Optimal DG placement in deregulated electricity market - School of ...

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 onl**in**e 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**, **in**clud**in**g size, is

formulated for two different objectives, namely, social welfare maximization and pr**of**it maximization. The candidate locations for **DG** **placement**

are identified on the basis **of** locational marg**in**al price (LMP). Obta**in**ed as lagrangian multiplier associated with active power flow equation for

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

bus, is proposed as another rank**in**g to identify candidate nodes for **DG** **placement**. The proposed rank**in**gs bridges eng**in**eer**in**g aspects **of** system

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

order to provide a scenario **of** variety **of** **DG**s 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 marg**in**al price; **Optimal** power flow; Electricity **market**; Social welfare

1. Introduction

**DG**s are considered as small power generators that complement

central power stations by provid**in**g **in**cremental capacity

to power system. Although **DG**s may never replace the central

power stations, these can be an attractive option when constra**in**ts

**in** transmission network prevent economic, or least expensive,

supply **of** energy reach**in**g demand. However, penetration and

viability **of** **DG** at a particular location is **in**fluenced by technical

as well as economic factors. The technical merits **of** **DG**

implementation **in**clude voltage support, energy-loss reduction,

release **of** system capacity, and improve utility system reliability

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

aga**in**st high **electricity** price. This **in**centive is enhanced with

vertical unbundl**in**g **of** utilities and **market** mechanisms such as

real time pric**in**g. By supply**in**g loads dur**in**g peak load periods,

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

hedg**in**g mechanism.

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

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

∗ Correspond**in**g 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** **DG**s **in** power system. Capacity **in**vestment plann**in**g **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, **in**clud**in**g artificial **in**telligence techniques,

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

also proposed for achiev**in**g the optimal **placement** **of** **DG**. An

optimization approach us**in**g GA for m**in**imiz**in**g the cost **of** network

**in**vestment and losses for a def**in**ed plann**in**g horizon is

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

level **of** **DG** for m**in**imiz**in**g the total cost **of** operation **in**clud**in**g

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

**placement** **of** **DG** for m**in**imiz**in**g real power losses **in** power distribution

system us**in**g GA is proposed **in** Ref. [6]. The gradient

and second order methods to determ**in**e the optimal location for

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

the m**in**imization **of** losses or l**in**e load**in**g is employed **in** Ref.

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

optimal **placement** **of** **DG** for loss m**in**imization is demonstrated

**in** Ref. [8]. Analytical methods for determ**in****in**g optimal location

**of** **DG** with the aim **of** m**in**imiz**in**g 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 m**in**imization is proposed **in** Ref. [10]. **Optimal**

**placement** **of** **DG** with Langrangian based approach us**in**g traditional

pool based OPF and voltage stability constra**in**ed 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, maximiz**in**g

social welfare and maximiz**in**g the pr**of**it **of** **DG** owner.

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

the OPF formulation deal**in**g with social welfare maximization

problem. Section 3 presents the methodology adopted to evaluate

the **placement** **of** **DG** where**in** the rank**in**gs used to identify

the candidate nodes for the **placement** are also discussed. The

OPF results and **in**ferences 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 dist**in**ct objective

functions, namely, social welfare maximization and pr**of**it maximization.

Social welfare is def**in**ed as the difference between

total benefit to consumers m**in**us 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

marg**in**al cost **of** produc**in**g the last unit **of** **electricity** [12].

The traditional OPF algorithm for cost m**in**imization is modified

to **in**corporate the demand bids, **in** addition to the generation

bids. LMP is determ**in**ed 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 **in**puts to OPF. The base case OPF based on social

welfare maximiz**in**g algorithm evaluates the generation dispatch,

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

obta**in**ed are **in**dicator for identify**in**g candidate nodes for **DG**

**placement**. The **placement** is **in**tended to meet the demand at a

lower price by chang**in**g the dispatch scenario.

The pr**of**it 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 pr**of**it. As higher LMP

value might considerably lower the revenue mak**in**g the pr**of**it

negative.

