Abstract
The high penetration of distributed energy resources raises new challenges in microgrid operation due to their stochastic and intermittent characteristics. This exacerbates the difficulty of congestion management of microgrids in comparison with conventional power systems. In addition to intermittent generation of renewable resources, some other factors such as load forecasting errors and forced outage of generating units can lead to real-time congestion (RTC) in a microgrid. To implement real-time congestion management (RTCM), some approaches can be employed by the microgrid central controller (MGCC) including network reconfiguration using remote control switches, generation and up-grid power rescheduling and load shedding. In this paper, a two-stage programming model is proposed to find the optimal solution of RCTM under different temperature conditions. Therefore, following an unexpected condition and the occurrence of congestion, at the first stage, MGCC implements reconfiguration as the lowest-cost approach to mitigate RTC. Soccer league algorithm is employed in first stage to find the optimal network topology. Subsequently, based on the obtained results from the first stage, a programming model is applied at the second stage to completely eliminate the RTC. The proposed model minimizes a weighted objective function which includes the generation and up-grid rescheduling cost, load shedding cost and congestion clearing time. To improve the operational planning in unexpected conditions, the allowable congestion clearing time is determined based on multi-level thermal rate due to temperature conditions. The numerical results demonstrate the efficacy of the proposed model.
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Abbreviations
- \(p\) :
-
Index of switch
- \(t\) :
-
Index of hour
- \(m\) :
-
Index of PVs
- \(g\) :
-
Index of DGs
- \(n\) :
-
Index of WTs
- \(i,j\) :
-
Index of buses
- \(L\) :
-
Index of load
- \(l\) :
-
Index of branches
- \({N}_{\mathrm{l}}\) :
-
Number of branches
- \({N}_{\mathrm{p}}\) :
-
Number of RCSs
- \(k\) :
-
Number of scenarios that guarantee the radial topology of the network
- \(D\) :
-
Set of scenarios that guarantee the radial topology of the network
- \({N}_{\mathrm{L}}^{\mathrm{Resch}}\) :
-
Number of the participated loads in CM
- \({N}_{\mathrm{g}}^{\mathrm{Resch}}\) :
-
Number of the participated generators in CM
- \({T}_{\mathrm{l}}^{\mathrm{max}}\) :
-
Maximum allowed conductor temperature (°C).
- \({T}_{\mathrm{l}}^{\mathrm{min} }\) :
-
Minimum allowed conductor temperatures (°C).
- \({I}_{\mathrm{E},\mathrm{t}}^{\mathrm{max}}\) :
-
Emergency-term thermal rate
- \({I}_{\mathrm{s},\mathrm{t}}^{\mathrm{max}}\) :
-
Short-term thermal rate
- \({I}_{\mathrm{L},\mathrm{t}}^{\mathrm{max}}\) :
-
Long-term thermal rate
- \(t_{{{\text{clear}},{\text{L}}}}^{\max }\) :
-
Maximum long-term clearing time
- \(t_{{{\text{clear}},{\text{E}}}}^{\max }\) :
-
Maximum emergency-term clearing time
- \(t_{{{\text{clear}},{\text{s}}}}^{\max }\) :
-
Maximum short-term clearing time
- \({F}_{\mathrm{l}}^{\mathrm{max}}\) :
-
Maximum apparent flow of the lth line (MVA).
- \({P}_{\mathrm{g}}^{\mathrm{min}}\) :
-
Minimum allowed active power generation of the gth generator (kW).
- \({P}_{\mathrm{g}}^{\mathrm{max}}\) :
-
Maximum allowed active power generation of the gth generator (MW).
- \({Q}_{\mathrm{g}}^{\mathrm{max}}\) :
-
Maximum allowed reactive power generation of the gth generator (kVar).
- \({Q}_{\mathrm{g}}^{\mathrm{min}}\) :
-
Minimum allowed reactive power generation of the gth generator (kVar).
