Distributed Economic Model Predictive Control Research Articles

Virtually coupled train set control subject to space-time separation: A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a virtually coupled train set (VCTS) at a minimal but safe distance. To guarantee collision avoidance, the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the emergency braking (EB) trajectories of two successive units during the whole EB process. In this case, the minimal safety distance is usually numerically calculated without an analytic formulation. Thus, the constrained VCTS control problem is hard to address with space-time separation, which is still a gap in the existing literature. To solve this problem, we propose a distributed economic model predictive control (DEMPC) approach with computation efficiency and theoretical guarantee. Specifically, to alleviate the computation burden, we transform implicit safety constraints into explicitly linear ones, such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently. For theoretical analysis, sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC, employing compatibility constraints, tube techniques and terminal ingredient tuning. Moreover, we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS. Finally, experimental results demonstrate the performance and advantages of the proposed approaches.

Wind farm control using distributed economic MPC scheme under the influence of wake effect

As wind farms (WFs) expand in scale, there is a growing need for active power control to track the reference power benchmark issued by the grid dispatch center and also the imperative to reduce the fatigue load on key components of each wind turbine (WT). The presence of the wake effect causes a decrease in power generation for downstream WTs and an increase in the fatigue load. Consequently, the suppression of the wake effect has emerged as a critical control objective for WFs. For tackling the challenge, this article designs a hierarchical WF control framework. The upper-level controller employs a sequential convex programming (SCP) approach to maximize the WF's captured wind energy function and determine the optimal induction factors for the WTs. The lower-layer controller uses a distributed economic model predictive control (DEMPC) scheme to control the WT locally to achieve reference power tracking while reducing the fatigue load on each WT. Finally, the effectiveness of the designed algorithm was verified by conducting the simulation on a wind farm containing nine WTs.

A distributed economic model predictive control-based FPPT scheme for large-scale solar farm

Increasing solar-photovoltaic-power penetration necessitates the implementation of flexible power point tracking (FPPT) in solar farms. However, coordinating multiple solar photovoltaic (PV) power generation systems (SPVPGSs) poses a significant challenge due to their inherent intermittency and varying dynamic characteristics, complicating FPPT implementation. To overcome this challenge, this paper proposes a distributed economic model predictive control (DEMPC) scheme to achieve FPPT, while simultaneously enhancing overall economic performance in solar farms. By integrating solar farm control and local control into one optimal control framework, this scheme eliminates the need for power allocation, PV voltage reference calculation, and pulse width modulation. Leveraging the SPVPGS model and soft power constraint, DEMPC controllers are designed to achieve the economic targets of solar farms, which cooperate through a communication network to realize FPPT and economic optimization. Additionally, the strong nonlinearity of SPVPGS causes a non-convex mixed integer nonlinear programming (MINLP) problem, solved by a MINLP algorithm using finite converter switching states. Simulations under step-changed irradiance and power reference, as well as urgent maintenance conditions, demonstrate that the DEMPC-based FPPT scheme significantly outperforms the traditional hierarchical model predictive control-based FPPT scheme, presenting both superior dynamic response and enhanced economic performance in FPPT implementation.

PV/Hydrogen DC microgrid control using distributed economic model predictive control

The integration of hydrogen energy into a photovoltaic-dominated microgrid is now becoming a promising approach to improve the photoconversion efficiency and enhance the operating reliability. However, the energy management and power regulation of the Photovoltaic/Hydrogen DC microgrid face challenges due to the intermittency of photovoltaic (PV) power generation and the randomness of load. In this paper, a distributed economic model predictive control (DEMPC) scheme is developed for a PV/Hydrogen DC microgrid, which integrates the energy management, economic optimization, and power regulation into one optimal control framework. Based on the developed distributed converter-based mathematical model, three local controllers are designed to achieve the economic targets of PV subsystem, alkaline electrolyzer subsystem, and proton exchange membrane fuel cell subsystem respectively, which cooperate with each other through the communication network to realize the power supply–demand balance, DC bus voltage stability, and economic optimization. A mixed integer nonlinear programming algorithm utilizing the finite converter switching states is embedded into the DEMPC to solve the non-convex local optimization problems efficiently. The effectiveness and superiority of the proposed DEMPC scheme are verified by simulations under varying irradiance and load conditions, indicating that the DEMPC can achieve a comparable overall dynamic economic performance with a significantly reduced computation burden and power oscillation, compared to the centralized economic model predictive control (CEMPC).

