Abstract -- In this paper the authors propose a market

strategy of a microgrid incorporating a virtual power plant. For exemplification, a configuration consisting of different types of distributed generators are considered. The aim of the virtual power plant is to maximize the profit by appropriate bidding strategy on the electricity market and optimal use of the sources.

Index Terms--virtual power plant, distributed generation, smart grids

I. INTRODUCTION N the last two decades the power systems have been undergoing major changes. The first major change was the decentralization of the generation, transmission and

distribution sectors, and introduction of the power market, respectively. The power market was created aiming to increase the competition among all involved entities in directly commercializing electrical energy, and finally reduce the electrical energy price. The next changes have been focusing on re-innovating renewable energy sources and therefore distributed generation, which are now the priority as a measure for protecting the environment. This major change have already entered into force and aims to stimulate for smart solutions needed to help overcoming problems which push the power systems to their limits and lead to a better comfort to the network users.

There is a sustained trend of the interest for renewable energy sources (photovoltaics, wind generation, micro-hydro, etc.) or for low emission sources (micro-turbine, multifuel-CHP, bio-CHP, diesel, etc.), in general of small rated power, under 10 MW. Following the European Union strategy which foresees that member states aims to reach the 20% share of the renewable energy sources of the total electrical energy generation until 2020, the financial incentives to support the renewable energy sources have been increasing. Therefore, the small size sources will have bigger share in the generation sector, especially in the low voltage and medium voltage networks. Furthermore, these sources can be located either near the consumers or far from the consumers.

II. IMPACT OF THE SMALL SIZE SOURCES ON THE POWER GRID OPERATION

The expected increase in the number of units and the installed power in the distributed generators (DG) will affect the power system operation following the change from a

radial configuration, supplied from only one source (the higher voltage network), to a configuration with several sources. Furthermore, the lack in monitoring possibilities of the distributed generators would introduce higher uncertainty in the active powers balancing process for frequency control performed by the system operator and the need for more power reserves as ancillary service, which may lead to increased price of the electrical energy. On this line, the network operators must take into account the intermittency of some renewable energy sources. Because of their small size, the distributed generators cannot participate individually to the power market.

The Virtual Power Plant (VPP) might be a possible solution for a broad range of problems caused by the distributed generators. The VPP consists in aggregating several generation sources under a single entity, by monitoring and coordination in real time by a local operator, which can be the distribution operator or an independent operator. By aggregating several generation sources, the local operator can coordinate the operation of the sources so that it can balance its economical contracts from his own portfolio, while participating to the power market.

The idea of a virtual power plant can be also applied to a wider level in the case of wind power plants. For instance, by correlation with a hydro power plant the unbalances generated by the wind power plant, caused by the wind intermittency, can be covered by the hydro power plant, independently by the national system operator.

III. ELECTRICITY MARKETS IN ROMANIA The electricity market has been introduced in Romania in

2002, and in 2005 it undergone reorganization in order to increase the competitiveness by introducing specific markets for ancillary services as well for real-time balancing. The electrical energy is traded by three types of arrangements. The long-term contracts are traded through regulated contracts or by public auction within the Bilateral Contracts Centralized Market (BCCM), while the short-term arrangements are performed on a daily market called Day Ahead Market (DAM). The DAM’s clearing price is given by the intersection point between the selling offers curve and buying offers curve. DAM is a purely economic market since its mechanism does not take into account any technical restriction. On the ancillary services market (ASM), organized monthly or at two-week, power capacities are contracted, while the Balancing Market (BM), for real-time dispatch, is organized

Market strategy of distributed generation through the Virtual Power Plant concept

Lucian TOMA, IEEE Member, Bogdan OTOMEGA, Ion TRISTIU, IEEE Member Department of Electrical Power Systems, University “Politehnica” of Bucharest

E-mail: lucian@ieee.org

I

978-1-4673-1653-8/12/$31.00©2012 IEEE 81

on daily auctions. BCCM and DAM are administrated by the market operator, OPCOM, while ASM and BM are administrated by the TSO, Transelectrica.

DAM and BM are organized in a sequential manner. Therefore, a producer can offer secondary regulation reserve or tertiary reserve for downward regulation only if he owns contracts for electrical energy by any commercial arrangement, that is its units are synchronized with electrical network in the involved dispatch interval.

Figure 1 shows the development in time of the Day Ahead Market and Balancing Market.

