The growing adoption of DC (direct current) systems in a variety of industries, including automotive and renewable energy, is driving a transformation in power grids. This growing complexity requires increasingly sophisticated design and analysis tools.
Ampère Professional, from Electro Graphics, stands out as a solution for calculating DC electrical networks, meeting the demands of a constantly evolving market. Aligned with the IEC 61660-1 standard, the software offers precision and reliability in determining fault currents, a crucial aspect for ensuring the safety and performance of electrical systems.
According to the company, with Ampère Professional engineers and designers can:
- Analyze DC networks comprehensively: from small installations to large distribution systems;
- Ensure compliance with standards: ensuring that projects comply with technical requirements;
- Optimize equipment sizing: reducing costs and increasing efficiency;
- Increasing system reliability: identifying and mitigating potential risks.
Calculation of direct current faults according to IEC 61660-1
Electro Graphics says that Ampère Professional adds more functionality to fault calculations, improving the study of current transients in circuits defined in direct current.
Numerous studies attempt to clarify and fill the gaps on the subject, pending a new normative reference regarding direct current, such as the CEI EN 60909-0 standard, which is for alternating current systems.
Such studies indicate that the average errors committed by the IEC 61660-1 standard for calculating the maximum peak current are around 10% (both positive and negative), due to the increase in distances between sources and fault points, to the correction coefficients (which push the errors towards the negative), and not taking into account the subtransient reactances of the generators, especially if they are small.
Furthermore, transients towards the steady state are generally faster than in reality, as the model does not take into account the effect of capacities.
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Calculation model
The software does not use the correction coefficients, subject to possible future developments, currently providing more conservative values. The Ampère Professional calculation model also uses the subtransient reactances of the generators, improving the estimates of the standard in line with the studies provided by some articles.
According to Electro Graphics, the software was tested with examples of third-party calculations, verifying the reliability of the results within the limits of the errors indicated above. “To activate the new DC calculation model, in the Properties window, Calculation Setup tab, activate the Calculate DC fault transient currents (IEC 61660-1) check box,” they advised.
The standard establishes a generally valid calculation method for short-circuit currents. The proposed method provides for the calculation of the short-circuit current that passes through the fault point as the sum of the currents generated by different sources. The elements studied in the standard that contribute to the determination of this current are:
- Three-phase bridge rectifiers;
- Lead-acid batteries;
- Snubber capacitors;
- Independently excited DC motors.
The trend over time of the current generated by the different sources is correctly obtained using formulas (1), (2) and (3):
Where:
- ip is the peak short-circuit current;
- ik is the quasi-steady short-circuit current (1 sec.);
- tp is the peak time;
- τ1 is the rise time constant;
- τ2 is the descent time constant.
“If no maximum current is defined, ip = ik and tp are assumed to be equal to TK, which is the fault interruption time. The total short-circuit current is then obtained by superimposing the effects, thus adding up all the contributions to the fault arising from the sources involved in the calculation,” the company reported.
Where:
- j is the reference to the source in question;
- m is the number of sources supplying the fault;
- i(t) is the total short-circuit current;
- Tk is the fault interruption time.
The figure below represents the current trend given by formulas (1) and (2), which approximate the contribution to the fault of each source.
Approximate curve – Standard approximation function
The study of the transient as a superposition of effects depends on the time constants and the maximum values imposed by each source, obtaining a trend that can be wave-like with several maximum values before tending to the final value of the steady state.
The standard proposes a method to obtain a curve that approximates the transient as a whole, always described through formulas (1) and (2), useful for calculating electrodynamic stresses and thermal stresses, in accordance with IEC 61660-2.
“The software displays the curve (in green color) and allows you to print the values ip (peak short-circuit current), ik (quasi-steady short-circuit current in 1 sec.), tp (peak time), τ1 (rise time constant) and τ2 (fall time constant) following the rules established in paragraph 3.3 of the standard,” they explained.
These parameters are derived graphically from the interpolated curve created by summing all source contributions to the fault (blue line in Ampère graphs).
The four examples proposed in the figure describe typical transients, where the real transient trend is represented by the solid line. The dashed line represents the approximated function.
“It is interesting to note that in the two figures on the right the calculation of τ1 is conditioned by the rise time of the first peak. In fact, if the first peak is greater than 50% of the peak current, it controls the rising part of the function (see figure 22 of the standard)”, reported the company.
Coordination with EN 60909-0 standard
The direct current calculation method used by the software acts on direct current users by modifying the single-phase fault current values associated with the subtransient regime. Therefore, the results obtained from the maximum peak analysis are saved in the Ikm variable.
“Remember that Ikm is the current compared to the interruption capacity of the protections and, given its very nature, has the maximum component upstream or downstream of the fault”, they stated.
Furthermore, according to EN 60909-0, the Protection Limiting Curve is not applied to it, even if IEC 61660-1 in paragraph 2.1 asks to take this into account for the calculation of the maximum currents. The quasi-steady fault currents, calculated in one second, are instead saved in the variable Ik1(fn)max, which represents the permanent fault.
The results of the analysis determine the values of the peak current variables Ip1 (fn), calculated as the total current contribution (sum of the upstream-downstream and downstream-upstream components). As with EN 60909-0, the Protection Limiting Curves are applied to them.
The Fault Analysis advanced functions panel proposes the calculated current values and through the Print Management command on the panel it is possible to obtain printouts like the one in the figure.
Fault analysis
The Fault Analysis panel allows you to analyze faults in alternating current and direct current. For alternating current users, Ampère offers a fault transient analysis with verification of the interrupting and closing capacity if protection is assigned.
According to Electro Graphics, if the software does not find any problems, the window displays the maximum fault trend, exposing its characteristic parameters; data relating to the assigned protection are also displayed.
Furthermore, it is possible to study the different fault dynamics according to the conductors involved by clicking on the appropriate cells in the network. When an inconsistency is found, Ampère, with the help of red messages, signals the presence of the error, also specifying which type of fault constitutes a problem.
The Fault Analysis advanced functions panel proposes the current values and through the Print Management command on the panel it is possible to obtain printouts like the one in the figure below.
It is important to highlight some points about the values provided, as there are details that can cause confusion:
- The Fault Analysis panel shows different peak current values;
- The assumed Ip max value is relative to the maximum value among all faults;
- The Ipk value detected graphically, and highlighted in the fault transient graph, is relative to the selected fault type;
- Even for the same fault, the values may be slightly different;
- The graph also shows the asymmetric part of the current, in green, which decreases exponentially with time (time constant T), and this decrease is different for each type of fault.
In short, the software's Fault Analysis panel offers features for a complete assessment of electrical systems, allowing the identification of potential problems and detailed analysis of fault characteristics, thus ensuring the safety and reliability of electrical systems.
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