Joseph Warrington

Dynamic Vehicle Redistribution and Online Price Incentives in Shared Mobility Systems

This paper considers the efficient operation of shared mobility systems via the combination of intelligent routing decisions for staff-based vehicle redistribution and real-time price incentives for customers. The approach is applied to Londons Barclays Cycle Hire scheme, which the authors have simulated based on historical data. Using model-based predictive control principles, dynamically varying rewards are computed and offered to customers carrying out journeys, based on the current and predicted state of the system. The aim is to encourage them to park bicycles at nearby underused stations, thereby reducing the expected cost of redistributing them using dedicated staff. In parallel, routing directions for redistribution staff are periodically recomputed using a model-based heuristic. It is shown that it is possible to trade off reward payouts to customers against the cost of hiring staff to redistribute bicycles, in order to minimize operating costs for a given desired service level.

Policy-Based Reserves for Power Systems

This paper introduces the concept of affine reserve policies for accommodating large, fluctuating renewable in feeds in power systems. The approach uses robust optimization with recourse to determine operating rules for power system entities such as generators and storage units. These rules, or policies, establish several hours in advance how these entities are to respond to errors in the prediction of loads and renewable infeeds once their values are discovered. Affine policies consist of a nominal power schedule plus a series of planned linear modifications that depend on the prediction errors that will become known at future times. We describe how to choose optimal affine policies that respect the power network constraints, namely matching supply and demand, respecting transmission line ratings, and the local operating limits of power system entities, for all realizations of the prediction errors. Crucially, these policies are time-coupled, exploiting the spatial and temporal correlation of these prediction errors. Affine policies are compared with existing reserve operation under standard modeling assumptions, and operating cost reductions are reported for a multi-day benchmark study featuring a poorly-predicted wind infeed. Efficient prices for such “policy-based reserves” are derived, and we propose new reserve products that could be traded on electricity markets.

Stochastic optimal power flow based on convex approximations of chance constraints

This paper presents a computationally-efficient approach for solving stochastic, multiperiod optimal power flow problems. The objective is to determine power schedules for controllable devices in a power network, such as generators, storage, and curtailable loads, which minimize expected short-term operating costs under various device and network constraints. These schedules include planned power output adjustments, or reserve policies, which track errors in the forecast of power requirements as they are revealed, and which may be time-coupled. Such an approach has previously been shown to be an attractive means of accommodating uncertainty arising from highly variable renewable energy sources. Given a probabilistic forecast describing the spatio-temporal variations and dependencies of forecast errors, we formulate a family of stochastic network and device constraints based on convex relaxations of chance constraints, and show that these allow economic efficiency and system security to be traded off with varying levels of conservativeness. The results are illustrated using a simple case study, in which conventional generators plan schedules around an uncertain but time-correlated wind power injection.

Robust reserve operation in power systems using affine policies

A new scheme is presented for operating electrical reserves in constrained power systems in the face of a large uncertain future wind infeed. The approach uses robust optimization with linear decision rules to determine, via a constrained convex optimization, how power system entities such as generators and storage units should act on prediction errors once they become known. These rules are specified such that the power network constraints, namely matching supply and demand, respecting transmission line ratings, and the operating limits of individual power system entities, are satisfied for all possible realizations of the prediction error. The error is assumed to be bounded and may be correlated spatially and/or temporally. The decision rules are demonstrated and compared with simpler modes of reserve operation, and cost reductions are reported. Efficient prices for such “policy-based reserves” are derived, and it is concluded that they are of particular interest to grids where both a large wind infeed and a large storage capacity are present.

Predictive power dispatch through negotiated locational pricing

A predictive mechanism is proposed in order to reduce price volatility linked to large fluctuations from demand and renewable energy generation in competitive electricity markets. The market participants are modelled as price-elastic units, price-inelastic units, and storage operators. The distributed control algorithm determines prices over a time horizon through a negotiation procedure in order to maximize social welfare while satisfying network constraints. A simple flow allocation method is used to assign responsibility for constraint violations on the network to individual units and a control rule is then used to adjust nodal prices accordingly. Such a framework is appropriate for the inclusion of aggregated household appliances or other ‘virtual’ market participants realized through smart grid infrastructure. Results are examined in detail for a 4-bus network and then success is demonstrated for a densely-populated 39-bus network. Formal convergence requirements are given under a restricted subset of the demonstrated conditions. The scheme is shown to allow storage to reduce price volatility in the presence of fluctuating demand.

