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Research on Two-Stage Optimization Operation of Micro Grid of Energy Hub Facing Extreme Weather Events

Abstract: Climate change has led to an increasing number of extreme weather events in recent years. These natural disasters can cause serious infrastructure damages and even trigger massive power outages. This situation has led to a combination of energy sources to improve the resilience of the energy system in the face of low probability, highly destructive extreme weather events. This paper pro-poses an optimal operation model and a two-stage optimal operation model for energy hub mi-crogrid to cope with extreme weather events. This operation mode improves the resilience of the microgrid system to extreme weather events by optimizing the purchase, transmission, and storage of energy both within a single energy hub and a energy hub microgrid. By setting the load priority, total operating cost and load cutting value can be effectively reduced. Case studies are run in Matlab R2018a environment and solved by YALMIP toolbox and GUROBI solver. The simulation results show that the proposed microgrid model and the two-stage optimal operation mode can greatly improve the stability and resilience of the energy system, and enhance its ability to resist extreme weather events.

1. 引言

2. 能源枢纽微网两阶段优化运行模型

2.1. 能源枢纽的基本结构

Figure 1. Basic structure of energy hub

${X}_{0}=\left[\begin{array}{c}{X}_{01}\\ {X}_{02}\end{array}\right]=\left[\begin{array}{ccccc}{X}_{1}^{1}& \cdots & {X}_{k}^{g}& \cdots & {X}_{24}^{1}\\ {X}_{1}^{2}& \cdots & {X}_{k}^{g}& \cdots & {X}_{24}^{2}\end{array}\right]$ (1)

${Y}_{0}=\left[\begin{array}{c}{Y}_{01}\\ {Y}_{02}\end{array}\right]=\left[\begin{array}{ccccc}{Y}_{1}^{1}& \cdots & {Y}_{k}^{g}& \cdots & {Y}_{24}^{1}\\ {Y}_{1}^{2}& \cdots & {Y}_{k}^{g}& \cdots & {Y}_{24}^{2}\end{array}\right]$ (2)

${X}_{\text{0}}$${Y}_{\text{0}}$ 都包含两部分，分别为 ${X}_{\text{01}}$${X}_{\text{02}}$${Y}_{\text{01}}$${Y}_{\text{02}}$，它们分别代表第一阶段和第二阶段的电能和天然气购买量，如式(1)~(2)所示。

2.1.1. 冷热电联产装置(Combined Cool, Heat and Power, CCHP)

Figure 2. Basic structure of combined cool, heat and power (CCHP)

$\frac{{E}_{CCHP}}{{\eta }_{CCH{P}_{E}}}=\frac{\frac{{H}_{CCHP}}{{\delta }_{heat}}+\frac{{C}_{CCHP}}{{\delta }_{cool}}}{{\eta }_{CCH{P}_{T}}}$ (3)

$\frac{{H}_{CCHP}}{{\delta }_{heat}}+\frac{{C}_{CCHP}}{{\delta }_{cool}}={Y}_{0}\ast CV\ast {\eta }_{CCH{P}_{T}}$ (4)

${E}_{CCHP}={Y}_{0}\ast CV\ast {\eta }_{CCH{P}_{E}}$ (5)

${\eta }_{CCH{P}_{T}}=1-{\eta }_{CCH{P}_{E}}-{\eta }_{loss}$ (6)

${C}_{CCH{P}_{\Gamma }}\ge {\Gamma }_{CCHP}\ge 0$ (7)

2.1.2. 储能系统(Energy Storage System, ESS)

Figure 3. Basic structure of energy storage system

${\Gamma }_{S,s,k+1}={\Gamma }_{S,s,k}\ast \left(1-{\mu }_{\Gamma ,IN}\right)+{\Gamma }_{IN,s,k+1}\ast {\eta }_{\Gamma ,IN}-\frac{{\Gamma }_{OUT,s,k+1}}{{\eta }_{\Gamma ,OUT}}$ (8)

$0\le {\Gamma }_{IN,s,k}\ast {\eta }_{\Gamma ,IN}\le {\Gamma }_{S}^{\mathrm{max}}\ast {z}_{s\gamma ,s}$ (9)

