Waqquas Bukhsh

Local Solutions of the Optimal Power Flow Problem

The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades. This paper presents examples of local optima on a variety of test networks including modified versions of common networks. We show that local optima can occur because the feasible region is disconnected and/or because of nonlinearities in the constraints. Standard local optimization techniques are shown to converge to these local optima. The voltage bounds of all the examples in this paper are between ±5% and ±10% off-nominal. The examples with local optima are available in an online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/) and can be used to test local or global optimization techniques for OPF. Finally we use our test examples to illustrate the behavior of a recent semi-definite programming approach that aims to find the global solution of OPF.

Optimization-Based Islanding of Power Networks Using Piecewise Linear AC Power Flow

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.

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

Renewable energy sources such as wind and solar have received much attention in recent years, and large amounts of renewable generation are being integrated into electricity networks. A fundamental challenge in power system operation is to handle the intermittent nature of 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 of 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. The proposed model is illustrated on a 4-bus and a 39-bus system. Numerical results show that substantial benefits in terms of redispatch costs can be achieved with the help of demand side flexibilities. The proposed approach is tested on the standard IEEE test networks of up to 300 buses and for a wide variety of scenarios for renewable generation.

MILP islanding of power networks by bus splitting

A mathematical formulation for the islanding of power networks is presented. Given an area of uncertainty in the network, the proposed approach uses mixed integer linear programming to isolate unhealthy components of the network and create islands, while maximizing load supply. Rather than disconnecting transmission lines, the new method splits the network at its nodes, which are modelled as busbars with switches between lines, generators and loads. DC power flow equations and network constraints are explicitly included in the MILP problem, resulting in balanced, steady-state feasible islands. Numerical simulations on the IEEE 14-bus test network demonstrate the effectiveness of the approach.

A robust optimisation approach using CVaR for unit commitment in a market with probabilistic offers

The large scale integration of renewable energy sources (RES) challenges power system planners and operators alike as it can potentially introduce the need for costly investments in infrastructure. Furthermore, traditional market clearing mechanisms are no longer optimal due to the stochastic nature of RES. This paper presents a risk-aware market clearing strategy for a network with significant shares of RES. We propose an electricity market that embeds the uncertainty brought by wind power and other stochastic renewable sources by accepting probabilistic offers and use a risk measure defined by conditional value-at-risk (CVaR) to evaluate the risk of high re-dispatching cost due to the mis-estimation of renewable energy. The proposed model is simulated on a 39-bus network, whereby it is shown that significant reductions can be achieved by properly managing the risks of mis-estimation of stochastic generation.

Element position perturbation for a narrow spot beam with applications to satellite communication antennas

Design of array antennas for satellite applications is always a trade-off between physical constrains and pattern requirements. In this paper, the focus is on the design of a large array antenna fo ...

Synthesis of wind time series for network adequacy assessment

When representing the stochastic characteristics of wind generators within power system simulations, the spatial and temporal correlations of the wind resource must be correctly modelled to ensure that reserve and network capacity requirements are not underestimated. A methodology for capturing these correlations within a vector auto-regressive (VAR) model is presented, and applied to a large-scale reanalysis dataset of historical wind speed data for the British Isles. This is combined with a wind speed-to-power conversion model trained against historically metered data from wind farms on the Great Britain (GB) electricity system in order to derive a lightweight model for simulating injections of wind power across a transmission network. The model is demonstrated to adequately represent ramp rates, both at a site and network level, as well as the individual correlations between sites, while being suitable for network adequacy studies which may require the simulation of many years of operation.

Adequacy assessment of future electricity networks

Liberalisation of electricity markets, changing patterns in the generation and use of electricity and new technologies are some of the factors that result in increased uncertainty about the future operating conditions of our power system. In this context, planning for future investments in power system requires careful selection and assessment of future operating conditions. This paper revisits the notion of power system adequacy and highlights the need for consideration of some factors that have hitherto tended not to be part of a transmission expansion planning process, in particular in respect of the credible range of possible values of system operating conditions and transitions between successive operating states. Firstly, we present some definitions of power system operational regions. Secondly, we present a stochastic optimisation model that measures the adequacy of a transmission network for given future operating conditions. Uncertainties in demand and generation are modelled using a large number of scenarios. The optimisation model identifies the critical future operating conditions needing the special attention of a power system planner. The proposed model is simulated on a 39-bus network, whereby it is shown that this model can identify critical operating conditions that need the attention of a system planner.