IEEE Proof IEEE TRANSACTIONS ON POWER SYSTEMS 1 Transition Rates Assessment of Protective Relay Reliability Models With Incomplete Data J. Jedrzejczak and G. J. Anders, Fellow, IEEE Abstract—Usually the residence intervals in various states of power equipment are known, yet information about the number of transitions from one state to another is either missing or incomplete. This is mainly caused by a difficulty in recording of the state changes in the protection equipment or poor data acquisition and recording by power utilities. The transition rates are key parameters in all power system reliability models. Partial information on protection systems poses a challenge to construct or complete a transition rate matrix for reliability assessment. This paper addresses an issue of reliability evaluation of protective relays, operating in harmonic polluted environment. It presents a solution to the problem of finding transition rate matrix for a Markov chain of a simplified digital distance relay model. In this approach, the power system network and its associated protection is designed in a graphical preprocessor to Alternative Transients Program (ATPDraw). Parametric simulations of different circuit topologies during nominal and fault conditions are executed, processed, and analyzed automatically through batch and MAT- LAB scripts. Statistical calculations are implemented to obtain reliability parameters. An example is used to demonstrate the interactive protection system simulation, developed using the new approach. Index Terms—EMTP-ATP, failure analysis, frequency balance approach, harmonics, Markov process, power system reliability, protective relays, stochastic Markov models, transition rates. NOMENCLATURE A Protected power system component. R A Protective relay. UP Relay or component is in operating condition. DN Component or protection system is failed. ISO Relay tripped and isolated the protected component. λ 1 Primary relay’s (R A ) dependability failure rate. λ 2 Primary relay’s (R A ) unavailability failure rate. λ 3 Primary relay’s (R A ) security failure rate. μ 1 ,μ 2 Repair rates of the protected component ‘A’. γ 3 Automatic switching rate due to the main protective relay (R A ) trip command. Dependability is the probability that a relaying system will operate correctly. It is a measure of a relay’s ability to operate when required. Protection Unavailability is the probability that a relaying system will not respond when a fault occurs. Manuscript received January 13, 2016; revised April 25, 2016; accepted May 4, 2016. Paper no. TPWRS-00087-2016. The authors are with the Department of Microelectronics and Com- puter Science, Lodz University of Technology, Lodz 90-924, Poland (e-mail: mr.jak.jed@gmail.com; george.anders@p.lodz.pl). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2016.2564358 Security is the probability that a relaying system will not operate in those situations when tripping is not desired. I. INTRODUCTION T HE general increased complexity of modern power sys- tems, including the introduction of active networks, brings unpredictability of energy infeed into the distribution grid. Due to decentralized, often volatile power generation, system oper- ation is facing challenges that include fluctuating fundamental frequency or unpredictable direction of the power flow. Critical content of current and voltage harmonic components may vio- late domestic and international standards [1]–[3], and increases equipment malfunctions or damage on the consumer side. At the same time, the growing hazard of overloads on lines, trans- formers and other devices can cause system failure, which may evolve into a widespread disruption of supply and cascading outages [4]. To diminish the frequency of such events and to ameliorate their effects, it is necessary to evaluate economic and reliability constraints at both the planning and operating phases [5]. Power system automation is a key element in maintaining a required level of reliability. Its performance is affected in two ways [6]. First, when the relaying system fails to respond when called upon to operate in the presence of a fault. Protection does not operate at all or its tripping time is delayed—relay unavailability. The second impact is observed when the relaying system operates in those situations, when tripping is not desired—mal-trip operation. Dependability and security of protective relays has been examined thoroughly in many papers [7]–[9]. The topic of harmonic components, affecting these reliability indices is covered in [10]–[13]; however, it is not a subject of existing relay reliability models [14]–[21]. The influence of low order harmonic components on solid state overcurrent relays, operating in both: overloaded conditions (1.2 to 2 times the pickup current) and during low magnitude faults, is presented in [10]. In this study, harmonic currents delay the tripping of the device and it is observed that the higher the THD I , the greater the variation of tripping time. Additionally, as the fundamental current magnitude increases, the harmonic effects on relay tripping are reduced. The impact of harmonics on the performance of overcurrent relays with passive harmonic filters is studied in [11]. IEEE 30-Bus system with heavy penetration of nonlinear loads is simulated using ETAP software. Both relay malfunctions (THD I above 20%) and wrong tripping sequence were observed. In [12] protection mal-operations are reported due to intermittent nature of DGs and rapidly changing harmonics (THD above 20%). A relay’s sensitivity reduction is experimentally proven in [13], where harmonic currents, circulating in the electric system, affect the shunt capacitor banks protection. 0885-8950 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.