- \({P}_{\mathrm{WM}}^{\mathrm{max}}\) :
-
Maximum allowable active power purchased from wholesale market
- \({P}_{\mathrm{WM}}^{\mathrm{min}}\) :
-
Minimum allowable active power purchased from wholesale market
- \({Q}_{\mathrm{WM}}^{\mathrm{min}}\) :
-
Minimum allowable reactive power purchased from wholesale market
- \({Q}_{\mathrm{WM}}^{\mathrm{max}}\) :
-
Maximum allowable reactive power purchased from wholesale market
- \({P}_{\mathrm{L}}^{\mathrm{min}}\) :
-
Minimum allowed active power consumed by the Lth load (MW).
- \({P}_{\mathrm{L}}^{\mathrm{max}}\) :
-
Maximum allowed active power consumed by the Lth load (MW).
- \({R}_{\mathrm{g}}^{\mathrm{up}}\) :
-
Ramp-up rate of the gth generator (kW/h).
- \({R}_{\mathrm{g}}^{\mathrm{Down}}\) :
-
Ramp-down rate of the gth generator (kW/h)
- \({\pi }_{\mathrm{g},\mathrm{t}}^{\mathrm{DG}}\), \({\pi }_{\mathrm{m},\mathrm{t}}^{\mathrm{PV}}\),\({\pi }_{\mathrm{n},\mathrm{t}}^{\mathrm{WT}}\) :
-
Contracted price with DG, PV and WT owners ($/kWh).
- \({\pi }_{\mathrm{t}}^{\mathrm{WM}}\) :
-
Wholesale market electricity price at time t ($/MWh).
- \({\pi }^{\mathrm{sw}}\) :
-
Cost of switching action ($)
- \({P}_{\mathrm{L},\mathrm{t}}\) :
-
Total power demand at time t (kW)
- \({P}_{\mathrm{g},\mathrm{t}}^{\mathrm{DG}}\) :
-
Output power of DG g at time t (kW)
- \({P}_{\mathrm{n},\mathrm{t}}^{\mathrm{WT}}\) :
-
Output power of WT n at time t (kW)
- \({P}_{\mathrm{m},\mathrm{t}}^{\mathrm{PV}}\) :
-
Output power of PV m at time t (kW)
- \(\Delta {Q}_{\mathrm{g}}\) :
-
Change in reactive power of the gth generator (kVar).
- \(\Delta {P}_{\mathrm{g}}\) :
-
Change in active power of the gth generator (kW).
- \(\Delta {Q}_{\mathrm{L}}\) :
-
Change in reactive power of the Lth load (kVar).
- \(\Delta {P}_{\mathrm{L}}\) :
-
Change in active power of the Lth load (kW).
- \(\Delta {P}_{\mathrm{WM}}\) :
-
Change in active power of up-grid (kW).
- \(\Delta {Q}_{\mathrm{WM}}\) :
-
Change in reactive power of up-grid (kVar).
