Overview

The generation and transmission expansion planning (GTEP) model is for investment decision analysis under various policies and energy transition scenarios. This model is a Mixed-Integer Linear Programming (MILP) Problem.

The objective of this model is to minimize total system costs, including fixed investment costs, variable operation costs, and penalties for non-compliance with policies. The techno-economic and environmental constraints of this model are budget constraints, power balance, transmission transfer limits, generator operation constraints, storage operation constraints, resource adequacy requirements, and policy constraints (i.e., renewable portfolio standards (RPS) and carbon emission limitations). The decision variables of this model include integer decision variables for investment in resources and continuous decision variables for operations in representative days.

Problem Formulation

Objective function

(1) Minimize total system cost:

\[\begin{aligned} \min_{\Gamma} \quad &\sum_{g \in G^{+}} \tilde{I}_{g} \times x_{g} + \sum_{g \in G, t \in T}VCG_{g} \times N_{t} \times \sum_{h \in H_{t}}p_{g,t,h} + \\ &\sum_{l \in L^{+}} \tilde{I}_{l} \times y_{l} + \\ &\sum_{s \in S^{+}} \tilde{I}_{s} \times z_{s} + \sum_{s \in S, t \in T} VCS \times N_{t} \times \sum_{h \in H_{t}} (c_{s,t,h} + dc_{s,t,h}) + \\ &\sum_{d \in D, t \in T} VOLL_{d} \times N_{t} \times \sum_{h \in H_{t}} p_{d,t,h}^{LS} + \\ & PT^{rps} \times \sum_{w \in W} pt_{w}^{rps} + \\ & PT^{emis} \times \sum_{w \in W} em_{w}^{emis} + \\ & \sum_{t \in T} DRC \times N_{t} \sum_{i \in I, h \in H_{t}} (dr_{i,t,h}^{UP} + dr_{i,t,h}^{DN}) \end{aligned}\]

\[\Gamma = \Bigl\{ x_{g}, y_{l}, z_{s}, f_{l,h}, p_{g,t,h}, p_{d,t,h}^{LS}, c_{s,t,h}, dc_{s,t,h}, dr_{i,t,h}^{DR}, dr_{i,t,h}^{UP}, dr_{i,t,h}^{DN}, soc_{s,t,h}, pt^{rps}, pw_{g,w}, pwi_{g,w,w'}, em^{emis}_{w}, a_{g,t}, b_{g,t} \Bigr\}\]

Constraints

(2) Generator investment budget:

\[\sum_{g \in G_{+}} \tilde{I}_{g} \times x_{g} \le IBG\]

(3) Transmission line investment budget:

\[\sum_{l \in L_{+}} \tilde{I}_{l} \times y_{l} \le IBL\]

(4) Storage investment budget:

\[\sum_{s \in S_{+}} \tilde{I}_{s} \times z_{s} \le IBS\]

(5) Power balance:

\[\sum_{g \in G_{i}} P_{g,t,h} + \sum_{s \in S_{i}} (dc_{s,t,h} - c_{s,t,h}) - \sum_{l \in LS_{i}} f_{l.t.h} \\ + \sum_{l \in LR_{i}} f_{l.t.h} = \sum_{d \in D_{i}} (P_{d,t,h} - P_{d,t,h}^{LS}) ; \forall i \in I, h \in H_{t}, t \in T\]

(6) Transmission power flow limit for existing transmission lines:

\[- F_{l}^{max} \le f_{g,l,t,h} \le F_{l}^{max}; \forall g \in G, l \in L^{E}, h \in H_{t}, t \in T\]

(7) Transmission power flow limit for new installed transmission lines:

\[- y_{l} \times F_{l}^{max} \le f_{g,l,t,h} \le y_{l} \times F_{l}^{max}; \forall g \in G, l \in L^{+}, h \in H_{t}, t \in T\]

(8) Maximum capacity limits for existing power generation:

\[0 \le p_{g,t,h} \le P_{g}^{max}; \forall g \in G_{E}, h \in H_{t}, t \in T\]

(9) Maximum capacity limits for installed power generation:

\[0 \le p_{g,t,h} \le P_{g}^{max} \times x_{g}; \forall g \in G_{+}, h \in H_{t}, t \in T\]

(10) Load shedding limit:

\[0 \le p_{g,t,h}^{LS} \le P_{g,t,h}; \forall d \in D_{i}, i \in I, h \in H_{t}, t \in T\]

(11) Renewables generation availability for the existing plants:

\[p_{g,h} \le AFRE_{g,t,h,i} \times P_{g}^{max}; \forall g \in G_{E} \cap G_{i} \cap (G^{PV} \cup G^{W}), i \in I, h \in H_{t}, t \in T\]

(12) Renewables generation availability for new installed plants:

\[p_{g,h} \le AFRE_{g,t,h,i} \times P_{g}^{max} \times x_{g}; \forall g \in G_{+} \cap G_{i} \cap (G^{PV} \cup G^{W}), i \in I, h \in H_{t}, t \in T\]

(13) Storage charging rate limit for existing units:

\[\frac{c_{s,t,h}}{SC_{s}} \le SCAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{E}\]

(14) Storage discharging rate limit for existing units:

\[\frac{dc_{s,t,h}}{SD_{s}} \le SCAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{E}\]

(15) Storage charging rate limit for new installed units:

\[\frac{c_{s,t,h}}{SC_{s}} \le z_{s} \times SCAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{+}\]

