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The State of the Art in Model Predictive Control Application for Demand Response

Review paper

Journal of Sustainable Development of Energy, Water and Environment Systems
Volume 10, Issue 3, September 2022, 1090401
DOI: https://doi.org/10.13044/j.sdewes.d9.0401
Amru Alqurashi
Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

Abstract

Demand response programs have been used to optimize the participation of the demand side. Utilizing the demand response programs maximizes social welfare and reduces energy usage. Model Predictive Control is a suitable control strategy that manages the energy network, and it shows superiority over other predictive controllers. The goal of implementing this controller on the demand side is to minimize energy consumption, carbon footprint, and energy cost and maximize thermal comfort and social welfare.  This review paper aims to highlight this control strategy's excellence in handling the demand response optimization problem. The optimization methods of the controller are compared. Summarization of techniques used in recent publications to solve the Model Predictive Control optimization problem is presented, including demand response programs, renewable energy resources, and thermal comfort. This paper sheds light on the current research challenges and future research directions for applying model-based control techniques to the demand response optimization problem.

Keywords: Stochastic MPC, robust MPC, energy management, demand response, renewable energy

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INTRODUCTION

Many countries expressed the need to make their power infrastructure more cost-effective, environmentally clean, and sociologically acceptable, thus sustainable. A considerable amount of the generated power is currently being lost due to various technical reasons: a) separated generation from end usage, b) outdated transmission and distribution lines, c) missing demand-responsive technology and policy infrastructures. Also, the load congestion bottlenecks in the existing grid raise barriers to integrating renewable forms of energy. The situation is exacerbated by increasing load demands and historically declining research and development investment by power utilities. Moreover, the dependency on centralized power generation is expected to increase emissions and raise electricity tariff prices [1]. Distributed resources such as renewable energy sources (RES) and demand response (DR) programs reduce transmission congestion, carbon footprint, and electricity price. However, DR's uncertainties increase the complexity of integrating them into the existing power grid. Therefore, energy management using the DR programs gained a lot of attention in recent years. Energy management can achieve different objectives such as minimizing the cost, reducing greenhouse gases, and minimizing the loss of generation, transmission, and distribution systems [2], [3]. DR programs can improve flexibility in the power system's operation and facilitate the low carbon transition in electricity production. The main objective of demand-side management is to mitigate the power supply's uncertainty and fluctuation, creating electricity demand flexibility. This demand flexibility increases the ability to integrate large penetrations of renewable energy. In other words, demand-side management utilizes distributed generators, including RES, using DR programs. Also, DR has a very high potential to improve power systems' performance in terms of energy saving, energy cost, emissions, and integrated RES. According to Energy Technology Perspectives Clean Energy Technology Guide [4], utilizing DR increases distributed generators' participation in the electricity market, which encourages installing more RES on the demand side and, as a result reducing transaction costs. The global market for DR has received a lot of attention. The wholesale demand response capacity in the United States grew to 28 GW and 35 GW from the retailer programs. In Italy, a total DR capacity of 280 MW was commissioned, while in Ireland, 415 MW was awarded in a four-year-head-action. In Japan, 1 GW was offered through different DR programs, such as the Interruptible load DR program and incentive-based DR programs.

Demand side management classification

As shown in Figure 1, the demand-side management can be classified into a demand reduction and DR. The demand reduction achieves using efficient appliances or changing consumer behavior. On the other hand, the demand response program can be an incentive-based program (dispatchable) or a price-based program (non-dispatchable). With a specific contract, the incentive DR programs allow the independent system operator (ISO) to reduce customers' loads. There are different types of incentive DR programs that can be set up for the customer. Some of these types are [5]-[10]:

  1. Direct load control (DLC): this gives the ISO direct control of the customer processes.

  2. Interruptible load: a customer contract with limited sheds.

  3. Emergency program: this allows the customers to respond to the emergency signal.

On the other hand, a price-based DR program influences customer consuming behavior by applying different tariffs throughout the day. There are different types of price-based DR program, some of which are:

  1. Time-of-use rates: a scheduled fixed price.

  2. Real-time pricing (RTP): the end customers have the wholesale price.

  3. Critical peak pricing: a less predetermined variant of time or use.

Utilizing the full potential of DR programs needs a control system that manages the energy network. Different control strategies have been applied to manage the demand side, such as classical, soft, and hard control strategies [11] [12]-[14]. Classical control, such as PID, is integrated with a predictive algorithm to enhance its ability to manage the building energy system. Soft control uses historical data for controlling the system, while the hard controller uses a model to determine future modus operandi. A hard controller's ability to foresee the upcoming system variability makes it more adaptive to the change. One of the best examples of the hard controller that has been used in building energy management is Model Predictive Control (MPC). MPC technique can adapt and update the model by using a feedback signal. This feature of the MPC allows the system to be rationalized with the new estimation or the measurement. As a result, the ongoing interval will be optimized based on estimating the future time interval. MPC mitigates future uncertainty by predicting the direction of the future and optimize the current decision. Moreover, the fast response of the MPC and the ability to incorporate several control operations makes MPC suitable for energy management optimization problems.

Considering the uncertainties of the power systems in energy management optimization problems will increase the solution's optimality. The difficulty of solving a real-time optimization problem that considers the uncertainty of the energy management problem can be tackled by different optimization techniques. Different review articles have been published on control strategies of demand-side energy management problems. In [5], the authors focused on the intelligent control system that achieved a building's comfort level using different control strategies such as a fuzzy logic controller and a neural network controller. On the other hand, the authors in [15] focused their review on agent-based control and model-based predictive control. In [16], the authors reviewed the supervisory and optimal control of the Heating, Ventilation, and Air Conditioning (HVAC) system in a building. The review paper in [17] focused on MPC's HVAC system theory and applications. Reference [18] provided different building energy management strategies such as MPC, fault detection, stochastic optimization, and robust optimization for residential and non-residential buildings. Unlike the aforementioned reviews, this present paper mainly focused on the recent journal publications that showed the MPC approach's capability to handle demand response optimization problems considering a high uncertainty level. In other words, this paper tries to summarize algorithms and techniques that have been used in recent publications to solve MPC optimization problem that includes RES, thermal comfort and different type of DR. Based on the uncertainty level, the optimization problems can be formulated as deterministic MPC, stochastic MPC, scenario approach MPC, or robust MPC. A comparison between different type of MPC formulations and MPC optimization methods are conducted. Also, this paper classifies the recent publications in demand-side management based on MPC formulations.

This paper is organized as follows: Section 2 provides an overview of different MPC formulations: deterministic MPC, stochastic MPC, scenario approach MPC, and robust MPC. Section 3 reviews the existing literature on the application of MPC in managing the demand side, focusing on the demand response. Section 4 concludes the paper and presents future research directions.

MODEL PREDICITIVE CONTROL

MPC is an optimization-based control technique that aims to drive the closed-loop system to an optimal operation set-point while meeting state, input, and output constraints. Using the MPC feedback mechanism, the optimization problem inside the moving horizon window is solved at each time step. Only the first control action is implemented, and the rest is discarded. Therefore, MPC can predict the evolution of the states over the prediction horizon. However, modeling a building for MPC is time-consuming since each building has a specific model [19]. To prepare a building model for demand response using MPC, white-box, black-box, or gray-box model structures have been used in the literature. The white-box modeling is developed based on the system's physical process, while the black-box model is developed based on measuring the inputs and outputs of the system [20]. Gray-box modeling is a mix of white-box and black-box approaches. For example, reference [21] applied the white-box approach for modeling, while reference [22] utilized the block-box approach. Gray-box modeling is used in [23], [24]. In terms of the simulation tool, researchers use different software environments for modeling buildings, such as DYMOLA [25], TRNSYS [26], EnergyPlus [27], and ESP-r [28]. A review paper in building modeling techniques can be found in [29]. After modeling the building, the optimal control strategy, such as MPC, can be applied.

Depending on data uncertainty, different optimization methods, such as deterministic, stochastic, and robust optimization, have been used to the formulated energy management problem. In the deterministic MPC formulation, the uncertainty parameters are assumed to be time-independent parameters (perfect prediction). Therefore, the deterministic formulation is less complicated, which lowers the computational time of solving the optimization problem. However, the perfect prediction assumption of the uncertainties in the deterministic approach is not realistic, which may lead to a sub-optimal solution. On the other hand, the stochastic approach is more realistic since it considers the uncertainties in the decision-making process. Nevertheless, the stochastic approach's computational time is very high due to the complexity of the formulation. Since stochastic MPC requires prior knowledge of the underlying probability distribution function for the uncertainties, which is hard to find for complex processes, robust MPC is an alternative MPC paradigm that can deal with uncertainty without knowing the probability distribution. This paradigm can be achieved by deriving a robust invariant set of the error system, which is the difference between the real and nominal systems. To construct the invariant set, a feedback control law is used (e.g., LQR based control law and feedback linearization). The robust MPC can then optimize the process performance online while maintaining the close loop state within the stability region. However, deriving a robust invariant set can be challenging.

Several papers have compared deterministic and stochastic optimization methods for demand-side energy management problems [30]-[32]. References [30], [31] applied deterministic and stochastic MPC on a single room with an HVAC system, while reference [30] applied MPC and weather prediction in integrated room automation by controlling the HVAC system. The result of these studies showed that deterministic and stochastic MPC had similar performance in terms of energy use. The authors in [33] compare the deterministic and robust MPC method in a single room. The result showed the robust MPC outperforms the deterministic in case of high uncertainty consideration. Comparison of deterministic, stochastic, and robust MPC optimization methods are shown in Table 1 [34]-[44]. In the following subsection, the deterministic MPC schemes will be given. In the second and third subsections, stochastic MPC formulations that utilize the uncertainties' probabilistic measures will be presented. Finally, another form of MPC, famously known as robust MPC, will be provided.