Distributed economic predictive control of integrated energy systems for enhanced synergy and grid response: A decomposition and cooperation strategy

The close integration of increasing operating units into an integrated energy system (IES) results in complex interconnections between these units. The strong dynamic interactions create barriers to designing a successful distributed coordinated controller to achieve synergy between all the units and unlock the potential for grid response. To address these challenges, we introduce a directed graph representation of IESs using an augmented Jacobian matrix to depict their underlying dynamics topology. By utilizing this representation, a generic subsystem decomposition method is proposed to partition the entire IES vertically based on the dynamic time scale and horizontally based on the closeness of interconnections between the operating units. Exploiting the decomposed subsystems, we develop a cooperative distributed economic model predictive control (DEMPC) with multiple global objectives that regulate the generated power at the grid’s requests and satisfy the customers cooling and system economic requirements. In the DEMPC, multiple local decision-making agents cooperate sequentially and iteratively to leverage the potential across all the units for system-wide dynamic synergy. Furthermore, we discuss how subsystem decomposition impacts the design of distributed cooperation schemes for IESs and provide a control-oriented basic guideline on the optimal decomposition of complex energy systems. Extensive simulations demonstrate that the control strategies with different levels of decomposition and collaboration will lead to marked differences in the overall performance of the IES. The standard control scheme based on the proposed subsystem configuration outperforms the empirical decomposition-based control benchmark by about 20%. The DEMPC architecture further improves the overall performance of the IES by about 55% compared to the benchmark.

Approximate Dissipativity of Cost-Interconnected Systems in Distributed Economic MPC

We consider dissipativity properties of interconnected systems in the context of distributed economic model predictive control (MPC), with the subsystems being interconnected through their stage cost functions. The isolated subsystems, i.e., when neglecting the coupled portion of the individual stage costs, are assumed to be dissipative with respect to a specific supply rate related to their local stage cost function, which is commonly used in an economic MPC context. Based on these local dissipativity properties and the interconnection structure, a corresponding (approximate) dissipativity property for the overall system is inferred, which is structured and provides performance bounds for overall system operation. The resulting structured dissipativity property is exploited in the design and analysis of a distributed economic MPC algorithm. Numerical examples visualize the theoretical findings and the effectiveness of the proposed algorithm.

Low-order dynamical model and distributed coordinated model predictive control for multi-stage belt conveyor systems

This work studies a distributed economic model predictive control (DEMPC) approach for multi-stage belt conveyor (BC) systems based on a novel low-order model. First, the existing BC finite element dynamic model is reduced to a low-order model with five micro-element segments. In describing the speed and acceleration range of the BC, the low-order model is consistent with the original model. Then, a DEMPC method is proposed for multi-stage BC systems. In this method, the state information of the adjacent BCs is used to express the collaborative cost function for the local optimization control problem. By using the obtained method, the economic performance is improved, and the energy consumption is reduced. Finally, hardware-in-the-loop simulation tests are utilized to demonstrate the benefits of the results gained.

Fuel Economy Optimization for Platooning Vehicle Swarms via Distributed Economic Model Predictive Control

Cooperation among multiple connected vehicles (CVs) brings swarm intelligence to our transportation systems and helps improve their performance. This study proposes a fuel economy optimization approach for a platooning vehicle swarm via distributed economic model predictive control (DEMPC). Within the DEMPC framework, each CV shares its assumed trajectory in the predictive horizon with its neighboring CVs at each control loop. With its neighbors’ and its own assumed trajectories, each CV first solves an open-loop control optimization problem for platoon formation, and then solves an open-loop economic optimization problem for direct fuel economy improvement. In particular, the optimal cost of the former optimization problem is used in the latter one to build an upperbound constraint for stability guarantee. The asymptotic convergence of assumed terminal states is given in the analysis, and the recursive feasibility of the two optimization problems are proved with an explicit constraint on the weight matrices in the open-loop control optimization problem. Based on these analyses, the asymptotic stability of the closed-loop system is finally proved through Lyapunov analysis. Numerical simulation results validate the effectiveness of the proposed approach in terms of closed-loop stability and fuel economy improvement. Note to Practitioners—This work aims to optimize the fuel economy for a swarm of vehicles running in a platoon. Existing approaches on platoon control mainly focus on the accurate tracking of the following vehicles, but this may cause aggressive control and hence lead to poor fuel economy. Therefore, this paper proposes a distributed economic model predictive control approach to explicitly optimize the fuel consumption rate of each vehicle. The proposed method can improve fuel economy and reduce communication requirements and burdens for platooning vehicle swarms. The paper assumes no communication time delay and packet drops, so the impact of unreliable communication will be studied in the future work.

