Simultanous EDRP and Unit Commitment

Simultanous EDRP and Unit Commitment Programming In Comparison With Interruptible Load Contracts Mir Mohammadreza Sahebi, Esmail Abedini Duki, Mohsen Kia, Soroudi Alirez, Mehdi Ehsan Sharif University of Technology, Center of Excellence in Power System Management & Control

Abstract Power system restructuring, electricity price variation in some hours of a day and growth in the fuel price, has led to more attention to Demand Side Management (DSM) programs for consumers. Two important issues in DSM programs are demand response (DR) and interruptible load management (ILM). DR is utilized to decrease the consumption in the peak load hours or critical hours of a day. This occurs by means of the customer behavior in response to the incentives. On the other hand, the curtailment of voluntarily loads in the critical hours considering the consumer requirements is an action which can be performed in DSM. In this paper, the effects of Emergency Demand Response Programming (EDRP) on the unit commitment cost reduction are investigated. The results are compared with the interruptible load contracts. The proposed methodology has been formulated as a Mixed Integer Linear problem and implemented in GAMS environment. The proposed model is applied to a 6-bus test system and a modified IEEE 118-bus system to demonstrate its effectiveness. Key words: Emergency Demand Response programming, Unit Commitment, Interruptible Load Contracts

1. Introduction 1.1. Motivation and Problem Description Limited energy sources used in power generations and low efficiency in power plants, motivated energy authorities to use consumption management policies. Demand Side Management (DSM) includes managerial methods to reduce the electricity consumption. Moreover, to have a complete competitive market, there should be enough motivations for customers to participate in power market operation. DSM programs have created such 1

opportunities for customers to be as players in the market[1]. Peak load shedding and increasing Load Factor (LF) considering of load curve variation in a year are the most common methods in DSM [2]. Moreover the time of peak load in a day varies from country to country due to various social, cultural, economic and climate conditions. According to FERC order 719, DSM programs has been categorized into two main categories[3]: I- Incentive-based programs: Incentive-based DSM programs pay participating customers to reduce their loads at times requested by the program sponsor, triggered either by a grid reliability problem or high electricity prices. The incentive-based DSM programs substantially have market based structures, and can be offered in both retail and wholesale markets. Well-known incentive-based programs are as follows: I-1- Direct Load Control (DLC) I-2- Interruptible/Curtail able Service (I/C) I-3- Demand Bidding/Buy Back I-4- Emergency Demand Response Program (EDRP) I-5- Capacity Market Program (CAP) I-6- Ancillary Service Markets (A/S) II- Time-based programs: Armed with these programs, customers tend to use less electricity at times when electricity prices are high. The time-based DSM programs are established to overcome flat or averaged electricity pricing flaws. Many types of these programs are designed in different independent system operators (ISO). Timebased programs are categorized as follows: II-1- Time-of-Use (TOU) program II-2- Real Time Pricing (RTP) program II-3- Critical Peak Pricing (CCP) Program 1.2. Literature Review An economic model for two DR programs namely "Interruptible/Curtail able program" and "capacity market program" has been developed in[4]. In [5] a model has been proposed for combined TOU and EDRP programs to show that demand and load shape could be changed due to the ISO policy in running of DR programs. In[6]

2

optimum TOU Program was performed for Iranian Power System. A stochastic model to schedule reserve provided by DR resources in wholesale electricity market has been presented in[7]. The model proposed in [8] evaluated the effects of EDRP on system and load point reliability of a deregulated power system. In[9] a new procedure for enhancing of spinning reserve by means of DLC program has been presented. 1.3. Contributions An electric demand-response activity is an action taken to reduce electricity demand in response to price, monetary incentives, or utility directives so as to maintain reliable electric service or avoid high electricity prices. The most important benefit of demand response is improved resource-efficiency of electricity production due to closer alignment between customers’ electricity prices and the value they place on electricity[10]. One of the Incentive based DR programs is EDRP that act based on the sensitivity of the demand on price changes. Considering the cost of UC and EDRP Simultaneously is a good way for studding the efficiency of EDRP method in comparison with other DSM methods. Furthermore, in this formulation we can calculate the optimum incentive price as a variable in the optimization problem. In This Paper, simultaneous implementation of UC and EDRP program has been used for a 4 week period. Also, to show the effectiveness of proposed methods, a 6 bus test system and the modified IEEE 118 Bus system are used as case studies. Results of this part have been compared to those of Interruptible Load Contracts (ILC) implementation. It shows a decrease in proposed method cost in comparison with ILC. 1.4. Paper Organization The rest of this paper is organized as follows: In section II, a model For EDRP is presented. Suggested objective function consisting of simultaneous EDRP and UC program in the 4 week period Considering Fuel Constraints is presented in section III. Section IV, implementation of ILC in UC program is shown. Section V presents the case studies and numerical results have been mentioned above. Finally the conclusion is presented in section VI. 2. Emergency Demand Response Programming The ISO by executing the demand response Program intends to decrease system peak load[11]. To do this, ISO applies price data and short term load prediction. Also, ISO offers a reward to the consumers to motivate