Comparison of MPC optimization methods

Optimization Methods

Reference

Complexity

Computational Speed

Accuracy

Robustness

Deterministic MPC

[34], [35]

Simple

High

Low

Low

Stochastic MPC

[36]-[38]

More complexity in joint chance-constrained compared to recourse problems

It leads to a considerable size expansion of the problem and eventually increases the computational burden

Very good

Good

Scenario Approach MPC

[39], [40]

Choosing approximations and models is difficult

It is inversely proportional to the number of samples

It depends upon the size of the sampling

It is very good for a large number of samples

Robust MPC

[41]-[44]

Very complex

Slow

High

High

Deterministic model predictive control

The mathematical formulation of the deterministic MPC for the class of nonlinear continuous system is as follows [34]:

minu(t)S(Δ)tktk+N[x(τ)TQx(τ)+u(τ)TRu(τ)dτ] (1a)

s.tx˜(t)=f(x˜˙(t),u(t)) (1b)

u(t)U,t[tk,tk+N] (1c)

x˜(tk)=x(tk) (1d)

x(t)X,t[tk,tk+N] (1e)

where u(t) is the decision variable defined over the prediction horizon length N. The control objective is to minimize a quadratic function that penalizes the deviations of the predicted states and inputs from their corresponding set-points (equation (1a)). The nominal model of equation (1b) is applied to predict the process of state evolution over the prediction horizon. To mitigate a feedback control scheme, the predicted model is initiated at each sampling time tk by the measured state from the real system x(tk). The input constraints U and state constraints X are enforced over the entire prediction horizon. The above MPC formulation can be applied to nonlinear discrete systems by replacing the nominal model of equation (1b) by the nominal discrete system (i.e., x(k+1) = fd (x(k), u(k), 0)) [35]. Up to this point, addressing the external disturbances and model uncertainties of the controlled process is not considered within the above deterministic MPC formulation. Such uncertainties will be taken into account via stochastic MPC paradigms, presented in the following subsection.

Stochastic model predictive control

A stochastic MPC algorithm can be developed using stochastic programming that can be reformulated as an optimal control problem considering the system's uncertainties. To understand how stochastic programming optimization problem is structured as an optimal control problem, the following stochastic discrete-time system is considered [36]:

xt+1=f(xt,ut,wt) (2)

yt=h(xt,ut,vt) (3)

where tN, x, and u are the state and input vectors, respectively. The disturbance vector w and v can represent a wide range of uncertainties with known probability distributions. The term f is the function that describes the system dynamics, while h is the function that describes the outputs. For full state-feedback control, the N-stage feedback control policy for stochastic MPC can be defined as follows:

π:=[π0(.),π1(.),πN1(.)] (4)

where π(.) is the Borel-measurable function for all i = 0...N-1. The stochastic discrete-time system can be formulated as a finite moving-horizon optimal control problem. By applying the MPC feedback mechanism, the value function of the resulting stochastic optimal control is commonly defined as follows:

VN:=Ext[i=0N1Jc(x˜i,ui)+Jf(x˜N)] (5)

where Jc and Jf are the stage cost function and the final cost function, respectively. Given the initial states, the term \tilde xi represents the predicted states at the time i. The objective function (equation (5)) is usually subjected to chance constraints. Using the conditional probability Prxt, the joint chance constraint over the prediction horizon formulation as follows [45], [46]:

Prxt[gi(y˜i)0,j=1,,s]β,i=1,,N (6)

where gi is the Borel-measurable function, y˜i is the predicted outputs at time i. s represents the number of inequality constraints, and the probability lower bound is represented by ?. By using value function (equation (5)) with joint chance constraints (equation (6)), the stochastic optimal control problem for the stochastic discrete-time system (2-3) can be formulated as follows [39], [40]:

VNo:=minπVN(xt,π) (7)

Subject to:

xi+1=f(xi,ui,wi)iZ[0, N1]yi=h(xi,ui,vi)iZ[0,N]Prxt[ gi(y˜i)0,j=1,,s ]βiZ[1,N]wi~PiiZ[0,N1]x˜0=xtiZ[0,N1]

where VoN is the function that represents the optimal value under the feedback control policy ρ(0). The optimal control sequence is implemented in a receding-horizon fashion (i.e., the first element of the optimal sequence π* is only applied between two consecutive time instants). Stochastic MPC is an optimal control scheme that aims to balance the trade-offs between fulfilling the overall control objectives and ensuring the satisfaction of the probabilistic constraints resulted from the uncertainty [36]-[38].

Scenario approach model predictive control

The scenario approach can be used to reformulate the stochastic optimization programming problem into a deterministic equivalent problem. To illustrate, a two-stage stochastic linear programming is used as an example. In two-stage stochastic programming with recourse, the decision-maker can take corrective actions (recourse decisions) after realizing the uncertainty over sequence stages. A general formulation for a two-stage stochastic linear programming with linear constraints is given by [47]:

minf(x)+E[Q(x,ω)] (8)

Subject to

Ax=b,xX (9)

where Q(x,ω) is the second stage optimal objective value

Q(x,ω)=ming(x,y,ω) (10)

Wωyω+Tωx=hω,yωY (11)

where ω is the probability distribution of the uncertain data for the second-stage, x represents the first-stage decision variable, and y represents the decision variable of the second-stage with the recourse action cost. Eω is the optimal objective value expectation of the second-stage decision variable. Q(x, ω) represents the recourse action cost. Wω represents the compensation of the system's variation of the Txhω. To overcome the difficulty of obtaining the random variable's probability distribution function, the continuous probability distribution can be approximated using a finite scenario set (s) with their probabilities (πs). As a result, the two-stage stochastic programming problem can be reformulated as a deterministic equivalent problem as follows:

minf(x)+SSπsqsTys (12)

Subject to

Ax=b (13)

Wωyω+Tωx=hω,yωY (14)

To apply the MPC algorithm, the deterministic optimization problem can be formulated as an optimal control problem. To have an accurate solution to the optimization problem, a large number of scenarios have to be generated to represent the system's uncertainties. However, including a high number of scenarios raises the computational time or causes an intractable problem. Different approaches have been used to overcome this issue [48]. One way to reduce the computational time is to apply scenario reduction techniques [49], [50], which reduces the number of scenarios. As a result, the computational time is reduced, whereas the solution accuracy is compromised. Another way to circumvent the issue of a high number of scenarios is by using an online MPC algorithm [51]-[53].

Robust model predictive control

The decision in the robust optimization can be a one-stage decision that has to be taken before the uncertainty is realized, and no corrective action can be taken after the realization of the uncertainty. The robust optimization can also be formulated as multiple stages, where the decision can be taken depending on the flow of the uncertainty realization. It is worth noting that it is challenging to incorporate the dynamic of the uncertainty in the robust optimization [54]. The general robust optimization formulation is [55]:

minfo(x¯),S.t.fi(x¯,u¯i)0,i=1,2,m (15)

where fo(x¯) is the objective to be optimized, and fi(x¯,u¯i) is the system constraints. f0 and fi are RnR functions. x is a vector of decision variables, and u¯i is the parameter uncertainties of the uncertainty set (Ui). m is the number of uncertain parameters. A comprehensive survey of robust optimization can be found in [56]. The robust optimization problem can be formulated as a robust MPC optimization problem, iteratively over a finite-moving horizon window. In other words, given the initial state, the state-feedback control law is used to minimize the worst-case scenario subjected to control input and output constraints [57]. The summary of the formulations of MPC optimization methods is shown in Table 2.

Formulations of MPC optimization methods

Optimization Methods

Objective Function

Constraints

Deterministic MPC

minu(t)S(Δ)tktk+N [ x˜(τ)TQx(τ)+u(τ)TRu(τ)]dτ

x˜(t)=f(x˜˙(t),u(t))u(t)U,t[ tk,tk+N ]x˜(tk)=x(tk)x(t)X,t[ tk,tk+N ]

Stochastic MPCVN0:=minπVN(xt,π)

xi+1=f(xi,ui,wi)iZ[0,N1]yi=h(xi,ui,vi)iZ[0,N]Prxt[ gi(y˜i)0,j=1,,s ]βiZ[1,N]wi~PiiZ[0,N1]x˜0=xtiZ[0,N1]

Robust MPC

minfo(x¯),

fi(x¯,u¯i)0,i=1,2,m

DEMAND SIDE MANAGEMENT VIA MODEL PREDICTIVE CONTROL

Buildings account for 40% of our worldwide energy consumption [58], [59]. Therefore, the need for controlling building energy consumption has received much attention. Many researchers investigate the potential of reducing electricity bills and greenhouse gases by optimizing energy usage in a building [60], [61]. According to [62], up to 35% of energy could be saved by selecting an optimal temperature set-point. Also, using the internet of energy technology is substantial for managing the energy network in a building. Internet of energy facilitates monitoring and controlling the flow of information between sources and loads. Taking advantage of the internet of energy technology, the fast ability to feed the control system with updated information helps the controller algorithm make an optimal decision [63]-[65]. As a result of this technology, many researchers applied the MPC technique on building energy management systems and showed that the MPC has better performance over other controllers in terms of transient and steady-state responses. Also, the MPC approach provides the ability to account for multivariable control action, which can be applied to optimize generation and demand response. MPC is considered one of the best control strategies for optimizing the energy flow within a building due to its inherent advantages, such as anticipatory control actions, handling uncertainty, and the time-varying system. MPC techniques can incorporate energy conservation strategies and disturbance rejection in its algorithm [17] [66]. However, there are several challenges when MPC is implemented, such as control design and building modeling. The decision to use the MPC strategy for a building mainly depends on its cost and performance [67].

In general, the controller's goal in a building energy management system can be categorized as follows. 1) minimize the operational cost, 2) maximize the utilization of RES, 3) achieve thermal comfort level by using a minimal amount of energy. 4) minimize the peak load or reschedule it. To achieve the control goal using MPC strategies, an optimal control optimization problem has to be formulated to minimize an objective function considering several constraints. The objective is usually to minimize the energy cost, but multi-objectives can minimize the cost and guarantee thermal comfort. Also, time-dependent constraints can be used for different comfort levels. Constraints can also be constructed to limit some of the parameters. Various Constraints can be considered in the MPC, such as equipment, energy match, economic, environmental, and political constraints.

Smart home energy management

Figure 2 illustrates the basic methodology of MPC for a building. The design parameters and predicted disturbances are the inputs to the MPC. Considering these inputs, the MPC optimizer minimizes the objective function is subjected to the constraints and the dynamic of the building model. Using the feed mechanism, the MPC controller applied only the first step of the solution and discarded the rest. In each time step, the MPC is updated with the current states. Based on the DR program, the MPC controller can manage the different types of loads to minimize energy costs. For example, the storage loads and the shiftable loads can be feed during the off-peak hours, where the electricity price is low.