Multiobjective Platooning of Connected and Automated Vehicles Using Distributed Economic Model Predictive Control

This paper considers the multi-objective platooning control problem of a group of connected and automated vehicles (CAVs) with bidirectional topologies. A new distributed economic model predictive control (DEMPC) algorithm is presented to reconcile the conflict of the control objectives of tracking, safety, stability and fuel economy of the heterogeneous vehicle platoon with guaranteed string stability. Using transient engine energy efficiency indices and cooperative performance of tracking and string stability, two distributed receding horizon optimal control problems are orderly formulated by a Lyapunov-based coupling constraint. Moreover, a new concept of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -string stability is defined for the platoon with bidirectional topologies. Some distributed terminal conditions are then derived to guarantee the recursive feasibility and asymptotic stability of the DEMPC as well as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -string stability of the platoon in the presence of constraints. Compared to traditional platooning control, the new DEMPC has a 4.2% energy-saving of vehicles while achieving the cooperative tasks of the platoon in several simulation scenarios.

Intrusion-Detector-Dependent Distributed Economic Model Predictive Control for Load Frequency Regulation With PEVs Under Cyber Attacks

With the participation of a significant number of plug-in electric vehicles (PEVs), it is really challenging to achieve economic-effective in load frequency control (LFC) while sustaining satisfiable system performance. To tackle this challenge, a new distributed economic model predictive control (DEMPC) strategy is proposed for the LFC with the large-scale PEV participation. In the light of the vulnerability of LFC to false data injection (FDI) attacks, a model-based χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> intrusion detection unit is integrated with the proposed DEMPC. This model-based intrusion detection unit can not only monitor the FDI attacks, but also generate a model-based state prediction for the DEMPC once the data is identified as compromised. Then, an event-triggering mechanism is presented to reduce the computation and communication burdens of each area controller. Simulation studies of a four-area power system are conducted and the results validate the effectiveness of the proposed intrusion detection unit and event-triggering conditions for the DEMPC.

Robust distributed economic model predictive control based on differential dissipativity

AbstractIn this article, a robust distributed economic model predictive control (DEMPC) approach is developed for plant‐wide chemical processes. The proposed approach achieves arbitrary feasible setpoints that may vary frequently, attenuates the plant‐wide effects of unknown disturbances and minimizes a plant‐wide economic cost. In this approach, a plant‐wide process is represented as a network of process units and each process unit is controlled by an individual controller which shares a plant‐wide optimization economic objective and stability conditions through the network. To ensure the convergence of process variables to arbitrary setpoints, a contraction condition is developed for the DEMPC, based on the contraction theory. To deal with the effects of interactions among process units, the concept of dissipativity is adopted. Using sum‐separable control contraction metrics, a reference‐independent robust stability condition is developed to ensure the plant‐wide disturbance effects (under interactions among process units) to be attenuated in terms of differential ℒ2 gain and represented by a plant‐wide differential dissipativity condition, which is converted into the differential dissipativity conditions that individual controllers need to satisfy. This approach facilitates the optimization of plant‐wide economic costs with global constraints in a distributed way, allowing efficient implementation of alternating direction method of multipliers (ADMM). The proposed approach is illustrated using a reactor‐separator process.

Hierarchical smart energy management strategy based on cooperative distributed economic model predictive control for multi‐microgrids systems

Hierarchical smart energy management strategy based on cooperative distributed economic model predictive control for <scp>multi‐microgrids</scp> systems

Distributed economic MPC for LFC of multi-area power system with wind power plants in power market environment

The rising penetration of renewable energy and the diverse power transaction mechanisms in power market environment (PME) make the control problem of the power system more difficult. Considering environmental pressure and market competition pressure, it is more important to ensure the economic operation of power system in the control process. This paper presents a novel distributed economic model predictive control (DEMPC) strategy for the load frequency control (LFC) problem of a practical multi-area power system incorporating wind power plants (WPPs) in PME. Meanwhile, the real time economic optimization is achieved by integrating the economic factors into the objective function. A distribution company (DISCO) participation matrix (DPM) is applied to visualize the liberalization of power transactions between the DISCOs and dispatchable generation companies (DGENCOs). Area participation factors (apfs) are introduced to present the allocation of uncontracted load demands. The DEMPC controllers solve the optimization problem of power system with external disturbances and constraints including frequency fluctuation constraint, control input constraints, output power of WPP constraint and pitch angle constraint of the wind turbine. Response results for a three-area power system including WPPs and thermal power plants demonstrate the certain improvement of the system performance with the participation of wind turbines and the high-efficiency of the proposed DEMPC strategy.

