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Cost-Effective Operation Risk-Driven µPMU Placement in Active Distribution Network Considering Channel Cost and Node Reliability

  • Research Article-Electrical Engineering
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Abstract

This paper studies optimal micro-PMU (µPMU) placement problem in active distribution networks (ADNs) for complete observability. Minimum procurement cost of μPMUs in extensive distribution networks and minimum loss of observability (LOB) during islanding operations are two important aspects of observability analysis. Because of complexities, modern ADNs require maximum observability during islanding operations. Therefore, this paper proposes a novel objective function considering μPMU-channel cost and risk of operation (RoOP) of system nodes in the integer linear programming framework. The index RoOP is incorporated as a metric for node reliability. A novel zero-injection bus (ZIB) modeling is proposed using topology transformation. Consideration of RoOP is essential for active distribution networks, where islanding operations may appear due to unreliable branch and node outages. Incorporation of RoOP ensures minimum total system operation risk (TSOR), minimum LOB, and higher total system observability in ADNs. Accurate RoOP is evaluated using Markov chain model and Monte Carlo simulation. The proposed objective function considering only channel cost is tested first on IEEE 34-, 69-, and 123-bus systems and found substantial savings compared to existing literature. Situations like single μPMU outage, existence of ZIB effect, and conventional meters are considered to validate the effectiveness of the proposed formulation. Further, simulation conducted on the IEEE 34-bus system considering channel cost and RoOP depicts that the proposed method successfully achieves 13.21% lesser TSOR and 2.44% higher measurement redundancy compared to the case without considering RoOP. Eventually, 0% LOB is ensured for the maximum number of possible islanding situations.

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Abbreviations

PMU:

Phasor measurement unit

μPMU:

Micro-phasor measurement unit

ADN:

Active distribution network

BCGA:

Binary coded genetic algorithm

BILP:

Binary integer linear programming

BOI:

Bus observability index

CF-PSO:

Constriction factor particle swarm optimization

CT:

Current transformer

DG:

Distributed generation

EVs:

Electric vehicles

GA:

Genetic algorithm

IM:

Injection measurement

ILP:

Integer linear programming

LOB:

Loss of observability

UOB:

Unobservable buses in islanded and grid connected networks

MCS:

Monte Carlo simulation

MCM:

Markov chain model

MST:

Minimum spanning tree

OPP:

Optimal PMU placement

OPD:

Observability propagation depth

OμPP:

Optimal μPMU placement

PFM:

Power flow meter

PDC:

Phasor data concentrator

PT:

Potential transformer

SCADA:

Supervisory control and data acquisition

SD:

Standard deviation

SORI:

System observability redundancy index

TSO:

Total system observability

TSOR:

Total system operation risk

WAMS:

Wide area measurement system

ZIB:

Zero-injection bus

\(\lambda\) :

System component failure rate

\(\lambda_{{\text{n}}}\) :

System component failure rate under normal weather condition

\(\lambda_{{\text{a}}}\) :

System component failure rate under adverse weather condition

\(\lambda_{{{\text{avg}}}}\) :

Average component failure rate under normal as well as adverse weather condition

\(\mu\) :

System component repair rate

A :

Connectivity matrix

\(C_{{\upmu {\text{PMU}}}}\) :

Cost of a single-channel μPMU

\(C_{{\upmu {\text{PMU}}\_\max }}\) :

Maximum procurement cost when all buses are equipped with µPMUs

\(C_{{{\text{ch}}}}\) :

Cost per single channel

\(m_{1}\) :

Multiplying factor of multi-objective function

\(m_{2}\) :

Multiplying factor of multi-objective function

N :

Number of buses in network

n :

Number of dummy buses

\(N_{1}\) :

Expected time duration of normal weather condition

\(P_{{\text{U}}}\) :

Probability of unavailability considering normal and adverse weather effect

\(P_{{{\text{aOH}}}}\) :

Probability of overhead line failure under adverse weather condition

\(P_{{{\text{aTF}}}}\) :

