Special issue on “Optimal design and operation of energy systems”

In the attempt to tackle the issue of climate change, governments across the world have agreed to set global carbon reduction targets. [...]

State Transition Tensors for Continuous-Thrust Control of Three-Body Relative Motion

Overview of Canada's energy storage related research activities: A perspective

Accurate solution of differential-algebraic optimization problems

Practical Methods for Optimal Control using Nonlinear Programming

This work is concerned with the maximum principles for optimal control problems governed by 3-dimensional Navier--Stokes equations. Some types of state constraints (time variables) are considered.

Process engineers routinely use optimization in designing and operating complex systems as a means to improve their performance. Optimization has thus become a major enabling area over the years, where it has evolved from a methodology of academic interest into a technology that has and continues to make a significant impact on industry. To date, most rigorous optimization implementations have been for the design and operation of lumped systems using steady-state simulation and optimization technologies. However, a majority of natural as well as industrial systems either are inherently transient, have important transients between steady-state phases, and/or are spatially distributed. Interest in dynamic optimization and optimal control of process systems has grown significantly over the last few decades and much progress has been achieved in solution strategies. Despite its great potential, however, seldom has this technology made an impact on the process industry sector yet. Its implementation does not come without a cost. It requires a thorough understanding of the underlying phenomena, which is hardly compatible with the limited effort and time that can usually be spent for modeling. Moreover, a high level of expertise is still needed for the solution of optimal control problems (OCPs), which is itself a consequence of the lack of sufficiently fast and reliable numerical solution techniques. In this special issue of Optimal Control Applications and Methods, we have provided a selection of articles that address some of these issues and apply advanced techniques for the optimal operation, control and estimation of complex process systems. Bonilla et al. [1] propose a new method for solving nonconvex OCPs. Their method relies on a homotopy-based approach, whereby the original nonconvex OCP is gradually transformed into a simpler convex OCP by varying an homotopy parameter. A special structure is assumed for the nonconvex OCP, namely the dynamic system is control-affine and the cost function penalizes deviations from a given reference trajectory, which makes the method well suited for model predictive control (MPC) applications. They demonstrate their methodology on two case studies, a simple parameter estimation problem and the optimal control of an isothermal chemical reactor with Van de Vusse reactions and input multiplicities. They find that the likelihood of finding a global solution to the original nonconvex OCP is greatly improved compared to standard local optimization techniques. The paper by Aliyev and Gatzke [2] presents a nonlinear MPC formulation with prioritized constraint handling. This formulation is particularly relevant for control problems that have relatively limited degrees of freedom compared to the number of control objectives of interest. It ensures that the constrained optimization problem remains feasible at each MPC execution. They develop an implementation of prioritized MPC that is computationally efficient. A closed-loop test on multivariate refinery facility simulation with significant nonlinearity and input multiplicity is investigated. Because first principles’ models are difficult to obtain for such processes, second-order

Optimal HVAC Control as Demand Response with On-site Energy Storage and Generation System

Electric-thermal energy storage using solid particles as storage media

In this article, we study an abstract constrained optimization problem that appears commonly in the optimal control of linear partial differential equations. The main emphasis of the present study is on the case when the ordering cone for the optimization problem has an empty interior. To circumvent this major difficulty, we propose a new conical regularization approach in which the main idea is to replace the ordering cone by a family of dilating cones. We devise a general regularization approach and use it to give a detailed convergence analysis for the conical regularization as well as a related regularization approach. We showed that the conical regularization approach leads to a family of optimization problems that admit regular multipliers. The approach remains valid in the setting of general Hilbert spaces and it does not require any sort of compactness or positivity condition on the operators involved. One of the main advantages of the approach is that it is amenable for numerical computations. We consider four different examples, two of them elliptic control problems with state constraints, and present numerical results that completely support our theoretical results and confirm the numerical feasibility of our approach. The motivation for the conical regularization is to overcome the difficulties associated with the lack of Slater's type constraint qualification, which is a common hurdle in numerous branches of applied mathematics including optimal control, inverse problems, vector optimization, set-valued optimization, sensitivity analysis, variational inequalities, among others.