Rolling Unit Commitment and Dispatch With Multi-Stage Recourse Policies for Heterogeneous Devices

We present a rolling decision-making process for electrical power systems, in which unit commitment, dispatch and reserve policies are co-optimized in order to minimize expected short-run operating costs in the presence of uncertainty arising from demand and renewable infeeds. The uncertainty is assumed to be bounded, with estimated first and second moment statistics available. The rolling “look-ahead” process employs a planning horizon of several hours, with re-optimization taking place each time the first step has been implemented. We present an expected-cost formulation incorporating multi-stage recourse on continuous decision variables-plans for adjusting the dispatch in the light of future information to be discovered at each stage of the optimization horizon. The generic formulation allows the flexibility of devices such as energy storage units to be exploited in the reserve mechanism. We demonstrate using closed-loop numerical tests that significant reductions in the cost of accommodating uncertainty are attainable relative to a time-decoupled reserve mechanism. In contrast to previous results, we show that a time-coupled cost function is not required for this benefit to be observed. In addition, we show that relaxing binary unit commitment decisions after the first step of the horizon brings significant computational speed-ups, and in some cases also reduce closed-loop system operation costs.

Negotiated predictive dispatch: Receding horizon nodal electricity pricing for wind integration

Rapid wind fluctuations make the systematic operation of electricity markets with high wind power penetration difficult. A novel dynamic pricing mechanism is presented, which uses a receding horizon principle to allow forecasts of wind power and demand to be incorporated as soon as they are available, and is shown to be capable of reducing dispatch costs on the hours timescale in volatile wind conditions. Incorporating a time horizon is shown to allow market participants to plan generator ramping decisions and storage operation better than when prices are set in a decoupled manner for sequential time steps. The scheme repeatedly updates proposed prices based on the degree to which the corresponding power outputs planned by the market participants violate constraints on the transmission network. The schemes operating rules, based on the theory of Lagrangian relaxation, are presented algorithmically. Results are demonstrated on a 39 bus network modified to include a large quantity of wind power, as well as conventional generators, loads, and storage.

Optimal transmission line switching for large-scale power systems using the Alternating Direction Method of Multipliers

It is known that in some cases, switching some transmission lines of an electric power system off may improve the optimal economic dispatch cost. This modification of the economic dispatch problem is known as optimal transmission line switching. Unfortunately, the modified problem involves binary decision variables which make the problem difficult to solve for large-scale power systems. This paper presents a method that scales well for large power systems, based on a decomposition approach known as the Alternating Direction Method of Multipliers (ADMM). The problem is broken into a convex component and a series of binary rounding operations, coupled via a penalty function. The output of the ADMM algorithm is post-processed in order to obtain a near-optimal solution to the original problem at relatively low computational cost. We measure the ADMM solution against a convex relaxation of the original problem, thereby certifying its quality without needing to solve the original combinatorial problem. The method is illustrated using the Polish 2383-bus test system.

Rule-based price control for bike sharing systems

The recent increase in popularity of shared mobility systems, in which users take a bicycle or car from a geographically-dispersed public pool in order to complete part of a journey, is due in part to improved technologies for tracking and billing customer journeys. In many schemes, a customer can start and end a journey at different docking stations and is billed according to a set fee structure. However, a given system generally becomes imbalanced due to asymmetry of demand for such “one-way” services across the system and throughout the day, and the resulting cost of employing staff to redistribute the systems vehicles is significant. This paper describes how dynamic customer prices, varying geographically as a function of the current and expected future state of the system, could be used as control signals to improve service rates. Such signals could be communicated to customers using existing ICT infrastructure. We show, using an agent-based model parameterized with historical data from Londons Barclays Cycle Hire scheme, that simple proportional price control rules can improve service rates without the need to resort to conventional bike redistribution staff. In addition we analyze the performance obtained and discuss system design issues.

Optimal unit commitment accounting for robust affine reserve policies

We describe a new approach to robust unit commitment for an electricity network, which couples the switching decisions to a set of time-coupled redispatch rules in order to minimize the expected cost of operation over a planning horizon. We assume bounded uncertainties arising from imperfect predictions of loads and intermittent renewable infeeds. We refer to the time-coupled redispatch rules as affine reserve policies, and they apply not only to generators but to other continuously-controllable devices such as energy storage units or demand response installations, which are modelled as generic mixed logical-dynamical systems. We use a lumped-parameter example to demonstrate that unit commitment decisions coupled with affine reserve policies can reduce the number of time periods in which expensive peaking plants need to be employed, and that the effect is present for a wide range of parameter values. An important benefit is that the approach allows the uncertainty of future energy storage levels to be managed more tightly than existing formulations would allow.