Increase the Reliability of Operation of Protection DC traction substation

For protection of direct current (DC) traction substation is proposed to use centralized differential protection. Estimation of reliability indicators is carried out on the basis of the method of Markov chains. The obtained results allow to make a conclusion about the prospects of implementing this protection.


Introduction
To protect special electrical installations of DC traction substation, current protections of transformers and rectifiers [1], special DC protections [2], and ground protections are used. These technical solutions are characterized by low selectivity and outdated element base. The purpose of research is the development of highly reliable centralized differential protection (CDP) for DC traction substation.

Realization of proposed protection
The CDP proposed by the authors is based on the differential principle in combination with the double entry method [3,4]. To describe the principle of protection, consider the fragment of the DC traction substation shown in fig. 1.
For the scheme ( fig. 1) construct a unidirectional graph ( fig. 2a) with vertices and arcs, where vertices V1 to V13 of the graph are protected items, and arcs e1 -e14, respectively, the branches of current transformers (CT), current sensors (CS) and circuit breakers. The arcs that characterize the branch of the CT, CS and switches, display the facts switching and have a weight that represents information about the magnitude flowing in the branch current obtained by measurement using the appropriate CT and CS.
The next step is the definition of range of protection based on the topology of scheme with the position of the isolators. As a result, possible transition to a new form of the graph ( fig. 2b) by deleting the arcs e3-e6, e9, e10 and merge the vertices V6-8 (V6*) and V9-12 (V7*).
For determining the location of fault, protection compares the currents on differential principle for particular regions and detects potentially damaged item. For all graph vertices with degree >1 compile equations. Then it is determined whether to trigger starting on fault in the region, or there is a CT, CS or communication lines (CL) fault. The presence of a fault is determined using the method of double entry. Since each arc of the graph is reflected with the same weight (current value) in the matrices twice: as an arc, associated with the vertex directed to one matrix, and as the arc associated with the vertex directed from another matrix, in the case getting wrong values is the sum of incoming and outgoing currents in the two matrices becomes incorrect, but the total differential current of the whole network remains equal to zero. In case of observance of rule of detection of the fault and maintaining a sum of currents for the entire network is equal to zero, a CT, CS or CL fault is detected.
Signs of the functioning of the differential protection for different ratios of currents and the results of performing matrix operations for this scheme is shown in Table 1. Variables SMV1...SMV7, obtained as a result of matrix operations, determine the conditions for the presence of short circuit in the protection zone. The SUM variable determines the total differential current.
As a result, depending on the ratio of the currents in the scheme as well as results of operations on matrices it can implement the reliable operation of the differential protection of DC traction substation. This provides not only the action of protection in case of damage on each site, but excluded its excessive action when damaged current transformers and current sensors.

Quantitative assessment of the reliability of the proposed protection
To quantify the advantages of the proposed technical solutions from the point of view of reliability, using the method of Markov chains. This method is often used to describe the processes of failure and repair with the elementary streams, and is most suitable for calculating reliability of system of relay protection (SRP) [5,6]. The distribution laws of failure and repair will accept exponential.
Taking into account specificity of the analyzed differential protection, define two types of protection failures [7]: undesired-tripping protection failures (in the absence of fault on the protected object), and fail-tooperate protection failures (in case of fault on the protected object).This approach is used in several papers, e.g. [8].
In fig. 3 presents two variants of the relay protection system organization is presented. In first case ( fig. 3a)  We will calculate reliability indexes for both cases. The initial data for calculations are obtained on the basis of [9,10] and from manufacturers of protection devices. The data is presented in Table 2.

Mode 1: absence of fault on the protected object
In fig. 4 shows  Define the probability ) ( 1 t P that the system is in state E1, which is an emergency, for random time t. Form a system of differential equations describing a graph, where ) (t P w -the probability of location the system in state without failures Ew.
Normalizing expression, the meaning of which is that the researched system located in state E1 or Ew as constituting a complete group of events, has the form As at the initial moment of operation of the system at t = 0 the system is in state without failures: As a result of solve the system of differential equations a function of the unreadiness probability  ) Make an assessment of the probability of failure-free operation of the SRP. The graph for the calculation will look similar as the graph in fig. 5 with the difference that it will not be possible to transition from state E1 to Ew, that is excludes repair rate μ1. This circumstance is due to the fact that when system fails (transition to absorbing state E1), the experiment is finished -the system cannot leave this state.
Due to absence of repair instead of a system of differential equations (1), the result will be an expression of the probability of failure-free operation (PFFO), with exponential distribution law: In fig. 6 shown the dependences of the function of the unreadiness probability of SRP, and functions of the PFFO on the average time between checks. a)

Mode 2: in case of fault on the protected object
The calculation of reliability indicators for the damage mode on the protected object is per-formed separately for the following damages using the approach described above: short circuit in the transformer, short circuit in the rectifier, short circuit on 3.3 kV buses. Analysis of numerical calculations of indicators of reliability of the relay protection ( fig. 6, 7) shows: -developed protection in the mode 2 has higher indicators of reliability than standard technical solution on average up to 5 times; -the obtained calculation ratio can be used in the methods of practical reliability analysis of centralized relay protection of DC traction substation.

Conclusions
1. Proposed a new principle of organization of the centralized differential protection of DC traction substation.
2. Developed technical solutions allow to detect the current transformers, current sensors and communication channels faults, and having high reliability.
3. Protection can be adapted to changes in the configuration of the DC traction substation.
4. The proposed technical solution can increase the reliability of the differential relay protection, what follows from by the results of practical calculations.