International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 1722

ISSN 2229-5518

Calculation of Nodal Pricing with Rescheduling of

Generators in Deregulated Power System

M. Bharathi1, J. Srinivasa Rao2

1M.Tech Student, Department of Electrical & Electronics Engineering, QIS College of Engineering & Technology,

Ongole, A.P, India.

2Associate Professor, Department of Electrical & Electronics Engineering, QIS College of Engineering & Technology, Ongole, A.P, India.

Abstract - The main objective of deregulation is to create competitive environment between producers and consumers. The transmission congestion is one of the technical problems that particularly appear in the deregulated power system. If congestion is not managed we face the problems of electricity price improvement, security and stability problems. Congestion relief can be handled using FACTS device such as TCSC and with the optimal power flow, where electricity price will be reduced. These FACTS devices are optimally placed on transmission system using Sensitivity approach method. The proposed methods are carried out on IEEE 14 bus system by using power world simulator 17 software.

Keywords - Deregulated power system, Nodal price, Optimal Power Flow (OPF), Thyristor Controlled Series Compensators (TCSC).

—————————— ——————————

In present days all our basic needs are relates with electricity. As the population increases, the demand for electricity increases. People are expecting better quality of

supply at most economical prices. This could only be achieved by unbundling the generation, transmission and distribution business and having sufficient competition in the power generation business. Overall this phenomenon is generally termed as deregulation. To induce efficient use of both the transmission grid and generation resources by providing correct economic signals, a nodal price or spot price theory for the deregulated power systems was developed [1], [2].

The deregulated electricity markets had to deal with number of issues such as congestion, losses, pricing, ancillary services, market power etc. [4]. The most fundamental of these is the problem of congestion. Fundamental concept on which these congestion management techniques are based on the Nodal price also called the Spot Price.

Nodal price is the marginal cost of supplying the next increment of electric energy at a specific bus while considering the generation marginal cost and the physical limits of the transmission system. More general Nodal price decomposition was presented in [7], [8], [9] with three components: marginal energy, loss, and congestion components.

Many of these now established technologies fall under the title of FACTS [10] (Flexible AC Transmission Systems). Introducing FACTS technology is used to controlling power

and losses in transmission line. To achieve minimum losses in transmission line, find the optimal place of transmission line & locate the FACTS device. Thyristor Controlled Series Capacitor (TCSC) is a variable impedance type FACTS device and is connected in series within the transmission line to increase the power transfer capability, improve transient stability, and reduce transmission losses [11].

Thyristor controlled series compensator (TCSC) is connected in series with transmission lines. It is equivalent to a controllable reactance inserted in series with a line to compensate the effect of the line inductance. The net transfer reactance is reduced and leads to an increase in power transfer capability. The basic structure of TCSC, shown in Figure 1.

Figure 1: Basic structure of Thyristor Controlled Series Capacitor

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The transmission line model with a TCSC connected between the two buses *i *and *j *is shown in Fig 3. Equivalent model is used to represent the transmission line. TCSC can be considered as a static reactance of magnitude equivalent

to−𝑗𝑋𝐶 . The controllable reactance is directly used as

control variable to be implemented in power flow equation

∗ = 𝑃

− 𝑄

= 𝑉∗ 𝐼

(1)

Figure 3: Model of Transmission line with TCSC.

𝑆𝑖𝑗

𝑖𝑗

𝑖𝑗

𝑖 𝑖𝑗

The active and reactive power loss in the line having TCSC

= ��𝑉𝑖 − 𝑉𝑗 �𝑌𝑖𝑗 + 𝑉𝑖 (𝑗𝐵𝑐 )�(2)

can be written as

𝑐 𝑐

∗ ∗ 𝑃𝐿 = 𝑃𝑖𝑗 + 𝑃𝑗𝑖

= 𝑉𝑖 {�𝐺𝑖𝑗 + 𝑗�𝐵𝑖𝑗 + 𝐵𝑐 �� − 𝑉𝑖 𝑉𝑗 (𝐺𝑖𝑗 + 𝑗𝐵𝑖𝑗 )}(3)

′ 2 2 ′

𝐺 + 𝑗𝐵 = 1 (4)

𝑅 +𝑗𝑋 −𝑗𝑋

= 𝐺𝑖𝑗 �𝑉𝑖

+ 𝑉𝑗 � − 2𝑉𝑖 𝑉𝑗 𝐺𝑖𝑗 cos(𝛿𝑖 − 𝛿𝑗 )(9)

