Purchase Strategies for Power Retailers Considering Load Deviation and CVaR

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Energy Procedia 158 Energy Procedia 00(2019) (2017)6658–6663 000–000 www.elsevier.com/locate/procedia

10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China

Purchase Strategies for Power Retailers Considering Load Deviation The 15th International Symposium on District Heating andLoad CoolingDeviation Purchase Strategies for Power Retailers Considering and CVaR and CVaR Assessing the of using the heat demand-outdoor a feasibility a Yanmin Guoa, Ping Shaoa, Jun Wangbb, Xun Doubb*, Wenhao Zhaobb Yanminfunction Guo , Pingfor Shao Jun Wang , Xun Dou *, Wenhao Zhao forecast temperature a ,long-term district heat demand China Electric Power Research Institute,Nanjing 210003,Jiangsu Province,China a

Electricand Power Research Institute,Nanjing Province,China College of ElectricalaChina Engineering Control Science,Nanjing TECH 210003,Jiangsu University,Nanjing 211816, Jiangsu Province,China a,b,c a a b c c b College of Electrical Engineering and Control Science,Nanjing TECH University,Nanjing 211816, Jiangsu Province,China b

a

I. Andrić

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b

Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract The power market has been divided into two parts in this paper, one is the main purchase market which includes the forward The power market dividedmarket, into two onemarket is the for main purchasedeviations. market which includes the forward contract market andhas thebeen day-ahead theparts otherinisthis the paper, real-time balancing A multi-objective unified contract market and thehas day-ahead market, the other at is minimizing the real-timethe market for balancing A multi-objective unified power purchase model been established aiming total purchase cost deviations. and the CVaR, considering the load Abstract power purchase been established aiming at minimizing total purchase and the themodel CVaR,ofconsidering the load deviations whichmodel we usehas probabilistic statistics to quantify. Then, anthe example is used tocost verify the power purchase deviations which use probabilistic statistics to quantify. Then, proposed an example used to verify the model of the power purchase combination. Thewe results show that the power purchase strategy in is this paper can provide a reference for the power District heating are commonly addressed in the literature as one mostcan effective for for decreasing the combination. The networks results show that theinpower purchase strategy proposed in of thisthe paper providesolutions a reference the power retailers to occupy a favorable position the diversified market competition. greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat retailers to occupy a favorable position in the diversified market competition. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Copyright © 2018 Elsevier Ltd. All rights reserved. © 2019 The Published by Elsevier Ltd. prolonging the investment return period. Copyright ©Authors. 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy This ismain an open access article under the CCthe BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) The scope of this paper is to assess feasibility of using the heat demand temperature function for heat Energy demand Selection and peer-review under responsibility of the scientific committee of the 10–thoutdoor International Conference on Applied (ICAE2018). Peer-review under responsibility of thelocated scientific committee of ICAE2018 The as 10th Conference forecast. The district of Alvalade, in Lisbon (Portugal), was –used a International case study. The district on is Applied consistedEnergy. of 665 (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: load deviation; CVaR; purchase strategy; power retailer renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: load deviation; CVaR; purchase strategy; power retailer compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The liberalization of the power market madewithin the demand-side more andcorresponds the markettohas The value of slope coefficient increased on has average the range of participants 3.8% up to 8% perdiversified decade, that the The liberalization of theheating powerhours market hasThe made the demand-side participants moreondiversified and the market has become and [1-2]. power had to formulate purchase to decreasemore in theactive number of competitive of 22-139h during retailers the heating season (dependingreasonable the combination ofstrategies weather and become more and competitive The power retailers had to formulate purchase strategies lower costs andactive risksconsidered). considering allocation characteristics in 7.8-12.7% thereasonable face ofpercompetitive pressures. A renovation scenarios Ondifferent the[1-2]. otherresource hand, function intercept increased for decade (depending on to the lower costs and risks considering different resource allocation characteristics in the face of competitive pressures. A reasonable combination of purchase make power retailers advantageous the market coupled scenarios). The values suggestedcan could be used to modify theoccupy functionan parameters for the position scenarios in considered, and reasonable combination of purchase can make power retailers occupy an advantageous position in the market improve the [3-4]. accuracy of heat demand estimations. competition Conditional value-at-risk (CVaR) can effectively weigh the risks and benefits of the power retailers'

competition [3-4]. Conditional value-at-risk (CVaR) can effectively weigh the risks and benefits of the power retailers' © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-25-5813-9517; fax: +86-25-5813-9187. * E-mail Corresponding Tel.: +86-25-5813-9517; fax: +86-25-5813-9187. address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]