As previously discussed, the MPC formulation can be categorized into deterministic MPC, stochastic MPC, scenario approach MPC, and robust MPC. The main difference in these formulations is how the system's uncertainties are considered on the optimization problem. Researchers used all these formulations to develop an MPC algorithm that can manage the building's energy system. Regardless of the MPC formulation, the MPC algorithm's implementation can be centralized, decentralized, distributed [68], [69]. Table 3 summarizes the techniques and evaluation of recent publications' contributions to utilizing RES, thermal comfort, cost reductions, shaving, shifting, or shaping load peaks for buildings' energy consumption, and characteristics of the demand response [30], [32], [70]-[107].

MPC formulations for demand-side energy management

Formulation

Ref

Techniques

Utilized RES

Thermal Comfort

Reduce Cost

Load Peak

DR

Deterministic MPC

[70]

EMPC

No

No

Yes

Shaving 26%

TOU

[71]

Mixed-Integer Nonlinear Programming, EMPC

PV

Yes

Yes

Shifting

Price-Based.

[72]

Artificial Neural Networks Dynamic Programming

Wind

Yes

Yes

Shaping

Control Load

[73]

MINLP Branch …Bound Algorithm

No

Yes

Yes

Shaving

Auxiliary Services

[74]

Cluster Analysis

PV

Yes

Yes

Yes

DLC

[75]

Proposed Algorithm

PV

Yes

Yes

Shaving %23

Ancillary Services

[76]

Mixed-Integer Linear Programming

PV

No

7%

Shaving

TOU

[77]

Linear State-Space Model, Discretized

Wind

No

Yes

Shaving

Dispatchable

[78]

Quadratic Program

No

Yes

Yes

Shaving

No

[79]

Exponentially Weighted Moving Average Algorithm

Yes

Yes

Yes

Shifting

DCL

[80]

Linear Quadratic Method Monte Carlo

No

Yes

Energy Saving 43%

Shaving

No

[81]

Linear Quadratic Method Monte Carlo

No

Yes

Energy Saving 43%

Shaving

No

[82]

Mixed-Integer Programming

Solar Thermal

Yes

Yes

Shifting

Price-Based

[83]

Cooperative Optimization, EMPC

No

Yes

15%

Shifting

No

[84]

Discrete Quadratic Programming

No

No

Yes

Shifting

Incentive-Based

[85]

Adaptive Approach

Wind, PV

Yes

46%

Shaving

TOU

Stochastic MPC

[30]

Probabilistic Constraints Factorial Simulation

No

Yes

Yes

No

No

[32]

Discrete Algorithm Sampling Algorithm

No

Yes

Yes

Shaving

No

[86]

Monte Carlo Probabilistic Constraints

PV

Yes

Yes

Shafting

DCL

[87]

Monte Carlo Probabilistic Constraint

No

Yes

Yes

No

No

[88]

Probabilistic Time-Varying Constraint

No

Yes

Yes

Shaving

Incentive-Based

[89]

Two-Stage Optimization Discrete

No

No

7.5%

Shifting

Price-Based

[90]

Quadratic Programming

No

No

Yes

No

No

Scenario Approach MPC

[91]

Discrete, Markov Chain, Monte Carlo

Wind

No

12%

Shifting

DCL

[92]

Probabilistic Monte Carlo

Solar

Yes

20%

Ramp Shaving 50%

RTP

[93]

Probabilistic Gaussian Distribution

No

Yes

Yes

Shifting

RTP

[94]

Mixed-Integer Linear Programming

Solar

Yes

25%

No

Price-based

[95]

EMPC Stochastic State Space

No

Yes

Yes

Shifting

TOU

[96]

EMPC Probabilistic, Scenario

No

No

9-32%

Shaving

RTP

[97]

Sequential Linear Programming, EMPC

Wind, PV Solar

Yes

21%-75%

Shifting

Price-Based

[98]

Probabilistic Search

No

Yes

Energy Savings 35%

Shaving

Incentive-Based

[99]

Neural Network Predictive Control

Wind PV

No

Yes

Shaving

Reliability

Robust MPC

[100]

Fuzzy Model

No

Yes

Yes

Yes

No

[101]

Quadratic Programming

No

Yes

Yes

Shaving

Incentive-Based

[102]

Mixed-Integer Linear Programming

No

Yes

yes

Shifting

TOU

[103]

EMPC, Decomposition Control Variables

PV

No

No

yes

No

[104]

EMPC, Min-max Worst Case Approach

PV

No

Yes

Yes

Price-Based

[105]

Adaptive Robust MPC

No

Yes

Energy Savings 20%

Shaving Shifting

Real-time- Based

[106]

Robust Constraints Satisfaction

No

Yes

yes

Shifting

No

[107]

Linear Matrix Inequalities

No

Yes

Yes

Shifting

Price-Based

Deterministic model predictive control in demand response

The uncertainty parameters usually come from solar irradiation, occupancy, RES, and weather forecast in the energy management optimization problem. These uncertainty parameters are assumed to be time-independent parameters in the deterministic MPC approach. A vast body of literature applied deterministic MPC to manage energy networks in a building [70]-[79]. Table 3 shows the techniques and controller objectives for each reference that applied the deterministic MPC approach.

A group of publications [70], [73], [77] used the hot water system in a building as an energy storage system. Based on the DR, the authors in [70] used an EMPC controller that optimized hot water system consumption by determining the optimal set-point of water temperature. Reference [77] proposed an MPC controller scheme that aggregated electric water heaters and provided the ISO with ancillary services. Also, the authors in [73] proposed an MPC controller scheme that aggregated thermostatically controlled appliances and provided them to the ISO as ancillary services.

A few publications [71], [72], [74], [75], [79] have directly dealt with the issue of the generation intermittency of renewable energy by using DR programs. References [79] and [74] used the DLC program to balance the renewable generation fluctuation by applying distributed and centralized MPC algorithms. The authors in [79] control the HVAC and the water level to shape the load while [74] controls the thermostat set-points for air conditioners. Reference [75] developed an MPC framework that optimizes the interaction between renewable generation and the battery storage system while maintaining the comfort level and reducing peak load. The authors in [72] proposed an MPC strategy to reduce the fluctuation of wind energy by regulating grid consumption and on-site energy generation and controlling the elastic loads. By modeling the building's behavior and weather forecasting, [71] proposed an EMPC controller that can match demand with fluctuations in supply.

In [76], MPC based on a deep reinforcement learning method was used to utilize dispatchable loads and storage resources in a DR program. A prototype was installed to demonstrate the performance of their control method using the internet of things devices. In [78], a machine learning technique for MPC was applied to minimize energy usage and guarantee the end-user comfort level. Using machine learning reduced the hardware and software complexity of the controller and, as a result, the implementation cost. Experiments were conducted in [80], [81] to show the MPC performance's superiority to minimize energy consumption while maintaining comfort. Reference [82] proposed a nonlinear model predictive controller that optimizes the energy usage and comfort level based on a linear thermal model, which reduces the problem complexity, resulting in reducing the computational time.

Stochastic model predictive control in demand response

In building energy management, researchers have used stochastic MPC formulation to include uncertainties such as occupancy, ambient temperature, solar radiation, and renewable energy generation. Table 3 shows the techniques and controller objectives for each reference that applied the stochastic MPC approach. In contrast with the deterministic approach, the stochastic MPC considers the uncertainty in the decision-making process. To include uncertainties in the DR optimization problem, chance-constrained is usually used in a stochastic MPC algorithm. For instance, reference [86] proposed a chance-constrained MPC to take into account the uncertainties of ambient temperature and PV generation. The developed model optimizes the scheduling of the controllable appliances based on energy cost, thermal comfort, and PV system. Chance constraints can be transformed into deterministic using a sample-based method and discrete convolution integrals, as shown in [32]. This reference considers the uncertainties of occupancy loads and weather and used stochastic MPC to control small-scale HVAC systems while guaranteeing the occupancy's comfort level. However, using chance constraints on a large system sometimes leads to computational intractability issues. To overcome this problem, the authors in [87] developed a closed-loop disturbance feedback formulation to reduce the conservatism of the problem. This reference used Monte-Carlo simulations to validate the chance-constrained solution. The stochastic algorithm was capable of considering the weather forecast and ensure temperature preferences and DR requests. The authors in [30] and [88] focused on including weather prediction uncertainty in the stochastic MPC to increase energy efficiency and maintain the thermal comfort level. The authors compared the predictive controller and rule-based controller with a stochastic MPC controller, which outperforms both controllers. A recent publication [89] compared deterministic and stochastic MPC of HVAC plants and showed that the deterministic solution fails to capture uncertainties, resulting in economic penalties. On the other hand, the stochastic MPC approach was more prepared to handle the uncertainties, leading to cost savings.

Scenario approach model predictive control in demand response

Stochastic MPC based on chance constraints is difficult to be solved. Therefore, some researchers use a scenario approach to reformulate the stochastic MPC optimal problem to a deterministic equivalent problem. Table 3 shows the techniques and controller objectives for each reference that applied the scenario approach MPC. The system's uncertainty can be captured using a sampling method based on the probability distribution function [108].

The Monte-Carlo technique is commonly used to sample a probability distribution randomly. Applying the Monte-Carlo technique, reference [91] used energy storage as a DR to shave the load and reduce wind generation fluctuation. In this reference, the wind generation and customer behavior uncertainties were considered in the scenario-based MPC to maximize social welfare.

Another approach to include the uncertainty in MPC algorithms is using the Markov chain modeling framework. For instance, the wind power uncertainty was modeled in [91] using the Markov chain Monte-Carlo method.

The high penetration of renewable resources increases the probabilistic variations of power generation. These probabilistic variations can be handled using energy storage systems and DR programs. However, some of the DR programs may increase the system's uncertainty due to the customer's behavior. Therefore, the online MPC approach can be more adaptable to the probabilistic variations of the model and enhance the solution's accuracy [91], [92], [99].

A real-time optimization framework MPC can utilize thermal mass storage and energy storage systems to control power flow between the grid, a PV system, and a commercial building [92]. Reference [99] developed a real-time MPC algorithm based on a neural network technique that manages the energy system in a zero-energy building.

Considering the uncertainties of the model, such as solar irradiation, occupancy, renewable energy resources, and weather forecast, the energy management stochastic optimization problems are formulated to minimize the operational cost of integrating renewable energy resources, DR, and controllable, and storage devices Figure 2 [93]-[98]. The authors in [93] took advantage of a commercial building's flexible operation and proposed an MPC strategy that considered real-time pricing and thermal comfort level. To increase the model's accuracy, the authors consider the uncertainty of cooling demands in their stochastic optimization problem. In [92], the authors applied MPC to optimize the HVAC system and the storage devices considering thermal comfort constraints and external temperature uncertainty. Reference [95] investigated the EMPC strategy's ability to utilize a high penetration of renewable energy in the system to reduce the operational cost and maintain the system's reliability. On the other hand, reference [96] applied EMPC on supermarket refrigeration systems, which enable it to be used as ancillary services. In [95], the authors used sequential linear programming to achieve an EMPC strategy that reduces computational time and minimizes the energy cost significantly. In contrast, the authors in [98] used cloud parallel computation to consider the full complexity simulation in the proposed MPC algorithm.