In general, optimal control problems rely on numerically rather than analytically solving methods, due to their nonlinearities. The direct method, one of the numerically solving methods, is mainly to transform the optimal control problem into a nonlinear optimization problem with finite dimensions, via discretizing the objective functional and the forced dynamical equations directly. However, in the procedure of the direct method, the classical discretizations of the forced equations will reduce or affect the accuracy of the resulting optimization problem as well as the discrete optimal control. In view of this fact, more accurate and efficient numerical algorithms should be employed to approximate the forced dynamical equations. As verified, the discrete variational difference schemes for forced Birkhoffian systems exhibit excellent numerical behaviors in terms of high accuracy, long-time stability and precise energy prediction. Thus, the forced dynamical equations in optimal control problems, after being represented as forced Birkhoffian equations, can be discretized according to the discrete variational difference schemes for forced Birkhoffian systems. Compared with the method of employing traditional difference schemes to discretize the forced dynamical equations, this way yields faithful nonlinear optimization problems and consequently gives accurate and efficient discrete optimal control. Subsequently, in the paper we are to apply the proposed method of numerically solving optimal control problems to the rendezvous and docking problem of spacecrafts. First, we make a reasonable simplification, i.e., the rendezvous and docking process of two spacecrafts is reduced to the problem of optimally transferring the chaser spacecraft with a continuously acting force from one circular orbit around the Earth to another one. During this transfer, the goal is to minimize the control effort. Second, the dynamical equations of the chaser spacecraft are represented as the form of the forced Birkhoffian equation. Then in this case, the discrete variational difference scheme for forced Birkhoffian system can be employed to discretize the chaser spacecraft's equations of motion. With further discretizing the control effort and the boundary conditions, the resulting nonlinear optimization problem is obtained. Finally, the optimization problem is solved directly by the nonlinear programming method and then the discrete optimal control is achieved. The obtained optimal control is efficient enough to realize the rendezvous and docking process, even though it is only an approximation of the continuous one. Simulation results fully verify the efficiency of the proposed method for numerically solving optimal control problems, if the fact that the time step is chosen to be very large to limit the dimension of the optimization problem is noted.

Integrating renewable energy and energy storage systems provides a way of operating the electrical grid system more energy efficiently and stably. Thermal storage and batteries are the most common devices for integration. One approach to integrating thermal storage on site is to use ice in combination with the cooling system. The use of ice storage can enable a change in the time variation of electrical usage for cooling in response to variations in PV availability, utility prices, and cooling requirements.A number of studies can be found in the literature that address optimal operation of onsite PV systems with batteries or ice storage. However, although it is a natural and practical question, it is not clear which integrated storage system performs better in terms of overall economics. Ice storage has low initial and maintenance costs, but there is an efficiency penalty for charging of storage and it can only shift electrical loads associated with building cooling requirements. A battery’s round-trip efficiency,on the other hand, is quite consistent and batteries can be used to shift both HVAC and non-HVAC loads. However, batteries have greater initial costs and a significantly shorter life. This research presents a tool and provides a case study for comparing life-cycle economics of battery and ice storage systems for a commercial building that has chillers for cooling and an on-site photovoltaic system. A model predictive control algorithm was developed and implemented in simulation for the two systems in order to compare optimal costs. The effect of ice storage and battery sizing were studied in order to determine the best storage sizes from an economic perspective and to provide a fair comparison

A numerical method for an optimal control problem with minimum sensitivity on coefficient variation

As global energy demand and warming increase, there is a need to transition to sustainable and renewable energy sources. Integrating different systems to create a hybrid renewable system enhances the overall adoption and deployment of renewable energy resources. Given the intermittent nature of solar and wind, energy storage systems are combined with these renewable energy sources, to optimize the quantity of clean energy used. Thus, various optimization strategies have been developed for the integration and operation of these hybrid renewable energy systems. Existing studies have either reviewed hybrid renewable energy systems or energy storage systems, however, these studies ignored energy storage systems integrated with hybrid renewable energy systems. This study offers a comprehensive analysis of the optimization methods used in hybrid renewable energy systems (HRES) integrated with energy storage systems (ESS). We examined the optimization models used in the integration of HRES and ESS, their objectives, and the common constraints. Based on our review, capacity and CO2 emissions constraints were frequently used in hybrid optimization techniques that are effective approaches for integrating HRES and ESS. This research supports the move towards sustainable, clean energy solutions by combining an analysis of energy storage techniques with the optimization of hybrid renewable energy systems.

Techno-economic analysis of long-duration energy storage and flexible power generation technologies to support high-variable renewable energy grids