𝐿 𝐿 𝑐

𝑐 + 𝑄𝑐

From the above equations the real and reactive power

equations can be written as

= −�𝑉𝑖

𝑗 𝑖𝑗

𝑄𝐿 = 𝑄𝑖𝑗

𝑠ℎ

𝑗𝑖

𝑖 𝑗

𝑖𝑗

𝑖 𝑗

2 + 𝑉2 ��𝐵′ + 𝐵

� + 2𝑉 𝑉 𝐵′ cos(𝛿

− 𝛿 )(10)

𝑃𝑖𝑗 = 𝑉2 𝐺 − 𝑉 𝑉 𝐺 cos(𝛿 − 𝛿 ) − 𝑉 𝑉 𝐵 sin�𝛿 − 𝛿 � (5)

𝑟𝑖𝑗

Where 𝐺 =

𝑖𝑗

𝑟𝑖𝑗 2

𝑄𝑖𝑗 = −𝑉2 �𝐵 + 𝐵 �

2 +(𝑥𝑖𝑗 −𝑥𝑐 )

′ (𝑥𝑖𝑗−𝑥𝑐)

− 𝑉𝑖 𝑉𝑗 𝐺𝑖𝑗 sin�𝛿𝑖 − 𝛿𝑗 �

𝐵𝑖𝑗 =− 𝑟2 +(𝑥

−𝑥 )2

+ 𝑉𝑖 𝑉𝑗 𝐵𝑖𝑗 cos�𝛿𝑖 − 𝛿𝑗 �(6)

𝑖𝑗

𝑖𝑗 𝑐

Similarly the real and reactive powers from bus *j *to *i *can

also be represented replacing *Vi *by *V*j.

Figure 2: Modal of transmission line.

The real and reactive power flow from bus- i to bus -j, of a line having series impedance and a series reactance are,

The change in the line flow due to series capacitance can be

represented as a line without series capacitance with power

injected at the receiving and sending ends of the line

asshowninFigure

Figure 4: Injection Model of TCSC.

The real and reactive power injections at bus-i and bus-j can be expressed as

𝑃𝑖𝑐 =

2 ∆𝐺

− 𝑉 𝑉 �∆𝐺

cos(𝛿 − 𝛿 � +

𝑐 = 𝑉2 𝐺 ′ − 𝑉 𝑉 𝐺 ′ cos(𝛿

− 𝛿 ) − 𝑉 𝑉 𝐵′ sin�𝛿 − 𝛿 � (7)

𝑉𝑖

𝑖𝑗

𝑖 𝑗

𝑖𝑗

𝑖 𝑗

𝑃𝑖𝑗

𝑖 𝑖𝑗

𝑖 𝑗

𝑖𝑗

𝑖 𝑗

𝑖 𝑗

𝑖𝑗

𝑖 𝑗

∆𝐵

sin(𝛿 − 𝛿 )] (11)

𝑖𝑗

𝑖 𝑗

𝑐 = −𝑉2 �𝐵′ + 𝐵 �

2 ∆𝐺

− 𝑉 𝑉 �∆𝐺

cos(𝛿 − 𝛿 � −

𝑄𝑖𝑗

𝑖 𝑖𝑗

𝑠ℎ

′

𝑃𝑗𝑐 = 𝑉𝑗

𝑖𝑗

𝑖 𝑗

𝑖𝑗

𝑖 𝑗

− 𝑉𝑖 𝑉𝑗 𝐺𝑖𝑗 sin�𝛿𝑖 − 𝛿𝑗 �

+ 𝑉𝑖 𝑉𝑗 𝐵𝑖𝑗 cos�𝛿𝑖 − 𝛿𝑗 �(8)

∆𝐵𝑖𝑗 sin(𝛿𝑖 − 𝛿𝑗 )](12)

𝑄𝑖𝑐 = −𝑉2 ∆𝐵 − 𝑉 𝑉 �∆𝐺 sin(𝛿 − 𝛿 �

Similarly the real and reactive powers from bus *j *to *i *can

also be represented replacing *Vi *by *V*j.