Robust model predictive control in demand response

The robust optimization deals with the range or region of a deterministic uncertainty while taking into account the worst-case scenario over the predetermined deterministic uncertainty set. Since robust optimization does not need probability distribution, it is preferable when the probability distribution is difficult to obtain from uncertain data. The robust optimization approach uses an uncertainty set that covers all the possible outcomes of the uncertain parameters. Thus, the optimality and feasibility of a solution are guaranteed within any realizations of the uncertainty set. Therefore, the uncertainty set must be carefully constructed to guarantee computational tractability. The objective is to find the optimal solution considering the worst-case scenario; hence, there is no need to include a large number of scenarios, like in the case of stochastic programming. Considering the worst-case scenario increases the reliability of solutions but leads to very costly (conservative) solutions. Therefore, by adding a constraint to the uncertainty set, a trade-off between the cost and reliability can be optimized [109], [110].

Due to the conservative solution and the implementation complexity of robust MPC optimization [111], a few researchers have applied robust MPC to the DSM optimization problem. Table 3 shows the techniques and controller objectives for each reference that applied the robust MPC. The authors in [101] formulated a min-max robust optimization problem taking into an account comfort level, controllable load, and electricity price. Considering the uncertainties of load predictions and ambient temperature, authors in [100] applied a fuzzy interval model to define the uncertainty bounds in the robust MPC formulation. The authors in [102] formulate a robust MPC optimization problem that optimizes multiple energy forms considering source-network-load flexibilities. In [103], [104], the authors propose a robust MPC that guarantees an optimal energy dispatch in a smart micro-grid considering bounded demand uncertainty. An adaptive robust MPC is presented in [105] to perform online estimation of uncertain parameters of the building, while the adaptive robust MPC proposed in [106] relies on recursive set membership identification to updated the close-loop operation in each time step. Robustness analysis to state estimation for a hybrid ground coupled heat pump system is applied in [107] using robust MPC. The result shows that robust method did not improve the state estimation for the investigated system.

CONCLUSION AND FUTURE DIRECTIONS

A smart grid advances two-way communication between the generation and end-users. This advancement of smart grid communication technologies allows consumers to participate in the electricity market through DR programs. Various DR programs have been used to optimize the participation of the demand-side. Utilizing the full potential of DR programs needs a control system that manages the energy network. Different methods of controlling techniques have been applied to manage the demand response in the literature. This paper provides a review of different MPC formulations, which are deterministic MPC, stochastic MPC, scenario approach MPC, and robust MPC. The deterministic MPC approach has the lowest computational time and most straightforward formulation comparing to other approaches. However, the perfect prediction assumption for the uncertainties may lead to a sub-optimal solution. The stochastic MPC approach considers the uncertainties in the decision-making process, resulting in a more realistic solution. The significant challenges of the stochastic approach are computing time and obtaining the probability distribution of the random variables. On the other hand, robust MPC deals with uncertainty without knowing the probability distribution by constructing an uncertainty set, which leads to a robust solution. However, the robust MPC solution is very costly since it considers the worst-case scenario.

The demand-side management optimization problems are subject to various uncertainties, including weather forecast, solar irradiation, occupant thermal comfort level, and electricity price. The high penetration of renewable distributed generation, such as wind and solar, has added additional uncertainties in the demand side due to the renewable energy sources fluctuations. However, these fluctuations can be mitigated by using an energy storage system. Smart grid capabilities also facilitate the utilization of the demand response programs to handle the demand side's uncertainties. Utilizing DR programs can increase power system reliability, reduce energy consumption, and minimize operational costs. To this end, an MPC strategy considers design parameters and predicted disturbances to come up with optimal control actions that maximize social welfare. Since the computing power has been improving, recent publications focus on including the uncertainties of the system in the MPC formulation. The main research challenge is how to optimize the energy flow and cost, considering the variability of the renewable energy, weather forecast, solar irradiation, thermal comfort, DR programs, and emission constraints. Most of the researchers applied the stochastic approach and considered some of these constraints. A few researchers used robust MPC since it generates a conservative solution.

The objective of implementing MPC on the demand side is to minimize energy consumption, carbon footprint, and energy cost; and maximize thermal comfort and social well-fare. However, several challenges can face researchers when considering the MPC in the demand response optimization problem. These challenges can be summarized as follows:

  • Modeling a building for MPC implementation.

  • Considering all kinds of uncertainties, such as weather prediction, RES, DR programs, and occupancy, in one model.

  • Reducing the computational time to solve the optimization problem.

  • Affordability and availability of the communication infrastructure to collect system measurements.

  • Handling big data that is collected from the system.

These challenges cause an observable discrepancy in the simulation results in the publications. A comprehensive model that considers all these challenges is needed. Taking advantage of smart grid technologies and cloud computing, artificial intelligence, and machine learning combined with MPC strategy has the potential to overcome these challenges and provide a cost-effective solution and ensure the security and reliability of the power system.

NOMENCLATURE

Abbreviations

DCL

Direct Control Load

DR

Demand Response

DSM

Demand Side Management

EMPC

Economic Model Predictive Control

ESS

Energy Storage System

HVAC

Heating, Ventilation, and Air Conditioning

ISO

Independent System Operator

MILP

Mixed-Integer Linear Programming

MINLP

Mixed-Integer Nonlinear Programming

MPC

Model Predictive Control

R…D

Research and Development

RES

Renewable Energy Sources

RTP

Real-Time Pricing

TOU

Time of Use

Variables

u(t)

Decision variable for the class of nonlinear continuous system

(t)

State variable for the class of nonlinear continuous system

xt

State vectors for the stochastic discrete-time system

ut

Input vectors for the stochastic discrete-time system

W

Disturbance vector can represent a wide range of uncertainties with known probability distributions for the stochastic discrete-time system

v

Disturbance vector can represent a wide range of uncertainties with known probability distributions for the stochastic discrete-time system

X

First-stage decision for the two-stage stochastic linear programming

y

Second-stage decision for the two-stage stochastic linear programming

ω

Probability distribution of the uncertain data for the second-stage

Vector of decision variables for the robust optimization formulation

i

Parameter uncertainties of the uncertainty set for the robust optimization formulation