$0\le \frac{{\Gamma }_{OUT,s,k}}{{\eta }_{\Gamma ,OUT}}\le {\Gamma }_{S}^{\mathrm{max}}\ast \left(1-{z}_{s\gamma ,s}\right)$ (10)

$0\le {\Gamma }_{S,s,k}\le {\Gamma }_{S1}^{\mathrm{max}}$ (11)

2.1.3. 负荷模型

Figure 4. Basic structure of load

${D}^{\Gamma }={\sum }_{j=1}^{3}{D}_{j}^{\gamma }$ (12)

${D}^{\Gamma }=\left[\begin{array}{cccccc}{D}_{1,1}^{\Gamma }& {D}_{1,2}^{\Gamma }& \cdots & {D}_{1,k}^{\Gamma }& \cdots & {D}_{1,24}^{\Gamma }\\ {D}_{2,1}^{\Gamma }& {D}_{2,2}^{\Gamma }& \cdots & {D}_{2,k}^{\Gamma }& \cdots & {D}_{2,24}^{\Gamma }\end{array}\right]$ (13)

${D}_{j}^{\gamma }=\left[\begin{array}{cccccc}{D}_{j,1,1}^{\gamma }& {D}_{j,1,2}^{\gamma }& \cdots & {D}_{j,1,k}^{\gamma }& \cdots & {D}_{j,1,24}^{\gamma }\\ {D}_{j,2,1}^{\gamma }& {D}_{j,2,2}^{\gamma }& \cdots & {D}_{j,2,k}^{\gamma }& \cdots & {D}_{j,2,24}^{\gamma }\end{array}\right]$ (14)

${L}_{\gamma ,s,2}^{\lambda }={\sum }_{j=1}^{3}{\sum }_{k=1}^{24}\left({\omega }_{j}^{\lambda }\ast {l}_{\gamma j,s,2,k}^{\lambda }\right)$ (15)

${l}_{\gamma j,s,2,k}^{\lambda }\le {D}_{j,2,k}^{\gamma }$ (16)

${\omega }_{j}$ 是用于估算负荷削减所造成的惩罚成本的重要系数，负荷等级越高(即j的值越小)，该系数的值就越大。由于第1阶段的能源供应充足，因此负荷削减只在第2阶段进行。负荷削减在一定程度上可以提高极端天气下多能系统的弹性和稳定性。

2.2. 能源枢纽微网的基本结构

Figure 5. Basic structure of micro grid of energy hub

2.3. 能源枢纽微网两阶段优化运行模型

2.3.1. 目标函数

$\Omega$ 表示微网中所有EH的集合。在这个模型中，我们将能源枢纽用A、B、C进行编号，即 $\Omega =\left\{\text{A},\text{B},\text{C}\right\}$

$f=\mathrm{min}{\sum }_{\lambda \in \Omega }{f}_{\lambda }=\mathrm{min}{\sum }_{\lambda \in \Omega }\left\{{W}_{ope,1}^{\lambda }+E\left({W}_{cur,2}^{\lambda }+{W}_{ope,2}^{\lambda }\right)\right\}$ (17)

${W}_{ope,1}^{\lambda }=\mathrm{max}\left({X}_{01}^{\lambda },0\right)\ast {W}_{1}+\mathrm{min}\left({X}_{01}^{\lambda },0\right)\ast {Q}_{\text{1}}+{Y}_{01}^{\lambda }\ast {V}_{\text{1}}$ (18)

${W}_{ope,2}^{\lambda }={\sum }_{{p}_{\lambda ,s}\in {P}_{\lambda }}\left(\mathrm{max}\left({X}_{02,s}^{\lambda },0\right)\ast {W}_{2}\ast {p}_{\lambda ,s}+\mathrm{min}\left({X}_{02,s}^{\lambda },0\right)\ast {Q}_{2}\ast {p}_{\lambda ,s}+{Y}_{02,s}^{\lambda }\ast {V}_{2}\ast {p}_{\lambda ,s}\right)$ (19)

${W}_{cur,2}^{\lambda }={\sum }_{s\in S}\left({\eta }_{1}\ast {L}_{e,s,2}^{\lambda }+{\eta }_{2}\ast {L}_{c,s,2}^{\lambda }+{\eta }_{3}\ast {L}_{h,s,2}^{\lambda }\right)$ (20)

