Kristian Edlund

The potential of Economic MPC for power management

Economic Model Predictive Control is a receding horizon controller that minimizes an economic objective function rather than a weighted least squares objective function as in Model Predictive Control (MPC). We use Economic MPC to operate a portfolio of power generators and consumers such that the cost of producing the required power is minimized. The power generators are controllable power generators such as combined heat and power generators (CHP), coal and gas fired power generators, as well as a significant share of uncontrollable power generators such as parks of wind turbines. In addition, some of the power consumers are controllable. In this paper, the controllable power consumers are exemplified by large cold rooms or aggregations of super markets with refrigeration systems. We formulate the Economic MPC as a linear program. By simulation, we demonstrate the performance of Economic MPC for a small conceptual example.

A taxonomy for modeling flexibility and a computationally efficient algorithm for dispatch in Smart Grids

The word flexibility is central to Smart Grid literature, but to this day a formal definition of flexibility is still pending. This paper present a taxonomy for modeling flexibility in Smart Grids, denoted Buckets, Batteries and Bakeries. We consider a direct control Virtual Power Plant (VPP), which is given the task of servicing a portfolio of flexible consumers by use of a fluctuating power supply. Based on the developed taxonomy we first prove that no causal optimal dispatch strategies exist for the considered problem. We then present two heuristic algorithms for solving the balancing task: Predictive Balancing and Agile Balancing. Predictive Balancing, is a traditional moving horizon algorithm, where power is dispatched based on perfect predictions of the power supply. Agile Balancing, on the other hand, is strictly non-predictive. It is, however, explicitly designed to exploit the heterogeneity of the flexible consumers. Simulation results show that in spite of being non-predictive Agile Balancing can actually out-perform Predictive Balancing even when Predictive Balancing has perfect prediction over a relatively long horizon. This is due to the flexibility-synergy-effects, which Agile Balancing generates. As a further advantage it is demonstrated, that Agile Balancing is extremely computationally efficient since it is based on sorting rather than linear programming.

Introducing Model Predictive Control for Improving Power Plant Portfolio Performance

Abstract This paper introduces a model predictive control (MPC) approach to construction of a controller for balancing power generation against consumption in a power system. The objective of the controller is to coordinate a portfolio consisting of multiple power plant units in an effort to perform reference tracking and disturbance rejection in an economically optimal way. The performance function is chosen as a mixture of the l 1 -norm and a linear weighting to model the economics of the system. Simulations show a significant improvement of the performance of the MPC compared to the current implementation consisting of a distributed PI controller structure, both in terms of minimising the overall cost but also in terms of the ability to minimise deviation, which is the classical objective.

Intraday Trading of Wind Energy

In this paper, we tackle the problem of a wind power producer participating in a short-term electricity market that allows for the continuous, but potentially illiquid, intraday trading of energy. Considering the realistic case of a wind farm operating in the western Danish price area of Nord Pool, we build a simple but effective algorithm for the wind power producer to fully benefit from the Elbas intraday market. We then investigate the sensitivity of the obtained benefits to the maximum volume of energy the wind power producer is willing to trade in the intraday market, the ultimate aim of the trade (either to decrease energy imbalances or to increase profits) and to the installed capacity of the wind farm. Our numerical results reveal that the wind power producer can substantially increase his revenues by partaking in the intraday market but with diminishing returns to scale-a result that we attribute to the low liquidity of Elbas.

On Propagating Requirements and Selecting Fuels for a Benson Boiler

In this paper, the problem of optimal choice of sensors and actuators is addressed. Given a functional encapsulating information of the desired performance and production economy the objective is to choose a control instrumentation from a given set to comply with its minimum. The objective of the work is twofold: reformulation of the business objectives into mathematical terms and providing solution to the given optimization. Commonly, there exist overall business objectives which dictate how a plant should be instrumented and operated either directly or indirectly. The work shows how to propagate a global objective to local subsystems. Particular focus is on a boiler in a power plant operated by DONG Energy - a danish energy supplier. The business objectives have been propagated to the actuator level to allow for selection of an actuator configuration.

A primal-dual interior-point linear programming algorithm for MPC

Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm is implemented in Matlab and its performance is compared to an active set based LP solver and linprog in Matlabs optimization toolbox. Simulations demonstrate that the new algorithm is more than one magnitude faster than the other LP algorithms applied to this problem.

Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem

We consider a virtual power plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the discrete virtual power plant dispatch problem (DVPPDP). First, the nondeterministic polynomial time (NP)-completeness of the discrete virtual power plant dispatch problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms hill climber and greedy randomized adaptive search procedure (GRASP). The algorithms are tuned and tested on portfolios of varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of \(10^{5}\) units) at computation times on the scale of just 10 s, which is far beyond the capabilities of the optimal algorithms we have tested. In particular, GRASP sorted shows with the most promising performance, as it is able to find solutions that are both agile (sorted) and well balanced, and consistently yields the best numerical performance among the developed algorithms.

Market integration of Virtual Power Plants

We consider a direct control Virtual Power Plant, which is given the task of maximizing the profit of a portfolio of flexible consumers by trading flexibility in Energy and Power Markets. Spot price optimization has been quite intensively researched in Smart Grid literature lately. In this work, however, we develop a three stage market model, which includes Day-Ahead (Spot), Intra-Day and Regulating Power Markets. This allows us to test the hypothesis that the Virtual Power Plant can generate additional profit by trading across several markets. We find that even though profits do increase as more markets are penetrated, the size of the profit is strongly dependent on the type of flexibility considered. We also find that penetrating several markets makes profits surprisingly robust to spot price prediction errors.

Economic MPC for Power Management in the SmartGrid

Abstract To increase the amount of green energy (e.g. solar and wind) significantly a new intelligent electrical infrastructure is needed. We must not only control the production of electricity but also the consumption in an efficient and proactive manner. This future intelligent grid is in Europe known as the SmartGrid. In this paper we demonstrate the use of Economic Model Predictive Control to operate a portfolio of power generators and consumers such that the cost of producing the required power is minimized. With conventional coal and gas fired power generators representing the controllable power production and a significant share of renewable energy, such as parks of wind turbines, representing the uncontrollable power generators we have demonstrated how the addition of controllable consumers, such as large cold rooms or supermarkets with a thermal capacity, can infuse the desired flexibility of the grid for utilization of more green energy and also lower the total cost. We formulate the supply-demand constraint as a probabilistic constraint, thereby robustifying the solution against uncertainties in power demand. We use small conceptual examples for simulations.

A riccati based homogeneous and self-dual interior-point method for linear economic model predictive control

In this paper, we develop an efficient interior-point method (IPM) for the linear programs arising in economic model predictive control of linear systems. The novelty of our algorithm is that it combines a homogeneous and self-dual model, and a specialized Riccati iteration procedure. We test the algorithm in a conceptual study of power systems management. Simulations show that in comparison to state of the art software implementation of IPMs, our method is significantly faster and scales in a favourable way.