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Abstract

Electric Power Systems Research 77 (2007) 1627–1636

Optimal DG placement in deregulated electricity market

Durga Gautam, Nadarajah Mithulananthan ∗

Electric Power System Management, Energy Field of Study, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand

Received 19 August 2006; received in revised form 14 November 2006; accepted 16 November 2006

Available online 29 December 2006

This paper presents two new methodologies for optimal placement of distributed generation (DG) in an optimal power flow (OPF) based wholesale

electricity market. DG is assumed to participate in real time wholesale electricity market. The problem of optimal placement, including size, is

formulated for two different objectives, namely, social welfare maximization and profit maximization. The candidate locations for DG placement

are identified on the basis of locational marginal price (LMP). Obtained as lagrangian multiplier associated with active power flow equation for

each node, LMP gives the short run marginal cost (SRMC) of electricity. Consumer payment, evaluated as a product of LMP and load at each load

bus, is proposed as another ranking to identify candidate nodes for DG placement. The proposed rankings bridges engineering aspects of system

operation and economic aspects of market operation and act as good indicators for the placement of DG, especially in a market environment. In

order to provide a scenario of variety of DGs available in the market, several cost characteristics are assumed. For each DG cost characteristic, an

optimal placement and size is identified for each of the objectives. The proposed methodology is tested in a modified IEEE 14 bus test system.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Distributed generation; Locational marginal price; Optimal power flow; Electricity market; Social welfare

1. Introduction

DGs are considered as small power generators that complement

central power stations by providing incremental capacity

to power system. Although DGs may never replace the central

power stations, these can be an attractive option when constraints

in transmission network prevent economic, or least expensive,

supply of energy reaching demand. However, penetration and

viability of DG at a particular location is influenced by technical

as well as economic factors. The technical merits of DG

implementation include voltage support, energy-loss reduction,

release of system capacity, and improve utility system reliability

[1]. Economical merit, on the other hand, encompasses hedge

against high electricity price. This incentive is enhanced with

vertical unbundling of utilities and market mechanisms such as

real time pricing. By supplying loads during peak load periods,

where the cost of electricity is high, DG can best serve as a price

hedging mechanism.

DG can have a great value in a highly congested area where

LMPs are higher than elsewhere. In such situation, it can serve

∗ Corresponding author. Tel.: +66 2 524 5405; fax: +66 2 524 5439.

E-mail address: mithulan@ait.ac.th (N. Mithulananthan).

0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsr.2006.11.014

the local load and effectively reduce the load. The placement of

DG, however, should be carried out with due consideration to

its size and location. The placement should be optimal in order

for the maximum benefit of DG implemented in the network.

Improper placement in some situations can reduce benefits and

even jeopardize the system operation.

Numerous techniques are proposed so far to address the viability

of DGs in power system. Capacity investment planning of

distributed generation under competitive electricity market from

the perspective of a distribution company is proposed in Ref. [2].

An approach for optimal design of grid connected DG systems

in relation to its size and type to satisfy on-site reliability and

environmental requirements is presented in Ref. [3]. Besides,

several optimization tools, including artificial intelligence techniques,

such as genetic algorithm (GA), tabu search, etc., are

also proposed for achieving the optimal placement of DG. An

optimization approach using GA for minimizing the cost of network

investment and losses for a defined planning horizon is

presented in Ref. [4]. GA has been used to obtain penetration

level of DG for minimizing the total cost of operation including

fixed and variable cost in Ref. [5]. The method for optimal

placement of DG for minimizing real power losses in power distribution

system using GA is proposed in Ref. [6]. The gradient

and second order methods to determine the optimal location for


1628 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636

the minimization of losses or line loading is employed in Ref.

[7]. An iterative method that provides an approximation for the

optimal placement of DG for loss minimization is demonstrated

in Ref. [8]. Analytical methods for determining optimal location

of DG with the aim of minimizing power loss are proposed

in Ref. [9]. Placement and penetration of distributed generation

under LMP based standard market design with the objective of

generation cost minimization is proposed in Ref. [10]. Optimal

placement of DG with Langrangian based approach using traditional

pool based OPF and voltage stability constrained OPF

formulations is proposed in Ref. [11].

Present study encompasses the placement of DG in a pool

based wholesale electricity market with centralized dispatch.