${W}_{\text{1}}$${W}_{2}$ 表示第1和第2阶段的购电单价， ${Q}_{\text{1}}$${Q}_{2}$ 表示第1和第2阶段的售电单价， ${V}_{\text{1}}$${V}_{2}$ 表示第1和第2阶段的购气单价，它们均为向量，具体表达式如式(21)~(23)所示。

${W}_{1}=\left[\begin{array}{ccccc}{w}_{1}^{1}& \cdots & {w}_{k}^{1}& \cdots & {w}_{24}^{1}\end{array}\right]$${W}_{\text{2}}=\left[\begin{array}{ccccc}{w}_{1}^{\text{2}}& \cdots & {w}_{k}^{\text{2}}& \cdots & {w}_{24}^{\text{2}}\end{array}\right]$ (21)

${Q}_{1}=\left[\begin{array}{ccccc}{q}_{1}^{1}& \cdots & {q}_{k}^{1}& \cdots & {q}_{24}^{1}\end{array}\right]$${Q}_{2}=\left[\begin{array}{ccccc}{q}_{1}^{2}& \cdots & {q}_{k}^{2}& \cdots & {q}_{24}^{2}\end{array}\right]$ (22)

${V}_{1}=\left[\begin{array}{ccccc}{v}_{1}^{1}& \cdots & {v}_{k}^{1}& \cdots & {v}_{24}^{1}\end{array}\right]$${V}_{\text{2}}=\left[\begin{array}{ccccc}{v}_{1}^{2}& \cdots & {v}_{k}^{2}& \cdots & {v}_{24}^{2}\end{array}\right]$ (23)

${L}_{e,s,2}^{\lambda }={\sum }_{j=1}^{3}{\sum }_{k=1}^{24}\left({a}_{\lambda ,j}\ast {l}_{ej,s,2,k}^{\lambda }\right)$ (24)

${L}_{c,s,2}^{\lambda }={\sum }_{j=1}^{3}{\sum }_{k=1}^{24}\left({b}_{\lambda ,j}\ast {l}_{cj,s,2,k}^{\lambda }\right)$ (25)

${L}_{h,s,2}^{\lambda }={\sum }_{j=1}^{3}{\sum }_{k=1}^{24}\left({c}_{\lambda ,j}\ast {l}_{hj,s,2,k}^{\lambda }\right)$ (26)

${a}_{\lambda ,j}$${b}_{\lambda ,j}$${c}_{\lambda ,j}$ 则分别表示不同等级负荷的削减惩罚系数，j代表负荷级数，且有 $\left\{1,2,3\right\}\in j$，其值越小，代表负荷关键度越高，其削减成本越高。

2.3.2. 约束条件

${X}_{s,k}^{g,\lambda }+{Y}_{s,k}^{g,\lambda }\ast CV\ast {\eta }_{CCHP}^{E}={\sum }_{j=1}^{3}\left({D}_{j,g,k}^{E,\lambda }-{\epsilon }_{g}\ast {l}_{ej,s,2,k}^{\lambda }\right)+{E}_{g,s,k}^{IN,\lambda }\ast {\eta }_{E,IN}-\frac{{E}_{g,s,k}^{OUT,\lambda }}{{\eta }_{E,OUT}}+{\sum }_{l,r\in \Omega }T{E}_{lr}$ (27)

${Y}_{s,k}^{g,\lambda }\ast CV\ast {\eta }_{CCHP}^{T}=\frac{{C}_{CCHP,g,s,k}^{\lambda }}{{\delta }_{cool}}+\frac{{H}_{CCHP,g,s,k}^{\lambda }}{{\delta }_{heat}}$ (28)

${C}_{CCHP,g,s,k}^{\lambda }\ast {\eta }_{C}+\frac{{C}_{g,s,k}^{OUT,\lambda }}{{\eta }_{C,OUT}}-{C}_{g,s,k}^{IN,\lambda }\ast {\eta }_{C,IN}={\sum }_{j=1}^{3}\left({D}_{j,g,k}^{C,\lambda }-{\epsilon }_{g}\ast {l}_{cj,g,s,k}^{\lambda }\right)$ (29)