KirschenD StrbacG. Transmission networks and electricity markets Fundamentals of power system economics 2004 141-204 https://doi.org/10.1002/0470020598.ch6 AlamM.S ArefifarS.A. Energy Management in power distribution systems: review, classification, limitations and challenges IEEE Access 2019 7 92979-93001 https://doi.org/10.1109/ACCESS.2019.2927303 RafiqueS.F JianhuaZ. Energy management system, generation and demand predictors: a review IET Generation, Transmission … Distribution 2017 12 3 519-530 https://doi.org/10.1049/iet-gtd.2017.0354 IEA Demand Response IEA Paris https://www.iea.org/reports/demand-response 2020 VardakasJ.S. ZorbaN. VerikoukisC.V. A survey on demand response programs in smart grids: Pricing methods and optimization algorithms IEEE Communications Surveys … Tutorials 2014 17 1 152-178 https://doi.org/10.1109/COMST.2014.2341586 PalenskyP DietrichD Demand side management: Demand response, intelligent energy systems, and smart loads IEEE transactions on industrial informatics 2011 7 3 381-388 https://doi.org/10.1109/TII.2011.2158841 SchellerF Provoking residential demand response through variable electricity tariffs-a model-based assessment for municipal energy utilities Technology and Economics of Smart Grids and Sustainable Energy 2018 3 1 7 https://doi.org/10.1007/s40866-018-0045-x ParrishB HeptonstallP. GrossR The potential for UK residential demand side participation System Architecture Challenges: Supergen+ for HubNet 2016 UddinM A review on peak load shaving strategies Renewable and Sustainable Energy Reviews 2018 82 3323-3332 https://doi.org/10.1016/j.rser.2017.10.056 MeyabadiA.F DeihimiM.H. A review of demand-side management: Reconsidering theoretical framework Renewable and Sustainable Energy Reviews 2017 80 367-379 https://doi.org/10.1016/j.rser.2017.05.207 DounisA.I CaraiscosC Advanced control systems engineering for energy and comfort management in a building environment-A review Renewable and Sustainable Energy Reviews 2009 13 6-7 1246-1261 https://doi.org/10.1016/j.rser.2008.09.015 YuZ.J. Control strategies for integration of thermal energy storage into buildings: State-of-the-art review Energy and Buildings 2015 106 203-215 https://doi.org/10.1016/j.enbuild.2015.05.038 PereraD.W.U. Pfeiffer>C. SkeieN.-O. Control of temperature and energy consumption in buildings-A review International Journal of Energy … Environment 2014 5 4 ThieblemontH Predictive control strategies based on weather forecast in buildings with energy storage system: A review of the state-of-the art Energy and Buildings 2017 153 485-500 https://doi.org/10.1016/j.enbuild.2017.08.010 ShaikhP.H. A review on optimized control systems for building energy and comfort management of smart sustainable buildings Renewable and Sustainable Energy Reviews 2014 34 409-429 https://doi.org/10.1016/j.rser.2014.03.027 WangS MaZ Supervisory and optimal control of building HVAC systems: A review Hvac…R Research 2008 14 1 3-32 https://doi.org/10.1080/10789669.2008.10390991 AframA Janabi-SharifiF. Theory and applications of HVAC control systems-A review of model predictive control (MPC) Building and Environment 2014 72 343-355 https://doi.org/10.1016/j.buildenv.2013.11.016 Mariano-HernandezD A review of strategies for building energy management system: Model predictive control, demand side management, optimization, and fault detect … diagnosis Journal of Building Engineering 2020 101692 https://doi.org/10.1016/j.jobe.2020.101692 PrivaraS Building modeling as a crucial part for building predictive control Energy and Buildings 2013 56 8-22 https://doi.org/10.1016/j.enbuild.2012.10.024 AmasyaliK El-GoharyN.M. A review of data-driven building energy consumption prediction studies Renewable and Sustainable Energy Reviews 2018 81 1192-1205 https://doi.org/10.1016/j.rser.2017.04.095 HazyukI GhiausC. PenhouetD Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part I-Building modeling Building and Environment 2012 51 379-387 https://doi.org/10.1016/j.buildenv.2011.11.009 FanC A novel methodology to explain and evaluate data-driven building energy performance models based on interpretable machine learning Applied Energy 2019 235 1551-1560 https://doi.org/10.1016/j.apenergy.2018.11.081 KreseG Determination of a Building's balance point temperature as an energy characteristic Energy 2018 165 1034-1049 https://doi.org/10.1016/j.energy.2018.10.025 MacarullaM estimation of a room ventilation air change rate using a stochastic grey-box modelling approach Measurement 2018 124 539-548 https://doi.org/10.1016/j.measurement.2018.04.029 Modeleon The software dymola https://www.modelon.com/products/dymola/ TRNSYS The software, transient system simulation too https://www.trnsys.com/ ZhaoJ EnergyPlus model-based predictive control within design-build-operate energy information modelling infrastructure Journal of Building Performance Simulation 2015 8 3 121-134 https://doi.org/10.1080/19401493.2014.891656 StrachanP ESP-r: Summary of validation studies Energy Systems Research Unit University of Strathclyde Scotland, UK 2000 AfrozZ Modeling techniques used in building HVAC control systems: A review Renewable and Sustainable Energy Reviews 2018 83 64-84 https://doi.org/10.1016/j.rser.2017.10.044 OldewurtelF use of model predictive control and weather forecasts for energy efficient building climate control Energy and Buildings 2012 45 15-27 https://doi.org/10.1016/j.enbuild.2011.09.022 Drgon̂aJ Explicit stochastic MPC approach to building temperature control in 52nd IEEE Conference on Decision and Control 2013 IEEE https://doi.org/10.1109/CDC.2013.6760908 MaY MatuŝkoJ BorrelliF Stochastic model predictive control for building HVAC systems: Complexity and conservatism IEEE Transactions on Control Systems Technology 2014 23 1 101-116 https://doi.org/10.1109/TCST.2014.2313736 MaasoumyM Handling model uncertainty in model predictive control for energy efficient buildings Energy and Buildings 2014 77 377-392 https://doi.org/10.1016/j.enbuild.2014.03.057 MagniL RaimondoD.M AllgowerF Nonlinear model predictive control Lecture Notes in Control and Information Sciences 2009 384 https://doi.org/10.1007/978-3-642-01094-1 CamachoE.F AlbaC.B Model predictive control 2013 Springer Science … Business Media MesbahA Stochastic model predictive control: An overview and perspectives for future research IEEE Control Systems Magazine 2016 36 6 30-44 https://doi.org/10.1109/MCS.2016.2602087 FarinaM GiulioniL ScattoliniR Stochastic linear model predictive control with chance constraints-a review Journal of Process Control 2016 44 53-67 https://doi.org/10.1016/j.jprocont.2016.03.005 HeirungT.A.N. Stochastic model predictive control-how does it work? Computers … Chemical Engineering 2018 114 158-170 https://doi.org/10.1016/j.compchemeng.2017.10.026 KallP Stochastic programming European Journal of Operational Research 1982 10 2 125-130 https://doi.org/10.1016/0377-2217(82)90152-7 BirgeJ.R LouveauxF Introduction to stochastic programming 2011 Springer Science … Business Media https://doi.org/10.1007/978-1-4614-0237-4 LeeY.I KouvaritakisB A linear programming approach to constrained robust predictive control IEEE Transactions on Automatic Control 2000 45 9 1765-1770 https://doi.org/10.1109/9.880645 GrimmG Nominally robust model predictive control with state constraints IEEE Transactions on Automatic Control 2007 52 10 1856-1870 https://doi.org/10.1109/TAC.2007.906187 YanZ WangJ Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks IEEE transactions on neural networks and learning systems 2013 25 3 457-469 https://doi.org/10.1109/TNNLS.2013.2275948 DongZ AngeliD Tube-based robust Economic Model Predictive Control on dissipative systems with generalized optimal regimes of operation in 2018 IEEE Conference on Decision and Control (CDC) 2018 IEEE https://doi.org/10.1109/CDC.2018.8619325 MillerB.L WagnerH.M Chance constrained programming with joint constraints Operations Research 1965 13 6 930-945 https://doi.org/10.1287/opre.13.6.930 PrekopaA On probabilistic constrained programming in Proceedings of the Princeton symposium on mathematical programming 1970 Citeseer KallP WallaceSW KallP Stochastic programming 1994 Springer ConejoA.J. CarrionM. MoralesJM Decision making under uncertainty in electricity markets 1 2010 Springer https://doi.org/10.1007/978-1-4419-7421-1_1 HeitschH RomischW A note on scenario reduction for two-stage stochastic programs Operations Research Letters 2007 35 6 731-738 https://doi.org/10.1016/j.orl.2006.12.008 DupacovaJ Growe-KuskaN RomischW Scenario reduction in stochastic programming: An approach using probability metrics 2000 Humboldt-Universitat zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät.... FrauendorferK Barycentric scenario trees in convex multistage stochastic programming Mathematical Programming 1996 75 2 277-293 https://doi.org/10.1007/BF02592156 HeitschH RomischW Scenario tree modeling for multistage stochastic programs Mathematical Programming 2009 118 2 371-406 https://doi.org/10.1007/s10107-007-0197-2 AlqurashiA EtemadiAH KhodaeiA Model predictive control to two-stage stochastic dynamic economic dispatch problem Control Engineering Practice 2017 69 112-121 https://doi.org/10.1016/j.conengprac.2017.09.012 GabrelV MuratC ThieleA Recent advances in robust optimization: An overview European journal of operational research 2014 235 3 471-483 https://doi.org/10.1016/j.ejor.2013.09.036 BertsimasD BrownDB CaramanisC Theory and applications of robust optimization SIAM review 2011 53 3 464-501 https://doi.org/10.1137/080734510 BeyerH.