Electricity Market Optimization(VI) - 机组组合问题的 GAMS 求解

根据之前的博客，我们考虑机组的启动成本只讨论考虑以下几种约束的机组组合问题：

• 功率平衡约束
• 火电机组启停约束和爬坡约束
• 备用容量约束
  min ⁡ ∑ t = 1 T ( C t g e n + C t u c + C t curt ) s.t. C t g e n = ∑ i ∈ [ G ] c i ( p i , t c ) C t u c = ∑ i ∈ [ G ] ( c i s u v i , t + c i s d w i , t ) C t curt = c curt [ ( P ‾ t w − p t w ) + ( P ‾ t pv − p t pv ) ] ∀ t ∈ [ T ] ∑ i ∈ [ G ] p i , t c + p t w + p t p v = D t ∀ t ∈ [ T ] P ‾ i u i , t ≤ p i , t c ≤ P ‾ i u i , t p t w ≤ P ‾ t w p t pv ≤ P ‾ t pv ∑ s = t − ( U T i − 1 ) t v i , s ≤ u i , t ∑ s = t − ( D T i − 1 ) t w i , s ≤ 1 − u i , t v i , t − w i , t = u i , t − u i , t − 1 p i , t c − p i , t − 1 c ≤ R i 60 + v i , t P ‾ i p i , t − 1 c − p i , t c ≤ R i 60 + w i , t P ‾ i u i , t ∈ { 0 , 1 } 0 ≤ v i , t , w i , t ≤ 1 p i , t + r i , t s ≤ P ‾ i u i , t p i , t + r i , t s + r i , t n s ≤ P ‾ i ∀ i ∈ [ G ] , t ∈ [ T ] r i , t s = 0 ∀ i ∈ [ G ] ∖ G S , t ∈ [ T ] r t r e q ≥ p i , t ∑ i ∈ [ G ] ( r i , t s + r i , t n s ) ≥ r t r e q ∑ i ∈ [ G ] r i , t s ≥ 0.5 r t r e q ∀ t ∈ [ T ] \begin{aligned} \min \quad & \sum_{t=1}^T \big(C_t^{\rm gen} + C_t^{\rm uc} + C_t^{\text{curt}}\big)\\\\ \text{s.t.} \quad & C_t^{\rm gen} = \sum_{i\in[G]} c_i(p^{\rm c}_{i,t}) \\\\ & C_t^{\rm uc} = \sum_{i\in[G]}\big(c^{\rm su}_i v_{i,t} + c^{\rm sd}_i w_{i,t} \big) \\\\ & C_t^{\text{curt}} = c^{\text{curt}} \Big[ (\overline{P}_{t}^{\text{w}} - p_{t}^{\text{w}}) + (\overline{P}_{t}^{\text{pv}} - p_{t}^{\text{pv}}) \Big] && \forall t \in [T] \\\\ & \sum_{i\in[G]} p_{i,t}^{\rm c} + p_{t}^{\rm w} + p_{t}^{\rm pv} = D_t &&\forall t \in [T] \\\\ & \underline{P}_{i}u_{i,t} \le p_{i,t}^{\rm c} \le \overline{P}_{i}u_{i,t} \\\\ &p_{t}^{\text{w}} \leq \overline{P}_{t}^{\text{w}} \\\\ & p_{t}^{\text{pv}} \leq \overline{P}_{t}^{\text{pv}}\\\\ & \sum_{s=t-(UT_i-1)}^t v_{i,s} \leq u_{i,t} \\ & \sum_{s=t-(DT_i-1)}^t w_{i,s} \leq 1-u_{i,t} \\\\ & v_{i,t} - w_{i,t} = u_{i,t} - u_{i,t-1} \\\\ & p_{i,t}^{\rm c} - p_{i,t-1}^{\rm c} \le R_i^{\rm 60} + v_{i,t}\underline{P}_i \\\\ & p_{i,t-1}^{\rm c} - p_{i,t}^{\rm c} \le R_i^{\rm 60} + w_{i,t}\underline{P}_i \\\\ & u_{i,t}\in\{0,1\} \\\\ & 0 \le v_{i,t}, w_{i,t} \le 1 \\\\ & p_{i,t} + r^{\rm s}_{i,t} \le \overline{P}_i u_{i,t} \\\\ & p_{i,t} + r^{\rm s}_{i,t} + r^{\rm ns}_{i,t} \le \overline{P}_i && \forall i \in [G],t \in [T] \\\\ & r_{i,t}^{\rm s} = 0 && \forall i \in [G]\setminus \mathcal{G}^{\rm S}, t \in [T] \\\\ & r^{\rm req}_t \ge p_{i,t} \\\\ & \sum_{i\in[G]} (r^{\rm s}_{i,t} + r^{\rm ns}_{i,t}) \ge r^{\rm req}_t \\\\ & \sum_{i\in[G]} r^{\rm s}_{i,t} \ge 0.5 r^{\rm req}_t && \forall t \in [T] \end{aligned} mins.t.​t=1∑T​(Ctgen​+Ctuc​+Ctcurt​)Ctgen​=i∈[G]∑​ci​(pi,tc​)Ctuc​=i∈[G]∑​(cisu​vi,t​+cisd​wi,t​)Ctcurt​=ccurt[(Ptw​−ptw​)+(Ptpv​−ptpv​)]i∈[G]∑​pi,tc​+ptw​+ptpv​=Dt​P​i​ui,t​≤pi,tc​≤Pi​ui,t​ptw​≤Ptw​ptpv​≤Ptpv​s=t−(UTi​−1)∑t​vi,s​≤ui,t​s=t−(DTi​−1)∑t​wi,s​≤1−ui,t​vi,t​−wi,t​=ui,t​−ui,t−1​pi,tc​−pi,t−1c​≤Ri60​+vi,t​P​i​pi,t−1c​−pi,tc​≤Ri60​+wi,t​P​i​ui,t​∈{0,1}0≤vi,t​,wi,t​≤1pi,t​+ri,ts​≤Pi​ui,t​pi,t​+ri,ts​+ri,tns​≤Pi​ri,ts​=0rtreq​≥pi,t​i∈[G]∑​(ri,ts​+ri,tns​)≥rtreq​i∈[G]∑​ri,ts​≥0.5rtreq​​​∀t∈[T]∀t∈[T]∀i∈[G],t∈[T]∀i∈[G]∖GS,t∈[T]∀t∈[T]​