+ ∆𝐵𝑖𝑗

2

cos(𝛿𝑖

− 𝛿𝑗 )](13)

𝑄𝑗𝑐 = −𝑉𝑗 ∆𝐵𝑖𝑗 + 𝑉𝑖 𝑉𝑗 �∆𝐺𝑖𝑗 sin(𝛿𝑖 − 𝛿𝑗 �

− ∆𝐵𝑖𝑗 cos(𝛿𝑖 − 𝛿𝑗 )](14)

𝑟𝑖𝑗 𝑥𝑐 (𝑥𝑐 −2𝑥𝑖𝑗 )

Where ∆𝐺𝑖𝑗 = (𝑟2 +�𝑥

−𝑥 )2�(𝑟2 +𝑥 2 )

𝑖𝑗

𝑖𝑗 𝑐

𝑖𝑗

𝑖𝑗

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2 2

−𝑥𝑐 (𝑟𝑖𝑗 − 𝑥𝑖𝑗 + 𝑥𝑖𝑗 𝑥𝑐 )

∆𝐵𝑖𝑗 = (𝑟2 + �𝑥

− 𝑥 )2 �(𝑟2 + 𝑥2 )

𝑖𝑗

𝑖𝑗 𝑐

𝑖𝑗

𝑖𝑗

This Model of TCSC is used to properly modify the

parameters of transmission line with TCSC for optimal location

Generally, the location of FACTS devices depends on the objective of the installation. The reactive power loss sensitivity factors with respect to these control variables may be given as follows [17]:

1. Loss sensitivity with respect to control parameter of

𝑋𝑖𝑗 TCSC placed between buses i and j,

If we ignore the constraints in the network, the total load of

410 MW should be dispatched solely on the basis of bids or

marginal costs of the generators in a way that minimizes the total cost of supplying the demand. We have assumed that these generators have the constant marginal cost over the entire range of operation. The generators are ranked in order of increasing marginal cost and loaded up to their capacity limit [20].

𝑃𝐴 = 125MW

𝝏__ __𝑸𝑳

𝟐 𝟐

𝑹𝒊𝒋𝟐−𝑿𝒊𝒋𝟐

𝒂𝒊𝒋 = 𝝏

𝑿𝒊𝒋

= [𝑽𝒊 + 𝑽𝒋 − 𝟐𝑽𝒊𝑽𝒋 𝐜𝐨𝐬(𝜹𝒊 − 𝜹𝒋)] (𝑹𝒊𝒋𝟐+𝑿𝒊𝒋𝟐)𝟐(15)

𝑃𝐵 = 285MW

Where, 𝑉𝑖 is the voltage at bus i,

𝑉𝑗 is the voltage at bus j,

𝑅𝑖𝑗 is resistance of line between bus i and j,

𝑋𝑖𝑗 is the reactance connected between bus i and j.

In 1962, Carpentier introduced a generalized nonlinear programming (NLP) formulation of the economic dispatch (ED) problem including voltage and other constraints. The problem was later termed as OPF. Today OPF plays a very important role in power system operation and planning.

4.1 **Example 3 Bus System**

For example consider a simple three bus system. For three bus system branch data and generator data is given below.

Table 1: Branch data for the three bus system.

𝑃𝐶 = 0MW

𝑃𝐷 = 0 MW (16)

The total cost of economic dispatch is

𝐶𝐸𝐷1 = 𝑀𝐶𝐴 𝑃𝐴 + 𝑀𝐶𝐵 𝑃𝐵 = (7.5*125+6*285)

= 2647.50 $/h(17)

We would calculate the branch flows using a power flow diagram, this will be given below. We can write the power balance equation at each bus or node as follows.

Figure 5: Basic dispatch in three bus system.

Node 1: 𝐹12 + 𝐹13 = 157.28 + 202.68 = 360 𝑀𝑊(18)

Node 2: 𝐹12 − 𝐹23 = 157.28 − 97.28 = 60𝑀𝑊(19)

Node 3: 𝐹13

+ 𝐹23

= 202.68 + 97.28 = 300 𝑀𝑊(20)

Table 2: Generator data for the three bus system.

Generator Capacity(MW) Marginal cost

($/MWh)

The above three equations are linearly dependent, so it is

difficult to solve these equations. For example subtracting node 2equation from node 1equation gives node 3 equation, then one equation is eliminated with no loss of information, we are left with two equations with three unknowns. This is hardly surprising because we have not

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taken into account the impedances of the branches. Our original problem can be decomposed into two simpler

𝑥𝐵 = 𝑥 + 𝑥 = 0.1 + 0.2 = 0.3 *p.u *(28)

𝐴 = 𝑥

= 0.2*p.u *(29)

problems. By using the super position theorem we can

easilyfindtheflows.