11:00 15:00 17:00

P [MW]

DAM

Close DAM Open BM Close BM

BalancingMarket

h-1 h

D-1 D

BC

DAM

Powerreserves

Time [ ]h

Balancingenergy

Fig. 1. Development in time of DAM and BM.

IV. THE VIRTUAL POWER PLANT CONCEPT

A. Technical issues The idea of a virtual power plant is today possible due to

the technological progress in the telecommunications, automation, metering and computation sectors. The backbone of the virtual power plant is the communication infrastructure, which allow remote control of the distributed generators according to a predefined methodology.

As illustrated in Figure 2, the distributed generators are connected to the control system located at the local operator through the communication infrastructure. Using forecast tools, optimization tools, information from the power market, etc., the local operator decide the strategy for participation to the power market.

It is assumed that in the VPP there are batteries for energy storage so that the wind power plants and the solar power plants can be considered with constant generation during one dispatching interval.

Generally, the unit commitment during various dispatching intervals of a day is performed on the basis of firm bids, without flexible changing possibilities, that is operation at constant values during one dispatching interval. This procedure is quite inflexible in the sense that any deviation from the day-ahead bid is corrected only by the system operator using regulation reserves.

The active powers balancing process is strongly related to the frequency control. A VPP could, for instance, participate to the frequency control by provision of fast tertiary reserve, both for the upward regulation and downward regulation, in the latter case also with the contribution from the controllable loads.

Hydro

μTurbine

Fuel cells

Bio-CHP

Storage

PV systemsWind-generation

Controllable loads

Diesel

LOCALCONTROLLER

Power Market

Hydro

μTurbine

Fuel cells

Bio-CHP

Storage

PV systemsWind-generation

Controllable loads

Diesel

LOCALCONTROLLER

Power Market

Fig. 2. Aggregation of distributed generators.

B. Economical Virtual Power Plant The idea: Several generation entities are aggregated to

form a single entity able to behave on the power market similar to a classical power plant. Participation on the market as independent entity is restricted by a minimum available power. For instance, in Romania the minimum power quantity that may be tendered on the market is 10 MW.

Besides the technical issues, the algorithm governing the local controller can include an objective function, which aims minimization of the global costs. In terms of availability of the primary resource (water, wind, sun), the total generation cost and the electrical energy price on the power market, the local operator, with the help of the algorithm implemented in the local controller, can decide for using mainly the generation sources from his portfolio or can choose to cover the electrical energy demand from the main grid.

Objectives: The market strategy of an economic VPP can be designed so that to: o Maximize the profit; it takes into account both the

generation costs and the power market price; o Minimize the generation costs, by coordinating the

generation entities; electrical vehicles and loads can also be included;

o Minimize the cost of energy bought from the power market;

o Coordinate between energy sold on the power market an energy/reserve sold as ancillary service.

o etc. Issues to be considered when formulating the economic

problem: • The customers may offer their availability to be

disconnected in any conditions. The loads can be used mainly in emergency conditions, but also when high forecast errors occur. This can be seen also as a technical problem. The supplier can use the generation facilities and the load from its portfolio to minimize the unbalance and avoid paying expensive balancing energy used by the system operator.

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• The total generation costs are determined mainly in terms of the cost of fuels (gas, liquid fuel, biomass, etc) and the technical availability of other units (with no fuel costs). The supplier can decide when to use certain generation units in terms of the load demand (from its portfolio) and the contracted power to be generated (sold).

• In terms of the expected costs on the power market, the supplier establish its strategy to minimize the generation cost. In this regard, the supplier needs a tool for price forecasting. If the market price is low, the supplier will choose to buy energy from the market while its generation units are kept at the minimum operating power limit or are shut-down. When the market price is above the break-even, the supplier will use his own resources to supply his own load and/or to sell energy on the market.

• The supplier can make its strategy to sell energy both on the day ahead market and the balancing market as tertiary reserve. For instance, if the supplier is not a balancing responsible party (BRP), it can make an agreement with a BRP for firm quantities, as a predefined generation curve (e.g. 24 values per day), that may be provided according to the technical rules (e.g., in Romania the fast tertiary reserve must be provided within 15 minutes);

• The economic problem must consider also the technical limitations of the generating units. In some cases, energy generation or provision of ancillary services can be performed in discrete steps rather than continuously;

• The renewable energy sources are dispatched inside the VPP irrespective of the costs taking into consideration their support for environment protection, that is for 1 MWh produced, the owner receives 1 green certificate. The generation costs of the wind power plants and the solar power plants are mainly due to the investment costs. With the support through the green certificates scheme, the generation cost can be considered very competitive as compared to the other types of generators.