DG is considered as a negative load. The placement problem is

formulated for the two different objectives, namely, maximizing

social welfare and maximizing the profit of DG owner.

The paper is organized in five sections. Section 2 sets out

the OPF formulation dealing with social welfare maximization

problem. Section 3 presents the methodology adopted to evaluate

the placement of DG wherein the rankings used to identify

the candidate nodes for the placement are also discussed. The

OPF results and inferences drawn from the same are covered in

Section 4. Several cases have been considered to depict possible

scenarios and results have been shown in graphical and tabular

format. The conclusions that can be drawn from the analysis are

presented in Section 5.

2. Problem formulation

The problem is formulated with two distinct objective

functions, namely, social welfare maximization and profit maximization.

Social welfare is defined as the difference between

total benefit to consumers minus total cost of production [12].

It is the sum of producers’ surplus and consumers’ surplus as

shown in Fig. 1. In general term, it represents the surplus to

society and is maximum when the market price is equal to the

marginal cost of producing the last unit of electricity [12].

The traditional OPF algorithm for cost minimization is modified

to incorporate the demand bids, in addition to the generation

bids. LMP is determined as the lagrangian multiplier of the

Fig. 1. Social surplus with quadratic supply and demand curves.

power balance equation in OPF. The generator and customer bids

are taken as inputs to OPF. The base case OPF based on social

welfare maximizing algorithm evaluates the generation dispatch,

demands and prices at each of the nodes. The nodal prices so

obtained are indicator for identifying candidate nodes for DG

placement. The placement is intended to meet the demand at a

lower price by changing the dispatch scenario.

The profit maximization problem is viewed from the perspective

of DG owner, who chooses to place DG at the load nodes.

In order for them to achieve maximum revenue out of the dispatched

power, placement and size of DG chosen should reduce

the LMP to a value that maximizes the profit. As higher LMP

value might considerably lower the revenue making the profit

negative.

2.1. Social welfare maximization

The objective function is formulated as quadratic benefit

curve submitted by the buyer (DISCO) minus quadratic bid

curve supplied by seller (GENCO) minus the quadratic cost

function supplied by DG owner.

N

max

(Bi(PDi) − Ci(PGi)) − C(PDGi) (1)

i=1

Alternatively, the maximization problem (1) can be formulated

as a minimization problem with multiplying the objective

function by −1.

N

min (Ci(PGi) − Bi(PDi)) + C(PDGi)

(2)

i=1

subject to

2.2. Equality constraints

The network for the transmission of electric energy is modeled

via the power balance equation at each node in the network.

The sum of power flows, active and reactive, injected into a node

minus the power flows extracted from the node has to be zero.

Pi = PGi + PDGi − PDi = vi

j=1

N

[vj{Gij cos(δi − δj)

+Bij sin(δi − δj}] (3)

Qi = QGi − QDi = vi

j=1

N

[vj{Gij sin(δi − δj)

−Bij cos(δi − δj}] (4)

2.3. Inequality constraints

Generation limits:

The generating plants have a maximum and minimum generating

capacity beyond which it is not feasible to generate due


D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636 1629

to technical or economic reasons. Generating limits are specified

as upper and lower limits for the real and reactive power

outputs.

Real power generation limits:

P min

Gi ≤ PGi ≤ P max

Gi

Reactive power generation limits:

Q min

Gi ≤ QGi ≤ Q max

Gi

Line flow limit:

The line flow limit specifies the maximum power that a

given transmission line is capable of transmitting under given

conditions. The limit can be based on thermal or stability considerations.

Thermal limits are usually considered for shorter

lines. The following constraint checks for the absolute power

flow both at sending and receiving ends of particular line to be

within the upper limit of the line.