𝑥2

12

0.3

𝐹12 = 𝐹 𝐴

+ 𝐹 𝐴 (21)

𝐹 𝐴 =

0.3 + 0.2

∗ 60 = 36𝑀𝑊(30)

𝐵 + 𝐹 𝐵 (22)

𝐹13 = 𝐹1 2

𝐵 0.2

𝐴 − 𝐹 𝐵 (23)

𝐹2

= ∗ 60 = 24𝑀𝑊(31)

0.3 + 0.2

𝐹23 = 𝐹1 2

The power flows in the original system are:

Let us consider the first problem. 300MW is injected at bus

1 and taken out at bus 3. Power flow along the paths A, B is

𝐹12 = 𝐹 𝐴 + 𝐹 𝐴 = 120 + 36 = 156 𝑀𝑊 (32)

1 2

𝐹 𝐴

+ 𝐹 𝐵

= 300𝑀𝑊(24)

𝐹13 = 𝐹 𝐵

+ 𝐹 𝐵

= 180 + 24 = 204𝑀𝑊 (33)

The reactances of paths A and B are

𝐹23 = 𝐹 𝐴

− 𝐹 𝐵

= 120 − 24 = 96𝑀𝑊(34)

𝑥 𝐴

= 𝑥12 + 𝑥23 = 0.1 + 0.2 = 0.3 *p.u*(25)

𝑥𝐵 = 𝑥 = 0.2 *p.u*

+

From the above results we conclude that the economic dispatch would overload the branch 1-2 by 30 MW because it would have to carry 156 MW when its capacity is only

126 MW. This is clearly not acceptable.

The economic dispatch minimizes the total production cost, but obtained solution is not acceptable because this is not satisfies the security criteria. Therefore we began least cost modifications that will remove the line overload. To reduce the flow on line 1-2, we can increase the generation at bus2 or bus 3.

Figure7: Flows for economic dispatch in three bus system.

Figure 6: Application of super position theorem to calculate line flows in three bus system.

Since these 300MW divides themselves between the two paths

bus 2 by 1MW. We neglect losses that must reduce the generation at bus 1 by 1MW.figure below shows the incremental re dispatch of the three bus system. In this

incremental flow ∆𝐹 𝐴 is the opposite direction to the flow 𝐹12, increasing the generation at bus 2 and reducing

𝐹 𝐴

𝐵

= 0.2 ∗ 300 = 120𝑀𝑊(26)

0.3+0.2

0.3

the generation at bus 1 will reduce the overload on branch

1-2.

𝐹1

= ∗ 300 = 180𝑀𝑊(27)

0.3 + 0.2

Similarly for second circuit 60 MW is injected at bus 1 and

taken out at bus 2. In this case, the impedances of the two paths are

Figure 8: Effect of incremental change in the generation at bus 2

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The reactances of paths A and B are

𝑥 𝐴 = 𝑥12 = 0.2 𝑝. 𝑢(35)

𝑥𝐵 = 𝑥13 + 𝑥23 = 0.3 𝑝. 𝑢(36)

Sum of two flows must be equal to 1 MW, we get

∆𝐹 𝐴 = 0.6𝑀𝑊 (37)

∆𝐹𝐵 = 0.4𝑀𝑊 (38)

Every megawatt injected at bus 2 and taken out at bus 1

thus reduces the flow on branch 1-2 by 0.6 MW. Line 1-2 is

overloaded by 30 MW, a total of 50MW of generation is shifted from bus 1 to bus 2 to satisfy line capacity constraint. Figure below shows the re dispatch and its superposition with the economic dispatch to obtain a constraindispatch.

(a) +

(b) =

(c)

Figure 9: Superposition of re dispatch of generation from bus 1 to bus

2 (b) on the economic dispatch (a) to produce a constrained dispatch that meets the constraints on line flows (c)

From the above figures it would be concluded that flow on the branch 1-3 is also reduces but the flow on the branch 2-3 is increases.

To produce the constrained dispatch generators connected at bus 1 must produce 360 MW to meet the local load of 50

MW and inject the 310 MW into the network. The generator at bus 2 must produce 50 MW and an additional 10 MW is taken from the network to supply a local load of 60 MW. The least cost generation dispatch is

𝑃𝐴 = 75 MW

𝑃𝐵 = 285 MW

𝑃𝐶 = 50 MW

𝑃𝐷 = 0 MW (39)

From the above equations, we comparing that output of

generator A has been reduced than that of output of

generator B, because the generator A has the highest

marginal cost.

