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

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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.

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Abbreviations

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

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

\(B_{i,t}^{\rm{c}}/B_{i,t}^{\rm{d}}\) :

Charging/discharging power of the power storage system of node i of the PDN at the tth hour

C uv :

Weymouth equation coefficient

\(C_t^{\rm{P}}/C_t^{\rm{Q}}\) :

Active/reactive power price of the utility grid at the tth hour

\(C_{i,t}^{{\rm{DPV}}}\) :

Operation cost of the distributed photovoltaic of node i in the distribution network, which is assumed to be a constant

COP AC :

Coefficient of performance of the absorption chiller in the mth microgrid

COP EC :

Performance coefficient of the electrical chiller in the mth microgrid

\(cm_m^{{\rm{HSS}}}\) :

Coefficient of the cost function of the heat storage system in the mth microgrid

\(cm_m^{{\rm{EC}}}/cm_m^{{\rm{AC}}}\) :

Coefficient of the cost function of the electrical chiller/absorption chiller in the mth microgrid

\(cm_m^{{\rm{WHB}}}\) :

Coefficient of the cost function of the waste heat boiler in the mth microgrid

\(C_{m,t}^{{\rm{gas}}}\) :

Purchased gas cost of the mth microgrids at the tth hour

\(C_{i,t}^{{\rm{DPV}}}\) :

Operation cost of the distributed photovoltaic of node i in the distribution network

\(C_{i,t}^{{\rm{ESS}}}\) :

Operation cost of the ESS of node i in the distribution network

\(E_{i,t}^{{\rm{ESS}}}\) :

Amount of electricity stored in the energy storage system of node i of the PDN at the tth hour

\(H_{m,t}^{{\rm{GB}}}\) :

Heating power production of the gas boiler of the mth microgrid at the tth hour

\(H_{m,t}^{{\rm{AC}}}\) :

Heating power absorption of the absorption chiller of the mth microgrid at the tth hour

\(H_{m,t}^{\rm{c}}/H_{m,t}^{\rm{d}}\) :

Charging/discharging power of the heat storage system in the mth microgrid at the tth hour

\(H_{m,t}^{\rm{D}}/H_{m,t}^{\rm{D}}\) :

Heating and cooling power loads of the mth microgrid at the tth hour

\(H_{m,min}^{{\rm{AC}}}/H_{m,\max }^{{\rm{AC}}}\) :

Minimum/maximum heating power consumption of the absorption chiller in the mth microgrid

\(H_{m,min}^{{\rm{WHB}}}/H_{m,\max }^{{\rm{WHB}}}\) :

Minimum/maximum heating power absorption of the waste heat boiler in the mth microgrid

\(H_{m,min}^{{\rm{GB}}}/H_{m,\max }^{{\rm{GB}}}\) :

Minimum/maximum heating power generation of the gas boiler in the mth microgrid

\(H_{m,min}^{\rm{c}}/H_{m,\max }^{\rm{c}}\) :

Minimum/maximum heating power charging of the heat power storage in the mth microgrid

\(H_{m,min}^{\rm{d}}/H_{m,\max }^{\rm{d}}\) :

Minimum/maximum heating power discharging of the heat power storage in the mth microgrid

I ij,t :

Current flowing in branch ij in the distribution network at the tth hour

\(kf_i^{{\rm{DPV}}}\) :

Minimum power factor of the distributed photovoltaic inverter of node i in the PDN

K G/K m :

Utility grid/microgrids located nodes correlation matrix

K ESS/K DPV :

ESS/distributed photovoltaic located nodes correlation matrix

l ij,t :

Square of the current flowing in branch ij in the distribution network at the tth hour

L NG :

Heating value of natural gas

\(m_i^{{\rm{ESS}}}\) :

Coefficient of the cost function of the node i of the electricity storage system (ESS) in the PDN

\(M_{m,t}^{{\rm{op}}}\) :

Operation cost of the mth the microgrids at the tth hour

\(M_{m,t}^{{\rm{HSS}}}\) :

Operation cost of the heat storage system in the mth microgrid at the tth hour

\(M_{m,t}^{{\rm{WHB}}}\) :

Operation cost of waste heat boiler in the mth microgrid at the tth hour

\(M_{m,t}^{{\rm{WT}}}\) :

Operation cost of the wind turbine of the mth microgrid at the tth hour, which is assumed to be a constant

\(M_{m,t}^{{\rm{AC}}}/M_{m,t}^{{\rm{EC}}}\) :

Operation cost of the absorption chiller/electrical chiller of the mth microgrid at the tth hour

P ij,t :

Active power flow in branch ij in the distribution network at the tth hour

\(P_{m,t}^{{\rm{EC}}}\) :

Active power consumption of the electrical chiller of the mth microgrid at the tth hour

\(P_{i,t}^{{\rm{DPV,max}}}\) :

Maximum forecasted active power production of the distributed photovoltaic of node i in the PDN at the tth hour

\(P_{m,t}^{\rm{D}}/Q_{m,t}^{\rm{D}}\) :