2.1. Social welfare maximization

The objective function is formulated as quadratic benefit

curve submitted by the buyer (DISCO) m**in**us quadratic bid

curve supplied by seller (GENCO) m**in**us the quadratic cost

function supplied by **DG** owner.

N

max

(Bi(PDi) − Ci(PGi)) − C(P**DG**i) (1)

i=1

Alternatively, the maximization problem (1) can be formulated

as a m**in**imization problem with multiply**in**g the objective

function by −1.

N

m**in** (Ci(PGi) − Bi(PDi)) + C(P**DG**i)

(2)

i=1

subject to

2.2. Equality constra**in**ts

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, **in**jected **in**to a node

m**in**us the power flows extracted from the node has to be zero.

Pi = PGi + P**DG**i − PDi = vi

j=1

N

[vj{Gij cos(δi − δj)

+Bij s**in**(δi − δj}] (3)

Qi = QGi − QDi = vi

j=1

N

[vj{Gij s**in**(δi − δj)

−Bij cos(δi − δj}] (4)

2.3. Inequality constra**in**ts

Generation limits:

The generat**in**g plants have a maximum and m**in**imum generat**in**g

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. Generat**in**g limits are specified

as upper and lower limits for the real and reactive power

outputs.

Real power generation limits:

P m**in**

Gi ≤ PGi ≤ P max

Gi

Reactive power generation limits:

Q m**in**

Gi ≤ QGi ≤ Q max

Gi

L**in**e flow limit:

The l**in**e flow limit specifies the maximum power that a

given transmission l**in**e is capable **of** transmitt**in**g under given

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

Thermal limits are usually considered for shorter

l**in**es. The follow**in**g constra**in**t checks for the absolute power

flow both at send**in**g and receiv**in**g ends **of** particular l**in**e to be

with**in** the upper limit **of** the l**in**e.

Sij ≤ S max

ij

Sji ≤ S max

ji

Bus voltage limit:

Voltage limits refer to bus voltage to rema**in** with**in** an allowable

narrow range **of** levels.

v m**in**

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; P**DG**i 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 **of**fer (bid) price at bus i;

C(P**DG**i)=a**DG**i + b**DG**i P**DG**i + c**DG**i(P**DG**i) 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 l**in**e ij; Gij denotes the conductance **of** the

l**in**e ij; QGi denotes reactive power generated at bus i; P max

Gi

and Pm**in** Gi denotes upper and lower real power generation

limits **of** generator at bus i; Qmax Gi and Qm**in**

Gi denote upper and

lower reactive power generation limits **of** generator at bus i;

vmax i and vm**in** 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 l**in**e ji.

and S max

ji denote the complex power flow limit for l**in**e ij

For base case OPF,

P**DG**i = 0

For load bus,

PGi = 0

For generator bus,

PDi = 0

P**DG**i = 0

2.4. Pr**of**it maximization

The pr**of**it maximization formulation constitutes two nested

blocks. The **in**ner block is handled by the **in**dependent 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 be**in**g one **of** the **market** participants, lies outside the

block and submits the **DG** size they are will**in**g to penetrate **in**

the **market**. ISO then runs OPF tak**in**g **in**to consideration the network

constra**in**ts. The objective **of** this OPF is to m**in**imize the

total costs. This block allows overall control and coord**in**ation **of**

generation and transmission. The LMP obta**in**ed from the OPF

is used by the **DG** owner **in** order to calculate the pr**of**it which

is evaluated as revenue m**in**us cost for the particular **DG**. The

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

The pr**of**it with **DG** **placement** at each **of** the node is evaluated

as:

Pr**of**iti = λi × P**DG**i − C(P**DG**i) (5)

where P**DG**i denotes the **DG** size at node i; λi denotes

the LMP at node i after plac**in**g **DG**; C(P**DG**i)=a**DG**i +

b**DG**iP**DG**i + c**DG**i(P**DG**i) 2 denotes the cost characteristic **of** **DG**

at node i.

