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A Two-Stage Stochastic Framework for an Electricity Retailer Considering Demand Response and Uncertainties Using a Hybrid Clustering Technique

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Abstract

Due to the highly volatile prices of pool market, a main source of an electricity retailer to meet its clients’ demand, retailers generally sign forward contracts in order to protect themselves from being exposed to the risk imposed by the uncertain pool prices. These contracts, however, decrease the retailer’s expected profit owing to their higher average prices compared with the pool market. In this paper, focusing on price-based demand response programs, a two-stage scenario-based stochastic framework is presented for the medium-term decision-making problem of an electricity retailer. This study would demonstrate that demand response programs can be an effective tool to hedge against the risk and an appropriate alternative yielding less involvement in costly forward agreements. The proposed model decides the optimal level of participation in the pool as well as forward market and determines the electricity rates offered to the clients. The objective is maximizing the expected value of the retailer’s profit, whereas the exposure risk is confined to a pre-specified level. Moreover, the scenarios required for the stochastic programming problem are generated using a hybrid clustering technique based on K-means and particle swarm optimization algorithms. The proposed model is mathematically described as a mixed-integer linear problem which is solvable through commercial software packages. The efficiency of the provided approach is evaluated via a realistic case study according to the available data from Spain electricity market.

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Abbreviations

\(\it {\text{bl}}\) :

Index of time blocks in time-of-use (TOU) rating scheme

\(f_{\text{b}}\) :

Index of base-load forward contracts

\(f_{\text{p}}\) :

Index of peak-load forward contracts

\(h,t\) :

Index of time periods

\(i\) :

Index of interruptible load contracts

\(\omega\) :

Index of scenarios

\(b_{t}^{\text{Peak}}\) :

Binary indicator which is equal to 1 if period t is in peak period, 0 otherwise

\(B\) :

Number of time blocks considered in TOU rating scheme

\(d_{t}\) :

Duration of time period t (h)

\(E_{t,h}\) :

Clients’ demand elasticity at hour t with respect to the sale price at hour h

\(M_{i}^{\text{IL}}\) :

Number of permitted interruptions related to interruptible load contract i

\(N_{\text{FB}}\) :

Number of signed base-load forward agreements

\(N_{\text{FP}}\) :

Number of signed peak-load forward agreements

\(N_{I}\) :

Number of interruptible load contracts

\(N_{T}\) :

Number of time periods

\(N_{\omega }\) :

Number of scenarios

\(P_{\omega ,t}^{C}\) :

Clients’ demand at scenario ω and period t (MWh)

\(P_{\omega ,t}^{{C{\text{flat}}}}\) :

Clients’ demand at scenario ω and period t under flat rating scheme (MWh)

\(P_{{f_{\text{b}} }}^{\text{FB,min}}\) :

Lower bound of the electricity purchased from base-load forward contract fb (MW)

\(P_{{f_{\text{b}} }}^{\text{FB,max}}\) :

Upper bound of the electricity purchased from base-load forward contract fb (MW)

\(P_{{f_{\text{p}} }}^{\text{FP,min}}\) :

Lower bound of the electricity purchased from peak-load forward contract fp (MW)

\(P_{{f_{\text{p}} }}^{\text{FP,max}}\) :

Upper bound of the electricity purchased from peak-load forward contract fp (MW)

\(P_{i}^{\text{IL,max}}\) :

Upper limit of the interruptible load related to contract i (MWh)

\(\alpha\) :

Confidence level

\(\beta\) :

Risk weight

\(\theta_{{{\text{bl}},t}}\) :

Binary indicator which is equal to 1 if hour t belongs to time block bl, 0 otherwise

\(\lambda_{{f_{\text{b}} }}^{\text{Base}}\) :

Price of base-load forward contract fb (€/MWh)

\(\lambda_{{f_{\text{p}} }}^{\text{Peak}}\) :

Price of peak-load forward contract fp (€/MWh)

\(\lambda_{\omega ,t}^{\text{Pool}}\) :

Pool market price at scenario ω and period t (€/MWh)

\(\lambda_{i}^{\text{IL}}\) :

Cost of interruptible load per unit related to contract i (€/MWh)

\(\lambda_{\omega ,t}^{\text{Sell}}\) :

Electricity sale price offered to clients at scenario ω and period t (€/MWh)

\(\lambda_{s}\) :

Service-related part of electricity sale price (€/MWh)

\(\lambda^{\text{Flat}}\) :

Electricity sale price under flat rating scheme (€/MWh)

\(\pi_{\omega }\) :

Probability of scenario ω

\(C^{\text{Forward}}\) :

Total cost of purchasing power through forward contracts (€)

\(C^{\text{Pool}}\) :

Expected net cost of trading in pool market (€)

\(C_{\omega }^{\text{Pool}}\) :

Net cost of trading in pool market at scenario ω (€)

\(C^{\text{IL}}\) :

Expected cost of interruptible load contracts (€)

\(C_{\omega }^{\text{IL}}\) :

Cost of interruptible load contracts at scenario ω (€)

\(\it {\text{CVaR}}\) :

Conditional value-at-risk (€)

\(P_{{f_{\text{b}} }}^{\text{Base}}\) :

Electricity purchased from base-load forward contract fb (MW)

\(P_{{f_{\text{p}} }}^{\text{Peak}}\) :

Electricity purchased from peak-load forward contract fp (MW)

\(P_{\omega ,t}^{\text{Pool}}\) :

Electricity energy traded in pool market at scenario ω and period t (MWh)

\(P_{\omega ,t,i}^{\text{IL}}\) :

Interrupted load related to contract i at scenario ω and period t (MWh)

\(\it {\text{PR}}\) :

Retailer’s expected profit (€)

\(\it {\text{PR}}_{\omega }\) :

Retailer’s profit at scenario ω (€)

\(\it {\text{IN}}\) :

Retailer’s expected income obtained by selling electricity to the clients (€)

\(\it {\text{IN}}_{\omega }\) :

Retailer’s income obtained by selling electricity to the clients at scenario ω (€)

\(U_{{f_{\text{b}} }}^{\text{Base}}\) :

Binary variable which is equal to 1 if base forward contract fb is signed, 0 otherwise

\(U_{{f_{\text{p}} }}^{\text{Peak}}\) :

Binary variable which is equal to 1 if peak forward contract fp is signed, 0 otherwise

\(U_{\omega ,t,i}^{\text{IL}}\) :

Binary variable which is equal to 1 if the customers’ load is interrupted with respect to contract i at scenario ω and period t, 0 otherwise

\(\eta_{\omega }\) :

Auxiliary variable employed in CVaR calculation (€)

\(\xi\) :

Value-at-risk (€)

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Guilan, Rasht, Iran

    Mostafa Nasouri Gilvaei & Alfred Baghramian

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  1. Mostafa Nasouri Gilvaei
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  2. Alfred Baghramian
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Correspondence to Alfred Baghramian.

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Nasouri Gilvaei, M., Baghramian, A. A Two-Stage Stochastic Framework for an Electricity Retailer Considering Demand Response and Uncertainties Using a Hybrid Clustering Technique. Iran J Sci Technol Trans Electr Eng 43 (Suppl 1), 541–558 (2019). https://doi.org/10.1007/s40998-018-0150-9

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  • DOI: https://doi.org/10.1007/s40998-018-0150-9

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