Abstract
This chapter proposes a model to demonstrate the impact of renewable energy sources, demand response (DR), and distribution feeder reconfiguration (DFR) on the optimal share of energy in distribution systems (DSs). The price-based DR program is adopted via load shifting mechanism. The proposed model determines optimal locations of RESs and DR in DSs to minimize the energy procurement cost as well as the cost of energy not supplied. Hence, a multiobjective optimization problem is formulated through a mixed-integer second-order cone programming (MISOCP) model, with a guaranteed global optimal solution. This model is solved via the ε-constraint method and Pareto optimal solutions obtained. The DFR is also considered to optimize the network topology. The proposed model is implemented on a standard 70-bus radial test system and solved by the General Algebraic Modeling System (GAMS) optimization software. According to simulation results, the proposed model is beneficial both from the reliability and economic perspectives.
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Abbreviations
- b, b′:
-
Index for network buses
- l :
-
Index for network feeders
- S b :
-
Set of all network nodes
- S dr :
-
Set of nodes participating in demand response
- S l :
-
Set of lines in distribution network
- S t :
-
Set of time periods
- t :
-
Index for operation intervals
- ϑ b, t :
-
Demand response decision variable of bus b at time period t
- \( {\mathrm{Bi}}_b^{\mathrm{dr}} \) :
-
Binary decision variable indicating whether bus b participates in DR or not
- \( {\mathrm{Bi}}_b^{\mathrm{pv}} \) :
-
Binary decision variable for installation of PV at bus b
- \( {\mathrm{Bi}}_l^r \) :
-
Binary decision variable to model the on/off status of feeder l
- \( {\mathrm{Bi}}_b^{\mathrm{w}} \) :
-
Binary decision variable for installation of WT at bus b
- CENS:
-
Cost of energy not supplied ($)
- ENSt:
-
Energy not supplied at time period t ($/h)
- I l, t :
-
Current flowing through the line l at time t (pu)
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{D}} \) :
-
Active/reactive demand of bus b at time period t with demand response (pu)
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{G}} \) :
-
Active/reactive power generation in bus b at time period t (pu)
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{net}} \) :
-
Net active/reactive power injection to bus b at time period t with demand response (pu)
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{pv}} \) :
-
Active/reactive power injection of bus b at time period t with PV (pu)
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{w}} \) :
-
Active/reactive power injection of bus b at time period t with WT (pu)
- TOC:
-
Total operation cost ($)
- V b, t :
-
Voltage magnitude at bus b at time t (pu)
- \( {\beta}_b^{+},{\beta}_b^{-} \) :
-
Coefficients for modeling the lower/upper limits of wind turbine reactive power output
- λ l :
-
Failure rate of branch l [failures/year]
- Γw/pv:
-
Rated active power of WT and PV connected to bus b (pu)
- \( {\Phi}_{\mathrm{t}}^{\mathrm{w}/\mathrm{pv}} \) :
-
Forecasted output of WT and PV at time period t(%)
- \( {\vartheta}_b^{\max /\min } \) :
-
Maximum/minimum demand flexibility at bus b(%)
- \( {I}_l^{\mathrm{max}} \) :
-
Maximum feeder of l capacity
- \( {\aleph}_t^{\mathrm{dr}} \) :
-
Energy rate of DR at time t in day-ahead market ($/MWh)
- \( {\aleph}_t^{\mathrm{pv}} \) :
-
Energy rate of PV at time t in day-ahead market ($/MWh)
- \( {\aleph}_t^{\mathrm{ups}} \) :
-
Pool market price at time t in day-ahead market ($/MWh)
- \( {\aleph}_t^{\mathrm{w}} \) :
-
Energy rate of WT at time t in day-ahead market ($/MWh)
- N dr :
-
Maximum number of nodes allowed to participate in demand response
- N pv :
-
Maximum number of nodes allowed to install the PV
- N w :
-
Maximum number of nodes allowed to install the wind plant
- \( {\left(P/Q\right)}_{b,t}^{\mathrm{D}0} \) :
-
Initial active/reactive demand of bus b at time period t without demand response (pu)
- R l :
-
Resistance of line l
- U l :
-
Average repair time of branch l [h]
- V min/max :
-
Maximum/minimum voltage magnitude
- VOLLt:
-
Value of lost load at time t ($/MWh)
- X l :
-
Reactance of line l
- CENS:
-
Cost of energy not supplied
- DFR:
-
Distribution feeder reconfiguration
- DERs:
-
Distributed energy resources
- DG:
-
Distributed generation
- DR:
-
Demand response
- DS:
-
Distribution system
- DSO:
-
Distribution system operator
- MISOCP:
-
Mixed-integer second-order cone programming
- PV:
-
Photovoltaic
- RESs:
-
Renewable energy sources
- TOC:
-
Total operation cost
- WT:
-
Wind turbine
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Hooshmand, E., Rabiee, A. (2020). Distribution Feeder Reconfiguration Considering Price-Based Demand Response Program. In: Nojavan, S., Zare, K. (eds) Demand Response Application in Smart Grids. Springer, Cham. https://doi.org/10.1007/978-3-030-32104-8_5
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