


ARTICLE 

Year : 2012  Volume
: 2
 Issue : 1  Page : 2431 

Congestion Management in Pool Electricity Markets with Loadability Limits
Charan Sekhar, Ashwani Kumar
Department of Electrical Engineering, NIT, Kurukshetra, India
Date of Web Publication  24Mar2012 
Correspondence Address: Charan Sekhar Department of Electrical Engineering, NIT, Kurukshetra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09768580.93219
Abstract   
In a restructured electricity market environment, when the producers and consumers of electric energy desire to produce and consume in amounts that would cause the transmission network to operate at or beyond one or more transfer limits, the system is said to be congested. The congestion in the system cannot be allowed to persist for a long time, as it can cause sudden rise in the electricity price and threaten system security and reliability. Congestion management (CM) is one of the most important challenging tasks of the Independent System Operator (ISO) in the deregulated environment. In this article, generators' reschedulingbased CM approach to manage transmission line congestion considering voltage stability limit has been presented for poolbased electricity market model. The results have also been obtained without taking loadability limit for comparison. The results have been obtained for IEEE 24 bus test system. Keywords: Bid function, congestion management, generator redispatch, loadability limit, pool electricity market
How to cite this article: Sekhar C, Kumar A. Congestion Management in Pool Electricity Markets with Loadability Limits. J Eng Technol 2012;2:2431 
1. Introduction   
With increasing demand of electricity all over the world, electric utilities are forced to meet the demand by installing more conventional power plants and also seeking other options of increasing generation using the renewable energy resources. The transmission network also needs expansion to transfer the growing demand of power. However, with increasing pressure from environmental concern and right of way problems, the utilities are going for multitransmission towers and using the existing transmission structure near to their physical limits. The transmission network thus restricted to carry power due to the transient stability, voltage stability, or thermal limits can violate its physical limits to carry more power which leads to the congestion in the transmission network. This congestion cannot be allowed to persist in the network for a long time in a competitive environment as it may threaten power system security and increase the price of electricity, thus causing market inefficiency. Congestion management (CM) is one of the critical and important tasks of SO and it manages the congestion using different techniques may be cost free or cost based ^{[1]} . Shirmmohamaadi et al. presented the basic transmission dispatch and CM model for CM ^{[2]} . The basic concepts of transmission management, dispatch model, and role of the SO and its model are presented nicely.
The CM methods can be cost free and noncost free. The ISO tries costfree methods first to manage transmission line congestion using transformer taps, rerouting of lines, or the outage of congested lines. However, the outage of lines can further aggravate the problem of congestion. These solutions may not help the ISO for CM and the ISO seeks other marketbased solutions to manage the congestion more effectively.
Many authors presented optimal power flowbased CM schemes minimizing the congestion cost by redispatching the generators ^{[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18]} . Fang and David ^{[3],[4]} proposed a transmission dispatch methodology as an extension of spot pricing theory in a pool and bilateral as well as multilateral transactions model. Prioritization of electricity transactions and willingnesstopay for minimum curtailment strategies have been investigated as a practical alternative to deal with the congestion. Authors in ^{[5]} proposed FACTSbased curtailmentbased strategy based on ^{[4]} for CM. Singh et al. ^{[6]} proposed approaches for CM based on OPF, which uses DC load flow model to minimize the congestion cost for poolco model and bilateral model. The nodal pricing theory has been applied in the pool model, whereas a method based on congestion cost allocation has been suggested for bilateral model. An optimal power flowbased approach using nodal congestion price signals for computing the optimal power output of generators has been proposed in ^{[7]} .
A combined zonal and Fixed Transmission Right (FTR) scheme for CM has been proposed in ^{[8]} . The combined scheme has been used with locational marginal prices (LMPs) to define zonal boundaries appropriately. An OPF approach based on DC load flow and AC load flow has been formulated to minimize the net cost of redispatch to manage interzonal and intrazonal congestion ^{[9]} . A novel Lagrangian Relaxationbased algorithm for area decomposition OPF, minimizing the congestion cost of redispatch to deal with the multizone CM, has been proposed in ^{[10]} . Both interzonal and intrazonal CM problem has been formulated. A similar method with augmented Lagrangian Relaxationbased algorithm has been proposed in ^{[11]} . Bompard et al. ^{[12]} developed a unified framework for mathematical representation of the market dispatch and redispatch problems, which is based on CM schemes and the associated pricing mechanisms. A unified framework has been used to develop meaningful matrices to compare the various CM approaches so as to assess their efficiency and effectiveness of the market signals provided to the market participants.
Kumar et al. proposed comprehensive survey of CM methods and categorized these methods based on their models for CM ^{[13]} . A CM approach based on real and reactive power congestion distribution factorbased zones and generator's rescheduling was proposed in ^{[14]} . Kumar et al. proposed distribution factorbased generators' rescheduling for CM ^{[15]} .
In the present work, generation reschedulingbased CM approach has been formulated along with the voltage stability constraint taken as loadability parameter. The approach has also been applied without loadability constraint for comparison. An optimal power flow problem using nonlinear programming approach has been solved using Conopt solver of GAMS ^{[19]} . The results have been obtained for IEEE 24 bus Reliability Test System ^{[20]} .