Sij ≤ S max

ij

Sji ≤ S max

ji

Bus voltage limit:

Voltage limits refer to bus voltage to remain within an allowable

narrow range of levels.

v min

i

≤ vi ≤ v max

i

where N denotes the total number of buses in the system; PGi

denotes real power generated at bus i; PDi denotes real power

demand at bus i; PDGi denotes the power supplied by the DG

at bus i. Bi(PDi)=aDi + bDiPDi − cDi(PDi) 2 , denotes purchaser

benefit functions at bus i; Ci =(PGi)aGi + bGiPGi + cGi(PGi) 2 ,

denotes the producer offer (bid) price at bus i;

C(PDGi)=aDGi + bDGi PDGi + cDGi(PDGi) 2 , denote the

cost characteristic of DG at bus i; vi denotes the voltage at

bus i; δi denotes the power angle at bus i; Bij denotes the

susceptance of the line ij; Gij denotes the conductance of the

line ij; QGi denotes reactive power generated at bus i; P max

Gi

and Pmin Gi denotes upper and lower real power generation

limits of generator at bus i; Qmax Gi and Qmin

Gi denote upper and

lower reactive power generation limits of generator at bus i;

vmax i and vmin i denote upper and lower limits of voltage at bus

i; Sij denotes the complex power transfer from bus i to bus j;

Sji denotes the complex power transfer from bus j to bus i;

Smax ij

and line ji.

and S max

ji denote the complex power flow limit for line ij

For base case OPF,

PDGi = 0

For load bus,

PGi = 0

For generator bus,

PDi = 0

PDGi = 0

2.4. Profit maximization

The profit maximization formulation constitutes two nested

blocks. The inner block is handled by the independent system

operator (ISO). In order to achieve the short-run economic

optimum, ISO collects the electric power bids from suppliers,

consumers and DG placement and size from DG owner. The

DG owner being one of the market participants, lies outside the

block and submits the DG size they are willing to penetrate in

the market. ISO then runs OPF taking into consideration the network

constraints. The objective of this OPF is to minimize the

total costs. This block allows overall control and coordination of

generation and transmission. The LMP obtained from the OPF

is used by the DG owner in order to calculate the profit which

is evaluated as revenue minus cost for the particular DG. The

process is iterative as LMP is also a function of DG penetration.

The profit with DG placement at each of the node is evaluated

as:

Profiti = λi × PDGi − C(PDGi) (5)

where PDGi denotes the DG size at node i; λi denotes

the LMP at node i after placing DG; C(PDGi)=aDGi +

bDGiPDGi + cDGi(PDGi) 2 denotes the cost characteristic of DG

at node i.

The optimization process will identify the node and corresponding

optimal DG size that will bring maximum profit to the

DG owner.

3. Methodology

For a specific combination of supplier and demand bid

curves, the base case OPF first calculates different electricity

prices for different nodes in the network. The nodal prices are

obtained from the lagrangian multipliers of the non-linear equality

constraints. The increasing functions for supplier bids and

decreasing functions for the consumer bids are treated as the

marginal cost or benefits of the bidder. The difference in prices

results from active line constraints and losses in the transmission

system.

To identify candidate nodes for the placement of DG, two

rankings are defined, namely, LMP based ranking and consumer

payment (CP) based ranking.

3.1. Locational marginal price (LMP) based ranking

LMP is the lagrangian multipliers associated with the active

power flow equations for each bus in the system. LMP at any

node in the system is the dual variable for the equality constraint

at that node [13]. LMP is generally composed of three

components, a marginal energy component (same for all buses),


1630 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636

a marginal loss component and a congestion component. Considering

the case of real power spot price at bus i, LMP is given

by:

LMPi = λ + λ ∂PL

∂Pi

NL

+

ij=1

μLij

∂Pij

∂P

LMPi = λ + λL,i + λC,i

(7)

where λ is the marginal energy component at the reference bus

which is same for all buses, λL,i = λ(∂PL/∂Pi) is the marginal loss

component and λC,i = μLij (∂Pij/∂Pi) is the congestion component.

Thus, the spot price at each bus is location specific and

differs by the loss component and the congestion component.

Theoretically, this location-based price equals the economically

efficient market value of electricity at that point, factoring into

account constraints everywhere in the system.

Higher LMP implies a greater effect of active power flow

equations of the node on total social welfare of the system. In

other words, higher LMP implies higher the generation pressed

by demand at that node. It thus provides indication that for

the objective of social welfare maximization, injection of active

power at that node will improve the net social welfare. As the

DG is assumed to inject real power at a node, the node with highest

LMP will have first priority for DG placement. Accordingly,

the load buses are ranked in descending order of LMPs with the

first node in the order as the best candidate for DG placement as

shown below.