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them to participate in this program. Large consumers which are able to curtail a portion or all of their loads, participate in this program voluntarily. This program has two main advantages: First, the “incentive price” determining before executing the program. Second, ISO do not force consumers who participate in the program to curtail their loads. It should be noted that the execution of this program leads to satisfactory results in the American power markets[12]. Today, the price of electricity is affected directly by the demand amount and the consumers adjust their demand according to the electricity price. Demand elasticity is defined as the sensitivity of demand with the change of electricity price[5]:

E =

¶q p0 dq = . ¶p q 0 dp

(1)

According to (1), the elasticity of ith load period with regard to jth load period is defined as below[13]:

E (i , j ) =

¶q (i ) p0 ( j ) dq (i ) = . ¶p ( j ) q 0 (i ) dp ( j )

(2)

Equation (2) shows the amount of the demand variation in thi period with regard to the price variations in thj period. As the price in one period increases, the intention of energy consumption decreases during that period. On the other hand, consumers intend to shift their loads to other periods if possible. Thus,“self elasticity” is negative and “cross elasticity” is positive. To handle price variations, consumers operate in two ways[14]: - Single period loads: These types of loads are not able to be shifted to other periods. To response against price variations, these loads could be truly disconnected or not. These loads just evaluated by“self elasticity” in the programming. - Multi period loads: These types of loads are able to be shifted to other periods. These consumers are eager to shift their consumption from peak load period to off-peak or low periods. These loads are evaluated by“cross elasticity” in the programming. Due to special characteristics of the electrical energy, small consumers respond to price variation hardly. So, they are categorized as single period loads. On the other hand, industrial consumers intend to decrease their load during peak load period and increase it during off-peak and low periods. They do this in order to decrease their operation costs. Thus, they are categorized as multi period loads. 4

The maximum consumer net surplus is achieved whenever the derivative of the Net Consumer Surplus (NCS) function regarding the consumption isequal to zero [15]:

¶NCS ¶ = {GCS (q (t )) - q (t ) p (tz ) + a (tz )(q 0 (t ) - q (t ))} = 0 ¶q (t ) ¶q (t )

(3)

Also, the Gross Consumer Surplus (GCS) is defined as:

GCS (q (t )) = GCS (q 0 (t )) + p (tz ) * (q (t ) - q 0 (t ))(1+

q (t ) - q 0 (t ) ) 2q 0 (t )å tz E (t ,tz )

(4)

Therefore the consumer’s load regarding to the incentive price is as follows[5]:

q (t ) = q 0 (t ).(1 +

å

tz

a (tz ).E (t , tz ) p (tz )

)

(5)

The execution of EDRP leads to an extra cost for ISO. The source of this cost is from the incentive price given to the consumers [5]:

C EDRP = a (tz )(q 0 (t ) - q (t )) = -

a (tz ) 2 q 0 (t ) åtz E (t , tz ) p (tz )

(6)

Equation (6) shows that the cost of EDRP execution is a function of incentive price. The ISO must reach the optimum cost regarding to the power production costs and extra cost due to EDRP. Therefore, in the proposed model in (6), parameter α is regarded as a variable like the rest of variables in unit commitment problem. So,α is calculated based on minimization of total system costs. 3. Objective Function In this paper, the cost of UC and EDRP are considered simultaneously as objective function. The objective function of Simultaneous EDRP and UC program has been shown in (7), as follows: Np N t Ng

min TC = min{å å å[ FC ,i ( Pi ,t ) . I i ,t +SU i ,t + SD i ,t ] + C EDRP }

(7)

p =1 t =1 i =1

As shown in (7), the main purpose is to reduce the total cost of generation units productions and obtaining the optimum cost of DR program. Equation (8) shows the nonlinear cost function of generation units:

