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Optimal Reserve Determination Considering Demand Response in the Presence of High Wind Penetration and Energy Storage Systems

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Abstract

Qualification of the reserve requirement of power systems in the presence of load uncertainties and renewable energy resources is one of the most important challenges of system operators. Especially, existence of wind turbines with unavoidable volatility in their generated powers makes this problem more serious. In this paper, is proposed a probabilistic method for optimal determining of the spinning and non-spinning reserves. In this method, the required optimal reserve level would be determined via simultaneously optimizing the operation cost (OC) and the expected energy not supplied (EENS) cost under security constraint unit commitment. That is, OC includes the cost of both reserve market and energy markets and EENS is computed using a piecewise linear function. The demand response program is considered to provide the reserve service from the demand side. These improve the power system reliability and also reduce the OC. Besides, energy storage systems have been included as a promising approach to diminish the uncertainties of wind power and electrical load. The method is formulated in a two-stage stochastic programming framework, where the first stage represents the day-ahead market, and the second stage deals with the real-time market. Also, a multi-step algorithm has been presented to implement the proposed model. Finally, the well-known 3-buses and 24-buses test systems would be used to verify the efficiency of proposed model.

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Abbreviations

\(n\) :

Index of system buses, from 1 to \(N_{\text{N}}\)

\(r\) :

Index of wind farm installation location

\(z\) :

Index of ESS installation location

\(i,f,h,k\) :

Index of conventional generating units, from 1 to \(N_{\text{G}}\)

\(j\) :

Index of loads, from 1 to \(N_{\text{L}}\)

\(e\) :

Index of ESS devices, from 1 to \(N_{\text{E}}\)

\(c\) :

Index of outage capacity levels, from 1 to \(N_{\text{c}}\)

\(m\) :

Index of energy blocks offered by conventional generating units, from 1 to \(N_{\text{B}}\)

\(t\) :

Index of time periods, from 1 to \(N_{\text{T}}\)

\(\omega_{\text{w}}\) :

Index of wind power scenarios, from 1 to \(N_{{\omega_{\text{w}} }}\)

\(\omega_{\text{l}}\) :

Index of load scenarios, from 1 to \(N_{{\omega_{\text{l}} }}\)

\(\varGamma\) :

Sets of transmission lines

\(Z\) :

Index of the iteration number of IMSA

\(C_{it}^{\text{SU}}\) :

Scheduled start-up cost ($)

\(P_{it}^{\text{S}}\) :

Power output of units in the DAM (MW)

\(P_{itm}^{\text{G}}\) :

Power output from mth block of energy offered by units in the DAM (MW)

\(L_{it}^{\text{S}}\) :

Power consumed of loads in the DAM (MW)

\(R_{it}^{\text{U}}\) :

Up-spinning reserve in the DAM (MW)

\(R_{it}^{\text{D}}\) :

Down-spinning reserve in the DAM (MW)

\(R_{it}^{\text{NS}}\) :

Non-spinning reserve in the DAM (MW)

\(R_{jt}^{\text{U}}\) :

Up-spinning reserve from demand side in the DAM (MW)

\(R_{jt}^{\text{D}}\) :

Down-spinning reserve from demand side in the DAM (MW)

\(R_{it}^{\text{GS}}\) :

All reserves of unit i in period t (MW)

\(R_{jt}^{\text{DS}}\) :

All reserves of load j in period t (MW)

\(R_{t}^{\text{R}}\) :

All operating reserves of generation side in period t (MW)

\(R_{t}^{\text{T}}\) :

Total reserves of both system generation side and demand side in period t (MW)

\(P_{i}^{{{\text{S}},{\text{WP}}}}\) :

Wind power in the DAM (MW)

\(P_{et}^{\text{Cha}} /P_{et}^{\text{Dis}}\) :

Charging/discharging power of ESS in the DAM (MW)

\(X_{et}^{\text{b}}\) :

Stored energy of ESS e in period t (MW)

\({\text{EENS}}_{t}\) :

Expected energy not supplied of system in period t (MW)

\(C_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{SU}}\) :

Start-up cost in the RTM ($)

\(C_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{A}}\) :

Start-up cost due to change in commitment status of units in DAM and RTM ($)

\(P_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{G}}\) :

Power output of units in the RTM (MW)

\(L_{{jt\omega_{\text{w}} \omega_{\text{l}} }}^{\text{C}}\) :

Power consumed of loads in the RTM (MW)

\(r_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{U}}\) :

Up-spinning reserve in the RTM (MW)

\(r_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{D}}\) :

Down-spinning reserve in the RTM (MW)

\(r_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{NS}}\) :

Non-spinning reserve in the RTM (MW)

\(r_{{jt\omega_{\text{w}} \omega_{\text{l}} }}^{\text{U}}\) :

Up-spinning reserve from demand side in the RTM (MW)

\(r_{{jt\omega_{\text{w}} \omega_{\text{l}} }}^{\text{D}}\) :

Down-spinning reserve from demand side in the RTM (MW)

\(r_{{itm\omega_{\text{w}} \omega_{\text{l}} }}^{\text{G}}\) :

Reserve deployed from the mth block of offered energy in the RTM (MW)

\(P_{{t\omega_{\text{w}} }}^{\text{WP}}\) :

