IEEE International Conference on Recent Advances and Innovations in Engineering (ICRAIE-2014),May 09-11, 2014, Jaipur, India

Dynamic Scheduling of Operating Energy and Reserve in Electricity Market with Ramp Rate

Constraints

Akanksha Bhatt Department of Electrical

Engineering M.LT.S., Gwalior, India

akankshabhatt07@gmail.com

Aayush Shrivastava Department of Electrical

Engineering M.LT.S., Gwalior India

mr.aayushshrivastava@gmail.com

Abstract- Earlier the economic dispatch problem was solved

for generation first and subsequently for reserve but nowadays in

electricity market these two operations are simultaneously

performed to increase the efficiency and reliability of the power

system. In this study, MATLAB based optimization solver

Sequential quadratic programming (SQP) is used to allocate the

static and dynamic dispatch in Electricity market based on price

bids submitted by the private and public GENCOS. The idea is

implemented on IEEE 17-units system with 57 buses for reserve

and energy cost optimization under all operating constraints. The

realistic representation of the power system is done where

constantly changing load demands, generator outages etc. are

included in the model. The SQP algorithm is found to model the

practical constraints like ramp-limits, reserve/energy coupling

constraints, power-balance and generation capacity limits.

Keywords- Block price characteristics; Dynamic energy and

reserve dispatch(DERD); ramp rate limits; Equality & inequality

contraints

I. INTRODUCTION

The dynamic energy and reserve dispatch (DERD) is proving to be the most important tool for optimizing the electrical power system operation in present restructured power system. Spinning reserve is playing a very significant function to maintain security and reliability in case of failures of generating units. The objective of the joint energy and reserve power allocation problem is to reach, the feasible schedule of generating unit and output of generation unit so as to match the load requirement at a certain time with optimal operation cost under different operational constraints. The deregulation of the electricity market has upgraded the efficiency and performance of the electrical industries. Spinning reserve (SR) power is one of the most significant back up services that is necessary for ensure the protected and reliable function of power system in the occurrence of unexpected events like, generator outages, sudden load changes, or both [3]. Spinning reserve is the accessible capacity of generation that can reach in short time to meet the demand. The issues related to generation and reserve dispatch in various areas of competitive market are more complex as compared to the conventional power dispatch [4]. Changes in planning and formulation are required to include additional constraints and transformed objectives. Generator price characteristics are affected by market behavior and the GENCOS can modify their block price bids for obtaining

[978-1-4799-4040-0/14/$31.00 ©2014 IEEE]

Manjaree Pandit Department of Electrical

Engineering M.LT.S., Gwalior, India

manjaree�@hotmail.com

Hari Mohan Dubey Department of Electrical

Engineering M.LT.S., Gwalior, India

harimohandubeymits@gmail.com

maximum profit. Energy and reserve have separate markets in conventional vertically integrated power systems where reserve is dispatched after the energy dispatch is completed. Thus a sequential dispatch is carried out for energy and reserve. This scenario suffers from some difficulties due to price fluctuations. The present market prefers a sequential dispatch of both commodities, i.e. energy and reserve to eliminate the earlier problems. The static energy and reserve dispatch (SERD) finds optimal operating schedules at a specific time and do not take into account the system behavior with changing load scenarios at different time moments. But the DERD takes into account the practical system operation at different time moments [2]. This is done by modeling the limit on the hourly climbing rate of a generator. Due to this additional constraint the computation process for DERD is more complex than that of a SERD but the solutions are more accurate and realistic[ 1].

