Transmission loss modelling and analysis with multiple linear regression

Unit commitment (UC) and economic dispatch (ED) are two crucial optimisation problems in the short term operational planning of power systems. For a given scheduling period, UC determines the optimal set of generating units to be in service whereas ED determines the economic distribution of generation values for a known set of generators. Both of these problems are modelled as aggregated supply and demand problems, and require an estimate of the transmission loss. Therefore the accuracy of the approximated transmission loss within these problems is vital in ensuring the optimality and feasibility of the solutions. The increasing penetration of renewable energy (RE) technologies into the grid has increased the volatility of the transmitted power, making it harder to approximate the transmission loss using existing techniques. A robust and reliable approximation is required, valid across a wide range of transmission values. Consider a power network with a set of nodes connected by transmission lines, with subset B of nodes with demand and subset N of nodes with generators. Let di be the real power demand at node i ∈ B, pj, the real power generated at node j ∈ N and L, the total real power transmission losses in the system.Without loss of generality let generator node 0 be the slack bus and write N0 = N\{0} for the generation nodes excluding the slack bus. This paper looks into a new way of modelling the aggregated transmission loss, using multiple linear regression. The fitted model's form is (Equation presented) where k = (1, . . ., n) is the observation number, ϵ(k) is the error and αij, βij and ηij are coefficients fitted using least squares. The proposed model does not rely only on a particular base case and does not make simplifying assumptions, as seen in previous models, though we do assume that the topology of the power network does not change. This makes the model more robust than existing approximations. In this paper the effect of power demand (load) at each demand point, power generation and voltage magnitudes for each generator are tested for eight different scenarios created using J.H. Chows 3-Machine 9-Bus benchmark problem which is quoted in Zimmerman et al. (2011). In each scenario we compare our proposed model with loss approximation models currently used in industry. From the analysis we see that our proposed model outperforms the existing models, and gives good approximations for a wide range of inputs. We also show that the performance measures used to compare the models can be used to determine a best base case. Finally, we show that by looking at the effect of voltage on how well our model fits, we are able to determine voltage limits for generators that are best, in the sense that they minimise the instability caused to load flows due to improper voltage magnitude values.