Optimal Bidding Strategy in Power Market before and after Congestion Management Using Invasive Weed Optimization

Power companies world-wide have been restructuring their electric power systems from a vertically integrated entity to a deregulated, open-market environment. Previously, electric utilities usually sought to maximize the social welfare of the system with distributional equity as its main operational criterion. The operating paradigm was based on achieving the least-cost system solution while meeting reliability and security margins. This often resulted in investments in generating capacity operating at very low capacity factors. Decommissioning of this type of generating capacity was a natural outcome when the vertically integrated utilities moved over to deregulated market operations. This study proposes an optimizing base and load demand relative binding strategy for generating power apprises of different units in the investigated system. Afterwards, congestion effect in this biding strategy is investigated. The described systems analysis is implemented on 5 and 9 bus systems and optimizing technique in this issue is the Invasive Weed Optimization algorithm; the results are then compared by GA. Finally, examined systems is simulated by using the Power World software; experimental results show that the proposed technique (Invasive Weed Optimization) is a high performance by compared GA for the congestion management purposes.


INTRODUCTION
Since the last two decades, many electric utilities world-wide have been forced to change their ways of doing business, from vertically integrated functioning to open-market systems.The reasons have been many and differed across regions and countries.
In developing countries, the main issues have been high demand growth associated with inefficient system management and irrational tariff policies, among others (Goncalves and Vale, 2003).This has affected the availability of capital investment in generation and transmission systems.In such a situation, many countries were forced to restructure their power sectors under pressure from international funding agencies.On the other hand, in developed countries, the driving force has been to provide the customers with electricity at lower prices and to offer them greater choice in purchasing electricity (Huang and Ping, 2001;Taylor et al., 2002).
In front of the days restructuring, the power grid used to be operated by vertically integrated utilities, who had control over both generation and transmission appliances (Perveen and Srivastava, 2000).
There are several methods to the congestion management.One of these methods is capacitance auction.Independent system operator auctions are some of the determined transmission generally (partially) in a short time and typically are transmissions which happens congestion to them.In the Pool Markets congestion management using Load flow and (LMP) is done (Henry et al., 2003;Lo et al., 2000).
The Independent System Operator (ISO) is a regulating entity autonomous from the electric companies and optimizes the overall system operation.Spot pricing theory is used for economic generation and load dispatch.Under the pool system, locational prices are computed by the marginal cost of optimal power flow solutions (Hajimirsadeghi and Lucas, 2009;Mehrabian and Yousefi-Koma, 2007).
In this study, Power Transfer Distribution Factors (PTDF) is used to congestion management implementation.
Following this tradition, in Mehrabian and Lucas (2006) proposed the Invasive Weed Optimization (IWO) a derivative-free, met heuristic algorithm, mimicking the ecological behavior of colonizing weeds.This algorithm is then applied to investigation the problem and also to analysis the effect of each unit to the local marginal price.Comparison the results obtained with GA reflects the superiority of IWO in a statistically significant fashion.
In a final manner, examined systems are simulated by using the Power World software to check the results (Power World, 2008;Power World Negative LMPs, 2008).In this study Invasive Weed Optimization (IWO) algorithm is utilized to optimal bidding strategy in power market; the evaluation is applied before and also after congestion management.The achieved results from Invasive weed optimization algorithm are finally compared with the Genetic algorithm.Experimental results show that in this purpose, the IWO algorithm has high performance and overcomes to GA method.

MATHDOLOGY
Problem formulation: The load flow p ij through the transmission line i-j is a function of the line reactance x ij , the voltage magnitude v i , v j and the phase angle between the sending and receiving end voltages δ i -δ j as shown in Eq. ( 1): ( ) The Transmission Line Relief (TLR) sensitivity values at all the load buses for the most overloaded transmission line are regarded and used for calculating the essential load curtailment for the alleviation of the transmission congestion.The TLR sensitivity at a bus k for a congested line i-j is S ij k and is computed as below: The excess power flow on transmission line i-j is written below: where, P ij = The Actual power flow through transmission line i-j ܲ ത = Flow limit of transmission line i-j (New England ISO, 2008;Yan, 1999).
The new load P k new at the bus k can be calculated by: where, new k P = Load after curtailment at bus k k P = Load before curtailment at bus k k ij S = Sensitivity of power flow on line i-j due to load change at bus k N = Total number of load buses Genetic Algorithm (GA): Our genetic algorithm is an ad-hoc one based on a classical structure.The outline steps are http://www.obitko.com/tutorias),(Kazemi et al., 2011)