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FC ,i ( Pi (t )) = ai Pi 2 (t ) + bi Pi (t ) + ci

(8)

If (8) is used in the optimization problem, a non-linear mixed integer function will be achieved. To avoid nonlinearity in the optimization problem, a piecewise linear cost function is used in this paper, as follows:

FC ,i ( Pi ,t ) = Fi ( Pi ,t min ).I i ,t + s i ,t 1 Pi ,t ,1 + ... + s i ,t ,n Pi ,t ,n 0 £ Pi ,t , k £ P + i ,t ,k

for

k = 1, 2,..., n

(9)

Where, Si,t is the cost function slope for thekth part and Pi,k is the unit generation production inkth part. The hourly UC constraints included in the optimization problem are listed below[16]: - The system power balance constraints - Real power generation constraints - Minimum up and down time constraints - Ramping up and down constraints - Reserve constraints - Transmission flow limits (line flow constraints have been considered using two-stage benders decomposition for faster convergence [17]) - Unit fuel constraints:

Fi

min

FGjmin £

Np Nt

£ åå ( Ff ,i ( Pitp ) + SU f , itp + SD f , itp ) £ Fi max

(10)

p =1 t =1

Np Nt

å åå (F

i ÎGj p =1 t =1

f ,i

( Pitp ) + SU f , itp + SD f , itp ) £ FGjmax

(11)

4. Interruptible Load Contracts If active units can’t meet demand, or demand supply cost in a bus is more than the cost of Interruptible Load contract (ILC), load will be interrupted in mentioned bus. For each bus, load interruption is defined in different hours; the equation for this purpose is described in (12), as follows[17]: L ì 0; if PLb - PGb - å S Lb f Ltp £ 0 ü ï ï L =1 =í NL ý S Lb f Ltp ; Otherwise ïî PLbtp - PGbtp -å ïþ L =1 N

LS btp

6

(12)

For Load Shedding (LS), there are also constraints, which are:

LS btp - PLbtp £ 0

(13)

0 £ LS btp £ M * ILS btp Where M is an assumptive large positive number. If binary variableILSbtp is equal to one, it means that LS occurs in the bus. Else, as shown by the equation (13), LS would be zero[18]. The contracts that are held between consumer and ISO for load shedding (based on IEEE 798 standard) are described as follows [19]: - The maximum number of curtailments per year for whole system: This is a long-term constraint and the LOLP calculation needs LS calculation weekly:

å å å LOLP = Np

Nt

Nb

p =1

t =1

b =1

ILS btp

N t *N p

£ LOLPfix

(14)

- The maximum number of curtailments per year for each bus:

LOLPb

å å = Np

Nt

p =1

t =1

ILS btp

N t *N p

£ LOLPfix ,b

(15)

- The maximum load curtailment in each bus:

LS btp £ LS b Max

(16)

- The maximum duration of each curtailment Considering ILC in UC, load interruption cost must be added to the total cost. Thus the cost function is as follows: Nb

C LS = å ILPb * LS btp

(17)

b =1

Np Nt Ng

minTC = min{ååå[ FC ,i ( Pi ,t ). I i ,t +SU i ,t + SDi ,t ] + CLS }

(18)

p =1 t =1 i =1

5. Numerical Studies To perform long term unit commitment with ILM and EDRP which their formulation were presented in sections V and VI, the mixed integer linear programming technique has been used. 7

In this paper, GAMS program and CPLEX method (an efficient method for solving MILP problems) has been utilized to solve the optimization problem[20]. In this section, proposed method was applied to the 6-bus test system and the modified IEEE 118 bus system, respectively. Then, the numerical results have been compared with each other in four following cases: a) Long term unit commitment considering fuel limits b) Long term unit commitment considering fuel limits and ILM (some of the interruptible load contracts) c)