2. Pool Market Model   
2.1 Pool Market Model
A pool electricity market is defined as a centralized market place that clears the market for the buyers and sellers bidding for purchase and supply of electricity. Electric power sellers/buyers submit bids to the pool for the amount of power that they are willing to trade in the market. Thus, under this model, one single entity, the Pool Company also called as PoolCo (usually system operator), purchases the power from the competing generators in the open market and generally sells it at a single market clearing price to the retailers/or consumers. Sellers in a power market would compete for the right to supply energy to the grid and not to specific customers. In this market, lowcost generators would especially be rewarded.
In the pool model shown in [Figure 1] ^{[21]} , competition is initiated in the generation business by creating more than one Generation Companies (GENCOs) and is gradually brought to the distribution side where retailers could be separated from Distribution Companies (DisCos) and where consumers could be allowed to phase in a choice of retail supply. The transmission system is centrally controlled by a combination of an Independent System Operator and a Power Exchange (ISO+PX), which is dissociated from all market participants and ensures open access. The ISO+PX operates the electricity pool to perform a pricebased dispatch and provides a platform for major option. This model was popular in England and Wales (E & W) System under the name "Contracts for Difference."
3. Congestion Management Model Based on Bid Function   
Transmission line CM has been obtained by rescheduling generators based on their qualifying bids in the market. For the generators to reschedule their generation up/down, their base case generation information is essential. This has been obtained solving optimal power flow problem with minimization of fuel cost. The nonlinear programming problem has been solved using GAMS CONOPT solver using MATLAB and GAMS interfacing ^{[19]} .
3.1 Base Case Real Power Output of Generators
The base case real power generation has been obtained by minimizing the marginal cost function of generators subject to their power generation limits, power flow limits, angle limits, and voltage limits. This optimal generation obtained after solving the OPF problem has been used for transmission line CM as a base generation data.
Minimize the fuel cost as an objective:
Subject to the following equality and inequality constraints:
(i) Power flow limit for a transmission line
Let complex voltages at busi and busj are V _{i} ∠δ_{i} and V _{j} ∠δ_{j} , respectively. The power flow equations are obtained as follows:
The apparent power from busi to busj is
From the equations (2.1), (2.2) the power flow equations for real and reactive power P _{ij} and Q _{ij} are obtained as
where
Similarly P _{ij} and Q _{ij} are given by:
(ii) Power injection balance equations at any busi: is given by:
where P _{gi} and Q _{gi} are real and reactive power generations, respectively, P _{di} and Q _{di} are real and reactive power demand, respectively, and P _{i} and Q _{i} are real and reactive power loss, respectively, at busi.
Inequality constraints
(i) Where the generation limits are taken as
(ii) The voltage limits are
(iii) The voltage angle limits are
Solving an optimization problem, the base case generation output is known.
3.2 CM Model without Loadability Factor
The objection function for three cases can be represented as below:
Objective function: minimize congestion cost CG
Where
Where
k1, k2 are generator cost coefficients for a bid function submitted to the ISO.
(a) Inequality constraints
(i) Up/down generation limits: the limits for are given by
(ii) Power flow limits for CM
(ii) Power flow limits for CM
(b) Equality constraints
(i) Change in generation limits
(ii) The power balance equation will become
Where
(ii) Power injection balance equation
Where
The voltage and angle constraints equations are same as (10) and (11). where
P_{g} Base case power generation
P_{d} Base case power demand
P_{gn} New power generation
Active power increment in generator at busi for CM
Active power decrement in generator at busi for CM
Price offered by generator at busi to increase its generation for congestion management
Price offered by the generator at busi to decrease its generation for congestion management
P_{i} Power injection at busi
The objective function for CM based on bid function with loadability factor is represented in the next section.
3.3 CM Model with Loadability Factor
In this formulation, the objective functions and respective constraints for transmission line CM are same as for the case without loadability factor for rescheduling of generator except the real power balancing equation. In this case, the base power generation is obtained solving the fuel cost minimization problem described in the previous section maximizing the loadability factor. The power injection equation can be written as:
The objective function along with the fuel cost minimization is
Maximize
In every case, load is multiplied with loadability factor in the real power injection balancing equation. The real power balancing in each case will become as follows:
The real power balancing equation becomes
The remaining equations for power injections and inequality constraints are same as discussed in the previous section.
4. Results and Discussions   
In this section, results have been obtained for three different cases of line congestion with bid function submitted by the GENCOs to the ISO. The bid data of generators are given in appendix [A1 ]. The results have been obtained for IEEE 24 RTS ^{[20]} . The results are presented in tabular and graphical form for all three cases. The cases for congestion in transmission lines have been considered assuming the power flow maximum rating in the corresponding lines below their base case power flows. For creating the congestion, the following lines have been taken as given below:
Case 1: For singleline (SL) congestion, power flow rating of 23 ^{rd} line connected between buses 14 and 16 has been taken as 2.60 p.u. compared with its given rating of 5.00p.u.
