A Multiperiod OPF Model Under Renewable Generation Uncertainty and Demand Side Flexibility

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 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 conventional power plants are determined. Second stage realizes the generation from renewable resources and optimally accommodates it by relying on demand-side flexibility. The benefits from its application are demonstrated and discussed on a 4-bus and a 39-bus systems. Numerical results show that with limited flexibility on the demand-side substantial benefits in terms of potential additional re-dispatch costs can be achieved. The scaling properties of the approach are finally analysed based on standard IEEE test cases upto 300 buses, allowing to underlined its computational efficiency.Comment: 8 pages, 10 figure

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

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

MILP formulation for controlled islanding of power networks

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

OATS : Optimisation and Analysis Toolbox for power Systems

Optimisation and Analysis Toolbox for power Systems analysis (OATS) is an open-source simulation tool for steady-state analyses of power systems problems distributed under the GNU General Public License (GPLv3). It contains implementations of classical steady-state problems, e.g. load flow, optimal power flow (OPF) and unit commitment, as well as enhancements to these classical models relative to the features available in widely used open-source tools. Enhancements implemented in the current release of OATS include: a model of voltage regulating on-load tap-changing transformers; load shedding in OPF; allowing a user to build a contingency list in the security constrained OPF analysis; implementation of a distributed slack bus; and the ability to model zonal transfer limits in unit commitment. The mathematical optimisation models are written in an open-source algebraic modelling language, which offers high-level symbolic syntax for describing optimisation problems. The flexibility offered by OATS makes it an ideal tool for teaching and academic research. This paper presents novel aspects of OATS and discusses, through demonstrative examples, how OATS can be extended to new problem classes in the area of steady-state power systems analysis

Risk and reliability assessment of future power systems

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 requirements of an electric power system. In this context, planning for future investments in a power system requires careful consideration of risk and reliability, and of the metrics with which these are measured. This paper highlights the need for consideration of a broader class of approaches to risk and reliability that have hitherto tended not to be an explicit part of the system development process in the electricity industry. We discuss a high level conceptual model that shows sources of uncertainty and modes of control for system operators and planners and offers a broad-brush approach to highlight risks at the planning stage. We argue that there is a need for new risk-informed criteria to help evaluate the necessary investments in electricity transmission systems. We further argue that the risk models that are developed for this purpose need to take better account of overall societal impact than is captured by traditional measures such as loss of load probability and loss of load expectation; societal impact should take account of frequencies of events with different levels of consequences, distinguishing, for example, between multiple small events and a single large event. This leads to discussion of a “disutility criterion” which has been previously studied in a health and safety context to distinguish between risk aversion and disaster aversion. This approach is new in the context of power systems

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

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

Optimal operation of the Western Link embedded HVDC connection

The Western Link is a new point-to-point embedded HVDC connection due to be commissioned in Great Britain in 2018. This paper investigates the optimal loading of the Western Link with respect to the wider transmission system. The work modelled a representation of behaviour of the wholesale market and system operator actions using mathematical optimisation in the form of an economic dispatch followed by an AC optimal power flow. A range of different system cases was studied using: a representative high voltage transmission network of Great Britain; system planned outages on AC circuits in parallel with the Western Link; system contingencies; and two possible post-contingency Western Link loading rules. It was concluded from the cases studied that the optimal dispatch of power on the Western Link is an affine function of power flow in the parallel AC circuits, modulated by system planned outages and the thermal rating of the Western Link

Comparative efficacy of two microdoses of a potentized homoeopathic drug, Cadmium Sulphoricum, in reducing genotoxic effects produced by cadmium chloride in mice: a time course study

BACKGROUND: Cadmium poisoning in the environment has assumed an alarming problem in recent years. Effective antimutagenic agents which can reverse or combat cadmium induced genotoxicity in mice have not yet been reported. Therefore, in the present study, following the homeopathic principle of "like cures like", we tested the efficacy of two potencies of a homeopathic drug, Cadmium Sulphoricum (Cad Sulph), in reducing the genotoxic effects of Cadmium chloride in mice. Another objective was to determine the relative efficacy of three administrative modes, i.e. pre-, post- and combined pre and post-feeding of the homeopathic drugs. For this, healthy mice, Mus musculus, were intraperitoneally injected with 0.008% solution of CdCl(2) @ 1 ml/100 gm of body wt (i.e. 0.8 mcg/gm of bw), and assessed for the genotoxic effects through such studies as chromosome aberrations (CA), micronucleated erythrocytes (MNE), mitotic index (MI) and sperm head anomaly (SHA), keeping suitable succussed alcohol fed (positive) and CdCl(2) untreated normal (negative) controls. The CdCl(2) treated mice were divided into 3 subgroups, which were orally administered with the drug prior to, after and both prior to and after injection of CdCl(2) at specific fixation intervals and their genotoxic effects were analyzed. RESULTS: While the CA, MNE and SHA were reduced in the drug fed series as compared to their respective controls, the MI showed an apparent increase. The combined pre- and post-feeding of Cad Sulph showed maximum reduction of the genotoxic effects. CONCLUSIONS: Both Cad Sulph-30 and 200 were able to combat cadmium induced genotoxic effects in mice and that combined pre- and post-feeding mode of administration was found to be most effective in reducing the genotoxic effect of CdCl(2) followed by the post-feeding mode