# Online Estimation of Short-Circuit Fault Level in Active Distribution Network
## 2 Short-Circuit Fault Level Estimation for Active Distribution Networks
### Proposed Estimation Scheme  
This paper aims to evaluate the potential fault level, which is expressed as the potential short-circuit current through the breaker. To investigate the extreme situation, three-phase short-circuit occurring  
Figure 1: The structure of a general radial distribution network. Figure 2: The equivalent circuit of the distribution network in question. exactly at the terminal of the breaker is considered. Hence, the power sources upstream rather than those downstream will contribute to the fault current through the studied breaker. Taking the breaker CB8 in Figures 1 and 2 as an example, the overall current through it, if the imaginary fault really happens, consists of the contribution from the upstream rotating generators and that from the upstream IBDGs. If \(Z_{eq}\) is known, then the former can be calculated by setting \(\dot{E}\), the value of 1.0 pu (per-unit value), as the internal electromotive forces of the rotating generators are practically close to their rated values. Concerning the latter contribution, it is usually limited within a range of 1.2 to 1.5 times the rated current [25; 26]. Such a multiplier is denoted as the overcurrent coefficient. Given the value of such a coefficient, the contribution from IBDGs to the fault current can be estimated, as long as their rated currents \(\dot{I}_{DC0}\) are known. Consequently, the estimation of the potential fault level is converted to the evaluation of two unknown parameters, i.e., \(Z_{eq}\) and \(\dot{I}_{DC0}\), even though no actual short-circuit fault occurs. An online method deriving these parameters from the measurements after a series of disturbances is proposed in the following paragraphs. All selected disturbances come from the normal phenomena, such as load fluctuations, instead of real short-circuit faults. Certainly, the information about whether the configuration of the upstream grid changes or not should be known during the estimation procedure. Otherwise, the undiscriminating disposal of the data, even though \(Z_{eq}\) and \(\dot{I}_{DC0}\) have already changed, is improper and might undermine the estimation accuracy. The proposed method in this paper benefits from an advanced algorithm to smartly detect, judge, and deal with various disturbances differently, thereby improving the estimation accuracy. The parameters of \(Z_{eq}\) and \(\dot{I}_{DC0}\) are proposed to be calculated on the basis of the voltage and current measurements after several continuous disturbances downstream to the studied circuit breaker and without re-configuration of upstream grids. In practice, the voltage at the breaker and the current through it can be measured by PMUs, taking their advantages on accurate synchronous sampling. The precision for the voltage/current amplitude and phase angle can reach 0.01% and 0.01\({}^{\circ}\), respectively [27]. Alternatively, they can also be measured by protection relays. The corresponding positive sequence phasors of voltage \(\dot{U}\) and current \(\dot{I}\) are obtained as well. In this paper, the subscript '0' is applied to denote the variables before disturbances, e.g., the measured voltage phasor \(\dot{U}_{0}\) and the current phasor \(\dot{I}_{0}\), respectively. After \(n\) downstream disturbances with enough identifiability, the relevant voltages and currents are recorded as a set of phasors i.e., \(\dot{U}_{1},\ \dot{U}_{2},\ \ldots\ \dot{U}_{n}\) and \(\dot{I}_{1},\ \dot{I}_{2},\ \ldots\ \dot{I}_{n}\). The following equations hold:  
\[\left\{ \begin{array}{l}\dot{E}_{0}=\dot{U}_{0}+\left(\dot{I}_{0}-\dot{I}_{ DC0}K_{0}\right)Z_{eq}\\ \dot{E}_{1}=\dot{U}_{1}+\left(\dot{I}_{1}-\dot{I}_{DC0}K_{1}\right)Z_{eq}\\ \ldots\\ \dot{E}_{n}=\dot{U}_{n}+\left(\dot{I}_{n}-\dot{I}_{DC0}K_{n}\right)Z_{eq}\end{array}  \right., \tag{1}\]  
where \(K_{i}\ (i=0,1,2\ldots n)\) is defined as the regulation factor to describe the IBDG output current with respect to its rated value as its output voltage changes.