We present in this paper an algebraic derivative method of the line current in order to detect the presence of series arcs in an AC or DC electrical installation. The first derivative is computed from a limited Taylor-McLaurin series transposed in Laplace space. The temporal estimation is achieved by integration over a sliding window of the product of a particular polynomial with the instantaneous current. The discrete version can be synthesized by a simple FIR filter. The tests, with and without series arc, are conducted on experimental currents (3-12 A) measured on domestic loads (resistors, vacuum drill, dimmer). The sampling frequency is set to 1 MHz. Short integration times (50 microseconds in AC and 200 microseconds in DC) are sufficient to observe, with high contrast, the derivative peaks due to the arc ignition. The detection is then performed by comparing the derivation filter output to its instantaneous noise level. The response time is equal to the integration duration. This method, simple to set up and easy to implement, is ideally suited for installations that do not use load switching current. I-Context and objectives Arc-fault detection, especially series arcing, is a key factor for increasing the safety of DC and AC power supply systems [1-2]. A series arc occurs in a galvanic interruption of the supply circuit. Involuntary separation of a contact point (breaking or disconnection) or insulation breakdown by carbon path, are the main causes of series arcs [3]. Less frequently, the arc can be initiated by a power overvoltage. Physically it is reflected in a current flow across the discontinuity. This results strong local temperature increase which causes the ionization of the air in the form of plasma. Since the current intensity is limited by the load, the average level takes no abnormal value which makes the series arcs detection very difficult and gives them a high hazard potential. In the presence of a series arc, the temporal shape of the current reveals :  disruptions in the average level in DC mode. The resistance of the arc being often low, the current slightly decreases.  discontinuities in the sinusoidal shape in AC mode. Spectrum analysis is the most often used detection method [4-6]. The frequency range is selected to avoid interferences caused by the load. Statistical analysis has proven advantages in some situations [7]. In the DC mode, the rupture detection can be achieved through the Page-Hinkley procedure which requires the selection of detection thresholds based on the noise level [8]. In the case of chaotic signals, multiple false detections can appear. The time-frequency or timescale decomposition can provide the frequency characteristics of the arc during its evolution [9-12]. Some authors propose detection based on the estimation of the impedance of the arc [13]. This method is more sensitive than the simple spectrum analysis, but requires knowledge about the arc voltage which is not actually possible in practical situations. Other methods rely on identifying a real-time model of the load [14-17]. An arc can be considered a non-linear and chaotic variable dipole; its apparition leads to a strong prediction error in the model. The proposed solutions are often restricted to special cases (single power system, known load, range of spectrum analysis tailored to the situation, unique ignition mode).