Invasive Weed Optimization (IWO):
The Invasive weed optimization algorithm was developed by Mehrabian and Lucas (2006).IWO algorithm is a new search method, which makes use of mechanisms inspired by the natural behavior of weeds in colonizing and seeking a suitable place for growth and reproduction.IWO algorithm is a numerical stochastic search algorithm mimicking natural behavior of weeds in colonizing and finding suitable place for growth and reproduction.This technique is motivated by a common phenomenon in agriculture that is colonization of invasive weeds.Weeds have shown very robust and versatile nature which turns them to undesirable plants in agriculture.Recent experiences in implementing the IWO algorithm in a number of different application domains (Mehrabian and Lucas, 2006;Hajimirsadeghi and Lucas, 2009) have shown considerable advantages over both classical algorithms and other bio-inspired techniques.The overall algorithm is summarized as below: Reproduction: Each member of the population is allowed to produce seeds conditional upon its own, as well as the colony's lowest and highest cost, such that, the number of seeds produced by a weed grows linearly from lowest possible seed for a weed with worst cost.

Spatial distribution:
The produced seeds are being randomly distributed over the d dimensional search space by normally distributed random numbers by a zero mean and variable variance.This step ensures that the genesis seeds will be generated around the parent weed, leading to a local search around each plant.However, the Standard Deviation (SD) of the random function is made to reduce over the iterations.
If Max sd and Min sd be the maximum and minimum standard deviation and if Pow be a real number, then the standard deviation for a particular iteration may be given as in Eq. ( 5): This step guarantee that the probability of dropping a seed in a distant area reduces nonlinearly with iterations, which results in grouping fitter plants and elimination of unsuitable plants.Since, this is a selection mechanism of IWO.
Competitive exclusion: If a plant leaves no offspring then it would go vanished, otherwise they would take over the world.Thus, there is a requirement of some kind of competition between plants for restricting maximum number of plants in a colony.At the first, the plants in a colony will reproduce fast and all the produced plants will be comprised in the colony, until the number of plants in the colony reaches a maximum value pop max .In any event, it is hoped that by this time the fitter plants have reproduced more than undesirable plants.After that, the seeds and their parents ranked together and those with better fitness survive and become reproductive (Mehrabian and Yousefi-Koma, 2007).The pseudo code for IWO is presented in Fig. 1.

BIDDING STRATEGY BEFORE CONGESTION MANAGEMENT FOR BOTH CASES
Bidding strategy is described by suggesting transactions in the market.Energy selling prices by the power generation units and energy purchasing prices by the clients are recommended to the power market.The whole market zones try to maximize the social welfare index.Bidding strategy with no congestion can be presented as below (Mehrabian and Yousefi-Koma, 2007;Viond et al., 2010): where, i = Customers load index j = Generators index NL = The number of consumption loads NG = The number of generators B i = The i th customer's profit function P j = The delivery power of j th unit C j = The j th generator's cost function d j = The quantity of consumption power in the j th unit Case A. 5 bus system: Bidding strategy after congestion management: Since the electricity market has been deregulated the participants have a variety of choices to improve their standing in the market.A set of different bidding strategies may be adopted by the participants in order to maximize their profit.In this study, by neglecting the losses in the load flow is advised and is as: where, the requirement power of consumption loads vector is described by consumption loads power differences.And ω is a weight matrix as ] [ 1 . ω in this study is advised as a 3×3 uniform one matrix (Sun et al., 2003;Silpa, 2007).