1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.038

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decision-making process [5-6]. In a certain risk environment, the power retailers need to allocate the amount of power purchased rationally in the multi-power market to obtain greater benefits [7-8]. Most of the existing researches are based on the superiority of CVaR in risk measurement to study the best economy in market transactions for power retailers [9-10], but there is not a lot of research to integrate the impact of load deviation on purchase for power retailers [11]. This paper divides the power purchase market into two purchase market, one is the main purchase market which includes the forward contract market and the day-ahead market, the other is the real-time balanced market that balances the load deviations. This paper formulates the power purchase strategy by establishing a multi-objective model aiming at minimizing the total purchase cost and the CVaR, considering the cost of balancing the deviations in the real-time market. Finally, by solving the model the results are analyzed and discussed. 2. Purchase Model for Power Retailers 2.1. Basic assumption From the central limit theorem of probability theory, the total load approximates the probability distribution in a given grid. Provided that the actual power demand of the power purchase subject obeys the normal distribution, as shown in Formula (1), where X t is the actual value of the load, Q t is the expectation of the forecast load,  2 t is the variance of the forecast load. The difference between the actual load and the forecast load is the deviation load which satisfies Formula (2). Y t represents the load deviation.

()

() ()

X (t )  N (Q (t ) , 2 (t ))

Y ( t )  N ( 0, 2 ( t ) )

()

(1) (2)

In the open electricity market, different time curves can be presented at different time periods. Assuming that the market price is subject to the normal distribution, as is shown in Equation (3), where Pi (t ) is the price of the day2 ahead market,  (t ) is its expectation, and  p (t ) is its variance. Using Pf to indicate the power price of the forward contract market, it is a fixed value in one day's power purchasing combination.

Pi (t )  N (  (t ),  p2 (t ))

(3)

The real-time market is more flexible than the main power market described above. Assuming that the price of the real-time market is Pr (t ) , its supply and demand balance sensitivity is  (t ) , which satisfies Formula (4). Real-time prices Pr (t ) can be expressed in Equation (5).

Pr (t ) − Pi (t ) X (t ) − Q(t ) Y (t ) =  (t ) = (t ) Pi (t ) Q(t ) Q(t ) Y (t ) = Pr (t )  (t ) Pi (t ) + Pi (t ) Q(t )

(4) (5)

It indicates that the purchased power is not enough when Y (t ) is greater than 0. The retailer needs to purchase power from the real-time market and this purchase price is represented by Prb (t ) .When Y (t ) is less than 0, it indicates that there is a surplus in purchased power. The retailer will sell it in the real-time market, and this price will be represented by Prs (t ) .They meet Equation (6) and (7) respectively.

Y (t ) Pi (t ) + Pi (t ) Q(t ) Y (t ) Prs (t ) = Pi (t ) + Pi (t ) − ( t ) Q(t )

Prb (t )  ( t ) =

(6) (7)

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2.2. Combination of power purchase Let the purchase amount of the forward contract market be Q1 (t ) , the amount of the day-ahead market is Q2 (t ) . Their relationship is shown in Equation (8), (9) and (10), where 1 (t ) and 2 (t ) indicate the combination coefficient.

Q1 (t ) = 1 (t )Q(t )

(8)

Q2 (t ) = 2 (t )Q(t ) 1 (t ) + 2 (t ) = 1

(9) (10)

On the basis of the above-mentioned combination strategy, C1 indicates the cost of power purchase in the forward contract market, C2 indicates the cost of the day-ahead market and Cr indicates the cost of balancing the deviation in the real-time market, as shown in Equation (11), (12) and (13). In Equation (13), f ( y ) represents the probability density function and satisfies Equation (14). In summary, the total cost of power purchased by the retailer is the sum of the costs of the three parts of the forward contract market, the day-ahead market and the real-time market, as shown in Equation (15).

