Active-reactive power scheduling of integrated electricity-gas network with multi-microgrids

Abstract

Advances in natural gas-fired technologies have deepened the coupling between electricity and gas networks, promoting the development of the integrated electricity-gas network (IEGN) and strengthening the interaction between the active-reactive power flow in the power distribution network (PDN) and the natural gas flow in the gas distribution network (GDN). This paper proposes a day-ahead active-reactive power scheduling model for the IEGN with multi-microgrids (MMGs) to minimize the total operating cost. Through the tight coupling relationship between the subsystems of the IEGN, the potentialities of the IEGN with MMGs toward multi-energy cooperative interaction is optimized. Important component models are elaborated in the PDN, GDN, and coupled MMGs. Besides, motivated by the non-negligible impact of the reactive power, optimal inverter dispatch (OID) is considered to optimize the active and reactive power capabilities of the inverters of distributed generators. Further, a second-order cone (SOC) relaxation technology is utilized to transform the proposed active-reactive power scheduling model into a convex optimization problem that the commercial solver can directly solve. A test system consisting of an IEEE-33 test system and a 7-node natural gas network is adopted to verify the effectiveness of the proposed scheduling method. The results show that the proposed scheduling method can effectively reduce the power losses of the PDN in the IEGN by 9.86%, increase the flexibility of the joint operation of the subsystems of the IEGN, reduce the total operation costs by $32.20, and effectively enhance the operation economy of the IEGN.

Graphical abstract

Keywords

combined cooling / heating / and power (CCHP) / integrated energy systems (IES) / natural gas / power distribution system / gas distribution system

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Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 51877033, 52061635103, 52007026, and 52077028).