Simultaneous EDRP and Unit commitment program considering fuel limits. The incentive price is

considered to be equal to the price of ILM contracts. d) Simultaneous EDRP and Unit commitment program considering fuel limits with determining of

optimized incentive price (Intelligent EDRP). 5.1. 6-Bus Test System Results 6-bus test system (shown in Figure 1. ) contains three generation units and seven transmission lines. Loads and spinning reserves are different in studying duration (672 hours or four weeks). Furthermore, transmission line constraints are considered. Case study's data are available in[21]. In this work, the day is divided to three different periods based on Load Curve (Low Peak, Off Peak and Peak). Also, the self and mutual elasticity values related to this system has been shown inTABLE I. TABLE II. Demonstrates the results of the optimization problem for the 6-bus test system in four different cases; at first, unit commitment has been carried out without EPDR and ILM which case“a”. So in this case the total cost is just the cost of unit commitment. In case“b”, proposed price for ILM is 25$/MW. Also LOLPfix is considered equal to 0.1. As shown in TABLE II. , the total cost in this case is less than the previous one. The changed load curve of this case has been presented for two days (48 hours) inFigure 2. In case “c”, long term unit commitment with EDRP has been considered according to equation (7), regarding an incentive price equal to 25$/MW (as same as the price of ILC).TABLE II. Obviously shows that the total cost has become less than two previous cases. Also, the other parameters inTABLE II. such as LF shows that EDRP leads to a better solution than ILM in total cost, peak reduction and flatting the load curve.

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Intelligent EDRP has been simulated in case“d”. In this program, the purpose is to calculate the deliverance reward to consumers in order to minimize the sum of generation cost and payments to the consumers according to the (7). In this case the optimized reward is 16.99$/MW. Calculating optimized reward paid to the consumers leads to the best total cost in case “d”. Figure 3. , shows the changed load curve of this case in four weeks (672 hours), also for two days (48 hours) is shown in Figure 4. According to the numerical results, by performing the EDRP, peak load have been reduced and transferred to other time periods. So LF has been increased. Furthermore, the intelligent EDRP cause the reduction in the total cost of simultaneous performing of UC and EDRP. It is concerned that withperforming this program better results are reached in aspect of LF and total cost in comparison with ILM contracts. 5.1. Modified IEEE 118-Bus System Results Modified IEEE 118-bus system contains 54 generation units and 186 transmission lines. Loads and spinning reserves are different in over the operation horizon under study (672 hours or four weeks). In addition, transmission line constraints are considered. This system's data are available in[21]. Also TABLE III. presents self and mutual elasticity values related to this system. TABLE IV. demonstrates the results of the optimization problem in modified 118-bus system for four different cases. For more comparing, figures 5 to 7 have been presented. The changed load curve of case 2 has been presented for two days (48 hours) inFigure 5. Figure 6. , shows the changed load curve of case 4 in four weeks (672 hours), and Figure 7. shows that in two days (48 hours). According to the numerical results, by performing the EDRP, peak load have been reduced and transferred to other time periods. So LF has been increased. Additionally, the intelligent EDRP caused the lowest total cost in comparison with three other cases. 6. Conclusion Due to the variation of electricity price in some hours of the day, DSM has been considered in restructured power systems. DSM programs have created such opportunities for customers to be as players in the market. In this paper, EDRP (as a method of DSM) was implemented on a 6-bus test system and a modified IEEE 118-bus

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system and the results were analyzed. From the numerical results, it is concluded that EDRP leads to LF improvement. It is also noticeable that results show more efficiency in comparison with the ILM programs. Moreover, simultaneous EDRP and UC leads to a more decrease in the total costs while the decrease rate of the peak value is as same as ILM. Additionally, the intelligent EDRP caused the lowest total cost in comparison with three other cases. It is also note worthy that the proposed optimization formulation consists of many integer and non-integer variables which cause more complexity and time consuming procedure. To overcome the deficiency the linearization approach is used in the proposed method, thus it should be appropriate for larger networks.

Appendix List of Symbols

TC

Total cost of unit commitment programming ($)

FC ,i ( Pi ,t ) Running cost of unit i in hour t

Pi ,t

Real power generation of unit i during hour t (MW)

I i ,t

Binary variable of generation unit commitment Equals 1 if generator is online during hour t, 0 otherwise)

SU i ,t

Startup cost of unit i during hour t

SDi ,t

Shutdown cost of unit i during hour t

Ff ,i (Pitp )

Fuel usage of unit i running during hour t in week p

Fi min

Minimum permissible fuel usage of unit i

Fi max

Maximum permissible fuel usage of unit i

FGjmin

Minimum permissible fuel usage of generation group Gj

FGjmax

Maximum permissible fuel usage of generation group Gj 10

SU f ,itp

Startup fuel usage of unit i during hour t in week p

SDf ,itp

Shutdown fuel usage of unit i during hour t in week

C EDRP

Cost of EDRP participation ($)