The optimization process will identify the node and correspond**in**g

optimal **DG** size that will br**in**g maximum pr**of**it to the

**DG** owner.

3. Methodology

For a specific comb**in**ation **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

obta**in**ed from the lagrangian multipliers **of** the non-l**in**ear equality

constra**in**ts. The **in**creas**in**g functions for supplier bids and

decreas**in**g functions for the consumer bids are treated as the

marg**in**al cost or benefits **of** the bidder. The difference **in** prices

results from active l**in**e constra**in**ts and losses **in** the transmission

system.

To identify candidate nodes for the **placement** **of** **DG**, two

rank**in**gs are def**in**ed, namely, LMP based rank**in**g and consumer

payment (CP) based rank**in**g.

3.1. Locational marg**in**al price (LMP) based rank**in**g

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 constra**in**t

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

components, a marg**in**al energy component (same for all buses),

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

a marg**in**al loss component and a congestion component. Consider**in**g

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 marg**in**al energy component at the reference bus

which is same for all buses, λL,i = λ(∂PL/∂Pi) is the marg**in**al 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 po**in**t, factor**in**g **in**to

account constra**in**ts 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 **in**dication that for

the objective **of** social welfare maximization, **in**jection **of** active

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

**DG** is assumed to **in**ject real power at a node, the node with highest

LMP will have first priority for **DG** **placement**. Accord**in**gly,

the load buses are ranked **in** descend**in**g 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 = **in**dex {max(LMP)} (9)

3.2. Consumer payment based rank**in**g

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 = **in**dex {max(CP)} (11)

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

pay for the **electricity**. The rank**in**g is **in**fluenced from the fact that

**market** for **DG** **placement** can be viewed from two standpo**in**ts.

(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 rank**in**g based on consumer payment is **in**tended to focus

on the later scenario where**in** total nodal payment is given the

priority rather than the high price. The rank**in**g will have overall

effect **of** reduc**in**g dom**in**ant loads **in** the system. In effect, LMP

goes down and the dom**in**ant customer would be better **of**f, 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 **in**tended

to br**in**g down the LMP, **DG** with operat**in**g cost higher than LMP

will f**in**d no **in**centive for **placement**. The **DG** with operat**in**g 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 pr**of**it 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 vary**in**g operat**in**g

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 reciprocat**in**g eng**in**es and gas turb**in**es 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** **DG**s considered **in** this work.

The cost comparison among the various units is made as per

the **in**cremental cost. Incremental cost is a function **of** power output

**of** the unit where slope **in**dicates cost to produce **in**cremental

quantity and **in**tercept **in**dicates no load cost. Other conditions

rema**in****in**g the same, the lesser the slope, the lower the **in**cremental

cost and higher the penetration. The cross**in**g over **of**

two different **in**cremental cost characteristics reveals that operational

cost effectiveness depends on power output. The cross**in**g

over is determ**in**ed by no load cost and slope **of** the curve. The

Table 1

Distributed generation data

**DG** ID a**DG** b**DG** c**DG**

**DG**1 0.002 15 0

**DG**2 0.004 19 0

**DG**3 0.04303 20 0

**DG**4 0.25 20 0

**DG**5 0.1 30 0

**DG**6 0.01 40 0

**DG**7 0.003 43 0

Note: a**DG**, b**DG**, c**DG** 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 certa**in** 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 accord**in**gly, **in**tersection at several po**in**ts. Hence,

the comparative study **of** operational cost among the units relies

on power output.

The **in**cremental cost characteristics **of** various **DG**s considered

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

**of** **DG**1 and **DG**2 is very small, their **in**cremental cost is almost

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

the **DG**6 and **DG**7. However, **DG**3, **DG**4 and **DG**5 show monotonically

**in**creas**in**g **in**cremental cost with crossover at several

po**in**ts.