- \({s}_{\mathrm{p},\mathrm{t}}\) :
-
Status of RCS p at time t (1: when the related RCS is opened, and 0: otherwise)
- \({R}_{\mathrm{l},\mathrm{t}}\left({T}_{\mathrm{t}}\right)\) :
-
Line resistance at time t with temperature T
- \({R}_{\mathrm{l}}\left({T}_{\mathrm{l}}^{\mathrm{max}}\right)\) :
-
Line resistance with maximum conductor temperatures
- \({R}_{\mathrm{l}}\left({T}_{\mathrm{l}}^{\mathrm{min}}\right)\) :
-
Line resistance with minimum conductor temperatures
- \({f}_{\mathrm{l},\mathrm{t}}^{\mathrm{penalty}}\) :
-
Thermal rate penalty function of the lth line at time t
- \({\mathrm{SeQ}}_{\mathrm{l}}^{\mathrm{L}}\) :
-
Line reactive power flow sensitivity with respect to reactive power load
- \({\mathrm{SeQ}}_{\mathrm{l}}^{\mathrm{WM}}\) :
-
Line reactive power flow sensitivity with respect to the up-grid reactive power
- \({\mathrm{SeQ}}_{\mathrm{l}}^{\mathrm{g}}\) :
-
Line reactive power flow sensitivity with respect to generator reactive power
- \({\mathrm{SeP}}_{\mathrm{l}}^{\mathrm{g}}\) :
-
Line active power flow sensitivity with respect to the generator active power
- \({\mathrm{SeP}}_{\mathrm{l}}^{\mathrm{WM}}\) :
-
Line active power flow sensitivity with respect to the up-grid active power
- \({\mathrm{SeP}}_{\mathrm{l}}^{\mathrm{L}}\) :
-
Line active power flow sensitivity with respect to active power load
- \({C}_{\mathrm{g}}\left(\Delta {P}_{\mathrm{g}}\right)\) :
-
Cost of change in active power of the gth generator
- \({C}_{\mathrm{L}}\left(\Delta {P}_{\mathrm{L}}\right)\) :
-
Cost of change in active power of the Lth load
- \({C}_{\mathrm{WM}}\left(\Delta {P}_{\mathrm{WM}}\right)\) :
-
Cost of change in purchased active power from wholesale market
- \({\gamma }_{\mathrm{l}}\), \({\lambda }_{\mathrm{l}}\) :
-
Conductance and susceptance of branch l
- \({V}_{\mathrm{i}}\) :
-
Voltage at bus i (p.u.)
- \({\Delta V}_{\mathrm{i},\mathrm{t}}\) :
-
Voltage deviations bus i
- \({\theta }_{\mathrm{l}}\) :
-
Voltage angle difference of branch l
- \({V}_{\mathrm{nom}}\) :
-
Nominal voltage.
- \({Q}_{\mathrm{i},\mathrm{t}}^{\mathrm{flow}}\) :
-
Net reactive power flow injected to bus i at time t (kW).
- \({P}_{\mathrm{i},\mathrm{t}}^{\mathrm{flow}}\) :
-
Net active power flow injected to bus i at time t (kW).
- \({Z}_{\mathrm{p},\mathrm{t}}^{+}\), \({Z}_{\mathrm{p},\mathrm{t}}^{-}\) :
-
Auxiliary variables
- \({I}_{\mathrm{i},\mathrm{j},\mathrm{t}}\) :
-
Current of line between bus i and bus j: at time t
- \({q}_{\mathrm{c}}\) :
-
Convection heat loss of the conductor (W/m).
- \({q}_{\mathrm{r}}\) :
-
Radiation heat loss of the conductor (W/m).
- \({q}_{\mathrm{s}}\) :
-
Imported heat due to heat gain rate from sun
- \({R}_{\mathrm{l},\mathrm{t}}\) :
-
Line resistance at time t
- \({T}_{\mathrm{l},\mathrm{t}}\) :
-
Temperature of the lth line at time t
- \({I}_{\mathrm{l},\mathrm{t}}\) :
-
Current the lth line at time t
- \({C}_{\mathrm{p}}\) :
-
Conductor thermal capacity (J/kg °C).
- m :
-
Mass per unit length of the conductor (kg/m).
- \({w}_{\mathrm{f}}\) :
-
Thermal rate weighting factor
- \({w}_{\mathrm{k}}\) :
-
Switch action weighting factor
- \({w}_{\mathrm{c}}\) :
-
Congestion management cost weighting factor.