Wind power generation in the RTM (MW)

\(S_{{t\omega_{\text{w}} }}\) :

Wind power generation spillage (MW)

\(P_{{et\omega_{\text{w}} \omega_{\text{l}} }}^{\text{Cha}} /P_{{et\omega_{\text{w}} \omega_{\text{l}} }}^{\text{Dis}}\) :

Charging/Discharging power of ESS in the RTM (MW)

\(f_{{t\omega_{\text{w}} \omega_{\text{l}} \left( {n,r} \right)}}\) :

Power flow through line (n, r) (MW)

\(U_{it}\) :

Commitment status of units in DAM

\(V_{{it\omega_{\text{w}} \omega_{\text{l}} }}\) :

Commitment status of units in RTM

\(U_{it}^{\text{Cha/Dis}}\) :

Commitment status of units in DAM

\(U_{{it\omega_{\text{w}} \omega_{\text{l}} }}^{\text{Cha/Dis}}\) :

Commitment status of units in RTM

\(d_{t}\) :

Duration of time period (h)

\(\gamma_{i}\) :

Probability of generators’ outage

\(p_{ct}\) :

Probability of the cth outage capacity level during period t

\(N_{\left( t \right)}\) :

Number of outage capacity levels during period t

\(\Delta C_{ct}\) :

Amount of the cth outage capacity during period t

\(\Delta R_{ct}\) :

Share of reserve corresponding to the cth outage capacity during period t

\(\Delta T\) :

Duration of time interval of two consecutive periods

\(\Delta T^{\text{SP}}\) :

Duration of time interval of spinning reserve delivery

\(\Delta T^{\text{NS}}\) :

Duration of time interval of non-spinning reserve delivery

\(\lambda_{it}^{\text{SU}}\) :

Start-up offer cost of units ($)

\(\lambda_{jt}^{\text{L}}\) :

Utility of electrical loads ($/MW h)

\(C_{itm}^{\text{G}}\) :

Marginal cost of the mth block of energy offered ($/MW h)

\(C_{t}^{\text{WP}}\) :

Marginal cost of the energy offer submitted by the wind farms ($/MW h)

\(C_{et}^{\text{ESS}}\) :

Marginal cost of the energy offer submitted by the ESS’s ($/MW h)

\(C_{it}^{{{\text{R}}^{\text{U}} }}\) :

Marginal cost of the up-spinning reserve by conventional units ($/MW h)

\(C_{it}^{{{\text{R}}^{\text{D}} }}\) :

Marginal cost of the down-spinning reserve by conventional units ($/MW h)

\(C_{it}^{{{\text{R}}^{\text{NS}} }}\) :

Marginal cost of the non-spinning reserve by conventional units ($/MW h)

\(C_{jt}^{{{\text{R}}^{\text{U}} }}\) :

Marginal cost of the up-spinning reserve by loads ($/MW h)

\(C_{jt}^{{{\text{R}}^{\text{D}} }}\) :

Marginal cost of the up-spinning reserve by loads ($/MW h)

\(V_{t}^{\text{S}}\) :

Wind spillage cost ($/MW h)

\({\text{VOLL}}_{t}\) :

Value of loss load ($/MW h)

\(\rho_{{\omega_{\text{w}} }}\) :

Probability of wind scenarios

\(\rho_{{\omega_{\text{l}} }}\) :

Probability of load scenarios

\(f_{{\left( {n,r} \right)}}^{\hbox{max} }\) :

Maximum capacity of line (n, r) (MW)

\(P_{i}^{\hbox{max} }\) :

Maximum capacity of units (MW)

\(P_{i}^{\hbox{min} }\) :

Minimum capacity of units (MW)

\({\text{RU}}_{i}\) :

Ramp-up rate of unit i (MW/min)

\({\text{RD}}_{i}\) :

Ramp-down rate of unit i (MW/min)

\(P_{e}^{{{\text{Cha}},\hbox{max} }}\) :

Maximum charging power of ESS’s (MW)

\(P_{e}^{{{\text{Dis}},\hbox{max} }}\) :

Maximum discharging power of ESS’s (MW)

\(X_{e}^{{{\text{b}},\hbox{max} }}\) :

Maximum energy stored in ESS’s (MW)

\(X_{e}^{{{\text{b}},\hbox{min} }}\) :

Minimum energy stored in ESS’s (MW)

\(X_{et0}^{\text{b}}\) :

Initial energy stored in ESS e at period t0 (MW)

\(X_{0}^{\text{b}}\) :

Initial energy stored in ESS’s (MW)

\(\chi /\eta\) :

Charging/discharging efficiency of ESS

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Authors and Affiliations

  1. Electrical Engineering Department, Imam Khomeini International University, Qazvin, Iran

    Mahdi MohammadGholiha, Karim Afshar & Nooshin Bigdeli

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  1. Mahdi MohammadGholiha
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  2. Karim Afshar
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  3. Nooshin Bigdeli
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Correspondence to Karim Afshar.

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MohammadGholiha, M., Afshar, K. & Bigdeli, N. Optimal Reserve Determination Considering Demand Response in the Presence of High Wind Penetration and Energy Storage Systems. Iran J Sci Technol Trans Electr Eng 44, 1403–1428 (2020). https://doi.org/10.1007/s40998-020-00328-2

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