Case 2: For twoline (2L) congestion case, the rating of 18 ^{th} line connected between buses 11 and 13 has been taken as 2.25 p.u. compared with its given rating of 5.00p.u. along with previous congested line.
Case 3: For threeline (3L) congestion case, rating of 11 ^{th} line connected between buses 7 and 8 has been taken as 1.50 p.u. compared with its given rating of 1.75p.u. along with previous two congested lines.
4.1 Generator Rescheduling Without Loadability Factor (WOL)
The up and down generation obtained for SL, 2L, and 3L congestion cases are given in [Table 1]. In the table base case optimal power generation, Pg and new Pg after removing congestion for all congestion cases are also given. The generators which are participating for the CM with their up and down generation, Pg, new Pg are also shown in [Figure 2] for a singleline congestion. For twoline and threeline congestion cases, the Pg, new Pg, up and down generation rescheduling has been shown in [Figure 3] and [Figure 4].  Figure 2: Generator rescheduling based on bid function for SL congested case
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 Figure 3: Generator rescheduling based on bid function for 2L congested case
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 Figure 4: Generator rescheduling based on bid function for 3L congested case
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For the singleline congested case, generator at bus 2 goes up generation and generator at bus 22 goes for down generation. These are the generators which provide minimum up and down regulation value to manage congestion. For twoline congestion, the generators at bus 2, 22 goes up generation and generators at bus 16 goes down generation which has minimum down bid value. Similarly, for threeline congestion generators at buses 2, 15, 21, 22, and 23 increases generation and generators at bus 7, 13, 16, 22, and 23 decreases generation for CM. The congestion cost for SL, 2L, and 3L congestion case is given in [Table 2]. It is observed that the cost for 2L and 3L congestion case is more than SL congestion case. This is due to the fact that with 3L congestion case, the power flow pattern changes in such a manner that the flow in the congested line increases and the up and down generation required is higher, thereby increasing the congestion cost.
4.2 Generator Rescheduling with Loadability Factor
The up and down generation obtained for singleline, twoline, and three line congestion cases are given in [Table 3]. In the table base case optimal power generation, Pg and new Pg after removing congestion for all congestion cases are also given. The generators which are participating for the CM with their up and down generation, Pg, new Pg are also shown in [Figure 5] for a singleline congestion. For twoline and threeline congestion cases, the Pg, new Pg, up and down generation rescheduling have been shown in [Figure 6] and [Figure 7].  Figure 5: Generator rescheduling based on bid function for SL congested case
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 Figure 6: Generator rescheduling based on bid function for 2L congested case
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 Figure 7: Generator rescheduling based on bid function for 3L congested case
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For the singleline congested case, generator at buses 2 and 7 goes up generation and at bus 18 goes down generation. For twoline congestion case, generators at bus 2, 7, 15, 22, and 23 goes up generation and at buses 13, 15, 16, 18, and 21 goes down generation. For three line congestion case, generators at bus 2, 15, 22, and 23 goes up generation and at buses 7, 13, 15, 16, 18, and 21 goes down generation. In this case also, the base case power generation is calculated using loadability factor. The congestion cost is given in [Table 4]. At higher loadability factor it is observed that the line flow pattern changes. Because of this congestion cost is more as scheduling values for managing congestion are higher for multiline congestion cases. Comparing the congestion cost with lodability factor, the congestion cost obtained is higher compared with the case without loadability case; however, for 3L case it is observed lower due to the fact that there are counter flows in the network and reduces flows. Due to this reduction in flows, the amount of generator rescheduling is obtained lower compared with the case without loadability. In [Table 5], the real and reactive power losses are given, and the loadability factor is also given in the Table. The reactive power loss increases with loadability and 3L case. This is due to the fact that lines absorb more reactive power due to the increase in the power flows. The real power loss slightly decreases for 3L case compared with 2L case and may be due the fact of counter flows in lines and thereby reducing the loss.
5. Conclusions   
From the above results and graphs we concluded that the congestion cost goes high with more number of lines getting congested in the network. We also observed that the congestion cost is higher with loadability factor. The congestion cost depends by how much amount the line is congested. This is clearly observed in the 3L congestion case. The congestion cost for 3L case is found lower compared with the case without loadability. This is attributed to the counter flows occurring in the network. The reactive power losses increase with lodability factor and multicongested lines. The real power loss also increase but found less for 3L case due to the counter flows in the network.
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Authors   
Charan Sekhar did his masters in Power Systems in Department of Electrical Engineering at NIT Kurukshetra in 2011. He has interests in the area of power system restructuring and congestion management.
Ashwani Kumar did his B. Tech. from GBPUA & Technology, Pant Nagar in 1988. He did his masters from Punjab University, Chandigarh in 1988 in honors and Ph.D. from IIT Kanpur in 2003. He is presently with the Department of Electrical Engineering at NIT Kurukshetra as an Associate Prof. He has interests in the area of Power system operation in deregulated environment, FACTS applications to power systems, distributed generation, demand side management, wind energy integration issues in deregulated markets. He is life member of ISTE, IEI, India and member IEEE/PES, USA.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