-G. SendhoffB Robust optimization-a comprehensive survey Computer methods in applied mechanics and engineering 2007 196 33-34 3190-3218 https://doi.org/10.1016/j.cma.2007.03.003 KothareM.V. BalakrishnanV MorariM Robust constrained model predictive control using linear matrix inequalities Automatica 1996 32 10 1361-1379 https://doi.org/10.1016/0005-1098(96)00063-5 Perez-LombardL OrtizJ PoutC A review on buildings energy consumption information Energy and buildings 2008 40 3 394-398 https://doi.org/10.1016/j.enbuild.2007.03.007 Urge-VorsatzD Energy use in buildings in a long-term perspective Current Opinion in Environmental Sustainability 2013 5 2 141-151 https://doi.org/10.1016/j.cosust.2013.05.004 DengS WangR DaiY How to evaluate performance of net zero energy building-A literature research Energy 2014 71 1-16 https://doi.org/10.1016/j.energy.2014.05.007 TorritiJ HassanMG LeachM Demand response experience in Europe: Policies, programmes and implementation Energy 2010 35 4 1575-1583 https://doi.org/10.1016/j.energy.2009.05.021 GhahramaniA Energy savings from temperature set-points and deadband: Quantifying the influence of building and system properties on savings Applied Energy 2016 165 930-942 https://doi.org/10.1016/j.apenergy.2015.12.115 KampelisN Evaluation of the performance gap in industrial, residential … tertiary near-Zero energy buildings Energy and Buildings 2017 148 58-73 https://doi.org/10.1016/j.enbuild.2017.03.057 HannanM.A. A review of internet of energy based building energy management systems: Issues and recommendations Ieee Access 2018 6 38997-39014 https://doi.org/10.1109/ACCESS.2018.2852811 HanJ SolankiSK SolankiJ Coordinated predictive control of a wind/battery microgrid system IEEE Journal of emerging and selected topics in power electronics 2013 1 4 296-305 https://doi.org/10.1109/JESTPE.2013.2282601 BordonsC CamachoE Model predictive control1 2007 Springer Verlag London Limited KillianM KozekM Ten questions concerning model predictive control for energy efficient buildings Building and Environment 2016 105 403-412 https://doi.org/10.1016/j.buildenv.2016.05.034 ScattoliniR Architectures for distributed and hierarchical model predictive control-a review Journal of process control 2009 19 5 723-731 https://doi.org/10.1016/j.jprocont.2009.02.003 NegenbornR.R MaestreJM Distributed model predictive control: An overview and roadmap of future research opportunities IEEE Control Systems Magazine 2014 34 4 87-97 https://doi.org/10.1109/MCS.2014.2320397 PeetersM CompernolleT Van PasselS Simulation of a controlled water heating system with demand response remunerated on imbalance market pricing Journal of Building Engineering 2020 27 100969 https://doi.org/10.1016/j.jobe.2019.100969 PerezK.X. BaldeaM EdgarTF Integrated HVAC management and optimal scheduling of smart appliances for community peak load reduction Energy and Buildings 2016 123 34-40 https://doi.org/10.1016/j.enbuild.2016.04.003 FinckC LiR ZeilerW Economic model predictive control for demand flexibility of a residential building Energy 2019 176 365-379 https://doi.org/10.1016/j.energy.2019.03.171 LiuM ShiY Model predictive control for thermostatically controlled appliances providing balancing service IEEE Transactions on Control Systems Technology 2016 24 6 2082-2093 https://doi.org/10.1109/TCST.2016.2535400 MahdaviN Model predictive control of distributed air-conditioning loads to compensate fluctuations in solar power IEEE Transactions on Smart Grid 2017 8 6 3055-3065 https://doi.org/10.1109/TSG.2017.2717447 BiyikE KahramanA A predictive control strategy for optimal management of peak load, thermal comfort, energy storage and renewables in multi-zone buildings Journal of building engineering 2019 25 100826 https://doi.org/10.1016/j.jobe.2019.100826 BrunoS GiannoccaroG La ScalaM A Demand Response Implementation in Tertiary Buildings through Model Predictive Control IEEE Transactions on Industry Applications 2019 55 6 7052-7061 https://doi.org/10.1109/TIA.2019.2932963 HalamayD.A. StarrettM BrekkenTK Hardware Testing of Electric Hot Water Heaters Providing Energy Storage and Demand Response Through Model Predictive Control IEEE Access 2019 7 139047-139057 https://doi.org/10.1109/ACCESS.2019.2932978 Drgon̂aJ Approximate model predictive building control via machine learning Applied Energy 2018 218 199-216 https://doi.org/10.1016/j.apenergy.2018.02.156 ZhouK CaiL A dynamic water-filling method for real-time HVAC load control based on model predictive control IEEE Transactions on Power Systems 2014 30 3 1405-1414 https://doi.org/10.1109/TPWRS.2014.2340881 SalakijS Model-Based Predictive Control for building energy management. I: Energy modeling and optimal control Energy and Buildings 2016 133 345-358 https://doi.org/10.1016/j.enbuild.2016.09.044 YuN Model-based predictive control for building energy management: Part II-Experimental validations Energy and Buildings 2017 146 19-26 https://doi.org/10.1016/j.enbuild.2017.04.027 SchirrerA Nonlinear model predictive control for a heating and cooling system of a low-energy office building Energy and Buildings 2016 125 86-98 https://doi.org/10.1016/j.enbuild.2016.04.029 StainoA NagpalH BasuB Cooperative optimization of building energy systems in an economic model predictive control framework Energy and Buildings 2016 128 713-722 https://doi.org/10.1016/j.enbuild.2016.07.009 MiyazakiK Design and value evaluation of demand response based on model predictive control IEEE Transactions on Industrial Informatics 2019 15 8 4809-4818 https://doi.org/10.1109/TII.2019.2920373 MbunguN.T. An optimal energy management system for a commercial building with renewable energy generation under real-time electricity prices Sustainable cities and society 2018 41 392-404 https://doi.org/10.1016/j.scs.2018.05.049 GarifiK Stochastic model predictive control for demand response in a home energy management system in 2018 IEEE Power … Energy Society General Meeting (PESGM) 2018 IEEE https://doi.org/10.1109/PESGM.2018.8586485 OldewurtelF Stochastic model predictive control for building climate control IEEE Transactions on Control Systems Technology 2013 22 3 1198-1205 https://doi.org/10.1109/TCST.2013.2272178 OldewurtelF Energy efficient building climate control using stochastic model predictive control and weather predictions Proceedings of the 2010 American control conference 2010 IEEE https://doi.org/10.1109/ACC.2010.5530680 KumarR Stochastic model predictive control for central HVAC plants Journal of Process Control 2020 90 1-17 https://doi.org/10.1016/j.jprocont.2020.03.015 NasirH.A. Stochastic Model Predictive Control Based Reference Planning for Automated Open-Water Channels IEEE Transactions on Control Systems Technology 2019 ArastehF RiahyGH MPC-based approach for online demand side and storage system management in market based wind integrated power systems International Journal of Electrical Power … Energy Systems 2019 106 124-137 https://doi.org/10.1016/j.ijepes.2018.09.041 RazmaraM Building-to-grid predictive power flow control for demand response and demand flexibility programs Applied Energy 2017 203 128-141 https://doi.org/10.1016/j.apenergy.2017.06.040 CaoY DuJ SoleymanzadehE Model predictive control of commercial buildings in demand response programs in the presence of thermal storage Journal of Cleaner Production 2019 218 315-327 https://doi.org/10.1016/j.jclepro.2019.01.266 BianchiniG An integrated model predictive control approach for optimal HVAC and energy storage operation in large-scale buildings Applied Energy 2019 240 327-340 https://doi.org/10.1016/j.apenergy.2019.01.187 ZongY Challenges of implementing economic model predictive control strategy for buildings interacting with smart energy systems Applied Thermal Engineering 2017 114 1476-1486 https://doi.org/10.1016/j.applthermaleng.2016.11.141 HovgaardT.G. Model predictive control technologies for efficient and flexible power consumption in refrigeration systems Energy 2012 44 1 105-116 https://doi.org/10.1016/j.energy.2011.12.007 RuusuR Direct quantification of multiple-source energy flexibility in a residential building using a new model predictive high-level controller Energy Conversion and Management 2019 180 1109-1128 https://doi.org/10.1016/j.enconman.2018.11.026 Gomez-RomeroJ A probabilistic algorithm for predictive control with full-complexity models in non-residential buildings IEEE Access 2019 7 38748-38765 https://doi.org/10.1109/ACCESS.2019.2906311 MegahedT.F. AbdelkaderSM ZakariaA Energy management in zero-energy building using neural network predictive control IEEE Internet of Things Journal 2019 6 3 5336-5344 https://doi.org/10.1109/JIOT.2019.2900558 CartagenaO Munoz-CarpinteroD SaezD A Robust Predictive Control Strategy for Building HVAC Systems Based on Interval Fuzzy Models 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) 2018 IEEE https://doi.org/10.1109/FUZZ-IEEE.2018.8491442 HosseiniS.M. CarliR DotoliM A Residential Demand-Side Management Strategy under Nonlinear Pricing Based on Robust Model Predictive Control 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC) 2019 IEEE https://doi.org/10.1109/SMC.2019.8913892 LvC Model predictive control based robust scheduling of community integrated energy system with operational flexibility Applied energy 2019 243 250-265 https://doi.org/10.1016/j.apenergy.2019.03.205 NassourouM BlesaJ PuigV Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty Energies 2020 13 3 696 https://doi.org/10.3390/en13030696 NassourouM PuigV BlesaJ Robust optimization based energy dispatch in smart grids considering simultaneously multiple uncertainties: Load demands and energy prices IFAC-PapersOnLine 2017 50 1 6755-6760 https://doi.org/10.1016/j.ifacol.2017.08.1175 YangS An adaptive robust model predictive control for indoor climate optimization and uncertainties handling in buildings Building and Environment 2019 163 106326 https://doi.org/10.1016/j.buildenv.2019.106326 TanaskovicM Robust adaptive model predictive building climate control IFAC-PapersOnLine 2017 50 1 1871-1876 https://doi.org/10.1016/j.ifacol.2017.08.257 AntonovS HelsenL Robustness analysis of a hybrid ground coupled heat pump system with model predictive control Journal of Process Control 2016 47 191-200 https://doi.org/10.1016/j.jprocont.2016.08.009 ShapiroA Monte Carlo sampling methods Handbooks in operations research and management science 2003 10 353-425 https://doi.org/10.1016/S0927-0507(03)10006-0 HedmanK The application of robust optimization in power systems Final Report to the Power Systems Engineering Research Center PSERC Publication 2014 14-6 Ben-TalA El GhaouiL NemirovskiA Robust optimization 28 2009 Princeton University Press https://doi.org/10.1515/9781400831050 MayneD Robust and stochastic model predictive control: Are we going in the right direction? Annual Reviews in Control 2016 41 184-192 https://doi.org/10.1016/j.arcontrol.2016.04.006
REFERENCES
  1. Kirschen D., Strbac G., Transmission networks and electricity markets, Fundamentals of power system economics, pp 141-204, 2004, https://doi.org/https://doi.org/10.1002/0470020598.ch6
  2. Alam M., Arefifar S., Energy Management in power distribution systems: review, classification, limitations and challenges, IEEE Access, Vol. 7 , pp 92979-93001, 2019, https://doi.org/https://doi.org/10.1109/ACCESS.2019.2927303
  3. Rafique S., Jianhua Z., Energy management system, generation and demand predictors: a review, IET Generation, Transmission … Distribution, Vol. 12 (3), pp 519-530, 2017, https://doi.org/https://doi.org/10.1049/iet-gtd.2017.0354
  4. , , Demand Response, 2020
  5. Vardakas J., Zorba N., Verikoukis C., A survey on demand response programs in smart grids: Pricing methods and optimization algorithms, IEEE Communications Surveys … Tutorials, Vol. 17 (1), pp 152-178, 2014, https://doi.org/https://doi.org/10.1109/COMST.2014.2341586
  6. Palensky P., Dietrich D., Demand side management: Demand response, intelligent energy systems, and smart loads, IEEE transactions on industrial informatics, Vol. 7 (3), pp 381-388, 2011, https://doi.org/https://doi.org/10.1109/TII.2011.2158841
