Optimal Dispatch of Electrical Transmission Systems Considering Interdependencies with Natural Gas Systems

Abstract

This chapter presents a novel model to assess the interdependencies between electric power systems interconnected with natural gas systems. The impact from natural gas systems in the electric power system can be evaluated with the proposed model in normal operation and contingency situations. To reduce the impact of interdependencies, additional constraints to the optimal dispatch problem are formulated. The interdependency constraints can be integrated into the normal optimal power flow problem and security-constrained optimal power flow problem to improve the robustness of the electric power system. A co-simulation platform is built in MATLAB environment. We evaluate the proposed model using the IEEE 14-bus system and a corresponding natural gas transmission system. According to the simulation results, the reliability of the power system is improved when interdependency constraints are considered.

Appendices

Appendix

The electrical consumption data after re-dispatch are shown in Table 9.5. The information on the buses of the artificial natural gas system is presented in Table 9.6. The constant pressure node in the natural gas system is denoted as “CP,” and the constant flow rate node is denoted as “CQ.” The regular nodes are denoted as “L.” All pipelines are assumed to have equal lengths of 80 km and equal inner diameters of 635 mm. The upper bounds of the pipeline are set to be 15 Mm³/day. The data of the sources in the natural gas system are provided in Table 9.7.

Table 9.5 Electrical consumption data after re-dispatch

Table 9.6 Artificial 14-bus natural gas system data sheet of buses

Table 9.7 Artificial 14-bus natural gas system data sheet of sources

List of Abbreviations and Symbols

Abbreviations

IDI	Interdependency impact
ENG system	Electric natural gas system
PCIDI	Post-contingency interdependency impact
ONGF	Optimal natural gas flow
PDIPA	Primal-dual interior point algorithm
OPF	Optimal power flow
SCOPF	Security-constrained optimal power flow
PTDF	Power transfer distribution factor
LODF	Line outage distribution factor

Symbols

FkI, FkD, Fkm	Flow rates of injection, demand of node k, and pipeline km in m3/day
pb, pk, pkw	Base pressure, pressure at node k, and well pressure at node k in kPa
r km	Compression ratio at node k of pipeline km
G	Specific gravity of the gas delivered by pipeline, unitless
R	Ideal gas constant equals to 8.314 J/K/mol
γ	Ratio of specific heats of gas
Dkm, Lkm	Pipe inside diameter in mm, length of pipe in km
Zk, Zkm	Compressibility factors of nodes k and pipeline km
ηkmp, ηkmc	Efficiencies of pipeline and compressor station of pipeline km
Tb, Tf, Tk	Base, average gas flow temperature; temperature at node k in K
NN, NC, NP	Number of nodes, number of compressors, and number of pipelines
N S	Number of total contingency scenarios in natural gas system
M NG	Operational cost of natural gas system
CS km	Compressor station at pipeline km
P km E	Electric power consumption of compressor at pipeline km in kW
PiG, QiG	Active and reactive powers of generator at bus i
PiD, QiD	Active and reactive power demands at bus i
Pi, Qi	Active and reactive power flows at bus i
Vi, Iij	Per unit voltage of bus i and per unit current of line ij
aiE, biE, ciE	Coefficients of the thermal generator at bus i
N B	Number of buses
M E	Operational cost of electrical system

Functions and Operators

sign(x)	Function to extract the sign of variable x
$\underline{x},\overline{x}$	Lower and upper limits of variable x
≤,  ≥	Component-wise operators