bus system data:
In this section a 5 bus system by 3 generator units, 2 customers (loads) and 6 transmission lines is analyzed.Cost functions and profits to the presented system are described in Table 1.For a suitable analysis on the costs, two different states are demonstrated to the system.At the first, transmission lines before congestion assumed and the relative analysis on the 5 bus system implemented.Afterwards, congestion also implemented and the analysis executed on the system again.Bid values and attaining cost using GA and IWO are described in Table 2 and the results show a higher performance for IWO algorithm toward GA (Mehrabian  and Yousefi-Koma, 2007; Biskas et al., 2007).
Table 3 shows the line flows before and after congestion management at bus 5. From Table 3, in line 5, the line flow is about 6 MW more than the limited value which is decreased to 45 MW after congestion management.
From the Table 3 it is observed that after bidding strategy, line 5 has found some over loads.Simulation results show that in order to remove the congestion, the output power of generator 3 is decreased.In brief generators in bus 2 for consumption load ensuring are faced to genesis growing.Also the acquired social welfare index in the IWO is desirable rather than the GA.Notice that transmission lines losses are also calculated in this analysis.Table 4 shows the simulation results.
As you can see in Fig. 3, by increasing the output power of generator 2 into 100 MW congestion in transmission line, (the line which is between bus 2 and bus 4) is decreased.And the output power value on generator 3 is raised for the consumption load security.
Case B. 9 bus system: Bidding strategy model after congestion management: Since the electricity market has been deregulated the participants have a variety of choices to improve their standing in the market.A set of different bidding strategies may be adopted by the participants in order to maximize their profit.In this system Assessment, by spot the losses in the load flow is advised and is as: where, the requirement power of consumption loads vector is described by consumption loads power differences, and k is the number of transmission line and p is the number of generators in the 9 bus system (Kazemi et al., 2011).---------------------------------------------------------GA  ---------------------------------------------------- Gen 9 bus system data: In this study a 9 bus system by 3 generator units, 3 customers (loads) and 6 transmission lines is analyzed.Cost functions and profits to the presented system are described in Table 5.For a suitable analysis on the costs, two different states are demonstrated to the system (Power World, 2008;Viond et al., 2010).At the first, transmission lines before congestion assumed and the relative analysis on the 9 bus system implemented.Afterwards, congestion also implemented and the analysis executed on the system again.Bid values and attaining cost using GA and IWO are described in Table 6 and the results show a higher performance for IWO algorithm toward GA (Sun et al., 2003;Daalader et al., 2005).
In Table 7 the line flows before and after congestion management at 9 bus system.From Table 3, in line 3, the line flow is about 2.9 MW more than the limited value which is decreased to 47.6 MW after congestion management.
From the Table 7 it is observed that after bidding strategy, line 3 has found some over loads.Simulation results show that in order to remove the congestion, the output of generator 2 is decreased.In brief generators in bus 3 for consumption load ensuring are faced to genesis growing.Also the acquired social welfare index in the IWO is desirable rather than the GA.Notice that transmission lines losses are also calculated in this analysis.Table 8 shows the simulation results for 9 bus system.
Simulation results for 9 bus system: Simulation results of 9 bus system using Power World software shows that the line transmission 3 (the line that is Fig. 4: Mimic diagram of 9 bus system and power flow before congestion management-power world software Fig. 5: Mimic diagram of 9 bus system and power flow after congestion management-power world software between bus 4 and bus 5) has over load which by declining the value of generated power on generator 2 (to 153 MW) and increasing the generated power of generator 3, congestion of line 3 (using the sensitivity decreasing method) is decreased (rather than the flow power of transmission lines).Figure 4 and 5 show the analysis.
As you can see in Fig. 4, by increasing the output power of generator 3 of 85 to 105 MW congestion in transmission line, (the line which is between bus 4 and bus 5) is decreased and the output power value on generator 3 is raised for the consumption load security.

CONCLUSION
Depending on the structure and objectives of the electricity market, different congestion management methods are put into practice.Effective congestion management will help mitigate the effects of market power in electricity markets.In this study, the application of the Invasive Weed Optimization algorithm (IWO) is presented to congestion management in bidding strategy; experimental results are compared by the Genetic Algorithm (GA).It is considered that in IWO, the output power of generators and also social welfare indexes have more performance than the GA.These two algorithms are implemented on 5 and 9 bus systems and transmission line losses are envisaged.With regard to more boundaries and too problems of power flow implementation by Gauss-Sidel and Newton-Rap son methods, power world software is used.The OPF in Power World simulator provides the ability to optimally dispatch the generation in an area or group of areas while enforcing the transmission line limits.Final results show that using IWO in power flow systems and for congestion management purpose is a proper technique.

Fig. 1 :
Fig. 1: Pseudo code for IWO algorithm Initialization: A finite number of weeds are initialized at the same element position of the conventional array, which has a similar spacing of λ/2 between elements in neighbor.

Fig. 2 :
Fig. 2: Mimic diagram of 5 bus system and power flow before congestion management-power world software

Table 1 :
Related data for cost functions in 5 bus system

Table 2 :
Social welfare index before congestion management

Table 4 :
Simulation results

Table 6 :
Social welfare index before congestion management Algorithm

Table 8 :
Simulation results for 9 bus system Algorithm