The energy and reserve dispatch in static environment is solved using an LP-based approach [7]. The joint modeling of energy and reserve dispatch is presented in [8]. A cost-effective representation and dispatching of reserve with supply and demand side options can be found in [6]. A flexible real time combined dispatch of reserve and energy with flexible detailed modeling of demand-supply fluctuations and contingency cost is proposed [5]. An approach established on mixed integer nonlinear programming (MINP) for dispatching energy and reserve simultaneously is presented in [11]. A multi-agent based simulator for a energy/reserve market is modeled in [12]. Contingency-constrained reserve planning using security­constrained unit commitment model is given in [10]. Reliability and spot market efficiency in distributed generation can be maintained with demand response programs [9]. Nature inspired computational methods are also becoming very popular for solving complex optimization problems. Genetic algorithm (GA) [15], particle swarm optimization [16], differential evolution (DE) [1, 14, and 13], memetic algorithm (MA) [19] and harmony search (HS) [20] have proved efficient for the joint dispatch problem. Recently gravitational search algorithm has also found application for economic dispatch solution [18]. Interior point algorithm has been used for solving bid based dynamic economic dispatch for competitive market [17]. Sequential quadratic programming [22] is a very efficient algorithm which finds an attractive implementation in MATLAB environment. In DERD problem i) Generator cost

curves are replaced by price bids ii) Reserve bids are separate iii) Simultaneous dispatch is carried out in place of the traditional sequential dispatch iv) mutual coupling constraints for energy and reserve v) energy and reserve capacity limits vi) generator contingencies and vii) ramp rate limits are modeled. This paper presents the solution of the optimal DERD for the practical market environment using SQP algorithm formulated in MATLAB environment. The model is tested on three test cases of 17-unit, IEEE 57 bus system. The results are found to be better than results from recent literature.

II. OPTIMAL DYNAMIC DISPATCH OF ENERGY/ RESERVE

The SERD is conducted such that the demand is assigned to the committed generators for a specified time instant. For accurate representation of practical systems where the demand is varying continuously and the generator power output has to be adjusted constantly, the DERD model is most effective. The DERD allocates the energy as well as reserve of online generation to match with the forecast load requirement computed over a certain time period.

The costs associated with changing generated power from one time step to the other are also considered in DERD. The ramp rate limits of the generator need to be accurately modeled when joining the two consecutive time intervals of DERD problem. It is required to allocate the generation to the committed units in such a manner that their mechanical limits such as boiler and turbine stresses are within the permissible limits to avoid wear and tear. This operational limitation is modeled as a constraint on the rate of increase or decrease of the generator power output, known as ramp limit. The ramp rate limits change the upper and lower operational bounds of the generating units in a dynamic manner, with each time step.

The DERD solution is computed for many cosecutive smaller time steps and then performing a SERD optimization each time step such that the some of the time steps is equal to the total dispatch period. This paper presents the solution of dynamic energy and reserve dispatch (DERD) for a day which is divided into 24 time steps.

A. Optimi=ation Objective:

The main idea behind dynamic energy and reserve dispatch (DERD) is to reduce combined cost of energy and reserve of generating unit for a certain period of time. The sum of cost for N generating units, for the power dispatch consisting of 'T' number of time intervals can be written as,

T N Cost = L L [F(?, (t» + G(R, (t»] t�l i�l (1)

Pi(t )and Ri(t) are the generation and reserve power of i'h

unit at tlh interval; G(R{t)) and F(P;(t» are the reserve and energy bid prices of the it 1 generating unit at tlh interval of time correspondingly.

The constraints of DERD problem are:

B. Equality Constraints

i) Power equilibrium constraint for certain interval 't'

are given as:

N IF: (t) = PD(t) + �"(t) i�1 (2)

Power loss and Demand for time interval't' is given by PL(t) and PD(t) respectively.

2) Spinning reserve power constraint for time interval 't'

is shown as N 2.R, (t) = RD (t) 1=1 (3)

The reserve power demand for time interval't' is given as RD (t). C. inequality Constraints

i)

2)

Unit power generation capacity constraints

�min ��(t) ��max

Unit reserve power generation capacity constraints;

o � R i ( t ) � R ,max

. ,

(4)

(5) Pm;n pmax d Rmax b d ' Here" " an i are oun atlon of power

generating units 3) Unit reserve and generating power coupling constraints

P, ( t ) + R I ( t ) � Pi max

4) Unit ramp-rate constraints given by:

DR, �(F:(t)-F:(t-l»�UR,

(6)

(7) The ramp-rate limits, DRi and URi are the downward and

rising limits of the ith generating unit. The main goal of the DERD problem is to reduce the total cost of generating energy and reserve power shown by (1) with respect to the equality and inequality constraints specified by (2)-(7).