The total cost of constrained dispatch is

𝐶𝐸𝐷2 = 𝑀𝐶𝐴 𝑃𝐴 + 𝑀𝐶𝐵 𝑃𝐵 + 𝑀𝐶𝑐 𝑃𝑐

= (7.5*75+6*285+14*50)= 2972.5 $/h (40)

Comparing the costs this cost is higher than the cost of the

economic dispatch. The difference represents the cost of

achieving the security using this re dispatch.

Figure 10: Effect of incremental change in the generation at bus 3.

Reactances of paths A and B are

𝑥𝐵 = 𝑥13 = 0.2 𝑝. 𝑢 (41)

𝑥 𝐴 = 𝑥12 + 𝑥23 = 0.3 𝑝. 𝑢 (42)

And the sum of two flows must be equal to 1MW

∆𝐹 𝐴 = 0.4𝑀𝑊 (43)

∆𝐹 𝐵 = 0.6𝑀𝑊 (44)

Every MW is injected at bus 3 and taken out at bus 1 that

reduces the flow on the branch 0.4 MW and increases the flow on the branch 1-3. This means that we need to shift

75MW of generation from bus 1 to bus 3 to reduce the overload on the branch 1-2. Below figures shows the superposing this re dispatch on the economic dispatch reduces the flows through all the branches of the network.

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(a) +

(b)=

(c)

Figure 11: super position of the re dispatch of generation from bus 1 to bus 3 (b) on the economic dispatch (a) to produce a constrained dispatch that meets the constraints on line flows (c)

Flow on the branch 1-2 is equal to the maximum capacity of that branch. Total power produced at bus 1 is now reduced by 75 MW the generation dispatch of this case is

𝑃𝐴 = 50 MW

𝑃𝐵 = 285 MW

𝑃𝐶 = 0 MW

𝑃𝐷 = 75 MW (45)

The total cost of this constrained dispatch is

𝐶𝐸𝐷3 = 𝑀𝐶𝐴 𝑃𝐴 + 𝑀𝐶𝐵 𝑃𝐵 + 𝑀𝐶𝐷 𝑃𝐷

= (7.5*50+6*285+10*75) = 2835 $/h (46)

Let us compare the ways of removing the over load on the

branch 1-2. If we make use of the generation at bus 3 we

would re dispatch 75 MW. On the other hand we make use of the generation at bus 2 we would re dispatch 50 MW. This is because flow on the branch 1-2 is less sensitivity at bus 3 compared to bus 2. Since marginal cost of generator D is less compared to generator C. So case 2 is more preferred. The difference between the cost of constrained dispatch and the cost of economic dispatch is the cost used to make the system more secure.

𝐶𝑆 = 𝐶𝐸𝐷3 − 𝐶𝐸𝐷1 = 2835 − 2647.5 = 187.5 $/��h (47)

The nodal marginal price is equal to the cost of supplying an additional megawatt of load at the node under consideration by the cheapest possible means.

In our above three bus example output of generator D has been increased to remove overload on the branch 1-2. At node 1 it is clear that an additional megawatt of load should be produced by generator A. The marginal cost of generator A is lower than the marginal cost of generators C, D, while it is higher than the generator B. Generator B is already loaded up to their maximum capacity and therefore it is unable to produce additional megawatt.

The nodal marginal price at bus 1 is

𝜋1 = 𝑀𝐶𝐴 = 7.5 $/𝑀𝑊ℎ (48)

Increasing the generation at bus 1 then overload the branch

1-2. The next cheapest option is to increase the output of

generator D. Since generator is located at bus 3. So the nodal marginal price at bus 3 is

𝜋3 = 𝑀𝐶𝐷 = 10 $/𝑀𝑊ℎ (49)

Supplying an additional MW at bus 2 is more complex

matter we could generate it locally at bus 2 using the generator C. But it is more expensive because the marginal cost of generator C is 14 $/MWh, it is higher than all the generators marginal cost.

(a)

(b)

Figure 12: Incremental flows in the network due to an additional MW of load at node 2 when the MW is produced at (a) bus 1 (b) bus 3.