- \({w}_{\mathrm{t}}\) :
-
Congestion clearing time weighting factor
- \({t}_{\mathrm{clear}}\) :
-
Congestion clearing time
- \({t}_{\mathrm{est}}\) :
-
Estimated time to solve reconfiguration equation
- \({t}_{\mathrm{recon}}\) :
-
Reconfiguration Times
- \({t}_{\mathrm{clear},\mathrm{Resch}}\) :
-
Rescheduling Time
- \({\Delta Q}_{\mathrm{l}}\) :
-
Variation in reactive power flow in the lth line (kVar)
- \({\Delta P}_{\mathrm{l}}\) :
-
Variation in active power flow in the lth line (kW)
- \({P}_{\mathrm{l}}^{0}\) :
-
Initial value of active power flow of the lth line (kW)
- \({Q}_{\mathrm{l}}^{0}\) :
-
Initial value of reactive power flow of the lth line (kVar).
- \({P}_{\mathrm{l}}\) :
-
Active power flow of the lth line (kW).
- \({Q}_{\mathrm{l}}\) :
-
Reactive power flow of the lth line (kVar).
- \({T}_{\mathrm{a}}\) :
-
Ambient temperature (°C).
- φ :
-
Wind direction (degrees).
- \({V}_{\mathrm{W}}\) :
-
Wind speed (m/s)
- \({s}_{\mathrm{p},\mathrm{t},\mathrm{recon}}\) :
-
Status of RCS pth at time t after reconfiguration
References
Barbulescu C, Kilyeni S, Cristian DP, Jigoria-Oprea D (2010) Congestion management using open power market environment electricity trading. In: 45th international universities power engineering conference UPEC2010 2010 Sep. IEEE pp 1–6
Biegel B et al. (2012) Congestion management in a smart grid via shadow prices. In: IFAC Proceedings vol 4521, pp 518–523
Li R, Qiuwei Wu, Oren SS (2014) Distribution locational marginal pricing for optimal electric vehicle charging management. IEEE Trans Power Syst 29(1):203–211
O’Connell N et al (2012) Day-ahead tariffs for the alleviation of distribution grid congestion from electric vehicles. Electric Power Syst Res 92:106–114
Verzijlbergh RA, De Vries Laurens J, Lukszo Z (2014) Renewable energy sources and responsive demand. Do we need congestion management in the distribution grid?.". IEEE Trans Power Syst 29.5:2119–2128
Huang S, Qiuwei Wu (2018) Dynamic subsidy method for congestion management in distribution networks. IEEE Trans Smart Grid 9(3):2140–2151
Andersen PB, Junjie H, Kai H (2012) Coordination strategies for distribution grid congestion management in a multi-actor, multi-objective setting. In: Innovative Smart Grid Technologies (ISGT Europe), 2012 3rd IEEE PES International Conference and Exhibition on. IEEE, 2012
Hu J et al (2014) Coordinated charging of electric vehicles for congestion prevention in the distribution grid. IEEE Transactions on Smart Grid 5.2:703–711
Zhang, C et al. FLECH: a danish market solution for DSO congestion management through DER flexibility services. 133
Huang S, Qiuwei Wu (2018) Real-time congestion management in distribution networks by flexible demand swap. IEEE Transactions on Smart Grid 9(5):4346–4355
Daroj K, and Limpananwadi W (2008) Reactive power dispatch scheme evaluation for synchronous based distributed generators to reduce real power loss in distribution systems.In: Sustainable Energy Technologies, 2008. ICSET 2008. IEEE International Conference on. IEEE, 2008
Viawan FA, Karlsson D (2008) Voltage and reactive power control in systems with synchronous machine-based distributed generation. IEEE Trans Power Delivery 23(2):1079–1087
Huang S et al. (2014) Review of congestion management methods for distribution networks with high penetration of distributed energy resources. IEEE PES Innovative Smart Grid Technologies, Europe pp 1–6
Shariatkhah MH, Mahmoud RH, Ali A (2011) Load profile based determination of distribution feeder configuration by dynamic programming. PowerTech, 2011 IEEE Trondheim. IEEE, 2011
Merlin A, and Back G Search for a minimum loss operational spanning tree configuration for an urban power distribution system. In: Proceedings of the fifth Power System Conference (PSC)