Fig.I. show energy price and reserve price with power and reserve respectively. It represents price characteristics [11][15].

PGlk is the offering rate for energy of ith generator whereas

PRik is spinning reserve in kth power block. In kth price band, variables PGik and RRik represents energy and reserve values. More over the energy and reserve costs F(Pi) and G(Ri) for ith generator, supplying energy Pi and reserve R are given as [l3][17].

����gy 1 I I l$/mwIh)

PGik _ Power(mw)

���:�e L..,,11-===--'��K��-_""P�G�i (_k-_-I1..1..)I---=P�

IG-ik--

($I�Wk lh) L

' _

-:---;;;;--

...1. __ -''-__

' � _ " Reserve(mw) - PRi (k- 1 ) K PRik

Fig. 1. Block price characteristics for energy and reserve

FeP;) = PG(k-l) XPa(k-l) +(P; -Pa(k-l»)XPGi�if.··Pc(k-l) <P; S,Paik

tPG(k-l) Xp; ... if . .P; S,Pa(k-l)

PG(k-l) XPa(k-l) +(PaiCPa(k-l»)XPGik+(P;-PaiJXPG(k+l)··.if.··Paik <P;

(8)

G{R,)= PII(k-l) Xi??(k-l) +(R, -R,I(k-l»)XPRiit····.ij.··Pc(k-l) <P;S,PaRik

jP/I(k_l) XR, ... if··P;S,Pa(k_l)

PII(k-l) Xi??(k-l) +(i??ik -i??(k-l»)XPRik +(R, -R,IiJXPG(kll)··.if.··Paik <P;

(9) III. SEQUENTIAL QUADRATIC PROGRAMMING(SQP)

ALGORITHM

SQP is a mathematical method used for solving the nonlinear optimization problem with mixed, equality and inequality, constraints [22]. Because of higher convergence rate, this method is efficient for solving smooth constrained optimization tasks frequently found in engineering and mathematical issues. In fact for highly time-consuming and complex simulations this method is found to be very popular. To minimize total cost function over a dispatch period and satisfying the ramp rate limits and other constraints, non linear problem is formulated. This uses self-concordant barrier function for encoding set of convex solutions. It reaches an optimal solution by searching the feasible region extensible. Since its inception the SQP algorithm based approaches have made a huge impact on areas of optimization for solving the convex programming.

Nonlinear programming refers to minimization of a nonlinear objective function f(x) of m variables, subject to equation or equality, inequality constraints involving a vector of nonlinear functions gi(x). General convex programming problems are of the form;

min x I(x) sl. g,(x) � 0, i = 1,2 ..... m (10) (where f and , i = 1; 2; : : : ;m, are convex functions

defined for m number of variables ) SQP algorithms can provide the solution of large-scale technological1y significant problems. These algorithms are based on mathematical programming which is the biggest and main dramatic area of research in optimization. SQP methods have entirely altered the landscape of mathematical programming theory. The aim of using SQP methodology is to solve the convex programming, special conic programming problems and general programming.

A. Matlab implementation of SQP algorithm:

Matlab base provides a very easy execution of various non linear optimization algorithms. Mapping of Constraint and problem definition is obtainable in an extremely user friendly atmosphere using the special 'fmincon 'library function. The 'fmincon' function finds the constrained optimization of a function distinct over a number of variables.

fmincon attempts to solve problems of the form: min

X f(x) S.t: A* X s, B, Aeq * X = Beq (11 )

c(x) � O,ceq(x) = 0 (Nonlinear constraints )

LB s, x s, UB (Bounds)

(12 )

(13 )

The function 'fmincon' applied four various algorithms; i) Sequential quadratic programming (SQP) ii) Trust region reflective iii) Interior point iv) Active set. Any one of these algorithm can be selected by defining the option as given.

