## 7 The Impact of Uncertainty  
The probabilistic approach to the identification of Areas of Vulnerability is based on the impact of uncertainty on power system planning and operation.  
**Planning** is essentially a conceptual exercise. It involves finding a balance between the requisites and constraints that define the planning environment. The requisites can easily be described as meeting the design criteria, keeping a sense of proportion, providing adequate reserves and maintaining flexibility of implementation and simplicity of operation. The constraints are obviously related first of all to the physical environment and the existing level of technology.  
**Design** can be considered as the project definition of whatever facility is being planned. Evidently, when it comes to specifying the design characteristics, system simulation studies will be required. In this respect, it should be noted that the \"curse of dimensionality\" is highly over-rated. In fact, it can be shown that a very discrete number of tests is usually sufficient to define system performance under conditions of equipment malfunction.  
**Design criteria** can be defined in deterministic or probabilistic terms as a set of events to be coped with (such as the type of fault) or as a risk of failure (such as failure and repair rates). In the deterministic approach, the N-1 criterion is mostly used for transmission lines and power transformers. It is generally recognized that this criterion more than adequately covers the reliability requirements for substation supply. The same is not true, however, for substation design itself whose reliability depends on the arrangement of the equipment and its associated buswork. This subject has been studied quite extensively and probabilistic methods to evaluate the Loss of Load Expectancy (LOLE) of various configurations have been devised. Indeed, all design is geared ultimately to reliability and especially to its economic implications.  
**Reliability** can be defined as a measure of the ability of a device to perform its intended function. This performance is measured in terms of failure rate and repair rate and unavailability. The combination of these indices in a reliability evaluation results in a Markov Process that determines the probability of loss of load since all equipment has a certain expectancy of failure. Critical to this evaluation is the importance of dependable outage data: its collection in a systematic manner and its interpretation and application. There is such a data-collection system in Canada [6].  
This section begins, therefore, with the role of Probability Analysis in power system planning.  
_The Role of Probability Analysis_  
There has always been uncertainty in the design of power systems because of the random nature of equipment forced outages and surges in transmission lines. Those uncertainties have been addressed through a probability analysis involving risk-of-failure calculations. Generation and transmission uncertainties have been defined in terms of risk of failure by means of convolutions of the associated parameters.  
For example, with respect to forced outages on static compensators, the probability of having \(x\) devices in service out of a total of \(n\) similar devices is given by the equation in Figure 2[7].  
Similarly, with respect to the forced outages of 735 kV power transformers, the number of massive failures over a thirty-year period encompassing 4000 transformer years was one hundred failures resulting in a failure rate of 2.5 percent [8]. As shown in Figure 2, if \(k\) is the actual number of failures per year and \(\lambda\) is the expected number of failures per year, then \(k\) is a probability distribution shown in Figure 2.  
In this way one can estimate the cost of the unavailability of major equipment.