An economic problem regarding the electrical energy should be linked also with the thermal energy, as it is the case of CHP units.

C. Example of Virtual Power Plant Placing DG units in the distribution network avoids

transmission of electrical energy over long distances, from the big power plants through the transmission network and the distribution network. In the traditionally organized electrical networks, the power losses may count, in some European countries, up to 10% of the total load. Higher efficiency is also obtained by supporting the distributed generators to produce more power, as the conversion efficiency from one type of conventional energy to electrical energy is higher as compared to the classical power plants. For example, a gas engine producing in cogeneration (electrical energy and thermal energy) can reach up to 89% efficiency.

In this paper it is assumed that all distributed generators are located in the same distribution network. Also, the Virtual Power Plant include all distributed generators, i.e. one diesel engine unit, one gas engine unit, one PV power plant, one wind power plant (consisting of 4 units) and one hydro unit. On the other hand, the VPP may include a controllable load,

that is eligible for disconnection when the market price is too high.

DieselEngine

Hydro powerplant

Wind powerplant

PV powerplant

Controllableload

Load

Load

MV

HV

Powersystem

Controllableload

DistributionNetwork

Gas Engine

Load

Fig. 3. Configuration of the virtual power plant.

D. Market strategy The supplier, using the VPP facilities, may choose to

participate on the electricity market, if he is able to provide at least 10 MW using its DGs, or it can inject power into the distribution network based on an agreement with the distribution company, supplying the consumers from its portfolio.

The supplier can choose between using the DGs to normally provide electrical energy or/and to provide power reserves as ancillary service. While injection of electrical energy in the distribution network ensures a constant income for the DGs’ owners, provision of power reserves increases the risk in the market strategy. Power balancing in the distribution network is possible, independent of the frequency regulation performed by the system operator, but this issue is not the purpose of the present work.

The diesel engine and the gas engine can operate over long period at constant outputs as the liquid fuel can be stored for longer period operation and the gas can be supplied at constant pressure.

If appropriate water flow is available, the hydro-generator can operate at any output value as they are the most flexible synchronous generators.

However, the PV systems are dependent on the sun, and the wind generators are dependent on the wind, which are both variable in time. For the shake of simplicity, we will consider that the fluctuations in the output power of the PV power plant and the wind power plant are balanced using a special agreement.

The power flowing through the link with the transmission system (distribution substation) is considered flexible, allowing both imports and exports to the distribution network, although only the power specified in the bilateral contract is scheduled to flow from the transmission network to the distribution network.

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Assumes that the supplier has a bilateral contract for consumption with a generation entity located in the transmission network. The energy is absorbed from the transmission network through the HV/MV substation.

V. THE OPTIMIZATION PROBLEM The objective function An objective function of the virtual power plant can be the

target for the maximization of the benefits after participation in various market arrangements for selling electrical energy and power reserves, i.e.:

BenefitMAX where

Benefit Incomes Costs= − Incomes

The VPP can have incomes from participation on various power markets:

24 24 24

, , , , ,1 1 1

24 24

, ,1 1

DAM t DAM t BC t BC t L VPP t VPPt t t

g t g tt t

Incomes E c E c E c

R R

−= = =

+ −

= =

= + + +

+ +

∑ ∑ ∑

∑ ∑

,DAM tE is the energy traded by the VPP on the Day-Ahead Market in the dispatching interval t, in kWh;

,DAM tc – the DAM clearing price in the dispatching interval t, in m.u./kWh;

,BC tE – the energy traded by the VPP through Bilateral Contracts in the dispatching interval t, in kWh;

,BC tc – the energy price negotiated on the bilateral contracts market, in m.u./kWh;

,L VPP tE − – the energy provided to the costumers that are part of the VPP, in kWh;

VPPc – the supply energy price for the costumers that are part of the VPP, in m.u./kWh;

,g tR+ – the total power reserve provided by the VPP for the arrangements on the ancillary services market for upward regulation, in kWh;

,g tR− – the total power reserve provided by the VPP for the arrangements on the ancillary services market for downward regulation, in kWh;

