Research On Positioning Method Of Successive Approximation For Partial Discharge Source Based On Semidefinite Relaxation

Partial discharge (PD) is an electric discharge phenomena which initial producedby the internal insulation defects for the electrical equipment, it will be continuousdevelopment and deepening under the operating voltage, ultimately lead to the loss ofwhole insulation performance and causes failure. So the PD has been known as the“insulation tumors” that if it can not be try to early detection and “effectivegovernance” in time, which will from part to whole that it can make the equipmentlose insulation capacity completely and cause large area power failure of the powersystem finally. Hence, If the location of the PD source and its discharge quantities canbe obtained quickly and accurately, not only the insulation condition of the electricalequipment can be determined, but also potential fault can be eliminated and long-termsafe operation can be ensured. The PD location has been one of the research focuses inthe field of electric power.Obtaining the location of the PD source monitoring is one of the effective methodsto ensure the safe operation of equipment insulation for a power transformer and to aidin determining the level of danger caused by the insulation fault. The location has animportant reference value in drafting a maintenance strategy with high efficiency andpertinence and in reducing the time of power cut-off. However, there is no effective wayto realize the fault location accurate and reliable, which is an important problem inelectric power systems. The main reason is that the size of power transformer is hugeand complex structure, and the insulation structure includes a variety of type, locationand quantity of defect. In the process of localization computing, numerous factors caninevitably contribute to the difficulty of obtaining time delay accurately, time delayerror further affects the locating error. As well as the time difference positioningequations are established for equivalent wave velocity based on electromagnetic wavepropagation speed which also affects the accuracy of the localization to some extent.And there by resulting in the so-called “error amplifier” situation that can lead to lowpositioning accuracy and even positioning failure. Besides, the present time differenceof arrival (TDOA) positioning algorithm has three major difficulties, namely, itssensitivity to time delay error, easy local convergence or divergence, and a large amountof computational load and time. To some extent, these shortcomings restrict theapplication of UHF technology in transformer PD source positioning. Hence, for the problem of the time-delay error can inevitably exist during measuring time differencewhich leads to large location error pollution due to low time delay accuracy, and toreduce the dependency of the TDOA method on time delay accuracy. This paperintroduce that academic thought of "treatment after pollution", in order to solve theproblem of difficult to positioning PD accurate and quick for the transformer. The mainresearch work and innovative result can be shown below:(1) This paper propose an improved time delay estimation algorithm based on4-order cumulan, which uses the mathem-atical transformation of “relevant–shift-superposition” to obtain a statistical PD signal waveform form a large amount ofsamples for a same discharge source. After using the4-order cumulant to analysis thePD waveform and obtaining the time difference. This method can not only effectivelyeliminate level shaking and random disturbance of the PD signals which resulting fromthe uncertain propagation path of electromagnetic wave, but also can effectively restrainnoise and increase signal-noise rate (SNR) so as to improve the accuracy of time delaymeasurement.(2) Current issues on localization algorithms based on the TDOA method for thePD source include its sensitivity to time delay error, easy local convergence ordivergence, and the large amount of computational load and time. This paper proposes asemi-definite relaxation method for PD source location to solve time delay positioningequations using the solution to the convex optimization problem, which has thecharacteristic of its global optimal solution can be guaranteed. The proposed methodconverts nonlinear time delay equations into an equivalent convex optimization problemby equivalent transformation and rank-1relaxation, which is solved by semi-definiteprogramming to obtain a unique global optimum solution, extract a rank-1componentfrom the global optimal solution of relaxed semi-definite programming, and to serve asa good approximate of the original problem for the PD source. The method was used tolocalize a measured PD source signal in the laboratory, and the results were comparedwith those of positioning by the Newton-iterative method. The comparison showed thatthe method can reduce sensitivity for the time delay error as well as effectively solveTDOA location equations, thereby ensuring that the result is a unique global optimalsolution with high positioning efficiency. The localization algorithm problem is solvedwith the unavoidable and difficult-to-locate time delay error.(3) In order to reduce the dependency of the TDOA method on time delay accuracy,a novel PD source location approach based on successive approximation of multi-samples is proposed in this paper. The particle swarm optimization is employed torecurrently perform the optimization objective function which is established by therelationship between sample value obtained by traditional TDOA method and sensorarray that in turn determined the optimal location of the PD source. Results ofexperimental simulation shows that the proposed method can effectively solve theproblem of low location accuracy caused by the poor accuracy of time delaymeasurements for the PD source and ensure the accuracy of PD localization. Thepositioning result of the proposed method can potentially be better than that of thetraditional TDOA method, it indicates that the proposed method is with a good accuracyand effectivenessand. The error can satisfy the requirements of the PD positioningaccuracy up to several centimeters within few meters for transformer.(4) After the multi-samples are calculated by the semidefinite relaxation algorithmand the successive approximation positioning technology. The positioning results,which has higher accuracy, and solving the data problem of strong dispersion and largeerror in PD location by a single sample signal, and ensuring the accuracy of PDlocalization. The positioning error is reduced from tens of centimeters of the singlesample to few centimeters, and higher than the results calculated by average method. Bychoosing different m values, a small m is found to result in improved precision. Thus,choosing an appropriate m value can optimize calculation based on the number ofsamples.