Online Estimation of Power System Inertia Constant Under Normal Operating Conditions

Abstract

An online estimation method for the power system inertia constant under normal operating conditions is proposed. First of all, a dynamic model relating the active power to the bus frequency at the generation node is identified in the frequency domain using ambient data measured with the phasor measurement units (PMUs). Then, the inertia constant at the generation node is extracted from the unit step response of the identified model in the time domain using the swing equation. Finally, with the sliding window method and the exponential smoothing method, the estimated inertia constant is updated in real-time. Compared to the conventional methods using large disturbance data or field test data, the proposed method can estimate the inertia constant under normal operating conditions, and therefore, can provide the tracking trajectory of the power system inertia constant in real-time. The effectiveness of the proposed method is validated in the IEEE 39-bus system. The results show that the relative error of the identified inertia constant is below 5% and the identified inertia constant can be updated within 1s.

Analysis and Improvement of an Algorithm for the Online Inertia Estimation in Power Grids with RES

“…The inertia estimation algorithm [17] exhibits good performances in the IEEE-39-bus grid, but we got a quite poor accuracy in the IEEE-14 network, which motivates the analysis and improvements of the algorithm described in this section.…”

“…where 0 ,˙ f t=0 is the slope of f (t) in t = 0. The algorithm proposed in [17] allows estimating the inertia with time step ⌧ (update time), based on measurements of f and P collected within a moving time window of length W . The algorithm can be summarized as follows: 1. take measurements of f (t k ) and P (t k ) at times t k , within the time window, with sampling time t; 2. filter data through a 6-th order Butterworth low-pass filter with cut-off frequency 0.5Hz; 3. use data in the first T -long part of the time window (with T < W) to identify, through the n4sid algorithm [20], a discrete-time linear system of order n with input P (t k ) and output f (t k ); 4. use data in the rest of the window (of length W T ) to validate the identified system, by computing the fitting ratio…”

“…In [17] a system of order between 1 and 10 is identified through the n4sid algorithm, which automatically determines the order that yields the lower estimation error (⌫ closest to 0). Actually, a better system identification does not necessarily imply a better estimation of the inertia.…”

“…In this paper, we consider the algorithm proposed in [17], which allows us to track the inertia constant in real-time under normal operating conditions, given the data measured through phasor measurement units (PMUs) [18]. The method is based on the estimation of a linear model relating the active power fluctuations to the frequency fluctuations on a bus and the subsequent inertia constant extraction from the unit-step response of the identified model.…”

“…The main novelty elements of this paper are: (i) a critical discussion of the algorithm proposed in [17], including the choice of some parameters, (ii) a change of some parts of the algorithm, and (iii) the application of this algorithm to the estimation of the inertia in a standard network (the IEEE-14-bus power system), also with the addition of a PV power plant (in [17] a network without RES was considered). In particular, estimating the total inertia of the power system becomes much more challenging in the presence of RES providing synthetic inertia.…”