The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades. We have shown the existence of local solutions on a variety of test networks including slightly modified versions of common networks. Standard local optimization techniques are shown to converge to these local optima if started close enough to them. These test cases are available in an online archive [1] and can be used to test local or global optimization techniques for OPF.
In this paper, a flexible optimization-based framework for intentional islanding is presented. The decision is made of which transmission lines to switch in order to split the network while minimizing disruption, the amount of load shed, or grouping coherent generators. The approach uses a piecewise linear model of AC power flow, which allows the voltage and reactive power to be considered directly when designing the islands. Demonstrations on standard test networks show that solution of the problem provides islands that are balanced in real and reactive power, satisfy AC power flow laws, and have a healthy voltage profile.
This paper presents a flexible optimization approach to the problem of intentionally forming islands in a power network. A mixed integer linear programming (MILP) formulation is given for the problem of deciding simultaneously on the boundaries of the islands and adjustments to generators, so as to minimize the expected load shed while ensuring no system constraints are violated. The solution of this problem is, within each island, balanced in load and generation and satisfies steady-state DC power flow equations and operating limits. Numerical tests on test networks up to 300 buses show the method is computationally efficient. A subsequent AC optimal load shedding optimization on the islanded network model provides a solution that satisfies AC power flow. Time-domain simulations using second-order models of system dynamics show that if penalties were included in the MILP to discourage disconnecting lines and generators with large flows or outputs, the actions of network splitting and load shedding did not lead to a loss of stability
Abstract-Renewable energy sources such as wind and solar have received much attention in recent years, and large amount of renewable generation is being integrated to the electricity networks. A fundamental challenge in a power system operation is to handle the intermittent nature of the renewable generation. In this paper we present a stochastic programming approach to solve a multiperiod optimal power flow problem under renewable generation uncertainty. The proposed approach consists of two stages. In the first stage, operating points for the conventional power plants are determined. The second stage realizes generation from the renewable resources and optimally accommodates it by relying on the demand-side flexibilities and limited available flexibilities from the conventional generating units. The proposed model is illustrated on a 4-bus and a 39-bus system. Numerical results show that with small flexibility on the demand-side substantial benefits in terms of re-dispatch costs can be achieved. The proposed approach is tested on all standard IEEE test cases upto 300 buses for a wide variety of scenarios.Index Terms-Demand response; optimal power flow; power system modelling; linear stochastic programming; smart grids; uncertainty; wind energy. NOMENCLATURE Sets BBuses, indexed by b. T Discrete set of time intervals, indexed by t . Parameters b lSusceptance of line l .τ l Off-nominal tap ratio of line l .Min., max. real power outputs of conventional generator g .Real power demand of load d .Cost function for generator g . Cost of renewable generation spillage.Min., max. load flexibility of demand atMin., max. change in operating point ofMin., max. regulation of generator g .Downward, upward regulation cost for generator g .Cost of decreasing, increasing demand in the time period t . P max lMax power flow capacity of line l . Variables pReal power output of generator g .
This paper presents an investigation of the potential for coordinated charging of electric vehicles to i) reduce the CO 2 emissions associated with their charging by selectively charging when grid carbon intensity (gCO 2 /kWh) is low and ii) absorb excess wind generation in times when it would otherwise be curtailed. A method of scheduling charge events that seeks the minimum carbon intensity of charging while respecting EV and network constraints is presented via a time-coupled linearised optimal power flow formulation, based on plugging-in periods derived from a large travel dataset. Schedules are derived using real half-hourly grid intensity data; if charging in a particular event can be done entirely through use of renewable energy that would otherwise have been curtailed, its carbon intensity is zero. It was found that if 'dumb' charged from the current UK mainland (GB) grid, average emissions related to electric vehicle (EV) charging are in the range 35-56 gCO 2 /km; this can be reduced to 28-40 gCO 2 /km by controlled charging -approximately 20-30% of the tailpipe emissions of an average new petrol or diesel car sold in Europe. There is potential for EVs to absorb excess wind generation; based on the modelled charging behaviour, 500,000 EVs (20% of Scotland's current car fleet) could absorb around three quarters of curtailment at Scotland's largest onshore wind farm.
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