⎡ ⎤

LMP1

⎢ ⎥

⎢ LMP2 ⎥

⎢ ⎥


LMP = LMP3 ⎥

⎢ ⎥

(8)

⎢ ⎥

⎢ ⎥

⎣ . ⎦

LMPn

where n is the number of load locations.

Best location = index {max(LMP)} (9)

3.2. Consumer payment based ranking

CP calculated as the product of LMP and capacity of load is

considered as another criterion to segregate candidate nodes for

DG placement. Thus, the CP evaluated at the load bus i is the

product of LMP and load at bus i.

⎡ ⎤

CP1

⎢ ⎥

⎢ CP2 ⎥

⎢ ⎥


CP = LMPi × Loadi = CP3 ⎥

⎢ ⎥

(10)

⎢ ⎥

⎢ ⎥

⎣ . ⎦

CP4

Best location = index {max(CP)} (11)

CPi reflects the total amount the consumer at node i need to

pay for the electricity. The ranking is influenced from the fact that

market for DG placement can be viewed from two standpoints.

(6)

One scenario might be where price is high but load is relatively

small, while in the other, price is relatively low but load is high.

The ranking based on consumer payment is intended to focus

on the later scenario wherein total nodal payment is given the

priority rather than the high price. The ranking will have overall

effect of reducing dominant loads in the system. In effect, LMP

goes down and the dominant customer would be better off, as the

amount they need to pay would be less compared to no DG case.

The candidate nodes are iteratively selected for the

placement. The placement is carried out with several cost characteristics

assumed for DG. As the placement technique is intended

to bring down the LMP, DG with operating cost higher than LMP

will find no incentive for placement. The DG with operating cost

lower than those bided by supplier is expected to have higher

penetration while the one with higher cost is expected to have

smaller penetration.

4. Simulation results and discussion

The effects of DG penetration under the two scenarios,

namely, social welfare maximization and profit maximization,

are discussed in detail. The analysis is extended for the various

cost characteristics assumed for the DG.

4.1. Cost characteristics used for DG

Wide varieties of DG technologies with varying operating

characteristics are available in the market. To depict the variation,

assumptions are made for the cost characteristics. CHP

units, due to their heat recovery system can deliver power at

much cheaper price than the central generation. The technologies

such as fuel cells are characterized by their high cost while

technologies such as reciprocating engines and gas turbines lie

somewhere in the middle. In order to accommodate the varieties

of DG units, assumptions are made on the basis of the

cost characteristics of central generation. Table 1 shows the cost

characteristics of DGs considered in this work.

The cost comparison among the various units is made as per

the incremental cost. Incremental cost is a function of power output

of the unit where slope indicates cost to produce incremental

quantity and intercept indicates no load cost. Other conditions

remaining the same, the lesser the slope, the lower the incremental

cost and higher the penetration. The crossing over of

two different incremental cost characteristics reveals that operational

cost effectiveness depends on power output. The crossing

over is determined by no load cost and slope of the curve. The

Table 1

Distributed generation data

DG ID aDG bDG cDG

DG1 0.002 15 0

DG2 0.004 19 0

DG3 0.04303 20 0

DG4 0.25 20 0

DG5 0.1 30 0

DG6 0.01 40 0

DG7 0.003 43 0

Note: aDG, bDG, cDG are quadratic cost coefficient of DG.


D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636 1631

Fig. 2. Cost characteristic of various DG.

unit cheaper due to lower no load cost can prove to be expensive

beyond certain power output if the slope is large and vice versa.

The cost characteristic of DG units considered in modified

IEEE 14 bus test system is shown in Fig. 2.

The cost characteristics considered have wide variety of

slopes and accordingly, intersection at several points. Hence,

the comparative study of operational cost among the units relies

on power output.

The incremental cost characteristics of various DGs considered

in this study is shown in Fig. 3. As the quadratic component

of DG1 and DG2 is very small, their incremental cost is almost

constant for the entire range of output. Same is the case with

the DG6 and DG7. However, DG3, DG4 and DG5 show monotonically

increasing incremental cost with crossover at several

points.

4.2. Base case analysis

The social welfare maximization problem encompasses the

welfare of consumers as well as producers. The analysis

Fig. 3. Incremental cost characteristics of various DG.

