Xiaokang Xu Senior Staff Consultant xiaokang.xu@siemens.com	Feng Dong Senior Software Engineer feng.dong@siemens.com	Michael J.S. Edmonds Vice President / General Manager michael.edmonds@siemens.com

Risk and reliability are the two facets of a measure of the ability of the electric power system to deliver electricity to all points of utilization within accepted standards and in the amount desired. Both terms have the same implication. Higher risk means lower reliability, and vice versa. A general definition of risk is “probability x consequence.” In power systems, this concept can be applied to calculate certain reliability indices such as Expected Unserved Energy (EUE) which is “probability x lost MW” (consequence) and a measure on system reliability from customer point of view.

Risk assessment of power systems can be performed using a deterministic or probabilistic approach. The traditional deterministic methods for transmission planning and power system security assessment in real-time for system operations have been found to be inadequate in the new deregulated environment as power systems present a probabilistic behavior to some extent, such as random failures of equipment, load growth forecast uncertainties, energy import and export transactions on the volatile market, etc. Use of the probabilistic reliability method complimentary to the deterministic method is getting more and more attention in both system planning and operation. This increasingly requires quantification of benefits as a result of increased reliability or decreased risk.

The newly implemented reliability features in Siemens PTI’s PSS™E employ both deterministic and probabilistic reliability methods that can be used for risk assessment of power systems in a deregulated, competitive power market.

Methodology
The methodology used for risk assessment in PSS™E involves two major components: deterministic contingency analysis and probabilistic index computation (probabilistic reliability assessment) as shown in Figure 1. Deterministic contingency analysis uses the enumerative approach to evaluate each contingency and simulate sequences following a contingency. Based on deterministic contingency analysis results, outage statistics of contingencies are incorporated to calculate various probabilistic indices including probabilistic indices of overloads, voltage violations or voltage collapse, loss of load, expected unserved energy (EUE), etc. These indices can be used to measure weak points or risks in a system.

Figure 1 - Methodology of Risk Assessment in PSS™E

The deterministic contingency enumeration process in PSS™E uses built-in contingency ranking so that the user specified contingencies and automatically generated contingencies from rankers can be evaluated individually or combined with each other as multi-level contingencies as shown in Figure 2. It also features generation redispatch, non-divergent power flow solution algorithm, tripping simulation and corrective actions [1]. Probabilistic reliability assessment takes the results of deterministic contingency analysis as inputs, matches each tested contingency with its outage statistics and calculates the probabilistic indices for a type of problem specified by the user, as shown in Figure 3.

Figure 2 - Automatic Multi-Level Contingency Analysis in PSS™E

Figure 3 - Probabilistic Reliability Assessment Function in PSS™E

Probabilistic Models
There are two probabilistic outage models: an independent single element outage model and a multiple element outage model. An independent single outage is the failure of one unique component, and is not related in terms of its cause to any other failures that may occur at the same time. For each component, frequency and duration of the independent outage must be specified. The single element outage is modeled using a binary-state model. At any time, the element can be in one of two states: In Service (Available) and Outage (Unavailable). The transition to the outage state is called failure, and is assumed to occur at a constant rate, , in failures per year; whereas the transition to the in-service state is a restoration event, and is also assumed to occur at a constant rate, , in restorations per year. The mean duration that the equipment is in service is m years; while the mean duration that it is out of service is r years. Thus, the probability that the equipment is in service or out of service is:

    Or

And

The frequency to transition from in service state to outage state is equal to the frequency to transition from the outage state to the in service state, and is given by:

The average duration that the element is in the Outage State is:

Multiple element outages occurring simultaneously may come about in different ways, e.g. from the same cause, or from independent causes for each outage. Multiple element outages can be further divided into: multiple independent outage, common mode outage as well as substation-related outage or dependent multiple outage. The probability and frequency of an independent multi-element outage event can be computed directly from the frequencies and durations of the individual independent outages. For example, given two independent outages, the parameters of an equivalent double outage can be computed as follows:

And

And

where P_A and P_B are the individual probabilities of independent outages for elements A and B; F_A and F_B are the respective frequencies of independent outages for the two elements; and D_A and D_B are the corresponding average durations in hours. The probabilities and frequencies of common mode and substation-related outages cannot be derived directly from the single element outage statistics. These outage events must therefore be explicitly specified with their corresponding frequency of occurrence and outage duration.