A self-interested distributed economic model predictive control approach to battery energy storage networks

In this work, a dissipativity based distributed economic model predictive control (DEMPC) approach is developed for the operation of battery energy storage (BES) networks in residential microgrids. With the presence of a microgrid power market (MPM), control of the BES systems is formulated as a self-interested distributed control problem, as individual DEMPC controllers minimize their local economic cost functions based on the price prediction of MPM. Due to the intermittent nature of photovoltaic (PV) power generations and load demands, the DEMPC without proper coordination or constraints may lead to excessive energy trading and price oscillations in MPM. To solve this problem, dissipativity theory with dynamic supply rates is adopted in this paper to deal with the interactions between individual users and the MPM. The microgrid-wide performance requirement of attenuation of the net power fluctuations with respect to time-varying PV generation and demands, is converted into the dissipative trajectory constraints imposed on individual DEMPC controllers. The proposed approach is scalable as it does not require online iterative optimizations across the controller network. A case study is presented to illustrate the proposed method.

Distributed economic model predictive control with Safeness-Index based constraints for nonlinear systems

In this work, sequential and iterative distributed economic model predictive control (DEMPC) architectures are developed with constraints based on a metric (termed the Safeness Index) that is indicative of the safeness of operating a process at a given state in state-space. The DEMPC’s may have lower computation times than a centralized economic model predictive control (EMPC) design with Safeness Index-based constraints, without significantly limiting closed-loop economic performance, which enhances their practicality and ability to improve process operational safety. Sufficient conditions are derived under which the implementation strategies for the DEMPC’s guarantee closed-loop stability.

Distributed Economic MPC With Separable Control Contraction Metrics

In this letter, a flexible and scalable distributed economic model predictive control scheme is proposed for large-scale networked systems consisting of nodes with local self-interest economic objectives but a shared responsibility for stability of the interconnected network. In this letter, subsystems are controlled to track reference trajectories while optimizing their own economic costs during the transitions. A reference-independent stability constraint is introduced using a sum-separable control contraction metric. The proposed control design approach is thereby independent of both reference trajectories and the economic cost functions and as such suitable for flexible manufacturing. We observe that self-interested distributed optimization with shared responsibility for stability results in the same general problem formulation as network utility maximization, and make use of the alternating direction method of multipliers to coordinate the optimization. The proposed approach is illustrated with an example of distributed control of a network with 120 nodes, each of which is a three-state nonlinear system.

Distributed EMPC of multiple microgrids for coordinated stochastic energy management

The concept of multi-microgrids has the potential to improve the reliability and economic performance of a distribution system. To realize this potential, a coordination among multiple microgrids is needed. In this context, this paper presents a new distributed economic model predictive control scheme for the coordinated stochastic energy management of multi-microgrids. By optimally coordinating the operation of individual microgrids, this scheme maintains the system-wide supply and demand balance in an economical manner. Based on the probabilistic forecasts of renewable power generation and microgrid load, this scheme effectively handles the uncertainties in both supply and demand. Using the Chebyshev inequality and the Delta method, the corresponding stochastic optimization problems have been converted to quadratic and linear programs. The proposed scheme is evaluated on a large-scale case that includes ten interconnected microgrids. The results indicated that the proposed scheme successfully reduces the system wide operating cost, achieves the supply-demand balance in each microgrid, and brings the energy exchange between DNO and main grid to a predefined trajectory.

Distributed Economic Model Predictive Control of a Catalytic Reactor: Evaluation of Sequential and Iterative Architectures

The development and application of distributed economic model predictive control (DEMPC) methodologies to a catalytic reactor is considered. Two DEMPC methodologies are designed for sequential and iterative implementation, respectively. The DEMPC architectures are evaluated on the basis of the closed-loop performance and on-line computation time requirements compared to a centralized EMPC approach. For the catalytic reactor considered, DEMPC proves to be a viable option as it is able to give similar closed-loop performance while reducing the on-line computation time requirements relative to a centralized EMPC strategy.