Notations

Acronyms
A-R-OPF	Active-reactive optimal power flow
AC	Absorption chillers
ACOPF	Alternating current optimal power flow
CCHP	Combined cooling, heating, and power
DG	Distributed generators
DPV	Distributed photovoltaic
EC	Electric chillers
GB	Gas boilers
GDN	Gas distribution network
GT	Gas turbines
HSS	Heat storage systems
IEGN	Integrated electricity-gas network
MMG	Multi-microgrids
OID	Optimal inverter dispatch
PCS	Power conditioning systems
PDN	Power distribution network
P2G	Power to gas
SOC	Second-order cone
WHB	Waste heat boilers
Indices
i/j	Index of nodes in the PDN
ij	Index of branches in the PDN
I/J	Set of the beginning/ending nodes of the branches in the PDN
m	Index of the microgrids
M	Set of the nodes of the PDN where the microgrids are located
t	Index of time slots
uv	Index of branches in the GDN
u/v	Index of nodes in the GDN
U/V	Set of the beginning/ending nodes of the pipelines in the GDN
Parameters
B_{i,t}^{\mathrm{c}}/B_{i,t}^{\mathrm{d}}	Charging/discharging power of the power storage system of node i of the PDN at the tth hour
Cuv	Weymouth equation coefficient
C_t^{\mathrm{P}}/C_t^{\mathrm{Q}}	Active/reactive power price of the utility grid at the tth hour
C_{i,t}^{\mathrm{D}\mathrm{P}\mathrm{V}}	Operation cost of the distributed photovoltaic of node i in the distribution network, which is assumed to be a constant
COPAC	Coefficient of performance of the absorption chiller in the mth microgrid
COPEC	Performance coefficient of the electrical chiller in the mth microgrid
c{m}_m^{\mathrm{H}\mathrm{S}\mathrm{S}}	Coefficient of the cost function of the heat storage system in the mth microgrid
c{m}_m^{\mathrm{E}\mathrm{C}}/c{m}_m^{\mathrm{A}\mathrm{C}}	Coefficient of the cost function of the electrical chiller/absorption chiller in the mth microgrid
c{m}_m^{\mathrm{W}\mathrm{H}\mathrm{B}}	Coefficient of the cost function of the waste heat boiler in the mth microgrid
C_{m,t}^{\mathrm{g}\mathrm{a}\mathrm{s}}	Purchased gas cost of the mth microgrids at the tth hour
C_{i,t}^{\mathrm{D}\mathrm{P}\mathrm{V}}	Operation cost of the distributed photovoltaic of node i in the distribution network
C_{i,t}^{\mathrm{E}\mathrm{S}\mathrm{S}}	Operation cost of the ESS of node i in the distribution network
E_{i,t}^{\mathrm{E}\mathrm{S}\mathrm{S}}	Amount of electricity stored in the energy storage system of node i of the PDN at the tth hour
H_{m,t}^{\mathrm{G}\mathrm{B}}	Heating power production of the gas boiler of the mth microgrid at the tth hour
H_{m,t}^{\mathrm{A}\mathrm{C}}	Heating power absorption of the absorption chiller of the mth microgrid at the tth hour
H_{m,t}^{\mathrm{c}}/H_{m,t}^{\mathrm{d}}	Charging/discharging power of the heat storage system in the mth microgrid at the tth hour
H_{m,t}^{\mathrm{D}}/C_{m,t}^{\mathrm{D}}	Heating and cooling power loads of the mth microgrid at the tth hour
H_{m,min}^{\mathrm{A}\mathrm{C}}/H_{m,max}^{\mathrm{A}\mathrm{C}}	Minimum/maximum heating power consumption of the absorption chiller in the mth microgrid
H_{m,min}^{\mathrm{W}\mathrm{H}\mathrm{B}}/H_{m,max}^{\mathrm{W}\mathrm{H}\mathrm{B}}	Minimum/maximum heating power absorption of the waste heat boiler in the mth microgrid
H_{m,min}^{\mathrm{G}\mathrm{B}}/H_{m,max}^{\mathrm{G}\mathrm{B}}	Minimum/maximum heating power generation of the gas boiler in the mth microgrid
H_{m,min}^{\mathrm{c}}/H_{m,max}^{\mathrm{c}}	Minimum/maximum heating power charging of the heat power storage in the mth microgrid
H_{m,min}^{\mathrm{d}}/H_{m,max}^{\mathrm{d}}	Minimum/maximum heating power discharging of the heat power storage in the mth microgrid
Iij,t	Current flowing in branch ij in the distribution network at the tth hour
k{f}_i^{\mathrm{D}\mathrm{P}\mathrm{V}}	Minimum power factor of the distributed photovoltaic inverter of node i in the PDN
KG/Km	Utility grid/microgrids located nodes correlation matrix
KESS/KDPV	ESS/distributed photovoltaic located nodes correlation matrix
lij,t	Square of the current flowing in branch ij in the distribution network at the tth hour
LNG	Heating value of natural gas
m_i^{\mathrm{E}\mathrm{S}\mathrm{S}}	Coefficient of the cost function of the node i of the electricity storage system (ESS) in the PDN
M_{m,t}^{\mathrm{o}\mathrm{p}}	Operation cost of the mth the microgrids at the tth hour
M_{m,t}^{\mathrm{H}\mathrm{S}\mathrm{S}}	Operation cost of the heat storage system in the mth microgrid at the tth hour
M_{m,t}^{\mathrm{W}\mathrm{H}\mathrm{B}}	Operation cost of waste heat boiler in the mth microgrid at the tth hour
M_{m,t}^{\mathrm{W}\mathrm{T}}	Operation cost of the wind turbine of the mth microgrid at the tth hour, which is assumed to be a constant
