzo (ITA), 22-27 August 2004.

[12] Michael R. Bussieck, Michael C. Ferris, Alexander Meeraus. "Grid-Enabled Optimization with GAMS", September 2008.

[13] Federico Milano. "A Graphical and Open Source Matlab-GAMS interface for Electricity Market Models."

[14] João Tomé Saraiva. "Markets and Regulation". Doctoral Programme in Electrical and Computer Engineering at FEUP.

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[15] DIDIER HENRION. "Global Optimization Toolbox for Maple", IEEE CONTROL SYSTEMS MAGAZINE » OCTOBER 2006.

[16] Yohan Sutjandra. "Mathematical Programs with Equilibrium Constraints".

X. BIOGRAPHIES

M. Amin Salmani was born in Tehran, Iran. He received his BS degree in 2006 in electrical engineering from K.N.Toosi University of Technology Tehran/Iran. He is currently pursuing MS degree in this University and he is working in MAPNA Co. His research interests are in the areas of energy management, renewable energy,deregulated power system and distributed generation.

Seyed-Masoud Moghaddas-Tafreshi was born in Tehran, Iran. He obtained his PhD degree in 1995 in electrical engineering from Technical University of Vienna, Austria. Dr. Moghaddas-Tafreshi is now an Assistant Professor in the Power Engineering Department in Electrical Faculty of K.N.Toosi University of Technology in Tehran/Iran. His research interests are in the areas of Load and Energy Management, Renewable Energy,

Power System Operation & Planning of the deregulated power system. He has numerous postgraduate and undergraduate students in these fields. He is author of one book with title: Electrical Energy Generation Resources in the 21st Century and co-author/author of more than 50 published papers.