Cross-linked polyethylene (XLPE), ethylene propylene rubber (EPR), and their superior versions such as tree-retardant cross-linked polyethylene (TR-XLPE) are used to insulate the conductor of the cable. IEEE Trans Smart Grid 7(2):771–784, Mazzanti G (2007) Analysis of the combined effects of load cycling, thermal transients, and electrothermal stress on life expectancy of high-voltage AC cables. By taking these decisions, a cable may transit either to operating state or failed state at stage $$y + 1$$ from its previous states at stage $$y$$. The key idea is to save answers of overlapping smaller sub-problems to avoid recomputation. At stage $$y$$, new cable is replaced by old cable. Planning horizon and effective age after preventive maintenance. The optimal cost-effective maintenance policy was found for two maintenance periods, first from the years 2016–2030 $$({\text{stage}}:y = 0\,{\text{to}}\,14)$$ and second from the years 2016–2055 $$({\text{stage}}:y = 0\,{\text{to}}\,39). Maintenance activity such as preventive maintenance (PM) action reduces the failure probability; however, the PM methods can only detect some potential failure causes and other causes remain undetected. 2014). This has engendered a demand for high reliability and a need for the extension of cable life with minimum maintenance cost which can only be achieved by implementation of an effective maintenance policy. Your task is to find the lowest cost path from the root node to a leaf. The optimal policy improves the reliability by suggesting the appropriate time for preventive maintenance and replacement action. State tree showing expected future states of the cable. The PM decision at state \( a_{y }^{'}$$ can detect $${\text{PM}}\%$$ of failures and reduce the failure probability by the same percentage. The proposed probabilistic dynamic programming model is capable of finding the optimal decision policy with respect to optimal long-run cost for a cable with a known failure distribution and degradation level. $$, $${{\mathbb{h}}} \,( \ /{\text{kWh}})$$,$$ C_{\text{PM}} = \mathop \sum \limits_{m = 1}^{{\mathcal{M}}} C_{m} . A large number of reliability centered maintenance (RCM) optimization methods are presented for electrical power distribution system. [Dynamic Program] Given initial state , a dynamic program is the optimization. At the same time, maintenance practices and techniques are to detect faults in cable changes, as well. © 2021 Springer Nature Switzerland AG. High Volt Eng 41(4):1178–1187, Sachan S, Zhou C, Bevan G, Alkali B (2015b) Failure prediction of power cables using failure history and operational conditions. The chronological age of cable at 2016 would be $$a = a^{,} = 33$$. Dynamic Programming and Probability. In: Power systems conference and exposition, IEEE PES, pp 389–393, Dong X, Yuan Y, Gao Z, Zhou C, Wallace P, Alkali B, Sheng B, Zhou H (2014) Analysis of cable failure modes and cable joint failure detection via sheath circulating current. $$, $$\left\{ {0, \ldots ,Y - 1} \right\}$$, $$\left\{ {0, \ldots , {\mathbb{Z}}} \right\}$$,$$ p\left( {a^{'} } \right) = p(a)\left[ {1 - \mathop \sum \limits_{z = 1}^{{\mathbb{Z}}} {\text{PM}}_{z} \% } \right], $$, $$\left\{ {0, \ldots , A^{'} } \right\}$$, $${\mathbf{\mathcal{D}}} = \left\{ {\text{NA, PM, CM,RP}} \right\}$$,$$ {\text{NA}}:\left\{ {\begin{array}{*{20}ll} { } \\ {F_{\text{NA}} : P\left( {F_{{a_{y + 1 }^{'} }} |a_{y }^{'} ,{\text{NA}}} \right) = P\left( {a_{y + 1 }^{'} |a_{y }^{'} ,{\text{NA}}} \right) } \\ {\bar{F}_{\text{NA}} : P\left( {a_{y + 1 }^{'} |a_{y }^{'} ,{\text{NA}}} \right) = 1 - P\left( {a_{y + 1 }^{'} |a_{y }^{'} ,{\text{NA}}} \right),} \\ \end{array} } \right. $$,$$ {\text{Current}}\,{\text{cost}} = {\text{immediate}}\,{\text{cost}} + {\text{future}}\,{\text{cost}} . The result is a richer and more expressive formalism with a broad range of possible application areas. 2005). At any stage $$y$$ of the maintenance period, a cable can either be in an operating state with effective age $$a_{y}^{'}$$ or in failed state $$F_{{a_{y }^{'} }}$$. Four types of maintenance decisions are taken on a cable asset: “no action” NA, “preventive maintenance” PM, “replacement” RP, and “corrective maintenance” CM. We present a data-driven, probabilistic trajectory optimization framework for systems with unknown dynamics, called Probabilistic Differential Dynamic Programming (PDDP). Distribution systems the transmission and distribution of discrete probabilistic Programs cable will have age 1 when a decision to (! And consists of going right, then left, then P ( \! Methodology can also be useful in solving –nite dimensional problems, because the cable! Relevance of mathematical developments in dynamic programming algorithm: a solution for maintenance... 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