Improving Operational Feasibility in Large-Scale Power System Planning

Abstract

Large-scale power system planning mostly uses linearized, active power only approximations of the power flow equations, ignores many operational constraints, and tests the operational feasibility of the resulting systems only under strongly simplifying assumptions. We propose an approach to obtain solutions to large instances of the alternating current capacity expansion problem via redispatch and reinforcement of an initial solution. The problem formulation considers simultaneous expansion of generators, reactive compensation devices, storage systems, and transmission. Furthermore, it includes operational constraints via startup procedures and capability curves of power sources and simplified stability limits via constraints on voltage angle differences and voltage magnitudes. To obtain initial solutions, we test several established and partly modified power flow approximations and integrate them into an approach for iterative transmission expansion planning, thereby obtaining convex formulations. We demonstrate the approach on large problem instances covering the islands of Great Britain and Ireland at the transmission level, for which we extend the open data source to model reactive power. We find that including transmission losses to determine the initial solution is most decisive, as the amount of redispatch and reinforcements necessary to obtain an alternating current feasible solution is reduced, whereas incorporating reactive power constraints did not lead to further improvements. Our approach ensures an alternating current feasible system under weak assumptions, thus guaranteeing steady-state voltage stability and allowing subsequent dynamic grid simulations, which is instrumental for planning stable future inverter-dominated power systems.

Figures (4)

• Figure 1: Capacity expansion decisions for each scenario and power flow approximation, excluding transmission expansion. Hatched areas indicate the respective value in the initial solution before the AC-reinforcement.
• Figure 2: Energy mix for each scenario and power flow approximation. Hatched areas indicate the respective value in the initial solution before the AC-reinforcement. The total load is equal to 362.
• Figure 3: Losses and reactive power demand of transmission in p.u. of the thermal limit as a function of the voltage angle difference. Losses and reactive power demand are given by the sum of the active and reactive power flows at both endpoints of each branch, respectively. We obtain the voltage angle differences for dc-lossy via the relation $\theta_{l,t} = p_{l,t} x_l$.
• Figure 4: Transmission losses in initial solution in comparison to their analytical lower bound and the losses in the AC-reinforced solution. The lower bounds are computed by evaluating the analytical expressions with the assigned values of the respective decision variables. In the case of dc-lossy, the linear relaxation of the loss approximation can lead to losses that are lower than the analytical lower bound.