Abstract
Recently, the increasing penetration of wind energy has provided various ways to operate the system at low cost and low pollution. On the other hand, the noticeable uncertainties caused by the forecast error of wind speed restrict the utilization of wind energy. Moreover, it brings unprecedented challenges to maintain system adequacy. One prevailing solution is to maintain sufficient spinning reserve of thermal units, which is not affordable. This paper analyses the relationship between the operation cost and wind power uncertainty using AC unit commitment in the frame of a short-term market. Conditional value-at-risk is established in a percentage of the worst-case estimations on wind power scenario under uncertainty to achieve adequate trade-offs between optimal solution and risk aversion. Operation cost of generation, load shedding cost and reserve cost are optimally established by multi-objective optimization. Finally, the simulation is performed on the test system and the obtained results are evaluated and compared to demonstrate the research effectiveness.
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Abbreviations
- \({{C}}_{{{{i}},t1}}^{{SU}}\) :
-
Start-up cost of unit i in period t1 ($)
- \({\text{C}}_{{{\text{i}},T1}}^{{SD}}\) :
-
Shut-down cost of unit i in period t1 ($)
- \(C_{{iT1}}^{D}\) :
-
Energy cost of unit i in day-ahead market or period t1 ($/MWh)
- \(P_{{{\text{i}}T1}}^{{g\left( D \right)}}\) :
-
Power purchased from unit i in day-ahead market or period t1 (MW)
- \(C_{{{\text{i}}T1}}^{{SR\left( {UP} \right)}}\) :
-
Cost of spinning up reserve by unit i in day-ahead market or period t1 ($/MWh)
- \(R_{{{\text{i}}T1}}^{{SR\left( {UP} \right)}}\) :
-
Spinning up reserve scheduled by unit i in day-ahead market or in period t1 (MW)
- \(C_{{{\text{i}}T1}}^{{SR\left( {DN} \right)}}\) :
-
Cost of spinning down reserve by unit i in day-ahead market or in period t1 ($/MWh)
- \(R_{{iT1}}^{{SR\left( {DN} \right)}}\) :
-
Spinning down reserve scheduled by unit i in day-ahead market or period t1 (MW)
- \(C_{{{\text{i}}T1}}^{{{\text{NSR}}}}\) :
-
Cost of nonspinning reserve by unit i in day-ahead market or period t1 ($/MWh)
- \(R_{{{\text{i}}T1}}^{{{\text{NSR}}}}\) :
-
Nonspinning reserve scheduled by unit i in day-ahead market or period t1 (MW)
- \(C_{{{\text{w}}T1}}^{{\text{D}}}\) :
-
Offer cost of wind producer w in day-ahead market or period t1 ($/MWh)
- \(P_{{{\text{w}}T1}}^{{w\left( D \right)}}\) :
-
Power purchased from wind producer w in day-ahead market or period t1 (MW)
- \(C_{{{\text{j}}T1}}^{{L\left( D \right)}}\) :
-
Energy cost of consumer j in day-ahead market and period t1 ($/MWh)
- \(P_{{{\text{j}}T1}}^{{L\left( D \right)}}\) :
-
Power consumption of consumer j in day-ahead market or period t1 (MW)
- \(P_{{\text{S}}}^{{}}\) :
-
Probability of scenarios S
- \(C_{{{\text{i}}T2,{\text{S}}}}^{{}}\) :
-
Additional costs due to changes in the start-up or shut-down plan of unit i in real-time market or period t2 ($)
- \(r_{{{\text{i}}T2,{\text{S}}}}^{{}}\) :
-
Reserve deployed by unit i in scenarios S and real-time market or period t2 (MW)
- \(C_{{{\text{w}}T2}}^{{spill}}\) :
-
Cost of wind energy spillage from wind producer w in real-time market or period t2
- \(P_{{{\text{w}}T2,{\text{S}}}}^{{w\left( {oe} \right)}}\) :
-
Surplus power spilled of wind producer, compared to the pre-sale power on the day-ahead market in scenarios S and real-time market or period t2 (MW).
- \(C_{{{\text{j}}T2}}^{{{\text{l}}.sh}}\) :
-
Forced outage cost of consumer j in real-time market or period t2 ($).
- \(P_{{{\text{j}}T2,{\text{S}}}}^{{{\text{l}}.sh}}\) :
-
Power not supplied of consumer j in scenarios S and real-time market or period t2 (MW).
- \(b_{{{\text{w}}T2,{\text{S}}}}\) :
-
Binary variable that equals to 1 if wind producer is overproduction during period t2 and 0 otherwise.
- \(r_{{{\text{i}}T2,{\text{S}}}}^{{UP,wind}}\) :
-
Reserve deployed by wind producer in scenarios S and real-time market or period t2 (MW).
- \(r_{{{\text{i}}T2,{\text{S}}}}^{{UP{\text{,g}}}}\) :
-
: Reserve deployed by thermal unit in scenarios S and real-time market or period t2 (MW).
- \(P_{{\text{i}}}^{{{\text{min}}}}\) :
-
Minimum power production of unit i (MW).
- \(P_{{\text{i}}}^{{{\text{max}}}}\) :
-
Maximum power production of unit i (MW).
- \(P_{{\text{j}}}^{{L\left( {min} \right)}}\) :
-
Minimum amount of load j (MW).
- \(P_{{\text{j}}}^{{L\left( {\max } \right)}}\) :
-
Maximum amount of load j (MW).
- \(P_{{\text{w}}}^{{{\text{max}}}}\) :
-
Maximum power production of wind power producer w (MW).
- \(b_{{{\text{i}}T1}}^{{}}\) :
-
Binary Variable that equals to 1 if unit is online during period t1 and 0 otherwise.
- \(Ram_{{\text{i}}}^{UP}\) :
-
Ramp-up rate limit for thermal unit i
- \(Ram_{{\text{i}}}^{DN}\) :
-
Ramp-down rate limit for thermal unit i
- \(C_{{{\text{i}}T2,S}}^{{SU}}\) :
-
Start-up cost of unit i in scenarios S and real-time market or period t2 ($)
- \(C_{{{\text{i}}T2,S}}^{{SD}}\) :
-
Shut-down cost of unit i in scenarios S and real-time market or period t2 ($)
- \(\lambda _{{{\text{i}}T1}}^{{SU}}\) :
-
Start-up fixed cost of unit i in period t1 ($)
- \(S_{{t2S}} \left( {{\text{ni}},{\text{nj}}} \right)\) :
-
Apparent power flow through transmission line from bus ni to nj
- \(Y\left( {{\text{ni}},{\text{nj}}} \right)\) :
-
Admittance value form bus ni to nj
- \(V\left( {nj} \right)\) :
-
Voltage value of bus nj
- \({\text{V}}^{*} \left( {{\text{ni}}} \right)\) :
-
Voltage value of bus ni
- \(N_{{\text{j}}}\) :
-
The total number of consumer
- \(N_{{\text{i}}}\) :
-
The total number of thermal unit
- \(N_{{\text{S}}}\) :
-
The total number of scenarios
- \(N_{{\text{w}}}\) :
-
The total number of wind producer
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Hosseini-Firouz, M., Alemi, A., Alefy, B. et al. Unit Commitment Model under Uncertainty of Wind Power Producer. Iran J Sci Technol Trans Electr Eng 45, 1295–1309 (2021). https://doi.org/10.1007/s40998-021-00429-6
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DOI: https://doi.org/10.1007/s40998-021-00429-6