M_{m,t}^{\mathrm{A}\mathrm{C}}/M_{m,t}^{\mathrm{E}\mathrm{C}}	Operation cost of the absorption chiller/electrical chiller of the mth microgrid at the tth hour
Pij,t	Active power flow in branch ij in the distribution network at the tth hour
P_{m,t}^{\mathrm{E}\mathrm{C}}	Active power consumption of the electrical chiller of the mth microgrid at the tth hour
P_{i,t}^{\mathrm{D}\mathrm{P}\mathrm{V},\mathrm{m}\mathrm{a}\mathrm{x}}	Maximum forecasted active power production of the distributed photovoltaic of node i in the PDN at the tth hour
P_{m,t}^{\mathrm{D}}/Q_{m,t}^{\mathrm{D}}	Active and reactive power loads of the mth microgrid at the tth hour
P_t^{\mathrm{G}}/Q_t^{\mathrm{G}}	Active/reactive power transported from the utility grid at the tth hour
P_{i,t}^{\mathrm{D}}/Q_{i,t}^{\mathrm{D}}	Active and reactive power of node i of the PDN at the tth hour
P_{m,max}^{\mathrm{P}\mathrm{C}\mathrm{C}}/Q_{m,max}^{\mathrm{P}\mathrm{C}\mathrm{C}}	Maximum amount of active/reactive power traded at the point of common coupling between the mth microgrid and the PDN
P_{m,min}^{\mathrm{G}\mathrm{T}}/P_{m,max}^{\mathrm{G}\mathrm{T}}	Minimum/maximum active power production of the gas turbine in the mth microgrid
P_{m,min}^{\mathrm{E}\mathrm{C}}/P_{m,max}^{\mathrm{E}\mathrm{C}}	Minimum/maximum active power consumption of the electrical chiller in the mth microgrid
P_{t,min}^{\mathrm{G}}/P_{t,max}^{\mathrm{G}}	Minimum/maximum active power transported from the utility grid at the tth hour
P_{m,max}^{\mathrm{P}\mathrm{C}\mathrm{C}}/Q_{m,max}^{\mathrm{P}\mathrm{C}\mathrm{C}}	Maximum amount of active/reactive power traded at the point of common coupling between the mth microgrid and the PDN
Pm,t/Qm,t	Transported quantity of the mth microgrid of active/reactive power at the tth hour
P_{m,t}^{\mathrm{G}\mathrm{T}}/H_{m,t}^{\mathrm{G}\mathrm{T}}	Active/heating power production of the gas turbine at the tth hour
P_{i,t}^{\mathrm{D}\mathrm{P}\mathrm{V}}/Q_{i,t}^{\mathrm{D}\mathrm{P}\mathrm{V}}	Active/reactive power production of the distributed photovoltaic of node i of the PDN at the tth hour
Qij,t	Reactive power flowing in branch ij in the distribution network at the tth hour
Q_{t,min}^{\mathrm{G}}/Q_{t,max}^{\mathrm{G}}	Minimum/maximum reactive power transported from the utility grid at the tth hour
rij,t/xij,t	Resistance/reactance of branch ij in the distribution network
S_i^{\mathrm{D}\mathrm{P}\mathrm{V}}	Capacity of the distributed photovoltaic inverter of node i of the PDN
S_{m,t}^{\mathrm{H}\mathrm{S}\mathrm{S}}	Amount of heat stored in the electrical chiller at the tth hour
SO{C}_{i,min}^{\mathrm{E}\mathrm{S}\mathrm{S}}/SO{C}_{i,max}^{\mathrm{E}\mathrm{S}\mathrm{S}}	Minimum/maximum state of charge of the ESS in the node i in the PDN
Vmin,i,t/Vmax,i,t	Voltage limitations of node i in the distribution network
Vi,t	Nodal voltage in node i in the distribution network at the tth hour
Ui,t	Square of nodal voltage in node i in the distribution network at the tth hour
Ub,t	Voltage drop in branch b in the distribution network at the tth hour
w_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l}}/w_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l}}	Limitations of the gas supplied quantity from the gas well at the tth hour
wuv,t	Gas flow from node u to node v in the GDN at the tth hour
w_t^{\mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l}}	Gas production by node u in the gas well at the tth hour
w_{u,t}^{\mathrm{G}\mathrm{T}}/w_{u,t}^{\mathrm{G}\mathrm{B}}	Gas consumption by GT/GB at node u in the gas distribution system at the tth hour
ψmin/ψmax	Limitations of the gas nodal pressure in the GDN at the tth hour
ρc	Compression factor of the compressor
ψu,t	Gas nodal pressure in node u in the gas distribution network at the tth hour
ψct,t/ψcf,t	Gas nodal pressure of the inlet and outlet of the compressor in the GDN at the tth hour
{\eta }_m^{\mathrm{G}\mathrm{T}}	Efficiency of the gas turbine in the mth microgrid
{\eta }_m^{\mathrm{G}\mathrm{B}}	Efficiency of the gas boiler in the mth microgrid
{\eta }_m^{\mathrm{W}\mathrm{H}\mathrm{B}}	Efficiency of the waste heat boiler in the mth microgrid
{\eta }_i^{\mathrm{c},\mathrm{E}\mathrm{S}\mathrm{S}}/{\eta }_i^{\mathrm{d},\mathrm{E}\mathrm{S}\mathrm{S}}	Charging/discharging efficiency of the ESS of node i in the PDN
{\eta }_m^{\mathrm{c},\mathrm{H}\mathrm{S}\mathrm{S}}/{\eta }_m^{\mathrm{d},\mathrm{H}\mathrm{S}\mathrm{S}}	Charging/discharging efficiency of the heat storage system in the mth microgrid

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