Table 2

Ranking based on LMP

Rank Bus PD (MW) LMP ($/MWh)

1 14 33.91 54.644

2 11 39.68 54.413

3 10 12.65 52.229

4 9 26.26 50.698

5 13 10.7 50.501

6 7 19.89 49.204

7 4 56.05 47.758

8 12 11.18 46.658

9 5 26.52 43.636

is extended for various cost characteristics assumed for the

DG.

The system used in this study, modified IEEE 14 bus test

system, consists of 9 load buses and 5 generators. The loads are

assumed to be elastic with power factor of 0.91 (lagging). The

maximum social welfare is found to be 4425.31 $/h. The total

real power loss in the system is 7.042 MW. The generation, load

and LMP corresponding to the maximum social welfare for the

base case are determined at each node. Results revealed that

generator buses have lower values of LMP compared to the load

buses.

4.3. Candidate nodes for DG placement

The system has a maximum load of 56.05 MW at node 4.

Contrary to the node with maximum load, the highest LMP of

54.64 $/MWh is recorded at node 14 as shown in Table 2. This

shows high LMP should not necessarily be at the node with high

load. Load exceeding the transmission capacity at a particular

location might lead to high LMP. However, due to the loop flow,

loads at other nodes and overall network configuration do play a

role in determining LMP. The ranking of the load buses according

to LMP and consumer payment are shown in Tables 2 and 3,

respectively.

4.4. DG placement for social welfare maximization

The optimal DG size for each of the load bus is determined

from the social welfare maximizing problem. Results revealed

that there is an optimal DG size at each of the load bus for

which the net social welfare is maximum. However, the max-

Table 3

Ranking based on consumer payment

Rank Bus PD (MW) LMP ($/MWh) Consumer payment ($/h)

1 4 56.05 47.758 2676.84

2 11 39.68 54.413 2159.11

3 14 33.91 54.644 1852.98

4 9 26.26 50.698 1331.33

5 5 26.52 43.636 1157.23

6 7 19.89 49.204 978.67

7 10 12.65 52.229 660.70

8 13 10.7 50.501 540.36

9 12 11.18 46.658 521.64


1632 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636

imum net social welfare obtained from these optimal sizes is

different from one load bus to another. Another worth noticeable

point is that the placement as well as penetration of DG

is found to vary with the cost characteristics used. Even for the

same load bus, different optimal sizes are obtained when different

cost characteristics are used. The cheaper the unit the higher

the penetration and so is the net social welfare. This shows DG

penetration as well as social welfare is a function of DG cost

characteristics.

The study has been carried out to identify the optimal placement

and penetration when the DG is cheaper or expensive than

the existing central generation. The results associated with two

expensive DGs, namely, DG6 and DG7 are presented as sample

results. However, summary of the results for all DGs are given

in the end of this section.

4.5. Placement of DG6

The maximum net social welfare that can be achieved when

the placement of DG6 is carried out at different load buses is

shown in Fig. 4.

The corresponding optimal DG size at each of the load bus

is also shown in Fig. 5. For instance, if placement is to be carried

out at node 14, optimal size of DG for the social welfare

of 4577.18 $/h is 42.84 MW. Similarly, for placement at bus

11 the optimal size giving the social welfare of 4563.29 $/h is

48.69 MW and so on. It is interesting to note that net social welfare

is maximized for the case of DG at node 14. Hence, the

optimal placement of DG6 is node 14 with the optimal size of

42.84 MW. The social welfare maximization is found to capture

the first candidate node of LMP ranking given in Table 2. Moreover,

the ranking is found to capture first four candidate nodes

accurately in the same order.

The variation of net social welfare with respect to DG size for

node 14 is shown in Fig. 6. As apparent from the figure, beyond

the optimal size there is a reduction in net social welfare. For

non-optimal size same social welfare can be obtained for two

different sizes of DG. However, maximum net social welfare is

obtained only for the optimal DG size.

Fig. 4. Net social welfare at respective nodes with DG6.

Fig. 5. Optimal DG size at respective nodes with DG6.

4.6. Placement of DG7

The maximum net social welfare that can be achieved when

the placement of DG7 is carried out each of the load buses is

shown in Fig. 7. The maximum net social welfare of 4483.04 $/h

is obtained when the placement is made at node 14. Corresponding

optimal DG size is found to be 25.33 MW. The smaller

optimal size compared to the placement of DG6 can be attributed

to higher incremental cost of DG7.