(16) Storage discharging rate limit for new installed units:

\[\frac{dc_{s,t,h}}{SD_{s}} \le z_{s} \times SCAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{+}\]

(17) State of charge limit for existing units:

\[0 \le soc_{s,t,h} \le SECAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{E}\]

(18) State of charge limit for new installed units:

\[0 \le soc_{s,t,h} \le z_{s} \times SECAP_{s}; \forall h \in H_{t}, t \in T, s \in S_{+}\]

(19) Storage operation constraints:

\[soc_{s,t,h} = soc_{s,t,h-1} + \epsilon_{ch} \times c_{s,t,h} - \frac{dc_{s,t,h}}{\epsilon_{dis}}; \forall h \in H_{t}, t \in T, s \in S\]

(20) Daily 50% of storage level balancing for existing units:

\[soc_{s,1} = soc_{s,end} = 0.5 \times SCAP_{s}; s \in S_{E}\]

(21) Daily 50% of storage level balancing for new installed units:

\[soc_{s,t,1} = soc_{s,t,end} = 0.5 \times z_{s} SCAP_{s}; s \in S_{+}\]

(22) Resource adequacy:

\[\sum_{g \in G_{E}} (CC_{g} \times P_{g}^{max}) + \sum_{g \in G_{+}} (CC_{g} \times P_{g}^{max} \times x_{g}) \\ + \sum_{s \in S^{E}}(CC_{s} \times SCAP_{s}) + \sum_{s \in S^{E}}(CC_{s} \times SCAP_{s} \times z_{s}) \ge (1 + RM) \times PK\]

(23) RPS policy - State total renewable energy generation:

\[pw_{g,w} = \sum_{t \in T} N_{t} \times \sum_{h \in H_{t}} p+{g,t,h}; \forall g \in (\bigcup_{i \in I_{w}} G_{i}) \cap (G^{RPS}), w \in W\]

(24) RPS policy - State renewable credits export limitation:

\[pw_{g,w} \ge \sum_{w' \in WER_{w}} pwi_{g,w,w'}; \forall g \in (\bigcup_{i \in I_{w}} G_{i}) \cap (G^{RPS}), w \in W\]

(25) RPS policy - State renewable credits import limitation:

\[pw_{g,w'} \ge pwi_{g,w,w'}; \forall g \in (\bigcup_{i \in I_{w}} G_{i}) \cap (G^{RPS}), w \in W, w' \in WIR_{w}\]

(26) RPS policy - Renewable credits trading meets state RPS requirements:

\[\begin{aligned} \sum_{g \in (\bigcup_{i \in I_{w'}} G_{i}) \cap (G^{RPS}), w' \in WIR_{w}} pwi_{g,w,w'} - \sum_{g \in (\bigcup_{i \in I_{w}} G_{i}) \cap (G^{RPS}), w' \in WER_{w}} pwi_{g,w',w} + pt_{w}^{rps} \\ \ge \sum_{t \in T} N_{t} \times \sum_{i \in I_{w},h \in H_{t}} \sum_{d \in D_{i}} p_{d,t,h} \times RPS_{w};\\ w \in W \end{aligned}\]

(27) Cap & Trade - State carbon allowance cap:

\[\sum_{g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G^{F}} a_{g,t} - em_{w}^{emis} \le ALW_{t,w}; w \in W, t \in T\]

(28) Cap & Trade - Balance between allowances and emissions:

\[N_{t} \sum_{h \in H_{t}} EF_{g} \times p_{g,t,h} = a_{g,t} + b_{g,t-1} = b_{g,t}; g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G_{F}, w \in W, t \in T\]

(29) Cap & Trade - No cross-year banking:

\[b_{g,1} = b_{g,end} = 0; g \in G_{F}\]

(30) Binary variables:

\[x_{g} = \{0,1 \}; \forall g \in G_{+} y_{l} = \{0,1 \}; \forall l \in L_{+} z_{s} = \{0,1 \}; \forall s \in S_{+}\]

(31) Nonnegative variable:

\[a_{g,t}, b_{g,t}, p_{g,t,h}, p_{d,t,h}^{LS}, c_{s,t,h}, dc_{s,t,h}, dr_{i,t,h}^{DR}, dr_{i,t,h}^{UP}, dr_{i,t,h}^{DN},soc_{s,t,h}, pt^{rps}, pw_{g,w}, pwi_{g,w,w'}, em^{emis} \\ \ge 0\]

(32) Demand response (load shifting) constraints - 1:

\[dr_{i,t,h}^{DR} = DR_{i,t,h}^{REF} + dr_{i,t,h}^{UP} - dr_{i,t,h}^{DN}; \forall i \in I, h \in H\]

(33) Demand response (load shifting) constraints - 2:

\[\sum_{i=h}^{h+23} dr_{i,t,h}^{UP} = \sum_{i=h}^{h+23} dr_{i,t,h}^{DN}; \forall i \in I, h \in HD \text{{1, 25, 49, T-23}}\]

(34) Demand response (load shifting) constraints - 3:

\[DR_{i,t,h}^{REF} + dr_{i,t,h}^{UP} \le DR^{MAX}; \forall i \in I, h \in H\]

(35) Demand response (load shifting) constraints - 4:

\[dr_{i,t,h}^{DN} \le DR_{i,t,h}^{REF}; \forall i \in I, h \in H\]