= C1

T

Pf Q1 (t ) =

T

 (t ) P Q(t )

=t 1 =t 1 T

= C2

Pi (t )Q2 (t ) =

T

 (t ) P (t )Q(t ) i

(12)

1 T   Prb (t ) − Prs (t ) (t ) 2 t 1 1= −

(13)

=t 1 =t 1 + T

= Cr

(11)

f

1

2

P= r (t )  yf ( y )dy t

y2

− 2 1 e 2 ( t ) 2

f ( y) =

(14)

T

T

1 T   Prb (t ) − Prs (t ) (t ) 2 t 1 =

C = 1 (t ) Pf Q ( t ) + 2 (t ) Pi (t )Q (t ) +

=t 1 =t 1

(15)

2.3. CVaR model for power purchase Supposing P0 is the price of power sold by the retailer and the customer, the expected value of deviation of forecast load is 0 for the retailer. Ce is the expectation of the cost of power purchase, E ( R) indicates the expectation of profit and R represents actual profit considering load deviation, as shown in Equation (16) (17) (18). The loss function is shown in Equation (19).

= Ce

T

T

1 (t ) Pf Q(t ) + 2 (t ) Pi (t )Q(t )

(16)

=t 1 =t 1 T

= E ( R)

P Q(t ) − C t =1

= R

0

e

(17)

T

P X (t ) − C t =1

0

(18)

T

f =− R =C − P0 X (t ) t =1

(19)

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Based on the analysis of the CVaR model in the literature [12], taking m sample values of power demand and the day-ahead price. Then the approximate value of CVaR can be expressed by Equation (20), where α is the VaR under the constraint of certain confidence level and risk level, that is, the unit's maximum possible loss of the power retailer, + β is the confidence level of CVaR. − Rk −  represents the maximum between 0 and − Rk −  .

F = +



1 +  − Rk −    m(1 −  ) k =1 m



(20)

2.4. Purchase strategy for power retailers considering load deviation and CVaR The combination of a forward contract and a day-ahead transaction can not only ensure long-term stable power supply, but also adapt to the current scheduling mode of power generation and provide opportunities for further profitability when the market is favorable. A multi-target power purchase plan with the lowest power purchase cost and risk is formulated, considering the flexibility of real-time market transactions in terms of load deviations. The objective function is shown in Equation (21).

 min C ( 1 , 2 )  Z F= = (1 , 2 )    min F (1 , 2 )  s.t. 1 + 2 = 1

(21)

3. Results and Discussion Based on relevant historical data of a certain region, an example analysis of the purchase results for the power retailer based on the purchase strategy proposed in this paper on a certain day is performed. The relevant data is shown in Table 1. The price of the forward contract is 550 ¥/MW and the sale price is 570 ¥/MW. The unit of the power is 'MW'. Table 1. A regional power market related data time

1

2

3

4

5

6

7

8

9

10

11

12

Q

520

500

500

510

560

630

700

750

760

800

780

740

26

25

25

25.5

28

31.5

35

37.5

38

40

39

37

250

150

150

130

250

350

400

500

650

850

900

850

13

12

12

12.5

13.5

14

15

16

16.5

18

19

18.5

1.98

2.01

1.98

1.95

2.01

2.04

2.05

2.10

2.16

2.29

2.34

2.16

time

13

14

15

16

17

18

19

20

21

22

23

24

Q

720

720

760

800

850

880

900

870

780

710

650

560

36

36

38

40

42.5

44

45

43.5

39

35.5

32.5

28

800

650

500

550

840

850

950

940

650

500

400

350

18

17

16

16.5

18

19

20

19.5

16.5

16

15

14.5

2.17

2.18

2.15

2.15

2.28

2.27

2.38

2.37

2.16

2.17

2.04

2.03

q  



q  



3.1. Analysis of the Pareto front of the purchase strategy Based on the above data, NSGA-II algorithm is used to simulate the example in MATLAB. The population size pop is 1000 and the maximum evolution generation gen is 400. The Pareto front of the power purchase program in one day developed by the purchase combination strategy proposed in this paper is shown in Fig. 1.

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From the Fig. 1, it is concluded that lowering the CVaR is at the cost of increasing the total cost of the power purchase and vice versa. Power retailers need to weigh between low cost and low risk. Point A indicates that the decision is more inclined to low cost, point C is more likely to be low risk and point B is the relative compromise decision. The corresponding proportion of power purchases is shown in Fig. 4, in which the purchase of power during peak time is mainly based on forward contracts and even reaches a maximum value. In the valley time, the risk is lower if the purchase of power is mainly based on forward contracts and on the contrary, the cost is lower if it is dominated by the day-ahead market.