The optimal size of DG after placing DG7 at each of these

buses is shown in Fig. 8. From the figure it is revealed that no

DG is selected for node 5. As apparent from Table 2, node5is

the last candidate node for DG placement. Hence, the placement

is found to follow the ranking based on LMP.

The variation of net social welfare with respect to DG size

for the placement of DG7 at node 14 is shown in Fig. 9.

Results revealed that placements as well as sizes vary with

the cost characteristics. The summary of results corresponding

to the placement of all the seven DGs considered in the study is

given in Table 4.

Fig. 6. Social welfare vs. DG size for the placement of DG6 at node 14.


D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636 1633

Fig. 7. Net social welfare at respective nodes with DG7.

Fig. 8. Optimal DG size at respective nodes with DG7.

Interestingly, it is observed that for the placement of DG1

and DG2, social welfare is maximized when placement is made

at node 4. In other words, the placement is found to track first

candidate node of consumer payment based ranking rather than

LMP ranking. Furthermore, as shown in Table 4 the penetration

of DG1 and DG2 is higher compared to that of DG6 and DG7.

The higher penetration can be attributed to the lower incremental

cost as is apparent from Fig. 3. The cheaper the unit, the higher

Fig. 9. Social welfare vs. DG size for the placement of DG7 at node 14.

Table 4

Result summary for the placement of DG with different cost characteristics

DG Best location Optimal DG

size (MW)

Social welfare

($/h)

Remarks

DG1 Bus 4 202.62 8460.47 CP based ranking

DG2 Bus 4 195.05 7586.12 CP based ranking

DG3 Bus 9 141.28 6427.09 –

DG4 Bus 14 41.94 4993.77 LMP based ranking

DG5 Bus 14 50.38 4848.79 LMP based ranking

DG6 Bus 14 42.84 4577.18 LMP based ranking

DG7 Bus 14 25.33 4483.04 LMP based ranking

the penetration and so is the net social welfare. Hence, the lower

incremental cost followed by higher penetration is found to favor

consumer payment based ranking given in Table 3.

4.7. DG placement for profit maximization

The present discussion encompasses the placement of the

same DG characteristics as the one considered for social welfare

maximization.

4.8. Placement of DG6

Fig. 10 shows the corresponding maximum profit at each load

bus after the placement of DG6. Fig. 11 shows the optimal DG

size corresponding to the maximum profit at each of the load bus.

The maximum profit of 75.135 $/h is found for the placement at

node 14. The corresponding optimal DG size is 21.76 MW which

is less than the value obtained for social welfare maximization

shown in Fig. 5.

The variation of profit with the penetration of DG6 at load

bus 14 is shown in Fig. 12. The maximum profit is found for the

optimal size as shown in Fig. 11.

As the penetration increases, LMP at a node will reduce.

If the LMP reduces to a value making the consumer payment

lower than the operating cost of DG, profit for DG owner would

be negative. This is apparent from Fig. 12 which shows that

beyond the optimal DG size, profit will decrease and can even

be negative if the penetration reaches a higher value.

Fig. 10. Maximum profit at respective nodes with DG6.


1634 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636

Fig. 11. Optimal DG size at respective nodes with DG6.

Fig. 12. Profit vs. DG size for placement of DG6 at node 14.

4.9. Placement of DG7

The profit that can be achieved to DG owner with the placement

of DG7 and corresponding optimal sizes at each of the load

buses is shown in Figs. 13 and 14, respectively. The variation

of profit with the penetration of DG7 at load bus 14 is shown in

Fig. 15.

Fig. 13. Maximum profit at respective nodes with DG7.

Table 5

Result summary for the placement of DG with different cost characteristic

DG Best location Optimal DG

size (MW)

Profit ($/h) Remarks

DG1 Bus 4 119.43 2766.58 CP based ranking

DG2 Bus 4 119.43 2260.33 CP based ranking

DG3 Bus 9 105.38 1592.49 –

DG4 Bus 11 37.29 470.72 –

DG5 Bus 4 50.46 323.53 –

DG6 Bus 14 21.76 75.14 LMP based ranking

DG7 Bus 14 12.55 29.25 LMP based ranking

Fig. 14. Optimal DG size at respective nodes with DG7.