When sending bids on the DAM, the VPP manager can only forecast the clearing price. But, after market clearing, once the DAM clearing prince is known, the VPP can perform the internal dispatching, in terms of the available capacity of all distributed generators and VPP loads so that to maximize its benefits. Expenses

The total costs necessary for all distributed generators from the VPP to provide the electrical energy traded through various power markets, during 24 dispatching intervals (one day), is:

24 24 24 24

, , , ,1 1 1 1

g t g t g t L tt t t t

Costs C SU SD R+

= = = =

= + + −∑ ∑ ∑ ∑

where:

,g tC is the total cost of the energy generated by all generators in the dispatching interval t, in m.u., with

, , , , ,1

n

g t g i t g i i ti

C E c I=

= ∑ ;

, ,g i tE is the energy produced by the generator i, in the dispatching interval t, in kWh;

,g ic – the marginal costs of the generator i, in m.u./kWh;

,i tI – a binary variable denoting the operation state of the generator i in the dispatching interval t: 1 shows that the generator is on and o shows that the generator is off;

,g tSU – the cost involved for all generators to start-up in the dispatching interval t, in m.u.;

, , ,1

n

g t g i ti

SU SU=

= ∑

, ,g i tSU is the cost of the generator i involved for start-up in the dispatching interval t, in m.u.;

,g tSD – the cost of all generators involved for shut-down in the dispatching interval t, in m.u.;

, , ,1

n

g t g i ti

SD SD=

= ∑

,g tSD is the cost of the generator i involved for shut-down in the dispatching interval t, in m.u.;

,L tR+ – the total power reserve maintained available by all consumers for disconnection in the upward regulation during the dispatching interval t, in kWh;

The maximization of the objective function is subjected to

the following equality and inequality constraints: a) The power reserve The total power reserve that was traded for the dispatching

interval t and which must be kept available at every instant of time is the sum of all reserves that can ne provided by the distributed generators, i.e.:

, , , ,1

n

g t g i t i ti

R R I=

= ∑

where , ,g i tR is the power reserve ensured by distributed generator i for the dispatching interval t; b) The total load

The total load that must be supplied by the VPP, consisting on energy sold on the day-ahead market, energy sold by bilateral contracts and the energy sold for the VPP consumers, is:

, , ,load DAM t BC t L VPP tE E E E −= + + Considering that the VPP is involved in ancillary services provision, the total power capacity that must be dispatched is:

, ,load r load L tE E R+= + The distributed generators are too small to participate in the secondary frequency control. However, they can participate in the tertiary frequency control either with fast reserved

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(available within 15 minutes) or with slow reserve (available within 7 hours). c) Capability constraints of generators

It is assumed that all distributed generators are capable to provide power reserve for both the upward and downward regulation, except for the wind power plants and solar power plants, of which generated power is subjected to fluctuations of the wind and light, respectively. However, it is not compulsory that a distributed generator will be dispatched by the VPP coordinator to provide power reserve as ancillary service. If a distributed generator i is not taken into account when building up the power reserve, the generated power is subject to the generation capability constraints, i.e.:

, ,min , , , , ,maxg i g i t i t g iP P I P≤ ≤

However, if the distributed generator i is taken into account when building up the power reserve, the total amount of the generated power and the power reserve is subject to the generation capability constraints, i.e.:

, ,min , , , , , , , ,maxg i g i t i t g i t i t g iP P I R I P≤ + ≤

However, the PV panels and wind turbine systems are used at their actual available output, so that the limits are fixed to the available output, i.e. min,i availP P= and max.i availP P= .

d) Capability constraints of the loads It is assumed that the consumers can participate in the

upward regulation by disconnecting a certain part of the total load that is part of the VPP. Giving priority to productivity, the maximum load that can be disconnected in 10% of the total load ,L VPP tE − , i.e.:

, ,0 10%L t L VPP tR E −≤ ≤

The total load consists of the energy exported e) Regulation constraints The power reserve that can be provided by the distributed

generators in the required time for upward regulation, in the dispatching interval, is:

{ }, , , , , ,max , ,min 15 ;g i t up up i g i g i tR R P P= × −

where ,up iR is the ramp-up capability. The power reserve that can be provided by the distributed

generators in the required time for downward regulation, in the dispatching interval, is:

{ }, , , , , , , ,minmin 15 ;g i t down down i g i t g iR R P P= × −

where ,down iR is the ramp-down capability. f) Additional constraints There must be taken into account the some operation time

of the generators. Therefore some additional constraints must be fulfilled for any i generator:

, 1 , 1 , 0 , 1: 24oni t i i t i tT MUT I I t− −⎡ ⎤− × − ≥ ∀ =⎡ ⎤⎣ ⎦ ⎣ ⎦

, 1 , 1 , 0 , 1: 24offi t i i t i tT MDT I I t− −⎡ ⎤− × − ≥ ∀ =⎡ ⎤⎣ ⎦ ⎣ ⎦

, , 1 ,i t i t i tI I J−− ≤

, 1 , ,i t i t i tI I K− − ≤

, , 1 , ,i t i t i t i tI I J K−− ≤ − where:

, 1on

i tT − , , 1off

i tT − is the number of hours for which the generator has been on/off;

iMUT , iMDT – minimum up and down time limits of the generator i, in hours;

,i tJ – binary variable denoting the start-up decision for the generator;

,i tK – binary variable denoting the shut-down decision for the generator.

VI. CASE STUDY

In the study case we consider that the virtual power plant consists of 6 distributed generators. The minimum, maximum and available active powers as well as the generation costs are given in Table 1. Note that the generation costs are given only for simulation purposes and might not necessarily reflect real costs, as these can vary from one unit to another and from one country to another.

TABLE 1. ACTIVE POWER LIMITS AND GENERATION COSTS

Pmin Pmax Pavail Cost kW kW kW m.u./kWh DG1 (Wind power plant) 0 300 … 4.1 DG2 (PV power plant) 0 400 … 8.0 DG3 50 3000 3000 5.0 DG4 50 5000 5000 4.5 DG5 50 1600 1600 3.5 DG6 50 2000 2000 3.0

m.u. – Monetary Unit The diesel engine, gas engine and micro-hydro power plant may operate for an output power between the minimum and maximum limits, while for the PV power plant and the wind power plants the operation limits are restricted to the available power. Renewable energy sources are considered prioritizable generation units and they are dispatched according to their available power. Under the classical electricity market conditions, no matter of the generation costs (where the capital costs are the most important), the renewable energy units must accept the market price. This is because these units generate energy when the primary energy is available. In our case, because these units are part of the virtual power plant, similar to the others units, which are be located in a microgrid, they are remunerated according to their costs. Let us consider the generation capacity of the 6 distributed generators of the VPP for a 24 hours window as shown in Figure 4. The generation capacities of the DG1 (wind power plant) and the DG2 (solar power plant) are restricted to the profile provided in Figure 4, whereas the generation capacities of the other generators can take any value between the minimum and the maximum limits.

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2 4 6 8 10 12 14 16 18 20 22 24

0

1000

2000

3000

4000

5000

time [h]

Gen

erat

ion

[kW

h]

2 4 6 8 10 12 14 16 18 20 22 240

1000

2000

3000

4000

5000

time [h]

capa

city

[kW

]

DG4

DG6

DG3

DG5

DG1DG2

Fig. 4. Generation capacity.

Table 2 shows the values of the energy traded in the 3

market arrangements and the price for each dispatching interval.