GCS

Gross consumer surplus

NCS

Net consumer surplus

E (t , tz )

Price elasticity of the hour t versus period tz

a (tz )

Incentive price paid to the costumer in load period tz for voluntary load reduction ($/MWh)

p (tz )

Price of electricity in period tz ($/MWh)

q 0 (t )

Initial demand of costumer (MW)

q (t )

New demand of costumer after participation in EDRP

C LS

Cost of interruptible load programming participation ($)

LS btp

Load shedding in bus b at time t (MW)

ILPb

Bidding price for interruptible load in bus b ($/MWh)

ILS tp

Binary variable of interruptible load participation (equals 1 if load curtailment occurs during time t and week p, 0 Otherwise).

PLbtp

Demand at bus b during period t in week p (MW)

LS b max

Maximum amount of reduction that has been mentioned at bus b (MW)

f Ltp

Electricity flow in line l at time t in week p

LOLPfix ,b Line-nod Conjunction matrix LOLPfix

Desired value of LOLP for whole system

LOLPfix ,b

Desired value of LOLP for each bus

tz

Time period of consumption (included Peak, Off-peak, Low) 11

i

Index of generation units from 1 to Ng

t

Index of time running in a week from 1 to Nt (168 Hours)

p

Index of week number from 1 to Np

l

Index of line number from 1 to NL

References [1] FERC Staff, "Assessment of demand response and advanced metering", Federal Energy Regulatory

Commission, Docket AD-06-2-000 (2006) [2] U.S. Department of Energy, "Energy policy Act of 2005", section 1252, February 2006. [3] Federal Energy Regulatory Commission, "Wholesale Competition in Regions With Organized Electric

Markets", FERC Order No. 719. Available: http://www.ferc.gov. [4] H.A.Alami,

M.Parsa

Moghaddam,

G.Yousefi,

"Demand

Response

Modeling

Considering

Interuptible/Curtailable Loads And Capacity Market Programs", Applied Energy 2010, pp. 243–250. [5] H.A.Alami, G.Yousefi, M.Parsa Moghaddam, "Demand Response Model Considering EDRP and TOU

Programs", IEEE/PES 2008. [6] H.A.Alami, M.Parsa Moghaddam, G.Yousefi, "Optimum Time of Use Program Proposal for Iranian Power

Systems", Electric Power and Energy Conversion Systems, 2009. EPECS. [7] M.Parvania, M.Fotuhi Firuzabad, "Demand Response Scheduling by Stochastic SCUC", IEEE Transactions

on Smart Grid, vol. 1, NO. 1, June 2010. [8] R.Azami, Abbasi, J.Shakeri, A.Faraji Fard, "Impact of EDRP on Composite Reliability of Restructured

Power Systems", IEEE 2009 Bucharest Power Tech Conference, June 28th - July 2nd. [9] A.Yousefi, H.Aalami, E.Shayesteh, M.P.Moghaddam, "An Approach for Improving Spinning Reserve

Capacity By Means Of Optimal Utilization Of DR Program", Second IEEE International Conference on Power and Energy, Dec. 1-3 2008, Johor Baharu, Malaysia

12

[10] "Benefits of Demand Response in Electricity Markets and Recommendations for Achieving Them", U.S.

Department of Energy, 2006. [11] M.Fahliglu,

F.L.Alvarado, "Designing Incentive

Compatible Contracts for Effective Demand

Management", IEEE Transaction on Power Systems, Vol. 15, No 4, PP 1255-1260, Nov 2000. [12] Federal Energy Regulatory Commission, "Regulatory Commission Survey on Demand Response and Time

Based Rate Programs/Tariffs", August 2006, www.FERC.Gov. [13] J.G.Roos, I.E.Lane, "Industrial Power Demand Response Analysis for One Port Real Time Pricing", IEEE

Trans. on Power System, vol. 13, no. 1, pp. 159-164, Feb. 1998. [14] D.S.Kirschen and G.Strbac, "Fundamenals of Power System Economics", Willey 2004. [15] J. G. Roos, I. E. Lane, "Industrial power demand response analysis for one port real time pricing", IEEE

