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This article presents a Real-Time Iteration (RTI) scheme for distributed Nonlinear Model Predictive Control (NMPC). The scheme transfers the well-known RTI approach, a key enabler for many industrial real-time NMPC implementations, to the setting of cooperative distributed control. At each sampling instant, one outer iteration of a bi-level decentralized Sequential Quadratic Programming (dSQP) method is applied to a centralized optimal control croblem. This ensures that real-time requirements are met and it facilitates cooperation between subsystems. Combining novel dSQP convergence results with RTI stability guarantees, we prove local exponential stability under standard assumptions on the MPC design with and without terminal constraints. The proposed scheme only requires neighbor-to-neighbor communication and avoids a central coordinator. A numerical example with coupled inverted pendulums demonstrates the efficacy of the approach.

This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems with non-convex constraints. Moreover, our method exhibits a small communication footprint and it achieves a comparably high solution accuracy with a limited number of iterations, whereby the local subproblems are of low computational complexity. We illustrate the performance of the proposed method on a problem from energy systems, i.e., we consider an optimal power flow problem with 708 buses.

Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In applications, these schemes, however, often require solving large-scale optimization problems. Iterative techniques from distributed optimization are frequently proposed for complexity reduction. Yet, they achieve feasibility only asymptotically, which induces a substantial computational burden. This work presents an approximate dynamic programming scheme, which is guaranteed to deliver a feasible solution in "one shot", i.e., in one backward-forward iteration over all subproblems provided they are coupled by a tree structure. Our proposed scheme generalizes methods from seemingly disconnected domains such as power systems and optimal control. We demonstrate its efficacy for problems with nonconvex constraints via numerical examples from both domains.

The real-time operation of large-scale infrastructure networks requires scalable optimization capabilities. Decomposition schemes can help achieve scalability; classical decomposition approaches such as the alternating direction method of multipliers (ADMM) and distributed Newtons schemes, however, often either suffer from slow convergence or might require high degrees of communication. In this work, we present new primal decomposition schemes for solving large-scale, strongly convex QPs. These approaches have global convergence guarantees and require limited communication. We benchmark their performance against the off-the-shelf interior-point method Ipopt and against ADMM on infrastructure networks that contain up to 300,000 decision variables and constraints. Overall, we find that the proposed approaches solve problems as fast as Ipopt but with reduced communication. Moreover, we find that the proposed schemes achieve higher accuracy than ADMM approaches.

Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.

This paper is about computationally tractable methods for power system parameter estimation and Optimal Experiment Design (OED). Here, the main motivation is that OED has the potential to significantly increase the accuracy of power system parameter estimates, for example, if only a few batches of data are available. The problem is, however, that solving the exact OED problem for larger power grids turns out to be computationally expensive and, in many cases, even computationally intractable. Therefore, the present paper proposes three numerical approximation techniques, which increase the computational tractability of OED for power systems. These approximation techniques are bench-marked on a 5-bus and a 14-bus case studies.

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we apply data-driven predictive control to a discrete-time descriptor model obtained by discretization of the power-swing equations for a nine-bus system. Our results shows the efficacy of the proposed control scheme and they underpin the prospect of the data-driven framework for control of descriptor systems.

Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems with non-convex constraints for which classical decentralized optimization algorithms lack convergence guarantees. Moreover, classical decentralized algorithms usually exhibit only linear convergence. This paper presents an essentially decentralized primal-dual interior point method with convergence guarantees for non-convex problems at a superlinear rate. We show that the proposed method works reliably on a numerical example from power systems. Our results indicate that the proposed method outperforms ADMM in terms of computation time and computational complexity of the subproblems.

This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal feasibility of the iterates. Numerical results show that the proposed method can compete with the alternating direction method of multipliers in terms of communication requirements for a chain of masses example.

Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms, however, typically exhibit asymptotic convergence at a linear rate. This note proposes an essentially decentralized variant of the Conjugate Gradient algorithm (d-CG). The proposed method exhibits a practical superlinear convergence rate and comes with a priori computable finite-step convergence guarantees. In contrast to previous works, we consider sum-wise decomposition instead of row-wise decomposition which enables application in multi-agent settings. We illustrate the performance of d-CG on problems from sensor fusion and compare the results to the widely-used Alternating Direction Method of Multipliers.

Solving the power flow problem in a distributed fashion empowers different grid operators to compute the overall grid state without having to share grid models-this is a practical problem to which industry does not have off-the-shelf answers. In cooperation with a German transmission system operator we propose two physically consistent problem formulations (feasibility, least-squares) amenable to two solution methods from distributed optimization (the Alternating direction method of multipliers (ADMM), and the Augmented Lagrangian based Alternating Direction Inexact Newton method (Aladin)); with Aladin there come convergence guarantees for the distributed power flow problem. In addition, we provide open source matlab code for rapid prototyping for distributed power flow (rapidPF), a fully matpower-compatible software that facilitates the laborious task of formulating power flow problems as distributed optimization problems; the code is available under https://github.com/KIT-IAI/rapidPF/. The approach to solving distributed power flow problems that we present is flexible, modular, consistent, and reproducible. Simulation results for systems ranging from 53 buses (with 3 regions) up to 4662 buses (with 5 regions) show that the least-squares formulation solved with aladin requires just about half a dozen coordinating steps before the power flow problem is solved., Comment: 35 pages, 6 figures, 7 tables, journal submission

The integration of renewables into electrical grids calls for optimization-based control schemes requiring reliable grid models. Classically, parameter estimation and optimization-based control is often decoupled, which leads to high system operation cost in the estimation procedure. The present work proposes a method for simultaneously minimizing grid operation cost and optimally estimating line parameters based on methods for the optimal design of experiments. This method leads to a substantial reduction in cost for optimal estimation and in higher accuracy in the parameters compared with standard Optimal Power Flow and maximum-likelihood estimation. We illustrate the performance of the proposed method on a benchmark system.