We can see that in both cases the power flow on the branch

1-2 is increased. Since flow on the branch 1-2 is reached its maximum capacity so neither solution is acceptable. We would increase the generation at bus 3 by 2 MW and reduce it at bus 1 by 1MW. The net increase is additional load at bus 2. Below diagrams shows this.

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In summary, we observe that

= 11.25 $/𝑀𝑊ℎ (54)

Figure 13: Application of super position theorem diagrams.

The first diagram shows that if 1 MW is injected at bus 3 and taken out at bus 1, the flow on the branch 1-2 would decrease by 0.4 MW. The other diagram shows that another

1MW is injected at bus 3 and taken out at bus 2 increases

the flow on the branch by o.2 MW. This is acceptable because the total flow on the branch 1-2 is decreases by 0.2

MW and it is below the maximum capacity limit, and it is

not optimal 1 ∆𝐹12 = 0 2

∆𝑃1 ∆𝑃2 = 1𝑀𝑊

3 ∆𝑃3

Figure14: Formulation of an additional megawatt of load at bus 2

without changing the flow on the branch 1-2.

We can supply an additional megawatt at bus 2 by redispatching generation at buses 1 and 3 without overloading branch 1-2. We must have

∆𝑃1 + ∆𝑃3 = ∆𝑃2 = 1𝑀𝑊(50)

Using the sensitivities shown in the figure 12, we can also

write

• Generator A sets a price of 7.5 $/MWh at bus 1.

Generator B has the lowest marginal cost 6.0

$/MWh but has no influence on nodal prices

because it operates at its maximum capacity.

• Generator D has a nodal price of 10 $/MWh at bus

3.

• At bus nodal price is set to 11.25 $/MWh by a

combination of other generators.

The study has been conducted on the calculation of nodal prices of an IEEE14 bus system using power world simulator 17.0.

For this system nodal prices are calculated by placing the FACTS device TCSC in optimal location using sensitivity approach method and with optimal power flow method.

This system consists of 14 buses, 17 line sections, 5 generator buses and 8 load buses.

The below figure shows the transmission line flows. The nodal prices of IEEE 14 bus system is as follows.

Figure 15: single line diagram of IEEE 14 bus system.

0.6∆𝑃1 + 0.2∆𝑃3 = ∆𝐹12 = 0𝑀𝑊(51)

Solving the above two equations, we get

∆𝑃1 = −0.5 MW (52)

∆𝑃3 = 1.5 MW (53)

Supplying at minimum cost an additional megawatt at bus

2 therefore requires that we increase the output of

generator D by 1.5 MW and reduce the output of generator

A by 0.5 MW. Hence the nodal price at bus 2 is

𝜋2 = 1.5 𝑀𝐶𝐷 − 0.5 𝑀𝐶𝐴 = 1.5 ∗ 10 − 0.5 ∗ 7.5

Table 3: Nodal prices of IEEE 14 bus system

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4 | 5467.05 | 5000 | 138.56 | 328.49 |

5 | 5381.41 | 5000 | 112.49 | 268.92 |

6 | 5525.22 | 5000 | 270.55 | 254.67 |

7 | 5168.85 | 5000 | -169.94 | 338.79 |

8 | 5173.3 | 5000 | -163.85 | 337.14 |

9 | 5937.6 | 5000 | 590.19 | 347.4 |

10 | 5907.36 | 5000 | 590.19 | 367.61 |

11 | 5740.61 | 5000 | 408.99 | 331.62 |

12 | 5649.22 | 5000 | 296.73 | 352.48 |

13 | 5713.56 | 5000 | 325.27 | 388.29 |

14 | 5990.61 | 5000 | 491.62 | 498.99 |

Nodal price is sum of energy component cost, loss component cost and a congestion component cost. In IEEE

14 bus system congestion is formed so the congestion cost is included so the total nodal price is increases. To minimize the congestion cost we will use rescheduling of generators (optimal power flow control) so the total cost is decreases.

Figure 16: single line diagram of IEEE 14 bus system with OPF.

Table 4: Nodal prices of IEEE 14 bus system with OPF.

By using optimal power flow control congestion cost is zero but the losses cost is exist so we minimize the losses in the system by placing different FACTS devices like TCSC in optimal location using sensitivity approach method. By using TCSC congestion and losses are going to be reduced.

The sensitivity indices table of IEEE 14 bus system is shown below.