Options = optimset ('Algorithm', 'sqp')

Then the options set above are passed on to 'fmincon' for implementation of the SQP algorithm. To start optimization routine the fol1owing instructions are used.

x = fmincon (fun, xV, A, b, Aeq, beq, lb, ub, nonlcon, options)

Here, fun represents the objective function which is to be minimized, xO is the initial value of the problem variables, 'A, b, Aeq, beq' are the matrices of coefficients of linear equality and inequality constraints. The lower and upper limits on variables are defined by matrices 'lb' and 'ub' . The non linear equality and inequality constraints are computed by the 'nonlcon' function.

B. Condition for termination

In iterative optimization algorithms it is important to set guidelines for terminating the process at the correct instant . This condition affects the final solution significantly . Normal1y two criteria are employed for stopping an optimization routine .

1) By setting up maximum iteration counts.

2) By setting up the function tolerance.

3) By setting up function evaluation count. In matlab the above three option for stopping the optimization algorithms are implemented by setting the fol1owing options[21] :

options.MaxFunEvals = maxfun

option.MaxJter= iterrmax

option. TolFun= tolmax

Where maxfun, iterrmax and tolmax are user defined values.

IV . RESULTS AND DISCUSSION

The joint reserve and generation dispatch problem defined in Section-2 is analyzed on a standard IEEE 57 bus test power system consisting of 17 Generating units. The energy and reserve cost are taken from [8]. The load and reserve requirement for whole day 24 hour, the reserve/energy and ramp rate limits, cost characteristics can be found in [13].Dynamic energy dispatch is defined for three different case test of this system for the twenty four hour load reserve in normal operation as wel1 as under generator outage contingency. In this study the value of maxfun is 50000, Iterrmax is 1000 and tolmax is taken as 10.6 respectively.

A. Optimal dynamic dispatch for operating cost(case J)

Economic dispatch is carried out with cost optimization only using the sectional cost characteristic [8]. Ramp rate limits are included to compute the twenty four hour optimal schedule with cost optimization only. Fig 2 shows the changes of optimal operation cost along with load against time .The variation of generation cost along with load display that the applied methodologies identify the accurate relationship between two quantities.

x 10· !'I ----.--.--------• • • • • • ----- - - .- - .-------- • • - • • • • • • ------- • • •.• • • ------- • • • • • •

-.-.Ctt'!;n�I·:ltioll (".o�t : : : : 4.Ij c:::::::l Ucm . .::ruli uu luud t---------------�-------- -----!---------------- !

� J.O ---- - -- - ----L--- - -- - -------L - - - - --------- - J- - -- -..,..- : : :

I ' � :::::::::::::::::::::::::::::::::::::::::::.,_. u

1.

U.;., 10 HOllr 15 20

Fig. 2. Variation of optimal generation cost with hourly demand

25

B. Dynamic dispatch with cost and spinning reserve. (case 2)

The sequential quadratic algorithm is used to evaluate the combined dynamic dispatch on matlab platform. In Table.! result of generation and reserves are listed there. In fig.3 display the changes in generation cost along with reserve cost against the time. The changes of the optimized generation and reserve cost defined that the methodology is able to identify the accurate relation between quantities.

:< 10· 5.------------r---,--------.---�--,--------,

'0 HOlX -5 20 25 Fig. 3. Variation of optimal reserve/generation cost with hourly demand

Table II. Compare the optimal dynamic dispatch and spinning reserve results for hour 5 by using SQP algorithm and RDE [13]. From table is clear that the SQP algorithm is much better than the RDE because it take the less iteration to reach the feasible solution and give the quite good result.

C Optimal dynamic dispatch with cost and spinning reserve for generator outage contingency. (case 3)

The practical joint dynamic dispatch is computed using the sequential quadratic programming on Matlab platform and feasible values of generation and reserve for generator outage contingency are shows in Table.IV.