TABLE 2. ENERGY TRADED AND ENERGY PRICE

Time E-DAM E-BC E-VPP

h kWh/h m.u./kWh kWh/h m.u./kWh kWh/h m.u./kWh

1 1800 4.3 2500 5.5 2600 4

2 1700 4 2500 5.5 2600 4

3 1500 4 2500 5.5 2600 4

4 1600 4 2500 5.5 2600 4

5 1700 4 2500 5.5 2600 4

6 1900 5 3000 5.5 3100 4

7 2400 6.2 3500 5.5 3700 4

8 2600 6.7 3500 5.5 4000 4

9 2500 6.9 3500 5.5 4000 4

10 2500 6.9 3500 5.5 4000 4

11 2400 6.7 3500 5.5 4000 4

12 2400 6.7 3500 5.5 4000 4

13 2300 6.5 3000 5.5 3800 4

14 2200 6.5 3000 5.5 3800 4

15 2200 6.7 3300 5.5 4000 4

16 2300 6.7 3300 5.5 4000 4

17 2300 6.7 3300 5.5 4000 4

18 2500 6.9 3500 5.5 4500 4

19 2700 6.9 3500 5.5 4500 4

20 2800 6.7 3500 5.5 4500 4

21 2600 6.5 3000 5.5 4000 4

22 2200 6 2500 5.5 3500 4

23 2200 5.5 2500 5.5 3000 4

24 1900 4.8 2500 5.5 3000 4 A constant active power of 1000 kW maintained available as ancillary service reserve for upward regulation is added to the hourly generation profile. It is assumed that the availability costs of the power reserve was traded for the amount of 0.5 m.u./kWh. Figure 5 shows the energy profile traded through different arrangements, i.e. energy traded on the day-ahead market (E-DAM), energy traded by bilateral contracts (E-BC) and the energy sold to the consumers that are part of the VPP (E-

VPP). The total energy (E-Total) is the sum of the above mentioned energies.

2 4 6 8 10 12 14 16 18 20 22 240

2000

4000

6000

8000

10000

12000

time[h]

load

[kW

h/h]

E-VPPE-BCE-DAM

E-Total

Fig. 5. Load.

In order to have an image of the difference between the generation capacity and the total generation and reserve, Figure 7 shows their profile for a 24 hours time window.

2 4 6 8 10 12 14 16 18 20 22 240

2000

4000

6000

8000

10000

12000

14000

time [h]

Tota

l cap

acity

/gen

erat

ion

[kW

h/kW

h]

Capacity

Generation + Reserve

Fig. 7. The total capacity vs. the total generation.

Fig. 8. Individual generation of the DGs. The unit commitment obtained for the 24 dispatching intervals after applying the optimization problem is presented in Table 3. The values are also illustrated in Figure 8.

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TABLE 3. THE UNIT COMMITMENT

Time DG1 DG2 DG3 DG4 DG5 DG6

h kWh/h kWh/h kWh/h kWh/h kWh/h kWh/h

1 200 0 50 3050 1600 2000

2 200 0 50 2950 1600 2000

3 600 0 50 2350 1600 2000

4 900 0 50 2150 1600 2000

5 1300 0 50 1850 1600 2000

6 1800 20 50 2530 1600 2000

7 2100 50 50 3800 1600 2000

8 1900 90 50 4460 1600 2000

9 1600 140 50 4610 1600 2000

10 1500 220 50 4630 1600 2000

11 1300 240 50 4710 1600 2000

12 800 260 240 5000 1600 2000

13 700 300 50 4450 1600 2000

14 700 280 50 4370 1600 2000

15 500 270 130 5000 1600 2000

16 300 250 450 5000 1600 2000

17 500 200 300 5000 1600 2000

18 500 100 1300 5000 1600 2000

19 700 50 1350 5000 1600 2000

20 900 0 1300 5000 1600 2000

21 800 0 200 5000 1600 2000

22 700 0 50 3850 1600 2000

23 700 0 50 3350 1600 2000

24 500 0 50 3250 1600 2000 It can be seen that, as agreed, the DG1 (wind power plant) and the DG2 (solar power plant) are dispatched with their whole available power, while the others generators are dispatched in terms of their marginal costs. Therefore, DG4 and DG5 are dispatched with their entire capacity, the DG3 is mostly maintained at the minimum capacity in order to avoid start-ups and shut-downs, while DG4 is dispatched to cover the difference to the load.

2 4 6 8 10 12 14 16 18 20 22 240

1

2

3

4

5

6x 104

time [h]

Pro

fit [m

.u.]

Incomes

Profit

Costs (Expenses)

Fig. 9. Calculation of VPP profit.

Figure 9 illustrates the Incomes, the Expenses as well as the Profit resulted for the 24 dispatching intervals. We can see that profit peaks occurs during peaks of the DAM clearing price, which means during the morning and during the load peak.

VII. CONCLUSIONS In a microgrid where the consumers may own distributed

generators, aggregation of all DG units for establishing the market strategy may minimize the total costs. From technical point of view, aggregated behavior of DG units can help the supplier to balance its own contracts (portfolio) achieving a balance between the generated powers and the load demand, avoiding penalties that may be caused by imbalances.

VIII. ACKNOWLEDGEMENTS The work has been co-funded by the Sectoral Operational

Programme Human Resources Development 2007-2013 of the Romanian Ministry of Labour, Family and Social Protection through the Financial Agreement POSDRU/89/1.5/S/62557 and by the project no. PN-II-ID-PCE-2011-3-0693 developed through CNCS.

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