Trans. On power system, vol. 13, no. 1, pp. 159-164, Feb. 1998. [16] J.Wang, M.Shahidehpour, Z.Li, "Security Constrained Unit Commitment with Volatile Wind Power

Generation", IEEE Transactions on Power Systems, vol. 23, NO. 3, August 2008. [17] Mohammad Shahidehpour, Yong Fu, "Benders decomposition: applying Benders decomposition to power

systems", IEEE Power and Energy Magazine, Vol. 3, November March-April 2005, pp. 20-21. [18] M.Bozorg, E.Hajipour, S.H.Hosseini, "Interruptible Load Contracts Implementation in Stochastic Security

Constrained Unit Commitment", PMAPS 2010. [19] IEEE Standard 739-1984 "Recommended Practice for Energy Conservation and cost-effective planning in

Industrial facilities". [20] GAMS User Guide Available At Http://www.Gams.com. [21] L.Wu, M.Shahidhpour, T.Li, "Stochastic Security-Constrained Unit Commitment", IEEE Transactions on

Power Systems, Vol. 22, No. 2, May 2007, pp. 800-811. [22] The detailed 118-bus system data are given Websitewww.motor.ece. iit.edu/ data/SCUC_118.

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List of Figures ·

Figure 1: Single line diagram of sample 6-bus system

·

Figure 2: Results of applying UC and ILM with the price of 25$/MW for 6-bus system

·

Figure 3: Results of applying intelligent EDRP and UC in four weeks for 6-bus system

·

Figure 4: Results of applying intelligent EDRP and UC in 48 hours for 6-bus system

·

Figure 5: Results of applying UC and ILM with the price of 25$/MW for modified 118-bus system

·

Figure 6: Results of applying intelligent EDRP and UC in four weeks for modified 118-bus system

·

Figure 7: Results of applying intelligent EDRP and UC in 48 hours for modified 118-bus system

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TABLE I.

Elasticity Values for 6-bus Test System

Low Off Peak Peak 01:00-08:00 09:00-19:00 20:00-24:00 Low -0.1 0.016 0.0199 Off Peak 0.016 -0.1 0.012 Peak 0.0199 0.012 -0.1

TABLE II.

Optimization Results of UC Simultaneous with EDRP and ILM for the 6-bus test system

Case a Total Cost

Case b

Case c

Case d

2500326.00 2453792.20 2413499.35 2382726.87 64932 29910

Cost of EDRP Incentive Price($/MWh)

-

-

25

16.99

ILC Price ($/MWh)

-

25

-

-

LOLP

-

0.026786

-

-

LF

70.11

71.57

73.26

72.10

Peak Decrease % Peak to Valley Decrease % Energy Usage Decrease %

-

2.22

4.81

3.12

-

3.92

11.02

7.26

-

0.18

0.53

0.36

TABLE III.

Elasticity Values for Modified 118 Bus System

Low Off Peak Peak 01:00-08:00 09:00-19:00 20:00-24:00 Low -0.1 0.016 0.034 Off Peak 0.016 -0.1 0.092 Peak 0.034 0.09 -0.1

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TABLE IV.

Optimization Results of UC Simultaneous with EDRP and ILM for Modified 118 Bus system

Case a

Case b

Case c

Case d

Total Cost

21420570

21400270

21378540

21282320

Cost of EDRP

-

-

Incentive Price($/MWh)

-

-

25

ILC Price ($/MWh)

-

25

-

10.326 -

LOLP

-

0.084821

-

-

LF

73.772

78.035

76.148

75.71

Peak Decrease % Peak to Valley Decrease % Energy Usage Decrease %

-

5.92

4.8077

3.9615

-

1.3633

9.7257

8.014

-

0.48439

1.7422

1.4391

534182.708 364495.422

Figure 1. Single line diagram of sample 6-bus system

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Figure 2.

Results of applying UC and ILM with the price of 25$/MW for 6-bus system

Figure 3. Results of applying intelligent EDRP and UC in four weeks for 6-bus system

Figure 4. Results of applying intelligent EDRP and UC in 48 hours for 6-bus system

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Figure 5. Results of applying UC and ILM with the price of 25$/MW for modified 118-bus system

Figure 6. Results of applying intelligent EDRP and UC in four weeks for modified 118-bus system

Figure 7.

Results of applying intelligent EDRP and UC in 48 hours for modified 118-bus system

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