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

Rank**in**g 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 (lagg**in**g). 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 correspond**in**g to the maximum social welfare for the

base case are determ**in**ed 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 exceed**in**g 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** determ**in****in**g LMP. The rank**in**g **of** the load buses accord**in**g

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 determ**in**ed

from the social welfare maximiz**in**g 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

Rank**in**g 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 obta**in**ed from these optimal sizes is

different from one load bus to another. Another worth noticeable

po**in**t 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 obta**in**ed 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 exist**in**g central generation. The results associated with two

expensive **DG**s, namely, **DG**6 and **DG**7 are presented as sample

results. However, summary **of** the results for all **DG**s are given

**in** the end **of** this section.

4.5. Placement **of** **DG**6

The maximum net social welfare that can be achieved when

the **placement** **of** **DG**6 is carried out at different load buses is

shown **in** Fig. 4.

The correspond**in**g optimal **DG** size at each **of** the load bus

is also shown **in** Fig. 5. For **in**stance, 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 giv**in**g the social welfare **of** 4563.29 $/h is

48.69 MW and so on. It is **in**terest**in**g to note that net social welfare

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

optimal **placement** **of** **DG**6 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 rank**in**g given **in** Table 2. Moreover,

the rank**in**g 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 obta**in**ed for two

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

obta**in**ed only for the optimal **DG** size.

Fig. 4. Net social welfare at respective nodes with **DG**6.

Fig. 5. **Optimal** **DG** size at respective nodes with **DG**6.

4.6. Placement **of** **DG**7

The maximum net social welfare that can be achieved when

the **placement** **of** **DG**7 is carried out each **of** the load buses is

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

is obta**in**ed when the **placement** is made at node 14. Correspond**in**g

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

optimal size compared to the **placement** **of** **DG**6 can be attributed

to higher **in**cremental cost **of** **DG**7.

The optimal size **of** **DG** after plac**in**g **DG**7 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 rank**in**g based on LMP.

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

for the **placement** **of** **DG**7 at node 14 is shown **in** Fig. 9.

Results revealed that **placement**s as well as sizes vary with

the cost characteristics. The summary **of** results correspond**in**g

to the **placement** **of** all the seven **DG**s considered **in** the study is

given **in** Table 4.

Fig. 6. Social welfare vs. **DG** size for the **placement** **of** **DG**6 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 **DG**7.

Fig. 8. **Optimal** **DG** size at respective nodes with **DG**7.

Interest**in**gly, it is observed that for the **placement** **of** **DG**1

and **DG**2, 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 rank**in**g rather than

LMP rank**in**g. Furthermore, as shown **in** Table 4 the penetration

**of** **DG**1 and **DG**2 is higher compared to that **of** **DG**6 and **DG**7.

The higher penetration can be attributed to the lower **in**cremental

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

Fig. 9. Social welfare vs. **DG** size for the **placement** **of** **DG**7 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

**DG**1 Bus 4 202.62 8460.47 CP based rank**in**g

**DG**2 Bus 4 195.05 7586.12 CP based rank**in**g

**DG**3 Bus 9 141.28 6427.09 –

**DG**4 Bus 14 41.94 4993.77 LMP based rank**in**g

**DG**5 Bus 14 50.38 4848.79 LMP based rank**in**g

**DG**6 Bus 14 42.84 4577.18 LMP based rank**in**g

**DG**7 Bus 14 25.33 4483.04 LMP based rank**in**g

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

**in**cremental cost followed by higher penetration is found to favor

consumer payment based rank**in**g given **in** Table 3.

4.7. **DG** **placement** for pr**of**it maximization

The present discussion encompasses the **placement** **of** the

same **DG** characteristics as the one considered for social welfare

maximization.

4.8. Placement **of** **DG**6

Fig. 10 shows the correspond**in**g maximum pr**of**it at each load

bus after the **placement** **of** **DG**6. Fig. 11 shows the optimal **DG**

size correspond**in**g to the maximum pr**of**it at each **of** the load bus.

The maximum pr**of**it **of** 75.135 $/h is found for the **placement** at

node 14. The correspond**in**g optimal **DG** size is 21.76 MW which

is less than the value obta**in**ed for social welfare maximization

shown **in** Fig. 5.

