A Frequency and Duration Approach for Interconnected System Reliability Evaluation

The need to quantitatively evaluate the reliability of power systems is widely recognized. There are several probabilistic methods available at the present time which provide numerical indices to reflect the static adequacy of the installed generating capacity. The Frequency and Duration method utilizes the departure rates between the various generation states and the load char¬ acteristics to formulate cumulative probability and cumulative frequency indices of a load loss situation. This approach is re¬ sponsive to the variation of the generating unit mean failure and repair rates on the system reliability. The capacity model is expressed in the form of a table and obtained recursively by adding a generating unit to the table one at a time. It contains the various capacity outage states which may arise due to forced outages of individual generating units. A large capacity generating unit may have a multitude of subsystems in which component outage can cause a unit derating. It therefore may not be valid to apply a binary model to large units. A more realistic representation is to introduce other states into the binary model to create a multi-state model of a unit. These states are called derated states. The capacity model can be combined with the exact-state load model to produce an overall system description in terms of discrete margin states. A margin is defined as the difference between the available capacity and the system load and therefore a negative margin constitutes a load loss situation due to capacity deficiency. The positive, negative and zero margin states form a margin table. The interconnection between neighboring power systems nor¬ mally provides an effective means of improving the overall level of system reliability. When a power system encounters a load loss situation, assistance is generally available from the interconnecting system. This effect is brought about by the diversity in the probabilistic occurrence of load and capacity outages in the different systems. Consequently the risk level will be lower with intercon¬ nection than in isolated operation for a given operating reserve. The interconnection benefits depend on the installed capacity in each system, the total tie capacity, the mean failure and mean repair rates of the tie lines, the peak load and the type of agreement between the systems. This paper presents an approach which can readily in¬ corporate the physical characteristics of the interconnection fa¬ cilities. System A is interconnected with System B by several parallel tie lines as shown in Fig. 1. System B has agreed to assist SystemA up to the point at which it suffers load curtailment. The positive margin states in the margin table for single System B indicate its different possible capacity assistances to System A. The negative and zero margin states in System B do not provide any assistance and can therefore be merged into a state of 0 MW. The positive margins, on the other hand, can be constrained by the total transmission capacity which may restrict the flow of power from System B. Any states with positive margins greater than the tie capacity can be merged into a state of the same capacity as the total tie capacity. Those other states with positive margins less than the total tie capacity represent different possible levels of capacity assistance from System B. At this stage the assisting System B is viewed from System A as a fictitious multi-state generating unit at the other end of the re¬ pairable tie lines. This equivalent multi-state generating unit can be combined with the Markovian model of the tie lines to consider the effect of the failure and repair rates of the tie lines. The Markovian combination of the assisting System B and the tie lines is regarded as a tie line constrained multi-state generating unit and can be added into the capacity model of System A. The computation of the overall reliability indices of System A follows as if the interconnected systems were now one single system. The paper presents a complete set of recursive algorithms for incorporating a multi-state generating unit into an existing capacity model. It proceeds further to model the assisting system in an interconnected system as a multi-state generating unit. The in¬ clusion of tie line constraints in the multi-state unit representation of the assisting system provides a sequential approach to studies of multi-tie line interconnections. The systems interconnected by a single tie line become a special case. Effectively the assisting system is viewed as a tie line constrained multi-state unit to the system being studied. The approach used can be modified to cover different agreements and generalized to multi-area system reliability evaluation. The equations in the paper are implemented in a computer program which has been applied to the IEEE Reliability Test System for some selected studies.