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Confidence-level optimization in distribution grids for voltage droop controllers tuning

With a high penetration level of renewable energy productions,distribution grids face different issues such as overvoltages. The voltages are controlled by an On Load Tap Changer(OLTC) and the Distributed Generators (DGs) reactive powers. Commonplace controllers embed only local measurements and simple linear droop-like algorithms. Usually, control parameters are set during the DG connection stage regardless of the
stochastic nature of consumption and renewable powers. This approach is sufficient to keep the voltages within the specified range. However, a stochastic optimisation of these control settings could additionally reduce both losses and voltage
variances. Given a network model, the goal of this paper consists of computing the set of local controllers parameters which maximizes a combination of confidence levels. First, the linear Power Flow method generates a linear stochastic representation
of the grid and yields both voltages and powers assuming a Gaussian distribution of the inputs. Then, the confidencelevel optimal problem, which considers both voltages and PQ domain issues is solved. This novel method is applied on a real distribution grid and improves the voltage control with a lower computational burden than Monte-Carlo methods.

The studied distribution network includes thousands of buses, lines/cables, an OLTC and many DGS, for which the reactive power reference is assumed to be given by the
following linear controller:
Q_ref^i = alpha_i V_i + beta_i P_i + Q^0_i (1)
where Vi and Pi come from local measurements, the pair (Pi,Qi) should remain within a local prescribed (PQ) domain. The OLTC controller is also assumed to be linear. The
power flow model can be simplified using the linear model presented by Bolognani, which gives the node voltages (V) as a linear function of load/production active (P) and reactive (Q) powers, which are provided by short term forecasting (2):
V = AP + BQ + 1V_OLTC (2)
Since all stochastic inputs (loads, productions and OLTC tolerance) are assumed to be characterized by Gaussian distributions, the use of a linear model yields directly the stochastic distribution of outputs V . The confidence levels correspond to the probabilities that each voltage lies within the range [0:95; 1:05] per unit (eta_i) and each DG power lies within a local prescribed PQ domain (lambda_j ). The proposed optimization method maximizes the sum of confidence levels. A secondary objective aims to reduce the voltage variance of a specified set of nodes k, V (k) and with the weighting factor w > 0.

In this abstract, results are shown for only one MV feeder of a 2000-node network. This feeder has 45 nodes in two branches, 2 photovoltaic generators and 15 km of line/cable. The maximum consumption is 2.5 MW and 0.6 MVAR, the production capacities of the generators are 4.5 MW and 5 MW. The characteristics (mean and standard deviations) of forecast errors can be inferred from a measurement data base.
Production may cause the grid voltages to raise; the voltages of the sensitive node 31 (end of the feeder) lie in the domain [1:044; 1:067] per unit at the 95 % confidence level. All voltages are brought back into the specified domain (Fig. 1).

In the full paper version, the resolution of the stochastic optimal confidence level will be detailed. A comparison with a non-simplified model, for which load and production uncertainties are based on real (and thus non-Gaussian) measurement
data base, will be done.


Jérôme Buire    
Ecole Centrale de Lille

Frédéric Colas    
Arts et Métiers ParisTech

Jean-Yves Dieulot    
Polytech Lille

Léticia De-Alvaro    

Xavier Guillaud    
Ecole Centrale de Lille


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