Optimal placement of inertia and primary control in high voltage power grids

The energy transition's ultimate goal is to meet energy demand from human activities sustainably. Accordingly, the penetration of new renewable energy sources (RES) such as photovoltaic panels and wind turbines is increasing in most power grids. In their current configuration, RES are essentially inertialess, therefore, low inertia situations are more and more common, in periods of high RES production, making grid stability a high concern in power grids with high share of RES. It has been suggested that the resulting reduction of overall inertia can be compensated to some extent by the deployment of substitution inertia - synthetic inertia, flywheels, synchronous condensers aso. Of particular importance is to optimize the placement of the limited available substitution inertia. Here, we construct a matrix perturbation theory to optimize inertia and primary control placement under the assumption that both are moderately heterogeneous. Armed with that efficient tool, we construct simple but efficient algorithms that independently determine the optimal geographical distribution of inertia and primary control.

Aspects of the energy transition and their effects on power systems

Laurent Vincent Pagnier

Most European countries are committed to an energy transition which consists in the substitution of conventional CO2 emitting energy sources by new renewable energy sources (RES), in particular wind and solar power. As opposed to conventional energy sources, new RES are distributed, non-dispatchable, fluctuating and inertialess and have negligible marginal costs. In this thesis, we investigate the impact of the energy transition on the electricity sector in Europe. In the first part of this thesis, we investigate the future electricity production and prices in Europe. We develop a dispatch algorithm on an aggregated model of the pan-European power grid with which we study the future European productions. We show that, as the penetration of new RES increases, the transmission grids are more strongly used and that more flexibility is required from conventional generators. The existing infrastructures seem to able to absorb, through increased international power exchanges and usage of the existing pumped-storage hydroelectricity, the variations of new RES productions even for high penetrations. Then we investigate the effects of new RES on electricity prices. We explain why, due to their negligible marginal cost and their lack of dispatchability, they tend to drag electricity prices down and can be considered as a reduction of the load in the electricity pricing. In particular, photovoltaics decreases the volatility of electricity prices. We show that, in most European countries, the day-ahead electricity price is strongly correlated with the residual load, which is obtained by subtracting the non-dispatchable productions, in particular those of the new RES, from the load. From this observation, we build an effective price model based solely on the residual load with which the revenues of different electricity producers are evaluated. The second part of this thesis deals with disturbances in large transmission grids. The substitution of conventional generators by inertialess RES reduces the amount of inertia connected to power systems which might affect their reliability. To examine the propagation of disturbances in large transmission grids, we develop a dynamical model of the continental European transmission grid. We observe that the magnitude of the disturbance following a power loss depends on the fault location. We show that when inertia and primary control are uniformly distributed, the faults exciting the slowest eigenmodes of the network Laplacian are followed by the strongest disturbances. Reducing inertia on those eigenmodes, which are mostly located in the periphery of the grid, affects more its resilience than when the reduction occurs in its center. Finally, we use perturbation theory to derive algorithms for optimal placement of inertia and primary control when some mild inhomogeneities are present in their distributions. We show that,when the vulnerability of the whole grid is taken into account, a uniform distribution of inertia is optimal and the primary control is best placed in the periphery of the grid.

EPFL2019

Optimal Placement of Inertia and Primary Control: A Matrix Perturbation Theory Approach

Philippe Jacquod

The increasing penetration of new renewable sources of electrical energy reduces the overall mechanical inertia available in power grids. This raises a number of issues regarding grid stability over short to medium time scales. A number of approaches have been proposed to compensate for this inertia reduction by deploying substitution inertia in the form of synchronous condensers, flywheels or powerelectronic-based synthetic inertia. These resources are limited and expensive; therefore, a key issue is to determine how to optimally place them in the power grid, for instance, to mitigate voltage angle and frequency disturbances following an abrupt power loss. Performance measures in the form of H-2-norms have recently been introduced to evaluate the overall magnitude of such disturbances. However, despite the mathematical convenience of these measures, analytical results can only be obtained under rather unrealistic assumptions of a uniform damping-to-inertia ratio or a homogeneous distribution of the inertia and/or primary control. Here, we introduce and apply matrix perturbation theory to obtain analytical results for an optimal inertia and primary control placement in the case where both are heterogeneous. This powerful method allows us to construct two simple algorithms that independently optimize the geographical distribution of the inertia and primary control. The algorithms are then implemented for a numerical model of the synchronous transmission grid of continental Europe with different initial configurations. We find that an inertia redistribution has little effect on the grid performance but that the primary control should be redistributed on the slow modes of the network, where the intrinsic grid dynamic requires more time to damp frequency disturbances. For a budget-constraint optimization, we show that increasing the amount of primary control in the periphery of the grid, without changing the inertia distribution, achieves 90 % or more of the maximal possible optimization, already for relatively moderate budgets.

2019

Optimal Placement of Inertia and Primary Control: A Matrix Perturbation Theory Approach

Philippe Jacquod

2019

Aspects of the energy transition and their effects on power systems

Laurent Vincent Pagnier

EPFL2019