${H}_{CCHP,g,s,k}^{\lambda }+\frac{{H}_{g,s,k}^{OUT,\lambda }}{{\eta }_{H,OUT}}-{H}_{g,s,k}^{IN,\lambda }\ast {\eta }_{H,IN}={\sum }_{j=1}^{3}\left({D}_{j,g,k}^{H,\lambda }-{\epsilon }_{g}\ast {l}_{hj,g,s,k}^{\lambda }\right)$ (30)

${E}_{CCHP,g,s,k}^{\lambda }={Y}_{s,k}^{g,\lambda }\ast CV\ast {\eta }_{CCHP}^{T}\ast \frac{{\eta }_{CCHP}^{E}}{{\eta }_{CCHP}^{T}}$ (31)

${\eta }_{CCHP}^{T}=\text{1}-{\eta }_{CCHP}^{E}-{\eta }_{loss}$ (32)

${X}_{s,k}^{g}\le {C}_{T},{X}_{s,k}^{\text{1}}\le {C}_{l},{Y}_{s,k}^{\text{1}}\le {C}_{p}$ (33)

${X}_{s,k}^{\text{2}}\le {C}_{l}\ast {S}_{Ek,s},0\le {Y}_{s,k}^{\text{2}}\le {C}_{p}\ast {S}_{Gk,s}$ (34)

$0\le {\Gamma }_{g,s,k}^{IN}\ast {\eta }_{\Gamma ,IN}\le {\Gamma }_{S,\lambda }^{\mathrm{max}}\ast {z}_{\gamma ,s,k}$ (35)

$0\le \frac{{\Gamma }_{g,s,k}^{OUT}}{{\eta }_{\Gamma ,OUT}}\le {\Gamma }_{S}^{\mathrm{max}}\left(1-{z}_{\gamma ,s,k}\right)$ (36)

$0\le {\Gamma }_{g,s,k}^{S}\le {\Gamma }_{S1}^{\mathrm{max}}$ (37)

$0\le {\Gamma }_{CCHP,g,s,k}\le {C}_{CCH{P}_{\Gamma }}$ (38)

${l}_{\gamma j,g,s,k}\le {D}_{j,g,k}^{\Gamma }$ (39)

$-{C}_{TL\gamma ,lr}\le T{\Gamma }_{lr}\le {C}_{TL\gamma ,lr}$ (40)

3. 算例分析

3.1. 基本参数设置

Figure 6. Load curve of energy hub

Figure 7. Energy transaction price

Table 1. Basic parameters of CCHP and ESS

3.2. 负荷分级策略优势的算例验证

Figure 8. Load cutting penalizes cost comparisons

Table 2. Ratio of electrical load cutting in E H A (regardless of load priority setting)

Table 3. Ratio of electrical load cutting in E H A (considering load priority setting)

3.3. 两阶段协调优化运行模式优势的算例验证

$E{H}_{A}$ 为例，两种优化运行模式的比较结果如图9所示，其直观地展示了两种优化运行模式的结果。

(a)(b)

Figure 9. Comparison of system cost under two optimization modes

3.4. 能源枢纽微网在不同运行模式下的目标结果对比

Table 4. Five optimal operation structures of energy hub micro grid

Figure 10. Comparison of load cutting penalty cost (yuan)

Figure 11. Comparison of energy purchase costs (yuan)

Figure 12. Total cost comparison (yuan)

${C}_{add}={\sum }_{\lambda \in \Omega }{C}_{noco}^{\lambda }-{C}_{co}$ (41)

${C}_{ad{d}_{\lambda }}=\left({C}_{noco}^{\lambda }+{\sum }_{\theta \in \Omega ,\theta \ne \lambda }{C}_{co}^{\theta }\right)-{C}_{co}$ (42)

${\rho }_{\lambda }=\frac{{C}_{ad{d}_{\lambda }}}{{\sum }_{\lambda \in \Omega }{C}_{ad{d}_{\lambda }}}$ (43)

${C}_{\lambda }={\rho }_{\lambda }\ast {C}_{add}$ (44)

${C}_{add}=249312.21元$ (45)

${\rho }_{A}\approx 0.275$${\rho }_{B}\approx 0.307$${\rho }_{C}\approx 0.418$ (46)

${C}_{A}=68589.88元$${C}_{B}=76432.70元$${C}_{C}=104289.63元$ (47)

4. 结论

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