Profit maximization results reveal that there is no profit for

DG owner when the placement is carried out at bus 5.

Results show that even for the DG with same cost characteristic,

profit maximization comes up with the lower optimal size

compared to social welfare maximization as can be seen from

Tables 4 and 5.

4.10. Comparison between social welfare and profit

maximization

Tables 6 and 7 show the comparative study of results obtained

from two placement techniques. The placement of DG6 and DG7

Fig. 15. Profit vs. DG size for placement of DG7 at node 14.


Table 6

Comparison of results for placement of DG6

D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) 1627–1636 1635

DG Bus Social welfare maximization Profit maximization

Social welfare ($/h) LMP ($/MWh) PDG (MW) Profit ($/h) LMP ($/MWh) PDG (MW)

14 4577.18 40.86 42.84 75.135 43.67 21.76

11 4563.29 40.97 48.69 70.818 43 25.87

10 4537.51 40.87 43.32 56.611 42.79 22.08

9 4524.67 40.94 46.88 52.136 42.87 19.53

13 4508.79 40.86 42.8 46.013 42.19 23.6

7 4455.76 40.59 29.59 9.864 44.39 2.26

4 4519.41 41.02 50.98 20.618 43.97 5.26

12 4475.75 40.56 28.14 26.905 41.95 14.99

5 4441.02 40.45 22.44 10.629 41.3 8.8

Table 7

Comparison of results for placement of DG7

DG Bus Social welfare maximization Profit maximization

Social welfare ($/h) LMP ($/MWh) PDG (MW) Profit ($/h) LMP ($/MWh) PDG (MW)

14 4483.04 43.15 25.33 29.249 43.112 12.55

11 4462.79 43.15 24.32 19.109 44.553 12.61

10 4452.27 43.11 19.02 13.655 44.386 10.07

9 4443.48 43.10 17.28 9.131 44.085 8.63

13 4431.32 43.07 11.82 3.09 43.527 6.07

7 4428.72 43.01 2.26 3.127 44.392 2.26

4 4431.57 43.03 5.26 5.033 43.973 5.26

12 4427.19 43.03 5.47 0.959 43.354 2.78

5 4425.31 41.65 0.00 0 41.646 0.00

is observed for social welfare as well as profit maximization

problem. The corresponding values of LMP at each of the nodes

after placing the optimal size of DG are tabulated.

5. Conclusions

The paper proposes two new methodologies of DG placement

in an OPF based wholesale electricity market. Optimal placement

and size is identified for social welfare as well as profit

maximization problem. For each DG cost characteristics, there

is an optimal location and size for which the net social welfare is

becoming maximum. The same condition is found to hold true

for profit maximization, as well.

For the DG placement at a node, social welfare maximization

ends up with lower LMP value compared to profit maximization.

Accordingly, optimal DG size for profit maximization is

lower than that for social welfare maximization. This is due

to the fact that social welfare is concerned with consumer as

well as producers surpluses; however, profit is concerned only

with the surplus to producers which will acquire high value

as the price increases. The high LMP results in higher consumer

payment with a consequent increase in the revenue to DG

owner.

DG penetration is found to reduce the dispatch of central

generation. The optimal placement and penetration is found to

depend on the cost characteristics of DG as well as those of

central generations. The DG with incremental cost lower than

the central generation is found to have a higher penetration in the

system, and similarly, the one with higher incremental cost, the

lower penetration. Considerable reduction in central generation

dispatch is observed with high DG penetration.

LMP and consumer payment have been identified as tools

for screening candidate nodes for DG placement. The DGs with

lower incremental cost compared to central generating stations

have a higher penetration and is found to follow the ranking

made on the basis of consumer payment. On the other hand, the

DGs with higher incremental cost have lower penetration and is

found to follow the ranking made on the basis of LMP.

It has also been observed that a high penetration of DG can

also lead to negative profit for the DG owner. The situation is

found to prevail when LMP reduces considerably due to high DG

penetration. If the LMP reduces to a value making the consumer

payment lower than the operating cost of DG, profit for DG

owner would be negative. Under such scenario, DG owner will

find no incentive for placement.

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