The variation **of** pr**of**it with the penetration **of** **DG**6 at load

bus 14 is shown **in** Fig. 12. The maximum pr**of**it is found for the

optimal size as shown **in** Fig. 11.

As the penetration **in**creases, LMP at a node will reduce.

If the LMP reduces to a value mak**in**g the consumer payment

lower than the operat**in**g cost **of** **DG**, pr**of**it for **DG** owner would

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

beyond the optimal **DG** size, pr**of**it will decrease and can even

be negative if the penetration reaches a higher value.

Fig. 10. Maximum pr**of**it at respective nodes with **DG**6.

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

Fig. 11. **Optimal** **DG** size at respective nodes with **DG**6.

Fig. 12. Pr**of**it vs. **DG** size for **placement** **of** **DG**6 at node 14.

4.9. Placement **of** **DG**7

The pr**of**it that can be achieved to **DG** owner with the **placement**

**of** **DG**7 and correspond**in**g optimal sizes at each **of** the load

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

**of** pr**of**it with the penetration **of** **DG**7 at load bus 14 is shown **in**

Fig. 15.

Fig. 13. Maximum pr**of**it at respective nodes with **DG**7.

Table 5

Result summary for the **placement** **of** **DG** with different cost characteristic

**DG** Best location **Optimal** **DG**

size (MW)

Pr**of**it ($/h) Remarks

**DG**1 Bus 4 119.43 2766.58 CP based rank**in**g

**DG**2 Bus 4 119.43 2260.33 CP based rank**in**g

**DG**3 Bus 9 105.38 1592.49 –

**DG**4 Bus 11 37.29 470.72 –

**DG**5 Bus 4 50.46 323.53 –

**DG**6 Bus 14 21.76 75.14 LMP based rank**in**g

**DG**7 Bus 14 12.55 29.25 LMP based rank**in**g

Fig. 14. **Optimal** **DG** size at respective nodes with **DG**7.

Pr**of**it maximization results reveal that there is no pr**of**it for

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

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

pr**of**it 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 pr**of**it

maximization

Tables 6 and 7 show the comparative study **of** results obta**in**ed

from two **placement** techniques. The **placement** **of** **DG**6 and **DG**7

Fig. 15. Pr**of**it vs. **DG** size for **placement** **of** **DG**7 at node 14.

Table 6

Comparison **of** results for **placement** **of** **DG**6

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

**DG** Bus Social welfare maximization Pr**of**it maximization

Social welfare ($/h) LMP ($/MWh) P**DG** (MW) Pr**of**it ($/h) LMP ($/MWh) P**DG** (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** **DG**7

**DG** Bus Social welfare maximization Pr**of**it maximization

Social welfare ($/h) LMP ($/MWh) P**DG** (MW) Pr**of**it ($/h) LMP ($/MWh) P**DG** (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 pr**of**it maximization

problem. The correspond**in**g values **of** LMP at each **of** the nodes

after plac**in**g 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 pr**of**it

maximization problem. For each **DG** cost characteristics, there

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

becom**in**g maximum. The same condition is found to hold true

for pr**of**it maximization, as well.

For the **DG** **placement** at a node, social welfare maximization

ends up with lower LMP value compared to pr**of**it maximization.

Accord**in**gly, optimal **DG** size for pr**of**it 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, pr**of**it is concerned only

with the surplus to producers which will acquire high value

as the price **in**creases. The high LMP results **in** higher consumer

payment with a consequent **in**crease **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 **in**cremental cost lower than

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

system, and similarly, the one with higher **in**cremental 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 screen**in**g candidate nodes for **DG** **placement**. The **DG**s with

lower **in**cremental cost compared to central generat**in**g stations

have a higher penetration and is found to follow the rank**in**g

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

**DG**s with higher **in**cremental cost have lower penetration and is

found to follow the rank**in**g made on the basis **of** LMP.

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

also lead to negative pr**of**it 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 mak**in**g the consumer

payment lower than the operat**in**g cost **of** **DG**, pr**of**it for **DG**

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

f**in**d no **in**centive for **placement**.

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