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A.Prakash^{1}, M.Yuvaraj^{2}

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The proposes a new methodology for solve the Profit Based Unit Commitment (PBUC) problem. The UC problem is solving to Improved Preprepared Power Demand (IPPD) table. In a deregulated environment, generation companies (GENCOs) schedule their generators to maximize profits rather than to satisfy power demand The proposed approach has been tested on 3 and 10 units for a scheduling horizon of 24 Comparison of results of the proposed method with the results of previous published methods shows that the proposed approach provides better qualitative solution with less computational time.
Keywords 

Profit Based Unit Commitment (PBUC), Improved Preprepared Power Demand table (IPPD)  
NOMENCLATURE  
PF Profit of GENCOs  
RV Revenue of GENCOs  
TC Total cost of GENC  
F(Pij) Fuel cost function of jth generating unit at ith hour  
Xi j ON/OFF status of jth generating unit at ith hour  
Pij Output power of jth generating unit at ith hour  
SPi Spot price at ith hour  
T Number of hours  
N Number of generating units  
PDi Power demand at ith hour  
Rij Reserve jth generating unit at ith hour  
SR Spinning reserve at ith hour  
Pij min Min output power of jth generating unit at ith hour  
Pij max Max output power of jth generating unit at ith hour  
ai,bi,ci Coefficients of fuel cost of unit ‘i'  
Tj on Minimum time that the jth unit has been continuously online  
Tj off Minimum time that the jth unit has been continuously offline  
Tj up Minimum up time that the jth unit  
Tj down Minimum down time that the jth unit  
INTRODUCTION 

The Profit Based Unit Commitment (PBUC) problem is one of the most important optimization problems to relating power system operation under deregulated environment. Earlier, the power generation was dominated by vertically integrated electric utilities (VIEU) that owned most of the generation, transmission and distribution subsystems. Recently,the electric power utilities are unbundling these subsystems as part of deregulation process. Deregulation requires to unbundling of vertically integrated power system into generation (GENCOs), transmission (TRANSCOs) and distribution companies (DISCOMs). The main aim of deregulation is to create competition among generating companies and provide choice of different generation options at cheaper price to consumers. The main interest of GENCOs in the deregulation is maximization of their profit whereas in the VIEUs, the objective is to minimize the fuel cost function. This aspect leads to a change in strategies to solve existing power system problem caused under deregulation. Since the objective of GENCOs to maximization of their profit, the problem of UC needs to be termed differently as Profit Based Unit Commitment (PBUC). Generally, the GENCOs place bids depending on the price forecast, load forecast, unit characteristics and unit availability in different markets. Mathematically, the PBUC problem is a mixed integer and continuous nonlinear optimization problem, which is complex to solve because of its enormous dimensionality due to a nonlinear objective function and large number of constraints. The PBUC problem is divided into two sub problems. The first sub problem is the determination of status of the generating units and second sub problem is the determination of output powers of committed units.  
The previous efforts for solving PBUC problem were based on conventional methods such as dynamic programming and Lagrangian relaxation(LR) [3] methods. Due to the curse of dimensionality with increase in number of generating units, dynamic programming takes large amount of computational time to obtain an optimal solution. The Lagrangian Relaxation method provides fast solution but suffers from numerical convergence.  
It is observed from the literature survey that most of the existing algorithms have some limitations to provide qualitative solution within considerable computational time. Therefore it is necessary to find a simple and efficient method for solving unit commitment problem independent of dimensionality and selection of solution specific parameters. In this context a table called improved prepared power demand table (IPPD) is prepared using the available information of system generation limits and coefficients of fuel cost function(s).  
The proposed algorithm was implemented in MATLAB (7 Version). The formulation of the PBUC problem is introduced in Section II. The description of the algorithm for solving the PBUC problem is given in Section III. Simulation results of the proposed approach for various generating units are presented in Section IV. Conclusions are given in the last section.  
PROFIT BASED UNIT COMMITMENT PROBLEM FORMULATION 

The profitbased UC problem under competitive environment is an optimization problem and can be formulated mathematically by the following equations:  
a) The Objective function is maximization of profit for generating companies.  
Constraints 

The UC problem is subjected to equality and inequality constraints such as power balance equation, reserve constraint, limits of units, and the other constraints including the thermal constraints.  
Power balance equation 

The sum of the output powers of on line generators is equal to the forecasted system power demand in each period of time.  
Reserve constraint  
Limits of output powers of units 

Minimum up/down time constraint 

Minimum up and minimum down time constraints are incorporated in the unit commitment problems as follows.  
SOLUTION METHODOLOGY FOR UC 

Solution of the UC problem is obtained in the following steps: 

The PBUC problem involves an on and off decision for units depending on variations in power demand. In this paper, a simple approach has been proposed.  
Formation of the IPPD table: 

