Reliability Analysis

Reliability calculations are essential for the evaluation and comparison of electrical power systems in terms of both design and operation. Although non-stochastic contingency analyses (i.e. n-1) are able to highlight obviously unacceptable operational events, they cannot rank these events in terms of either frequency or duration. The DIgSILENT PowerFactory Reliability Analysis tool incorporates standard reliability assessment features together with sophisticated modelling techniques that enable all forms of reliability assessment to be carried out.

Failure models are defined using mean yearly failure frequency and repair duration data. For lines and cables, this data is entered in per-length terms. Detailed models are available for generators that enable de-rated states to be represented, with maintenance and common mode models also available.

Load forecast and growth curves can be imposed via time-varying load characteristics. Load models are additionally available for hard-to-predict industrial situations, and each can be assigned its own interruption cost using one of the following cost functions: cost/customer/interruption, cost/kW/interruption or cost/interruption.

All failure and load models can be represented either by the Markov method, where simple mean repair durations are modelled, or by the sophisticated Weibull-Markov method, where repair duration variance is additionally modelled. The Weibull-Markov model also has the unique property that annual interruption cost indices such as load and process (industrial) interruption costs can be calculated both analytically and quickly. Consequently, PowerFactory’s Reliability Analysis tool enables the comparison and justification of alternative investment proposals on a financial basis.

The basic calculation method used is analytical state enumeration. This method is very efficient, produces exact results and is flexible for addressing a wide range of reliability calculation problems. The network reliability analysis can be carried out on the basis of a simple connectivity check (primarily intended for distribution networks) or on the basis of AC load flow calculations which consider load curtailments due to overloading or voltage constraints (for bulk power system analysis).

The approach combines fast topological analysis for fault clearance, fault isolation and power restoration, with AC load flow and optimization techniques for addressing energy at risk, load transfer and load shedding.

Finally, the results of all reliability assessments can be presented in text format, as user-defined graphs, or within the single-line graphics environment.

Failure Models

The failure models for network reliability assessment include:

Failures of lines, cables, transformers, generators/external grids and busbars
Independent second failures ("n-2")
Common mode failures
Double earth faults
Protection/circuit breaker malfunction
Transient fault model (for momentary interruption indices)

In addition to the above-listed failure models, planned outages such as scheduled maintenance can also be considered.

Special failure models can be used by various network components to share failure data. The failure models hold stochastic failure information (mean yearly failure frequency for sustained, transient and earth faults on a per km basis, as well as mean repair durations). PowerFactory’s user-interface allows for both an easy setup, as well as for simple modification of input data for various studies.

The Maintenance feature simulates the effects of network reliability under predefined planned outage scenarios. Maintenance of individual network components can be modelled on an hourly basis.

State Enumeration

Based on the network model and the given failure data, the reliability analysis generates and analyses the resulting contingency cases.

In addition, the user can model load forecast and growth curves by imposing time-varying load characteristics. PowerFactory has a very efficient handling of the reliability assessment over time with varying load data, through the use of the following techniques:

Clustering of load states in the state enumeration algorithm
Analysing load variation correlations, thereby reducing the overall number of load states
Using linear approximation techniques to improve performance in the case of large numbers of load states

Failure Effect Analysis

The Failure Effect Analysis (FEA) simulates both the automatic and manual reactions to faults of installed protection and of the system operators during each reliability assessment. The FEA can be checked and fine-tuned in an interactive way to exactly match the real system and operator reactions.