Fig. 1. Pareto front of C and CVaR

Fig. 2. Comparison of purchase strategies

Fig. 3. Different confidence levels

B

A

C

1.0

λ1

λ2

0.9

proportion

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

1

6

11

time

16

21

1

6

11

time

16

21

1

6

11

time

16

21

Fig. 4. Distribution of power purchase ratio

3.2. Analysis of the compared to general strategy without considering load deviation Comparing the power purchase strategy in this paper with the general purchase strategy that only considers the cost and CVaR of purchase without the load deviation, the Pareto front of the cost and CVaR of one day purchase is shown in Fig. 2. The Pareto front obtained by the purchase strategy proposed in this paper is below the general purchase strategy. The purchase strategy considering load deviation and CVaR in this paper have a certain advantage over low-cost and low-risk targets relative to general power purchase strategies. 3.3. Analysis of the compared to different confidence levels For different confidence levels, the Pareto front after optimizing the purchase strategy in this paper is shown in Fig. 3, in which when the confidence level increases, the curve of the solution set shifts to the upper right, that is, at the

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same level of return, the higher the confidence level, the greater the CVaR. Conversely, the lower the confidence level, the smaller the CVaR. 4. Conclusions This paper studies the issue of purchase strategies for power retailers that consider the load deviations and CVaR. A multi-objective model for power purchase is established by analyzing the differences in different purchase markets, considering the impact of load deviations on the cost of purchases, based on the CVaR method. Solve the model and draw the following conclusion: • If power retailers prefer lower costs, they need to increase the percentage of purchasing in the day-ahead market. If power retailers are more inclined to low risk, they need to increase the percentage of purchasing in the forward contract market. • Power retailers can further reduce the cost of power purchase and expand investment efficiency in the face of equal risks, considering the impact of load deviations. • As the confidence level increases, the pareto front of the multi-objective function will move to the upper right. Both corresponding cost and CVaR will increase. Acknowledgements This research was supported by State Grid Science and Technology Project 'Research and Software R&D on the Framework of the Power Salesman Platform Considering Decision-Making in the New Market Model'(DZ71-17-019), the 'Six Talents Peak' Project (2015-ZNDW-005) in Jiangsu Province. Most significantly, China Electric Power Research Institute and Nanjing TECH University should be thanked for their funding, knowledge and development contributions in the study. References [1] Zhang Xiaoxuan, Xue Song, Yang Su, et al. International experience and lessons in power sales side market liberalization[J]. Automation of Electric Power Systems, 2016, 40(9): 1-8 (in Chinese). [2] ZENG Ming. Analysis of several issues in direct trade of new Electric reform[J]. China Power Enterprise Management, 2015(10):48-50. [3] ZHENG Yanan, ZHOU Ming, LI Gengyin. Models for large consumer electrical purchasing portfolio and contrastive analysis on them[J]. Power System Technology, 2011, 35(3): 188-194 (in Chinese). [4] Nojavan S, Mehdinejad M, Zare K, et al. Energy procurement management for electricity retailer using new hybrid approach based on combined BICA–BPSO[J]. International Journal of Electrical Power & Energy Systems, 2015, 73:411-419. [5] Mirza F M, Bergland O. Pass-through of wholesale price to the end user retail price in the Norwegian electricity market[J]. Energy Economics, 2012, 34(6):2003-2012. [6] Luo Q, Song Y Q, Jian X U, et al. AHP-Logit Based Decision-making Scheme for Competitive Electricity Retailer[J]. East China Electric Power, 2013. [7] Ahmadi A, Charwand M, Aghaei J. Risk-constrained optimal strategy for retailer forward contract portfolio[J]. International Journal of Electrical Power & Energy Systems, 2013, 53(1):704-713. [8] Wang L, Zhang L, Zhang F, et al. Decision-making and Risk Assessment of Purchasing and Selling Business for Electricity Retailers[J]. Automation of Electric Power Systems, 2018. [9] Kharrati S, Kazemi M, Ehsan M. Equilibria in the competitive retail electricity market considering uncertainty and risk management[J]. Energy, 2016, 106:315-328. [10] Masoud B, Mohammad N M, Ahad K. Optimal Price and Quantity Determination of Retailer Electric Contract and maximizing social welfare in Retail Electrical Power Markets with DG[J]. 2016. [11] Guo M, Chen H, Cong Z, et al. Optimal Marketing Strategy of Retailers Under Energy Deviation Penalty[J]. Automation of Electric Power Systems, 2017, 41(20):17-25. [12] Song M, Amelin M. Price-maker bidding in day-ahead electricity market for a retailer with flexible demands[J]. IEEE Transactions on Power Systems, 2018, PP(99):1-1.