Probabilistic Index Computation
PSS™E uses contingency enumeration methodology to calculate probabilistic indices. The base case and mutually exclusive contingency cases form a state space of an electricity system as shown in Figure 4. Each node represents an operation state: base case or a contingency case. The sum of probabilities of all states is equal to1. Probabilistic indices of system problems are computed by identifying the set of states that satisfy failure criteria and the transition rates from any state inside the set to a state outside of the set. In the figure, a yellow node represents a state that has violations; all yellow ones form the set S containing states that satisfy failure criteria. Failure criteria include branch overloads, bus voltages outside high or low limits, bus change exceeding deviation criteria and loss of load.

Figure 4 - System State Space Diagram

For example: the probability of system overload problems is calculated as:

where the set S consists of all cases that cause thermal overload problems, P_iOUT is the probability of state i. The frequency of system overload problems is calculated as:

The total frequency and probability are accumulative quantities for all contingencies (single or multiple) resulting in the problems. The duration is averaged for all failed contingencies. The composite indices combining probability and system problems are defined as [2]:

where V_i is the sum of amount of violations (overloads, voltage violations, loss of load, etc.); P_i is probability of an outage event causing violations; and S is the set of contingencies resulting in violations. The loss of load in MW/year and EUE in MWh/year measuring customer impacts are calculated as follows:

where m_i is load loss for outage event i (MW); f_i is frequency for load loss caused by outage event i (occurrence/year); d_i is duration for load loss outage event i (h). These probabilistic indices provide a better indication of power system reliability by taking into consideration the relative likelihood of different contingencies that may occur from system and customer standpoints.

Case Studies
Several reliability studies are performed with PSS™E on the IEEE Reliability Test System (RTS) [3] as shown in Figure 5. In the RTS, a peak load of 3,563 MW and an installed generation capacity of 4,764 MW are assumed. The transmission network consists mainly of 230 kV and 138 kV voltages. The large generation is located in the northern area and connected to 230 kV, and major loads are in the south and connected to 138 kV. Power is transferred from the north to the south via an interface comprised of 230 kV lines and 230/138 kV transformers.

Figure 5 - IEEE Reliability Test System

Application 1: Probabilistic Indices
A n-2 contingency analysis with tripping and corrective actions initiated is performed for the RTS system. Some typical historical outage data for major transmission equipment based on worldwide historical data sources is used for probabilistic index calculation. Table 1 shows a sample output of the probabilistic indices including the frequencies and durations of load losses and EUE as well as impact indices on individual bus and system-wide basis. The probabilistic results can also be graphically displayed, e.g. EUE indices on the impacted buses are displayed in red numbers in Figure 5.

Table 1 - Probabilistic Indices of Loss of Load

Application 2: Weak Point Analysis
The probabilistic indices can be used to rank weak points in a system to identify the components of the system that are experiencing the most severe reliability problems. Figure 6 is a contour diagram on the probability of the voltage problem at each bus; it clearly shows that buses 224 and 103 are the most vulnerable parts in the system and require voltage compensation to mitigate voltage problems and improve system reliability.

Figure 6 - Contour Diagram on Probabilities of Voltage Problems

Application 3: Probabilistic Reliability Margin
In deterministic reliability studies, the reliability margin can be defined as the maximum level of incremental power transfer that the system can handle without experiencing any defined reliability problems, e.g. n-1 compliance. The concept of deterministic reliability margin can be extended by applying a tolerance threshold to determine probabilistic reliability margin [2]. In the RTS system, power transfer from the north to the south is changed incrementally in the step size of 100 MW; both deterministic and probabilistic reliability assessments are performed for each transfer level. The probabilistic indices of voltage violations, overloads and overall system problems are plotted as a function of the incremental power transfer as shown in Figure 7.

Figure 7 - Probabilistic Indices and Reliability Margin with Power Transfer

References
[1] Feng Dong and Baldwin P. Lam, “Bulk Electric System Reliability”, Siemens PTI eNewsletter. Power Technology, September 2006.
[2] Nicolas Maruejouls, Vincent Sermanson, Stephen T. Lee and Pei Zhang, “Practical Probabilistic Reliability Assessment Using Contingency Simulation”, Presented at the IEEE Power Engineering Society's 2004 Power Systems Conference and Exposition, New York, New York, 10-13 Oct. 2004.
[3] Reliability Test System Task Force Report, “IEEE Reliability Test System”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No.6 November/December 1979.

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