Linear AC Three-Phase OPF Model for Active Distribution Networks with Unbalanced ZIP Loads

Pinto, Rafael Silva; Unsihuay-Vila, Clodomiro; Fernandes, Thelma Solange Piazza; Baran Junior, Antonio Rubens

doi:10.1590/1678-4324-2022220061

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Article - Engineering, Technology and Techniques • Braz. arch. biol. technol. 65 • 2022 • https://doi.org/10.1590/1678-4324-2022220061 copy

Linear AC Three-Phase OPF Model for Active Distribution Networks with Unbalanced ZIP Loads

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS

An AC linear optimal power flow model for unbalanced ZIP loads.
Model includes voltage regulators, distributed generation, and mutual impedance.
Results show deviations lower than 0.6% for voltage magnitude compared to a non-linear model.
Results show deviations lower than 3% for voltage angle compared to a non-linear model.

Abstract:

Although nonlinear Alternating Current (AC) Optimal Power Flow (OPF) may provide more accurate results compared to linearized OPF models, many ACOPF problems are complex and may require high, sometimes infeasible, computational time. The linear Direct Current OPF (DCOPF) has been widely used in power system analysis; however, it has limitations regarding reactive power analysis, and it may cause significant error in distribution networks with a high R/X ratio of feeders. Moreover, most of the existing formulations for the linear ACOPF do not consider mutual impedance for the lines and simplify the network as a single-phase system, which does not significantly represent unbalanced loads. This paper proposes a novel linear AC three-phase OPF formulation for unbalanced ZIP loads using current injection and considering delta and wye loads. The formulation is extended to include shunt capacitors, voltage regulators, and mutual impedance. The proposed methodology is illustrated using the IEEE 123-bus test system in case studies including/not-including voltage regulators, distributed generation, high R/X ratio, and mutual impedance. The results are very accurate compared with a nonlinear three-phase ACOPF model. The high computational performance and the accuracy of the proposed model considering distributed generation and high R/X ratio show its effectiveness in active distribution networks.

Keywords:
Three-phase Power Flow; Unbalanced Load; Linear Optimal Power Flow; Power Flow Current Formulation.

work	P/I	S/T	SC	LF/OPF	MI	LP	CP	VR
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Proposed Model	I	T	N	OPF	Y	Y	Y	Y

	MAE	MAPE (%)
Voltage magnitude (V)	8.9E-05	0.009
Voltage angle (θ)	1.1E-05	0.062
Active power flow (P_l)	1.9E-06	0.007
Reactive power flow (Q_l)	1.3E-05	0.107

	MAE	MAPE (%)
Voltage magnitude (V)	6.1E-04	0.061
Voltage angle (θ)	2.2E-04	1.360
Active power flow (P_l)	1.2E-04	0.204
Reactive power flow (Q_l)	7.6E-05	0.262

	MAE	MAPE (%)
Voltage magnitude (V)	5.8E-04	0.058
Voltage angle (θ)	1.8E-04	1.290
Active power flow (P_l)	9.9E-05	0.201
Reactive power flow (Q_l)	7.2E-05	0.244

	MAE	MAPE (%)
Voltage magnitude (V)	6.4E-03	0.639
Voltage angle (θ)	1.7E-03	2.911
Active power flow (P_l)	7.0E-04	1.986
Reactive power flow (Q_l)	1.7E-04	1.007

	MAE	MAPE (%)
Voltage magnitude (V)	3.9E-04	0.039
Voltage angle (θ)	9.7E-04	0.383
Active power flow (P_l)	6.6E-04	1.221
Reactive power flow (Q_l)	6.9E-05	0.278

	MAE	MAPE (%)
Voltage magnitude (V)	3.1E-03	0.315
Voltage angle (θ)	2.6E-04	0.941
Active power flow (P_l)	3.4E-04	2.667
Reactive power flow (Q_l)	1.5E-04	2.645

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