TABLE '- OPTIMAL GENERATION AND RESERVE COST FOR 24 HOURS AT DIFFERENT LOADS

Hour Load Reserve Generation Reserve Total cost iterations (Pd) (RD) cost ($) cost($) US($)/" MW MW 11 11

L F(l\) LG(�) - ; , I 1086 284 15327.82 5580 20907.82 136

2 1056 211 14823.8 3814 18637.8 140

3 986 139 13653.42 2242 15895.42 100

4 833 122 11146.01 1936 13082.01 110

5 1028 178 14355.01 3044 17399.01 110

6 1097 227 15512.63 5405 20917.63 147

7 1042 278 14590.6 5430 20020.6 83

8 1208 267 17418 7836 25254 148

9 1319 367 19462.7 7836 27298.7 122

10 1208 406 17418 8928 26346 139

II 1194 406 17173 8928 26101 112

12 1194 411 1717301 9068 2624101 104

13 1208 411 17418 9068 26486 141

14 1319 411 19462.75 9068 28530.75 100

15 1611 411 26064.83 9068 35132.83 93

16 1750 431 29313.2 9639 38952.2 108

17 2014 300 36368.25 5980 42348.25 60

18 2361 500 46910.4 11730 58640.4 12

19 2194 495 41547.5 11570 53117.5 53

20 1791 486 30382 11282 41664 118

21 1694 472 27940 10850 38790 124

22 1472 411 22720 9068 31788 118

23 1194 400 17347.91 8760 26107.91 77

24 1055 361 14807.01 7668 22475.01 143 Total cost 518335.9 183798 702133.9

US$ /day US$/day US$/day

TABLE II RESULT COMPARISON WITH RDE FOR HOUR 5

Unit Energy Reserve EnergyfRDEJ[131 ReservefRDEJ[131

MW MW

I 80 99.999 80 92

2 100 0 100 0 3 89.9976 50 88 50 4 79.9999 20 62 20 5 80.0002 00 80 0 6 79.9986 0 80 0 7 45.0002 0 45 0 8 44.9990 0 45 0 9 919645 0 136 0

10 86.0303 0 90 0 II 40.01124 0 40 0 12 0 0 0 0 13 39.9999 8 40 8 14 39.9999 0 40 0 15 49.9999 0 50 0 16 59.9999 20 40 20 17 0 0 0 0

Cost 14355.01 3044 14400.19 3043.0 US($)/H

Iterations 110 1000

In Flg.4 shows the vanatlOn of the generation and spmnmg reserve cost between case2 and case3. It is clearly seen that the operating cost in generator outage condition is greater as compare to the case 2. The graph has shows the Convergence

characteristics of energy and reserve dispatch in Fig.5. It indicates that the applied method generates the stable convergence behavior. The algorithm starts with user supplied initial values and reach the feasible optimal results were located very quickly within 150 iterations. In Fig.7 The algorithmic variation of step size of the variable is shown .As the algorithm proceeds towards the optimal solution, the initially step size are the large taken by the algorithm to reach the feasible result to give the optimal solution. Fig 6 shows variation of function evaluation counts with the progress of the algorithm.

Table 3 compares the SQP algorithm with the interior­point algorithm and analysis that the latter method takes greater time to reach optimal result

_ x 104 .� 5 ����������------r--------r-------' .- -- Glneration cost (casl 3) 3 � 4 -- Resme cost (ca,e 3) ............ � .... . B -- Glneration cost (casl 2)

; -- Resme cost (ca,e21 " t E 2

':I � :; '.:l i: = O �------�------�--�----�------�------� � 0 lC 15 20 25

Fig. 4. Comparision of optimal generation/reserve cost for case 2 and case 3

x '0' Current .t"uncnOll Vnlue: J8631.·�

2.2

1.E

' r, ." � 1.4 = =

� 1.2 Ii:

0.<

U.b 0.4 0 2C ·10 EC 80 1)) 120 '.1)

Fig. 5. Convergence characterstics of energy and reserve dispatch (Case 2)

TABLE III. COMPARISON OF SQP WITH INTERIOR POINT METHOD Method SQP iterations Interior- Iterations

point H-I 20907.82 136 20908.1 305

H-2 18637.8 140 18638.1 431

H-3 15895.42 100 15896.5 204

H-4 13082.01 110 13082.88 157

H-5 17399 01 110 17400.31 229

H-6 20917.63 147 20917.9 266

Total Function rvaluatiow: 5327

70,-------------,-----,------,-----,------,------,

60

, , , I I I 110 - -- - - - ---- t - - - --- - - - - i -- - - -- - - - - -i--- - - - - - - - -� - - - - - - - - - - t - - -- - - - - - - - - - - - - - - - -

, . , , , � 20 - -- - - - - - -- T - - - - -- - - - - .,------ - - - - -,-- - - - ------r - - - - - - ----r---- - - · - - - - - . - - - - - - -

I , I I I 10 .......... � .......... � ........... : ........... � .......... � .......... ......... .