Due to their large power draws and increasing adoption rates, electric vehicles (EVs) will become a significant challenge for electric distribution grids. However, with proper charging control strategies, the challenge can be mitigated without the need for expensive grid reinforcements. This manuscript presents and analyzes new distributed charging control methods to coordinate EV charging under nonlinear transformer temperature ratings. Specifically, we assess the trade-offs between required data communications, computational efficiency, and optimality guarantees for different control strategies based on a convex relaxation of the underlying nonlinear transformer temperature dynamics. Classical distributed control methods such as those based on dual decomposition and alternating direction method of multipliers (ADMM) are compared against the new Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) method and a novel low-information, look-ahead version of packetized energy management (PEM). These algorithms are implemented and analyzed for two case studies on residential and commercial EV fleets. Simulation results validate the new methods and provide insights into key trade-offs., Comment: 15 pages, 9 figures, journal

This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-$\alpha$. ALADIN-$\alpha$ is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Its user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-$\alpha$.

The integration of renewables into electrical grids calls for the development of tailored control schemes which in turn require reliable grid models. In many cases, the grid topology is known but the actual parameters are not exactly known. This paper proposes a new approach for online parameter estimation in power systems based on optimal experimental design using multiple measurement snapshots. In contrast to conventional methods, our method computes optimal excitations extracting the maximum information in each estimation step to accelerate convergence. The performance of the proposed method is illustrated on a case study.

This paper investigates the role of feasible initial guesses and large consensus-violation penalization in distributed optimization for Optimal Power Flow (OPF) problems. Specifically, we discuss the behavior of the Alternating Direction of Multipliers Method (ADMM). We show that in case of large consensus-violation penalization ADMM might exhibit slow progress. We support this observation by an analysis of the algorithmic properties of ADMM. Furthermore, we illustrate our findings considering the IEEE 57 bus system and we draw upon a comparison of ADMM and the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method.

Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems. In case of constrained non-convex optimization only a few algorithms are currently are available; often their performance is limited, or they lack convergence guarantees. This paper proposes a framework for decentralized non-convex optimization via bi-level distribution of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Bi-level distribution means that the outer ALADIN structure is combined with an inner distribution/decentralization level solving a condensed variant of ALADIN's convex coordination QP by decentralized algorithms. We prove sufficient conditions ensuring local convergence while allowing for inexact decentralized/distributed solutions of the coordination QP. Moreover, we show how a decentralized variant of conjugate gradient or decentralized ADMM schemes can be employed at the inner level. We draw upon case studies from power systems and robotics to illustrate the performance of the proposed framework.

This paper proposes a structure exploiting algorithm for solving non-convex power system state estimation problems in distributed fashion. Because the power flow equations in large electrical grid networks are non-convex equality constraints, we develop a tailored state estimator based on Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method, which can handle the nonlinearities efficiently. Here, our focus is on using Gauss-Newton Hessian approximations within ALADIN in order to arrive at at an efficient (computationally and communicationally) variant of ALADIN for network maximum likelihood estimation problems. Analyzing the IEEE 30-Bus system we illustrate how the proposed algorithm can be used to solve highly non-trivial network state estimation problems. We also compare the method with existing distributed parameter estimation codes in order to illustrate its performance.

Recently there has been considerable progress on the analysis of stability and performance properties of so-called economic Nonlinear Model Predictive Control (NMPC) schemes; i.e. NMPC schemes employing stage costs that are not directly related to distance measures of pre-computed setpoints. At the same time, with respect to the energy transition, the use of NMPC schemes is proposed and investigated in a plethora of papers in different contexts. For example receding-horizon approaches to generator dispatch problems, which is also known as multi-stage Optimal Power Flow (OPF), naturally lead to economic NMPC schemes based on non-convex discrete-time Optimal Control Problems (OCP). The present paper investigates the transfer of analytic results available for general economic NMPC schemes to receding-horizon multistage OPF. We propose a blueprint formulation of multi-stage opf including AC power flow equations. Based on this formulation we present results on the dissipativity and recursive feasibility properties of the underlying OCP. Finally, we draw upon simulations using a 5 bus system and a 118 bus system to illustrate our findings.

The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage-problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community.

The present paper discusses the application of the recently proposed Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method to non-convex AC Optimal Power Flow Problems (OPF) in a distributed fashion. In contrast to the often used Alternating Direction of Multipliers Method (ADMM), ALADIN guarantees locally quadratic convergence for AC OPF. Numerical results for 5 to 300 bus test cases indicate that ALADIN is able to outperform ADMM and to reduce the number of iterations by about one order of magnitude. We compare ALADIN to numerical results for ADMM documented in the literature. The improved convergence speed comes at the cost of increasing the communication effort per iteration. Therefore, we propose a variant of ALADIN that uses inexact Hessians to reduce communication. Additionally, we provide a detailed comparison of these ALADIN variants to ADMM from an algorithmic and communication perspective. Moreover, we prove that ALADIN converges locally at quadratic rate even for the relevant case of suboptimally solved local NLPs.