Probability of transformer failure under adverse weather condition

\(P_{{{\text{aF}}}}\) :

Probability of feeder line failure under adverse weather condition

\(P_{{{\text{int}}}}\) :

Probability of intentional service interruption

\(P_{{{\text{th}}}}\) :

Threshold value of probability of unavailability below which a branch is said to be safe from outage

\(P_{{\text{a}}}\) :

Overall branch failure probability under adverse weather condition

\(S_{1}\) :

Expected time duration of adverse weather condition

T:

Period under consideration

\(U\) :

Observability vector for new transformed topology

\(v\) :

Observability vector of original topology

X :

Solution vector

\(a_{ij}\) :

Connectivity information in binary value between two buses i and j

\(a_{Di}\) :

Connectivity information in binary value between dummy bus D and normal bus i

\({\text{BIC}}_{i}\) :

Basic infrastructure cost of µPMU at bus i

b :

Column vector of inequality constraint for optimization algorithm

\(A_{{{\text{eq}}}}\) :

Coefficient matrix of equality constraint for optimization algorithm

\(b_{{{\text{eq}}}}\) :

Column vector of equality constraint for optimization algorithm

\(C_{i}\) :

Ratio of cost for µPMU at bus i to the cost for µPMUs at all buses

\(d_{i}\) :

Degree for bus i

\(n_{{{\text{ch}} - i}}\) :

Number of extra channels required for bus i

\(n_{i}\) :

Durations of normal weather at interval i

\(p_{i}\) :

Bus factor for bus i

\(q_{j}\) :

Penalty factor assigned to cost function considering proposed ZIB modeling

\({\text{RoOP}}_{i}\) :

Risk of operation for bus i

\({\text{RoF}}_{i}\) :

Risk of failure for branch i

\(s_{j}\) :

Durations adverse weather at interval j

\(W_{i}\) :

Bus-weight factor for objective function without considering operation risk of nodes

\(W_{i}^{{\prime \prime }}\) :

Bus-weight factor for objective function considering operation risk of nodes

\(\omega_{j}\) :

Weight of dummy bus j

\(M_{j}\) :

Ratio of procurement cost of μPMU at dummy bus to the maximum procurement cost, i.e., \(C_{{\upmu {\text{PMU}}\_\max }}\)

\(x_{i}\) :

Binary decision variable for bus i

\(x_{{\text{D}}}\) :

Binary decision variable for dummy bus D

\(\gamma_{j}\) :

Number of buses in nonlinear term which corresponds to a particular Dummy bus j

lb:

Lower bound of decision variables for optimization algorithm

ub:

Upper bound of decision variables for optimization algorithm

E :

Set containing buses which are not dummy buses

G :

Set containing network vertices

H :

Set containing observability status attributes of vertices elements

\({\mathcal{P}}\) :

Set containing dummy buses

\(\mho\) :

Set of branches connected to bus i

\(\Phi\) :

Set of μPMU nodes

\({\mathcal{R}}\) :

Set containing radial buses

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Authors and Affiliations

  1. Electrical Engineering Department, NIT Durgapur, Durgapur, WB, India

    Manas Mukherjee & Biman Kumar Saha Roy

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  1. Manas Mukherjee
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Correspondence to Manas Mukherjee.

Appendices

Appendix A: Flow Chart of the Proposed Method Without Considering Risk of Operation of System Nodes

See Fig. 18.

Fig. 18
figure 18

Flow chart of the proposed method without considering system risk of operation (RoOP)

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Appendix B: Flow Chart of the Proposed Method Considering Risk of Operation of System Nodes

See Fig. 19.

Fig. 19
figure 19

Flow chart of the proposed method considering system risk of operation (RoOP)

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Mukherjee, M., Roy, B.K.S. Cost-Effective Operation Risk-Driven µPMU Placement in Active Distribution Network Considering Channel Cost and Node Reliability. Arab J Sci Eng 48, 6541–6575 (2023). https://doi.org/10.1007/s13369-022-07426-9

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