Table 5: Sensitivity indexes for IEEE 14 bus system.

Bus Number | MW Marg. Cost $/MWh | Energy cost $/MW h | Congestio n cost $/MWh | Losses cost $/MW h |

1 | 5000 | 5000 | 0 | 0 |

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7 | 4 | 5 | -0.1068 | -0.0986 | -0.0866 |

8 | 4 | 7 | -0.0102 | -0.0142 | -0.0217 |

9 | 4 | 9 | -0.0079 | -0.0079 | -0.0081 |

10 | 5 | 6 | -0.061 | -0.0678 | -0.0793 |

11 | 6 | 11 | -0.0059 | -0.0044 | -0.0027 |

12 | 6 | 12 | -0.0035 | -0.0026 | -0.0016 |

13 | 6 | 13 | -0.0185 | -0.0135 | -0.0072 |

14 | 7 | 8 | -0.0778 | -0.0787 | -0.0808 |

15 | 7 | 9 | -0.1297 | -0.1293 | -0.1288 |

16 | 9 | 10 | -0.00099 | -0.00087 | -0.00074 |

17 | 9 | 14 | -0.0037 | -0.0029 | -0.0018 |

18 | 10 | 11 | -0.0028 | -0.0022 | -0.0016 |

19 | 12 | 13 | 0.000152 | 0.000199 | 0.000235 |

20 | 13 | 14 | -0.0027 | -0.002 | -0.0011 |

From the above table 5 the line12-13 have the most positive sensitivity index. So this is the best location for placement of TCSC to relieve congestion and minimize the losses in the network. The single line diagram of IEEE 14 bus system after placing TCSC is shown below.

12-13.

After placing TCSC in line 12-13, the congestion in the network is relieved and also losses are minimized. So the nodal prices of the system are reduced. The nodal prices of IEEE 14 bus system with TCSC are shown below.

Table6: Nodal prices of IEEE 14 bus system with TCSC.

Comparison of Nodal prices without compensation, with

TCSC and with OPF are as follows.

Table 7.5: Nodal price list without compensation, with

TCSC and with OPF of an IEEE 14 bus system

Nodal prices $/MWh

Bus Number | MW Marg. Cost $/MWh | Energy cost $/MWh | Congestion cost $/MWh | Losses cost $/MWh |

1 | 5000 | 5000 | 0 | 0 |

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6500

6000

5500

5000

4500

1 3 5 7 9 11 13

without comp with TCSC with OPF

[6] A.J. Conejo, E. Castillo, R. Mínguez and F. Milano, "Locational

Marginal Price Sensitivities," IEEE Trans. Power Syst., vol. 20, no.

4, pp. 2026- 2033, Nov. 2005

[7] R. J. Kaye, F. F. Wu, and P. Varaiya, “Pricing for system security in *Proc. IEEE Winter Power Meeting*, 1992, Paper 92-WM-100-8.

[8] S. Oren, P. Spiller, P. Varaiya, and F. F.Wu, “Nodal prices and

Graph 1: Nodal price comparison without compensation, with TCSC

and with OPF of an IEEE 14 bus system.

The challenge for engineers is to produce and provide an electrical energy to consumers in a safe, economical and environmentally friendly manner under various constraints. In deregulated environment, the location of FACTS devices and their control can significantly affect the operation of the system.

In this paper a simple sensitivity approach is proposed, it will give a solution for determining optimal location of FACTS devices in a deregulated power system to relieve congestion on system and then nodal prices of the system reduces. An optimal power flow model minimizing the congestion cost for re - dispatch of generators and then congestion cost is reduces to zero, then nodal prices of the system reduces. This method was successfully tested on IEEE 14 bus system. The nodal prices with OPF and with FACT device were described in this paper.

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————————————————

M.BHARATHI is an M-Tech candidate at QIS college of Engineering

& Technology under JNTU, Kakinada. She received her B-Tech degree from QIS college of Engineering & Technology under JNTU Kakinada.

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ISSN 2229-5518

Her current research interests are FACTS applications on transmission systems, Power System Deregulation.

J.SRINIVASARAO is an associate professor in QIS College of Engineering &Technology at Ongole. He is a Ph.D candidate. He got his M-Tech degree from JNTU Hyderabad and his B-Tech degree from RVRJC Engineering College, Guntur. His current research interests are power systems, power systems control and automation, Electrical

Machines, power systems deregulation, FACTS applications.

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