  7. Scheller F., Provoking residential demand response through variable electricity tariffs-a model-based assessment for municipal energy utilities, Technology and Economics of Smart Grids and Sustainable Energy, Vol. 3 (1), pp 7, 2018, https://doi.org/https://doi.org/10.1007/s40866-018-0045-x
  8. Parrish B., Heptonstall P., Gross R., The potential for UK residential demand side participation, System Architecture Challenges: Supergen+ for HubNet, 2016
  9. Uddin M., A review on peak load shaving strategies, Renewable and Sustainable Energy Reviews, Vol. 82 , pp 3323-3332, 2018, https://doi.org/https://doi.org/10.1016/j.rser.2017.10.056
  10. Meyabadi A., Deihimi M., A review of demand-side management: Reconsidering theoretical framework, Renewable and Sustainable Energy Reviews, Vol. 80 , pp 367-379, 2017, https://doi.org/https://doi.org/10.1016/j.rser.2017.05.207
  11. Dounis A., Caraiscos C., Advanced control systems engineering for energy and comfort management in a building environment-A review, Renewable and Sustainable Energy Reviews, Vol. 13 (6-7), pp 1246-1261, 2009, https://doi.org/https://doi.org/10.1016/j.rser.2008.09.015
  12. Yu Z., Control strategies for integration of thermal energy storage into buildings: State-of-the-art review, Energy and Buildings, Vol. 106 , pp 203-215, 2015, https://doi.org/https://doi.org/10.1016/j.enbuild.2015.05.038
  13. Perera D., Pfeiffer >., Skeie N., Control of temperature and energy consumption in buildings-A review, International Journal of Energy … Environment, Vol. 5 (4), 2014
  14. Thieblemont H., Predictive control strategies based on weather forecast in buildings with energy storage system: A review of the state-of-the art, Energy and Buildings, Vol. 153 , pp 485-500, 2017, https://doi.org/https://doi.org/10.1016/j.enbuild.2017.08.010
  15. Shaikh P., A review on optimized control systems for building energy and comfort management of smart sustainable buildings, Renewable and Sustainable Energy Reviews, Vol. 34 , pp 409-429, 2014, https://doi.org/https://doi.org/10.1016/j.rser.2014.03.027
  16. Wang S., Ma Z., Supervisory and optimal control of building HVAC systems: A review, Hvac…R Research, Vol. 14 (1), pp 3-32, 2008, https://doi.org/https://doi.org/10.1080/10789669.2008.10390991
  17. Afram A., Janabi-Sharifi F., Theory and applications of HVAC control systems-A review of model predictive control (MPC), Building and Environment, Vol. 72 , pp 343-355, 2014, https://doi.org/https://doi.org/10.1016/j.buildenv.2013.11.016
  18. Mariano-Hernandez D., A review of strategies for building energy management system: Model predictive control, demand side management, optimization, and fault detect … diagnosis, Journal of Building Engineering, pp 101692, 2020, https://doi.org/https://doi.org/10.1016/j.jobe.2020.101692
  19. Privara S., Building modeling as a crucial part for building predictive control, Energy and Buildings, Vol. 56 , pp 8-22, 2013, https://doi.org/https://doi.org/10.1016/j.enbuild.2012.10.024
  20. Amasyali K., El-Gohary N., A review of data-driven building energy consumption prediction studies, Renewable and Sustainable Energy Reviews, Vol. 81 , pp 1192-1205, 2018, https://doi.org/https://doi.org/10.1016/j.rser.2017.04.095
  21. Hazyuk I., Ghiaus C., Penhouet D., Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part I-Building modeling, Building and Environment, Vol. 51 , pp 379-387, 2012, https://doi.org/https://doi.org/10.1016/j.buildenv.2011.11.009
  22. Fan C., A novel methodology to explain and evaluate data-driven building energy performance models based on interpretable machine learning, Applied Energy, Vol. 235 , pp 1551-1560, 2019, https://doi.org/https://doi.org/10.1016/j.apenergy.2018.11.081
  23. Krese G., Determination of a Building's balance point temperature as an energy characteristic, Energy, Vol. 165 , pp 1034-1049, 2018, https://doi.org/https://doi.org/10.1016/j.energy.2018.10.025
  24. Macarulla M., estimation of a room ventilation air change rate using a stochastic grey-box modelling approach, Measurement, Vol. 124 , pp 539-548, 2018, https://doi.org/https://doi.org/10.1016/j.measurement.2018.04.029
  25. , , The software dymola
  26. , , The software, transient system simulation too,
  27. Zhao J., EnergyPlus model-based predictive control within design-build-operate energy information modelling infrastructure, Journal of Building Performance Simulation, Vol. 8 (3), pp 121-134, 2015, https://doi.org/https://doi.org/10.1080/19401493.2014.891656
  28. Strachan P., ESP-r: Summary of validation studies, Energy Systems Research Unit, 2000
  29. Afroz Z., Modeling techniques used in building HVAC control systems: A review, Renewable and Sustainable Energy Reviews, Vol. 83 , pp 64-84, 2018, https://doi.org/https://doi.org/10.1016/j.rser.2017.10.044
  30. Oldewurtel F., use of model predictive control and weather forecasts for energy efficient building climate control, Energy and Buildings, Vol. 45 , pp 15-27, 2012, https://doi.org/https://doi.org/10.1016/j.enbuild.2011.09.022
  31. Drgon̂a J., , in 52nd IEEE Conference on Decision and Control, 2013
  32. Ma Y., Matuŝko J., Borrelli F., Stochastic model predictive control for building HVAC systems: Complexity and conservatism, IEEE Transactions on Control Systems Technology, Vol. 23 (1), pp 101-116, 2014, https://doi.org/https://doi.org/10.1109/TCST.2014.2313736
  33. Maasoumy M., Handling model uncertainty in model predictive control for energy efficient buildings, Energy and Buildings, Vol. 77 , pp 377-392, 2014, https://doi.org/https://doi.org/10.1016/j.enbuild.2014.03.057
  34. Magni L., Raimondo D., Allgower F., Nonlinear model predictive control, Lecture Notes in Control and Information Sciences, (384), 2009, https://doi.org/https://doi.org/10.1007/978-3-642-01094-1
  35. Camacho E., Alba C., , Model predictive control, 2013
  36. Mesbah A., Stochastic model predictive control: An overview and perspectives for future research, IEEE Control Systems Magazine, Vol. 36 (6), pp 30-44, 2016, https://doi.org/https://doi.org/10.1109/MCS.2016.2602087
  37. Farina M., Giulioni L., Scattolini R., Stochastic linear model predictive control with chance constraints-a review, Journal of Process Control, Vol. 44 , pp 53-67, 2016, https://doi.org/https://doi.org/10.1016/j.jprocont.2016.03.005
  38. Heirung T., Stochastic model predictive control-how does it work?, Computers … Chemical Engineering, Vol. 114 , pp 158-170, 2018, https://doi.org/https://doi.org/10.1016/j.compchemeng.2017.10.026
  39. Kall P., Stochastic programming, European Journal of Operational Research, Vol. 10 (2), pp 125-130, 1982, https://doi.org/https://doi.org/10.1016/0377-2217(82)90152-7
  40. Birge J., Louveaux F., , Introduction to stochastic programming, 2011
  41. Lee Y., Kouvaritakis B., A linear programming approach to constrained robust predictive control, IEEE Transactions on Automatic Control, Vol. 45 (9), pp 1765-1770, 2000, https://doi.org/https://doi.org/10.1109/9.880645
  42. Grimm G., Nominally robust model predictive control with state constraints, IEEE Transactions on Automatic Control, Vol. 52 (10), pp 1856-1870, 2007, https://doi.org/https://doi.org/10.1109/TAC.2007.906187
  43. Yan Z., Wang J., Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks, IEEE transactions on neural networks and learning systems, Vol. 25 (3), pp 457-469, 2013, https://doi.org/https://doi.org/10.1109/TNNLS.2013.2275948
  44. Dong Z., Angeli D., , in 2018 IEEE Conference on Decision and Control (CDC), 2018
  45. Miller B., Wagner H., Chance constrained programming with joint constraints, Operations Research, Vol. 13 (6), pp 930-945, 1965, https://doi.org/https://doi.org/10.1287/opre.13.6.930
  46. Prekopa A., , in Proceedings of the Princeton symposium on mathematical programming, 1970
  47. Kall P., Wallace S., Kall P., , Stochastic programming, 1994
  48. Conejo A., Carrion M., Morales J., , Decision making under uncertainty in electricity markets, 2010
  49. Heitsch H., Romisch W., A note on scenario reduction for two-stage stochastic programs, Operations Research Letters, Vol. 35 (6), pp 731-738, 2007, https://doi.org/https://doi.org/10.1016/j.orl.2006.12.008
  50. Dupacova J., Growe-Kuska N., Romisch W., Scenario reduction in stochastic programming: An approach using probability metrics, Humboldt-Universitat zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät...., 2000
  51. Frauendorfer K., Barycentric scenario trees in convex multistage stochastic programming, Mathematical Programming, Vol. 75 (2), pp 277-293, 1996, https://doi.org/https://doi.org/10.1007/BF02592156
  52. Heitsch H., Romisch W., Scenario tree modeling for multistage stochastic programs, Mathematical Programming, Vol. 118 (2), pp 371-406, 2009, https://doi.org/https://doi.org/10.1007/s10107-007-0197-2
  53. Alqurashi A., Etemadi A., Khodaei A., Model predictive control to two-stage stochastic dynamic economic dispatch problem, Control Engineering Practice, Vol. 69 , pp 112-121, 2017, https://doi.org/https://doi.org/10.1016/j.conengprac.2017.09.012
  54. Gabrel V., Murat C., Thiele A., Recent advances in robust optimization: An overview, European journal of operational research, Vol. 235 (3), pp 471-483, 2014, https://doi.org/https://doi.org/10.1016/j.ejor.2013.09.036
  55. Bertsimas D., Brown D., Caramanis C., Theory and applications of robust optimization, SIAM review, Vol. 53 (3), pp 464-501, 2011, https://doi.org/https://doi.org/10.1137/080734510
  56. Beyer H., Sendhoff B., Robust optimization-a comprehensive survey, Computer methods in applied mechanics and engineering, Vol. 196 (33-34), pp 3190-3218, 2007, https://doi.org/https://doi.org/10.1016/j.cma.2007.03.003
  57. Kothare M., Balakrishnan V., Morari M., Robust constrained model predictive control using linear matrix inequalities, Automatica, Vol. 32 (10), pp 1361-1379, 1996, https://doi.org/https://doi.org/10.1016/0005-1098(96)00063-5
  58. Lombard L., Ortiz J., Pout C., A review on buildings energy consumption information, Energy and buildings, Vol. 40 (3), pp 394-398, 2008, https://doi.org/https://doi.org/10.1016/j.enbuild.2007.03.007
  59. Urge-Vorsatz D., Energy use in buildings in a long-term perspective, Current Opinion in Environmental Sustainability, Vol. 5 (2), pp 141-151, 2013, https://doi.org/https://doi.org/10.1016/j.cosust.2013.05.004
  60. Deng S., Wang R., Dai Y., How to evaluate performance of net zero energy building-A literature research, Energy, Vol. 71 , pp 1-16, 2014, https://doi.org/https://doi.org/10.1016/j.energy.2014.05.007
  61. Torriti J., Hassan M., Leach M., Demand response experience in Europe: Policies, programmes and implementation, Energy, Vol. 35 (4), pp 1575-1583, 2010, https://doi.org/https://doi.org/10.1016/j.energy.2009.05.021
  62. Ghahramani A., Energy savings from temperature set-points and deadband: Quantifying the influence of building and system properties on savings, Applied Energy, Vol. 165 , pp 930-942, 2016, https://doi.org/https://doi.org/10.1016/j.apenergy.2015.12.115