Active and reactive power loads of the mth microgrid at the tth hour

\(P_t^{\rm{G}}/Q_t^{\rm{G}}\) :

Active/reactive power transported from the utility grid at the tth hour

\(P_{i,t}^{\rm{D}}/Q_{i,t}^{\rm{D}}\) :

Active and reactive power of node i of the PDN at the tth hour

\(P_{m,\max }^{{\rm{PCC}}}/Q_{m,\max }^{{\rm{PCC}}}\) :

Maximum amount of active/reactive power traded at the point of common coupling between the mth microgrid and the PDN

\(P_{m,\min }^{{\rm{GT}}}/P_{m,max}^{{\rm{GT}}}\) :

Minimum/maximum active power production of the gas turbine in the mth microgrid

\(P_{m,\min }^{{\rm{EC}}}/P_{m,max}^{{\rm{EC}}}\) :

Minimum/maximum active power consumption of the electrical chiller in the mth microgrid

\(P_{t,\min }^{\rm{G}}/P_{t,max}^{\rm{G}}\) :

Minimum/maximum active power transported from the utility grid at the tth hour

\(P_{m,\max }^{{\rm{PCC}}}/Q_{m,max}^{{\rm{PCC}}}\) :

Maximum amount of active/reactive power traded at the point of common coupling between the mth microgrid and the PDN

\({P_{m,t}}/{Q_{m,t}}\) :

Transported quantity of the mth microgrid of active/reactive power at the tth hour

\(P_{m,t}^{{\rm{GT}}}/H_{m,t}^{{\rm{GT}}}\) :

Active/heating power production of the gas turbine at the tth hour

\(P_{i,t}^{{\rm{DPV}}}/Q_{i,t}^{{\rm{DPV}}}\) :

Active/reactive power production of the distributed photovoltaic of node i of the PDN at the tth hour

Q ij,t :

Reactive power flowing in branch ij in the distribution network at the tth hour

\(Q_{t,\min }^{\rm{G}}/Q_{t,\max }^{\rm{G}}\) :

Minimum/maximum reactive power transported from the utility grid at the tth hour

r ij,t/x ij,t :

Resistance/reactance of branch ij in the distribution network

\(S_i^{{\rm{DPV}}}\) :

Capacity of the distributed photovoltaic inverter of node i of the PDN

\(S_{m,t}^{{\rm{HSS}}}\) :

Amount of heat stored in the electrical chiller at the tth hour

\(SOC_{i,\min }^{{\rm{ESS}}}/SOC_{i,\max }^{{\rm{ESS}}}\) :

Minimum/maximum state of charge of the ESS in the node i in the PDN

V min,i,t /V max,i,t :

Voltage limitations of node i in the distribution network

V i,t :

Nodal voltage in node i in the distribution network at the tth hour

U i,t :

Square of nodal voltage in node i in the distribution network at the tth hour

U b,t :

Voltage drop in branch b in the distribution network at the tth hour

\(w_{\min }^{{\rm{well}}}/w_{\max }^{{\rm{well}}}\) :

Limitations of the gas supplied quantity from the gas well at the tth hour

w uv,t :

Gas flow from node u to node v in the GDN at the tth hour

\(w_t^{{\rm{well}}}\) :

Gas production by node u in the gas well at the tth hour

\(w_{u,t}^{{\rm{GT}}}/w_{u,t}^{{\rm{GB}}}\) :

Gas consumption by GT/GB at node u in the gas distribution system at the tth hour

ψ min/ψ max :

Limitations of the gas nodal pressure in the GDN at the tth hour

ρ c :

Compression factor of the compressor

ψ u,t :

Gas nodal pressure in node u in the gas distribution network at the tth hour

ψ ct,t/ψ cf,t :

Gas nodal pressure of the inlet and outlet of the compressor in the GDN at the tth hour

\(\eta _m^{{\rm{GT}}}\) :

Efficiency of the gas turbine in the mth microgrid

\(\eta _m^{{\rm{GB}}}\) :

Efficiency of the gas boiler in the mth microgrid

\(\eta _m^{{\rm{WHB}}}\) :

Efficiency of the waste heat boiler in the mth microgrid

\(\eta _i^{{\rm{c,ESS}}}/\eta _i^{{\rm{d,ESS}}}\) :

Charging/discharging efficiency of the ESS of node i in the PDN

\(\eta _m^{{\rm{c,HSS}}}/\eta _m^{{\rm{d,HSS}}}\) :

Charging/discharging efficiency of the heat storage system in the mth microgrid

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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).

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Authors and Affiliations

  1. Department of Electrical Engineering, Northeast Electric Power University, Jilin, 132012, China

    Tao Jiang, Xinru Dong, Rufeng Zhang, Xue Li, Houhe Chen & Guoqing Li

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  1. Tao Jiang
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  3. Rufeng Zhang
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Correspondence to Rufeng Zhang.

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Jiang, T., Dong, X., Zhang, R. et al. Active-reactive power scheduling of integrated electricity-gas network with multi-microgrids. Front. Energy 17, 251–265 (2023). https://doi.org/10.1007/s11708-022-0857-1

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