° O�----J2 0�----4�O------6�O----�8 �O -----Jl0-0-----1J2�O -----J14 0 [t.�rjjt.i\lu

Fig. 6. Variation of function evaluations(counts) with the progress of the algorithm

TABLE IV. OPTIMAL DlSPATCH RESULTS FOR DIFFERENT HOURS( GENERATOR OUT AGE CASE)

HOUR3 HOUR 4 UNITS ENERGY RESERVE ENERGY RESERVE

(i) MW MW MW MW I 0 0 0 0 2 99.9999 19 100.0001 2 3 89.99729 50 89.99729 50 4 79.9999 20 39.9998 20 5 79.9989 0 80.0003 0 6 79.9984 0 79.99921 0 7 44.998 0 44.99972 0 8 44.9948 0 45 0 9 146.9886 0 90.00062 0

10 89.9886 0 81.06196 0 II 40.0039 0 39.99947 0 12 0 0 0 0 13 40.0003 30 40.0003 30 14 39.99823 0 39.99823 0 15 49.99823 0 50.00007 0 16 59.93917 20 11.98917 20 17 0 0 0 0

COST 14097 2806 11549.4 3742 US($)lH Iterations

100 110

Step Size: O.OOOIOM73 200,-----�----�----��----�----�------�----, 1 80 .......... , .......... , ........... : ........... , .......... , ......... .

. . , , 140 ----------�----.--.--:--.--.--.--:-----------:--------.--;--------_ • . - - -------

120 ......... , .. • -- .. . • • , .• . .. . .. . .. : ........... , .......... , ......... . _� 100 � UO ---------;.----------�-----------:-----------:--------.--�--.--.----

:: C:T T�r· •••• · •••• °u ;.w 4U GC UU Ttprntinn 1UU

Fig. 7. Variation of step size with the progress of the algorithm

1;lU

V. CONCLUSIONS

The joint energy and reserve dispatch plays a very significant role in restructure electricity market where separate bids are submitted for both commodities. Simultaneous allocation of reserve ensures that system reliability and security are maintained. This paper solves the joint dispatch model with complex equality and inequality constraints using SQP algorithm. The results are found to be feasible for different operating conditions such as load changes and generator contingencies. The results are validated with some previous results and interior point algorithm.

ACKNOWLEDGMENT

The financial support provided by University Grants Commission New Delhi for major research project received, vide F No.34-399/2008 (SR) dated, 24th December 2008 is sincerely acknowledged. The facilities and support provided by the M.I.T.S Gwalior administration is also acknowledge.

REFERENCES [I] X. Xia, A.M. Elaiw, "Optimal dynamic economic dispatch of

generation: A review", Electric Power Systems Research 80 (2010) 975-986.

[2] M. Pandit, L. Srivastava and K. Pal" "Static/dynamic optimal dispatch of energy and reserve using recurrent differential evolution", IET Generation, Transmission & Distribution, vol. 7, Issue 12, pp. 1401-1414, 2013 doi: 10.1049/iet-gtd.2013.0127

[3] S.Surender Reddy,B.K.Panigrahi,Rupam Kundu,R.Mukherjee,"Energy and spinning reserve scheduling for a wind thermal power system using CMA-ES with mean learning technique" International Elsevier Joumel of electrical power and energy system 53,march(2013) ,pp 113-122.

[4] M. Shahidehpour and M. Alomoush, "Restructured electrical power systems, operation, trading and volatility", IEEE Computer Application in Power, vol. I 5, no.2, April 2002, pp.60-62.

[5] A. Van Deventer, S. Chowdhury, S. P. Chowdhury, C. T. Gaunt, "Management of emergency reserves dispatching in electricity networks", IEEE International Conference on Power System Technology, Oct. 2010, ,pp. 1-5 .