  63. Kampelis N., Evaluation of the performance gap in industrial, residential … tertiary near-Zero energy buildings, Energy and Buildings, Vol. 148 , pp 58-73, 2017, https://doi.org/https://doi.org/10.1016/j.enbuild.2017.03.057
  64. Hannan M., A review of internet of energy based building energy management systems: Issues and recommendations, Ieee Access, Vol. 6 , pp 38997-39014, 2018, https://doi.org/https://doi.org/10.1109/ACCESS.2018.2852811
  65. Han J., Solanki S., Solanki J., Coordinated predictive control of a wind/battery microgrid system, IEEE Journal of emerging and selected topics in power electronics, Vol. 1 (4), pp 296-305, 2013, https://doi.org/https://doi.org/10.1109/JESTPE.2013.2282601
  66. Bordons C., Camacho E., , Model predictive control1, 2007
  67. Killian M., Kozek M., Ten questions concerning model predictive control for energy efficient buildings, Building and Environment, Vol. 105 , pp 403-412, 2016, https://doi.org/https://doi.org/10.1016/j.buildenv.2016.05.034
  68. Scattolini R., Architectures for distributed and hierarchical model predictive control-a review, Journal of process control, Vol. 19 (5), pp 723-731, 2009, https://doi.org/https://doi.org/10.1016/j.jprocont.2009.02.003
  69. Negenborn R., Maestre J., Distributed model predictive control: An overview and roadmap of future research opportunities, IEEE Control Systems Magazine, Vol. 34 (4), pp 87-97, 2014, https://doi.org/https://doi.org/10.1109/MCS.2014.2320397
  70. Peeters M., Compernolle T., Van Passel S., Simulation of a controlled water heating system with demand response remunerated on imbalance market pricing, Journal of Building Engineering, Vol. 27 , pp 100969, 2020, https://doi.org/https://doi.org/10.1016/j.jobe.2019.100969
  71. Perez K., Baldea M., Edgar T., Integrated HVAC management and optimal scheduling of smart appliances for community peak load reduction, Energy and Buildings, Vol. 123 , pp 34-40, 2016, https://doi.org/https://doi.org/10.1016/j.enbuild.2016.04.003
  72. Finck C., Li R., Zeiler W., Economic model predictive control for demand flexibility of a residential building, Energy, Vol. 176 , pp 365-379, 2019, https://doi.org/https://doi.org/10.1016/j.energy.2019.03.171
  73. Liu M., Shi Y., Model predictive control for thermostatically controlled appliances providing balancing service, IEEE Transactions on Control Systems Technology, Vol. 24 (6), pp 2082-2093, 2016, https://doi.org/https://doi.org/10.1109/TCST.2016.2535400
  74. Mahdavi N., Model predictive control of distributed air-conditioning loads to compensate fluctuations in solar power, IEEE Transactions on Smart Grid, Vol. 8 (6), pp 3055-3065, 2017, https://doi.org/https://doi.org/10.1109/TSG.2017.2717447
  75. Biyik E., Kahraman A., A predictive control strategy for optimal management of peak load, thermal comfort, energy storage and renewables in multi-zone buildings, Journal of building engineering, Vol. 25 , pp 100826, 2019, https://doi.org/https://doi.org/10.1016/j.jobe.2019.100826
  76. Bruno S., Giannoccaro G., La Scala M., A Demand Response Implementation in Tertiary Buildings through Model Predictive Control, IEEE Transactions on Industry Applications, Vol. 55 (6), pp 7052-7061, 2019, https://doi.org/https://doi.org/10.1109/TIA.2019.2932963
  77. Halamay D., Starrett M., Brekken T., Hardware Testing of Electric Hot Water Heaters Providing Energy Storage and Demand Response Through Model Predictive Control, IEEE Access, Vol. 7 , pp 139047-139057, 2019, https://doi.org/https://doi.org/10.1109/ACCESS.2019.2932978
  78. Drgon̂a J., Approximate model predictive building control via machine learning, Applied Energy, Vol. 218 , pp 199-216, 2018, https://doi.org/https://doi.org/10.1016/j.apenergy.2018.02.156
  79. Zhou K., Cai L., A dynamic water-filling method for real-time HVAC load control based on model predictive control, IEEE Transactions on Power Systems, Vol. 30 (3), pp 1405-1414, 2014, https://doi.org/https://doi.org/10.1109/TPWRS.2014.2340881
  80. Salakij S., Model-Based Predictive Control for building energy management. I: Energy modeling and optimal control, Energy and Buildings, Vol. 133 , pp 345-358, 2016, https://doi.org/https://doi.org/10.1016/j.enbuild.2016.09.044
  81. Yu N., Model-based predictive control for building energy management: Part II-Experimental validations, Energy and Buildings, Vol. 146 , pp 19-26, 2017, https://doi.org/https://doi.org/10.1016/j.enbuild.2017.04.027
  82. Schirrer A., Nonlinear model predictive control for a heating and cooling system of a low-energy office building, Energy and Buildings, Vol. 125 , pp 86-98, 2016, https://doi.org/https://doi.org/10.1016/j.enbuild.2016.04.029
  83. Staino A., Nagpal H., Basu B., Cooperative optimization of building energy systems in an economic model predictive control framework, Energy and Buildings, Vol. 128 , pp 713-722, 2016, https://doi.org/https://doi.org/10.1016/j.enbuild.2016.07.009
  84. Miyazaki K., Design and value evaluation of demand response based on model predictive control, IEEE Transactions on Industrial Informatics, Vol. 15 (8), pp 4809-4818, 2019, https://doi.org/https://doi.org/10.1109/TII.2019.2920373
  85. Mbungu N., An optimal energy management system for a commercial building with renewable energy generation under real-time electricity prices, Sustainable cities and society, Vol. 41 , pp 392-404, 2018, https://doi.org/https://doi.org/10.1016/j.scs.2018.05.049
  86. Garifi K., , in 2018 IEEE Power … Energy Society General Meeting (PESGM), 2018
  87. Oldewurtel F., Stochastic model predictive control for building climate control, IEEE Transactions on Control Systems Technology, Vol. 22 (3), pp 1198-1205, 2013, https://doi.org/https://doi.org/10.1109/TCST.2013.2272178
  88. Oldewurtel F., , Proceedings of the 2010 American control conference, 2010
  89. Kumar R., Stochastic model predictive control for central HVAC plants, Journal of Process Control, Vol. 90 , pp 1-17, 2020, https://doi.org/https://doi.org/10.1016/j.jprocont.2020.03.015
  90. Nasir H., Stochastic Model Predictive Control Based Reference Planning for Automated Open-Water Channels, IEEE Transactions on Control Systems Technology, 2019
  91. Arasteh F., Riahy G., MPC-based approach for online demand side and storage system management in market based wind integrated power systems, International Journal of Electrical Power … Energy Systems, Vol. 106 , pp 124-137, 2019, https://doi.org/https://doi.org/10.1016/j.ijepes.2018.09.041
  92. Razmara M., Building-to-grid predictive power flow control for demand response and demand flexibility programs, Applied Energy, Vol. 203 , pp 128-141, 2017, https://doi.org/https://doi.org/10.1016/j.apenergy.2017.06.040
  93. Cao Y., Du J., Soleymanzadeh E., Model predictive control of commercial buildings in demand response programs in the presence of thermal storage, Journal of Cleaner Production, Vol. 218 , pp 315-327, 2019, https://doi.org/https://doi.org/10.1016/j.jclepro.2019.01.266
  94. Bianchini G., An integrated model predictive control approach for optimal HVAC and energy storage operation in large-scale buildings, Applied Energy, Vol. 240 , pp 327-340, 2019, https://doi.org/https://doi.org/10.1016/j.apenergy.2019.01.187
  95. Zong Y., Challenges of implementing economic model predictive control strategy for buildings interacting with smart energy systems, Applied Thermal Engineering, Vol. 114 , pp 1476-1486, 2017, https://doi.org/https://doi.org/10.1016/j.applthermaleng.2016.11.141
  96. Hovgaard T., Model predictive control technologies for efficient and flexible power consumption in refrigeration systems, Energy, Vol. 44 (1), pp 105-116, 2012, https://doi.org/https://doi.org/10.1016/j.energy.2011.12.007
  97. Ruusu R., Direct quantification of multiple-source energy flexibility in a residential building using a new model predictive high-level controller, Energy Conversion and Management, Vol. 180 , pp 1109-1128, 2019, https://doi.org/https://doi.org/10.1016/j.enconman.2018.11.026
  98. Gomez-Romero J., A probabilistic algorithm for predictive control with full-complexity models in non-residential buildings, IEEE Access, Vol. 7 , pp 38748-38765, 2019, https://doi.org/https://doi.org/10.1109/ACCESS.2019.2906311
  99. Megahed T., Abdelkader S., Zakaria A., Energy management in zero-energy building using neural network predictive control, IEEE Internet of Things Journal, Vol. 6 (3), pp 5336-5344, 2019, https://doi.org/https://doi.org/10.1109/JIOT.2019.2900558
  100. Cartagena O., Munoz-Carpintero D., Saez D., , 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2018
  101. Hosseini S., Carli R., Dotoli M., A Residential Demand-Side Management Strategy under Nonlinear Pricing Based on Robust Model Predictive Control, 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), 2019, https://doi.org/https://doi.org/10.1109/SMC.2019.8913892
  102. Lv C., Model predictive control based robust scheduling of community integrated energy system with operational flexibility, Applied energy, Vol. 243 , pp 250-265, 2019, https://doi.org/https://doi.org/10.1016/j.apenergy.2019.03.205
  103. Nassourou M., Blesa J., Puig V., Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty, Energies, Vol. 13 (3), pp 696, 2020, https://doi.org/https://doi.org/10.3390/en13030696
  104. Nassourou M., Puig V., Blesa J., Robust optimization based energy dispatch in smart grids considering simultaneously multiple uncertainties: Load demands and energy prices, IFAC-PapersOnLine, Vol. 50 (1), pp 6755-6760, 2017, https://doi.org/https://doi.org/10.1016/j.ifacol.2017.08.1175
  105. Yang S., An adaptive robust model predictive control for indoor climate optimization and uncertainties handling in buildings, Building and Environment, Vol. 163 , pp 106326, 2019, https://doi.org/https://doi.org/10.1016/j.buildenv.2019.106326
  106. Tanaskovic M., Robust adaptive model predictive building climate control, IFAC-PapersOnLine, Vol. 50 (1), pp 1871-1876, 2017, https://doi.org/https://doi.org/10.1016/j.ifacol.2017.08.257
  107. Antonov S., Helsen L., Robustness analysis of a hybrid ground coupled heat pump system with model predictive control, Journal of Process Control, Vol. 47 , pp 191-200, 2016, https://doi.org/https://doi.org/10.1016/j.jprocont.2016.08.009
  108. Shapiro A., Monte Carlo sampling methods, Handbooks in operations research and management science, Vol. 10 , pp 353-425, 2003, https://doi.org/https://doi.org/10.1016/S0927-0507(03)10006-0
  109. Hedman K., The application of robust optimization in power systems, Final Report to the Power Systems Engineering Research Center, pp 14-6, 2014
  110. Ben-Tal A., El Ghaoui L., Nemirovski A., , Robust optimization, 2009
  111. Mayne D., Robust and stochastic model predictive control: Are we going in the right direction?, Annual Reviews in Control, Vol. 41 , pp 184-192, 2016, https://doi.org/https://doi.org/10.1016/j.arcontrol.2016.04.006

DBG