Jorge M et al (2006) Minimal loss reconfiguration using genetic algorithms with restricted population and addressed operators: real application. IEEE Trans Power Syst 21(2):948–954
Shirmohammadi D, Wayne Hong H (1989) Reconfiguration of electric distribution networks for resistive line losses reduction. IEEE Trans Power Deliv 4(2):1492–1498
Baran ME, Wu FF (1989) Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Delivery 4(2):1401–1407
Glamocanin V (1990) Optimal loss reduction of distribution networks. IEEE Trans Power Syst 5(3):774–781
Toune S et al (2002) Comparative study of modern heuristic algorithms to service restoration in distribution systems.". IEEE Trans Power Delivery 17(1):173–181
Nara K et al (1992) Implementation of genetic algorithm for distribution systems loss minimum re-configuration. IEEE Trans Power syst 7(3):1044–1051
Shariatkhah MH, and Mahmoud RH (2012) Using feeder reconfiguration for congestion management of smart distribution network with high DG penetration. pp 316–316
Franco JF et al (2013) A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation. Electric Power Syst Res 97:51–60
Abur A (1996) A modified linear programming method for distribution system reconfiguration. Int J Electr Power Energy Syst 18(7):469–474
Bogdan E et al (2008) Radial network reconfiguration using genetic algorithm based on the matroid theory. IEEE Trans Power Syst 23(1):186–195
Santos SF et al (2016) New multistage and stochastic mathematical model for maximizing RES hosting capacity—Part I: problem formulation. IEEE Trans Sustain Energy 8(1):304–319
Seppa TO (2002) Increasing transmission capacity by real time monitoring. Power Engineering Society Winter Meeting, 2002. IEEE. Vol. 2. IEEE, 2002
IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors, IEEE Standard 738TM-2012, Jan. 2013
Hur K, Boddeti M, Sarma N, Dumas J, Adams J, Chai S-K (2010) High-wire act. IEEE Power Energy Mag 8(1):37–45
Mahmoudian M, and Yousefi GR (2012) ATC improvement and losses estimation considering dynamic transmission line ratings. In: Electrical Engineering (ICEE), 2012 20th Iranian Conference on. IEEE, 2012
Electric Power Research Institute (EPRI) (2006) Increased power flow through transmission circuits: Overhead line case studies and quasi-dynamic rating,” EPRI, Palo Alto, CA, USA, Tech. Rep. 1012533
Moosavian N, Babak KR (2013) Soccer league competition algorithm, a new method for solving systems of nonlinear equations. Int J Intell Sci 4(01):7
Dutta S, Singh SP (2008) Optimal rescheduling of generators for congestion management based on particle swarm optimization. IEEE Trans Power Syst 23(4):1560–1569
Dariush S, Wayne Hong H (1989) Reconfiguration of electric distribution networks for resistive line losses reduction. IEEE Trans Power Deliv 4(2):1492–1498
International Electrotechnical Commission (2006) IEC 60287–1–1: Electric Cables—Calculation of the Current Rating—Part 1–1: Current Rating Equations (100% Load Factor) and Calculation of Losses—General. International Electrotechnical Commission: Geneva, Switzerland (2006)
International Electrotechnical Commission (1989) IEC 60853–2: Electric Cables—Calculation of the Cyclic and Emergency Current Rating of Cables Part 2: Cyclic Rating Factor Cable Greater than 18/30 (36) kv and Emergency Current Rating for Cables of All Voltages Publication 853–862, 1989
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Ehsani, I., Amirahmadi, M., Tolou-Askari, M. et al. Real-time congestion management for networked microgrids using optimal resources rescheduling and reconfiguration considering multi-level thermal rate. Electr Eng 105, 1025–1044 (2023). https://doi.org/10.1007/s00202-022-01713-2
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DOI: https://doi.org/10.1007/s00202-022-01713-2