[6] M. Rashidinejad, Y. H. Song and M. H. J. Dasht-Bayaz, "Contingency reserve pricing via a joint energy and reserve dispatching approach", Energy Conversion and Management, vol. 43, noA, March 2002, pp. 537-548.

[7] A. G. Bakirtzis, "Joint energy and reserve dispatch in a competitive pool using lagrangian relaxation", IEEE Power Engineering Review, vol. 18, no. II, Nov. 1998, pp. 60-62

[8] M. Xingwang, D. Sun and C. K wok, "Energy and reserve dispatch in a multi-zone electricity market", IEEE Transactions on Power Systems, vol. 14, no. 3, Aug 1999, pp. 913-919

[9] W. Jianhui, M. Shahidehpour and L. Zuyi , "Contingency-constrained reserve requirements in joint energy and ancillary services auction", IEEE Transactions on Power Systems, vol. 24, no. 3, August 2009, 1457-1468.

[10] P.Faria, Z. Vale, T. Soares, H. Morais, "Energy and reserve provision dispatch considering distributed generation and demand response", 3rd IEEE PES International Conference and Exhibition on Innovative Smart Grid Technologies, 2012 pp. 1 - 7.

[II] T. Soares, H .Morais, B.Canizes, , and Z. Vale, "Energy and ancillary services joint market simulation", Proc. 8th International Conference on the European Energy Market (EEM), 25-27,May 2011, pp. 262-267

[12] Y. Lin. and J. Zhong, "Energy and reserve dispatch in the integrated electricity market with sectional price offers", Proceeding of IEEE/PES Transmission and Distribution Conference and Exposition, April 2008, pp.!-6.

[13] Hejazi A., Mohabati H. R., Hosseinian S. H., and Abedi M., 'Differential evolution algorithm for security-constrained energy and reserve optimization considering credible contingencies', IEEE Transactions on Power Systems, 26,(3), 2011, pp. 1145-1155.

[14] K. Pal, M. Pandit and L. Srivastava, "Joint Energy and Reserve Dispatch in a Multi-area competitive Market Using Time-Varying Differential Evolution", International Journal of Engineering, Science and Technology, vol. 3, No.1, pp.87-106, 2011.

[15] E.N.Azadani, S.H. Hosseinian, B.Moradzadeh "Generation and reserve dispatch in a competitive market using constrained particle swarm optimization " International Journal of Electrical Power and Energy Systems, vol. 32, 2010, no.!, pp. 79-86.

[16] F. Wen and A.K.David, "Coordination of bidding strategies in day­ahead energy and spinning reserve markets", International Journal of Electrical Power and Energy Systems, vol. 24, no. 4, 2002, pp. 251-261.

[17] S.Mondal,A.Bhattacharya,S.Halder nee DeY,"Multi- objective economic emmision load dispatch solution using gravitational search algorithm and considering winf power penetration". International Elsevier Journel of electrical power and energy system 44june(2012),pp 282-292.

[18] W.Minlin,SJawchen,"Bid Based Dynamic Economic Dispatch with an efftcinent interior point algorithm" International Elsevier Journel of electrical power and energy system jan 2001,pp.51-57.

[19] M.A.Paqaleh and S. H. Hosseini, "Transmission constrained energy and reserve dispatch by hannony search algorithm", IEEE Power & Energy Society General Meeting, 26-30 July 2009, pp.1 - 8.

[20] N. Hazrati, M. R. Nejad, and A.A. Gharaveisi, "Pricing and allocation of spinning reserve and energy in restructured power systems via memetic algorithm", Large Engineering Systems Conference on Power Engineering, 10-12 Oct.2007, pp. 234 - 238.

[21] Matlab help file' www. Matworks.in/help/pdCdoc/optimloptim_tb.pdf' [22] R.F1etcher,"Sequential quadratic programming method", Springer Berlin

Heidelberg publisher non linear optimization lecture note in mathematics,20 I O,pp 165-214,DOI-0.I 007-978-3-642-11339-03.