The Failure Effect Analysis comprises:

Automatic fault clearance by protection devices
Automatic or manual fault isolation
Automatic or manual power restoration by network reconfiguration.
This includes sophisticated sectionalizing and strategic power restoration methods that operate in three distinct phases:
- Phase 1: Sectionalizing by remote controlled switch devices
- Phase 2: Sub-sectionalizing of strategic areas
- Phase 3: Full system restoration
Sectionalizing supports serial or parallel switch actions (based on station access times).
Overload alleviation by optimized generator re-dispatch, load transfer and load shedding, under consideration of load priorities and the amount of load that is available for shedding.
Under-voltage load-shedding

For classical bulk power system analysis, it is assumed that post-fault overloads may occur. A full AC load flow, incorporating basic generator re-dispatch and automatic tap changing, is used to analyse post-fault system conditions. Additional load transfer and/or load shedding will then be simulated.

In cases where it can be assumed that system restoration will not lead to any overloading, the overload alleviation can be omitted and a fast network connectivity analysis is sufficient.

System Indices and Results

PowerFactory’s Network Reliability Assessment calculates all common reliability indices. Among others, the following indices are available:

System indices (also available for user-defined feeders, zones, and areas):

SAIFI, System Average Interruption Frequency Index
CAIFI, Customer Average Interruption Frequency Index
SAIDI, System Average Interruption Duration Index
CAIDI, Customer Average Interruption Duration Index
ASIFI, Average System Interruption Frequency Index
ASIDI, Average System Interruption Duration Index
ASAI, Average Service Availability Index
ASUI, Average Service Unavailability Index
ENS, Energy Not Supplied
AENS, Average Energy Not Supplied
ACCI, Average Customer Curtailment Index
EIC, Expected Interruption Cost
IEAR, Interrupted Energy Assessment Rate
SES, System Energy Shed
LOLE, Loss of Load Expectancy
LOEE, Loss of Energy Expectation
LOLF, Loss of Load Frequency
LOLD, Loss of Load Duration
MAIFI, Momentary Average Interruption Frequency Index

Load Indices:

AID, Average Interruption Duration
ACIF, Average Customer Interruption Frequency
ACIT, Average Customer Interruption Time
LPIT, Load Point Interruption Time
LPIF, Load Point Interruption Frequency
LPENS, Load Point Energy Not Supplied
LPEIC, Load Point Expected Interruption Costs
LPCNS, Load Point Customers Not Supplied
LPPNS, Load Point Power Not Supplied
LPPS, Load Point Power Shed
LPES, Load Point Energy Shed
LPIC, Load Point Interruption Costs
TCIF, Total Customer Interruption Frequency
TCIT, Total Customer Interruption Time

Busbar Indices:

AID, Average Interruption Duration
LPIF, Yearly Interruption Frequency
LPIT, Yearly Interruption Time

Special Features

The Network Reliability Assessment is fully-integrated into PowerFactory, thus profiting from the extremely flexible data management and data handling for setting up individual studies.

High Flexibility

Each contingency case is created and analysed based on events (i.e. switch events, load shedding events, generator re-dispatch events). By default, the events are created automatically by the reliability calculation algorithm. This allows the user to analyse, adjust and fine-tune the individual cases in a very flexible manner. The reliability calculation will then consider the user-defined events for the FEA instead of creating them automatically.

Tracing of Individual Cases

The user can examine the results of a single fault by running the fault case of interest in the trace mode, a step-by-step analysis that sweeps over the individual actions of the FEA. The switching actions and load shedding/generator dispatch events created by the reliability calculation will then be applied to the network and the results can be viewed and analysed after each time step.

Powerful Output Tools for Result Representation

Results can be viewed in a variety of ways:

Formatted reports
Tabular result views (integrated into the PowerFactory Data Manager)
Graphical result representations
Various colouring modes

Contribution to Reliability Indices

Post-processing tools allow the calculation of individual components’ contributions to system indices. In this way the user can study the impact of certain network components (such as lines/cables, transformers, etc…) on the overall system indices. Likewise, loads can be grouped into load classes (industrial, agricultural, domestic, etc…) and their contribution to, for example, energy indices can be evaluated.

Development of Indices over Years

Taking into account the evolution of the network model and the failure data over time, PowerFactory supports the calculation and visualization of the reliability indices over years.