The procedure to form the IPPD table is given below.  
Step1 Determine minimum and maximum values of λ for all generating units at their ,min and Pi max. for each units two λ values are possible. Then arrange these λ va lues in ascending order and index them as λ (where j = 1,2,....2N ) (9)  
for all generators at each λ j value. Incorporate Pi,min and P i max as below.  
a. Setting of the minimum output power limit  
But, for must run generators  
b. Setting of the maximum output power limit  
Step3 λ values, output powers and sum of output powers (SOP) at each λ are arranged in the table in ascending o r d e r o f λ values. This t a b l e is known as the Improved Preprepared Power Demand (IPPD) table.  
The structure of IPPD table is as follows 

a. Entries of Column1 of IPPD table are evaluated λ values arranged in ascending order.  
b. Entries of Column2 to Column N+1 are output powers of each generating unit i subject to constraints on λ given in eqn. (9)(12).  
The last column of IPPD table consists of sum of output powers (SOP) of the generating units at each of the evaluated λvalue.  
Here, λ values a r e e v a l u a t e d a t m i n i m um a n d m a x i m um o u t p u t powers. For ‘N’ units system, 2N lambda values are calculated. Thus the IPPD table has 2N rows and N+2 columns for a system with N generating units. Assume that the power demand plus spinning reserve lies between SOPj1 N+2 and SOP j, N+2 Therefore j1th and jth rows from the IPPD table are selected and form a new table. This table is called Reduced IPPD (RIPPD) table.  
The RIPPD table gives the information of the status of the units at selected λ values and also the transition of commitment of units at one to other λ in the table. The unit commitment schedule for a time horizon having t intervals will be evaluated from this IPPD table (as explained in procedure below) given the power demand in each time interval.  
Formation of the Rippd Table: 

Profit is obtained only when the forecasted price at the given hour is greater than the incremental fuel cost of the given Therefore, the forecasted price is taken as the main index to select the Reduced IPPD (RIPPD) table from the IPPD table.  
There are two options to select the RIPPD table from the IPPD table.  
Option 1: At the predicted forecasted price, two rows from the IPPD table are selected such that the predicted forecast price lies within the lambda limits. Assume here that the corresponding rows are m and m+1.  
Option 2: At the predicted power demand, two rows from the IPPD table are selected such that the predicted power demand lies within the Sum of Powers (SOP) limits. Assume here that the corresponding rows are n and n+1.  
Therefore, the Reduced IPPD table is as follows:  
ⅰ If m<n, then the RIPPD table is selected based on  
option 1. Here, the power demand is modified as the SOP of m+1 row. In the PBUC problem, the power demand constraint is relaxed and it is not necessary to operate the generating units so as to meet power demand.  
ii If m>n, then the RIPPD table is selected option2.Once the RIPPD table is identified, the information about the Reduced Committed Units (RCU) table is generated by simply assigning +1 if the output power of the unit ‘i’ pi ≠ 0 and 0 if pi = 0 . The RCU table will have binary elements indicating the status of all units.  
Now, “incorporation of noload cost”, “recommitment of units” and “Inclusion of minimum up time and minimum down time constraints” in the PBUC problem need to be addressed.  
B. Incorporation Of No Load Cost  
Formulation of IPPD table is based on incremental fuel cost (λ). Therefore noload cost is not considered in IPPD table. In the fuel cost data, some generating units may have huge noload cost and less incremental fuel costs. Therefore incorporation of noload cost is needed to reduce the total fuel cost. In this paper, a simple approach is proposed to incorporate the noload cost.  
Step1 production cost of the units at average of minimum output power and maximum output power is evaluated for all units.  
Step 2 all units are arranged in ascending order of the production cost.  
Step 3 status of the units is also modified according to the ascending order of the production cost.  
Step 4 Last onstate unit at each hour is identified. Status of the units is changed as follows: If any unit on the left side of the last onstate unit is in off state then it is converted as on state unit.  
Decommitment Of Units 

The committed units may have excess spinning re serves due to a greater gap between the selected lambda values in the RIPPD table. Therefore, decommitment of units is necessary for getting more economical benefits.following steps are used to decommit the units.  
Step1 Identify the committed units.  
Step2 Last unit in the above order is decommitted and spinning reserve is checked. If reserve constraint is satisfied after decommit the unit, that unit is decommitted.  
Step3 Step 2 is repeated and possible units are decommitted without violating the reserve constraint. Inclusion of Minimum up time and minimum down time constraints If the off time of the unit is less than the minimum down time, then status of that unit will be off. If on time of the unit is less than the up time of the unit, then that unit will be on.  
TEST CASES AND SIMULATION RESULT 

The proposed approach has been implemented in MATLAB and executed .The proposed has been tested on 3 to 10 generating unit solve profit based unit commitment problems.  
Example 1 In this example, a 3generating unit system is considered. The fuel cost data of this 3unit system was obtained from given TABLE 1.  
In this example, lambda values are computed for all units at their minimum and maximum output powers and arranged in ascending order. For all lambda values, the output powers are evaluated and IPPD is formulated.  
CONCLUSION 

The Improved Preprepared Power Demand table has been proposed in this paper to solve Profit Based Unit Commitment (PBUC). While solving the PBUC problem. While solving the PBUC problem, information regarding the forecasted price is known. Simulation results for the proposed method have been compared with existing methods and also with traditional unit commitment. It is observed from the simulation results that the proposed algorithm provides maximum profit with less computational time compared to existing methods and is thus amenable for the realtime operation required in a deregulated environment.  
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