1. Introduction
Residential and commercial buildings consume a large share of the energy consumption in the E.U. and USA [
1]. Heating, ventilation, and air conditioning (HVAC) systems alone consume around 44% of the total energy required in commercial buildings, which necessitates the control of such systems [
2]. While the HVAC control in residential buildings and their participation in residential demand response have received a lot of attention [
3,
4,
5], coordination of commercial buildings still needs further research. Unlike residential buildings, commercial buildings are more challenging to optimize and coordinate. This is because a generalized model for commercial buildings cannot be easily achieved due to the complexity and customization of different commercial buildings, which stems from the fact that commercial HVAC systems consist of multiple parts (chillers, air handling units, variable or constant air boxes, etc.) and they can be configured in many ways.
To evaluate the potential of commercial buildings in participating in demand response, two years of smart meter data coming from an urban area in New York was used in [
6]. It was found that the demand characteristics of commercial buildings in which the strict temperature requirements coincide with the time of use on-peak period make it challenging for most commercial buildings to participate in demand-side management effectively. Different researchers proposed different control methodologies to help minimze the energy cost of commercial buildings and facilitate their integration into the grid [
7,
8,
9]. Model predictive control (MPC) is one of the most commonly used controllers for commercial HVAC optimization [
10]. Data-driven MPC was used in [
11] to optimally schedule the heating system in order to save energy while guaranteeing the thermal comfort for the occupants. A linearized random forest model was used to develop the data-driven MPC and it was found that the MPC could provide comparable performance with the conventional physics-based MPC. Stochastic model predictive control (SMPC) for commercial HVAC control was proposed in [
12], where a finite probability density function was used to reflect the uncertainties associated with the thermal loads of different zones. In [
13], a neural network was deployed to model the building temperature dynamics and a linear regression for the energy consumption. Experimental evaluation of data-driven optimization was conducted, where integer linear programming was used to minimize the energy costs while satisfying the thermal comfort. Other authors considered the use of reinforcement learning for whole-building HVAC control [
14,
15] to minimize the energy cost while maintaining the thermal comfort. The reinforcement learning allowed for the possibility of adopting more accurate nonlinear models of the HVAC system but the optimiality of the operation is not guaranteed.
A virtual battery model for a commercial building was developed in [
16], where data-driven and physics based-modeling were used to learn the building’s thermal characteristics. Then, a model predictive controller was developed to enable real-time ramping service participation. To ensure a fast response, the MPC was tested under different possible circumstances, where an input–output mapping is recorded and saved in a scheduler that is used for real-time control. All the previous works focused on the optimization of an individual commercial building.
To leverage the use of commercial buildings in providing grid services, some researchers developed more comprehensive controllers that are able to coordinate multiple buildings or resources. Agent-based modeling was proposed in [
17] to study the consumption behavior of commercial buildings participating in demand response under different market structures. The results illustrate that there is an obvious impact from commercial buildings with price-responsive demand on the electricity market. In [
18], the authors developed a generalized battery model for buildings with the aim of analyzing the buildings’ flexibility and ability to provide different grid services. The effect of lock-off time of virtual battery models was assessed in [
19]. It was found that with the lock-off time, the flexibility does not greatly change when following slow grid signals, but was much reduced when following fast signals.
Many researchers considered centralized coordination of commercial buildings and resources. Centralized coordination of buildings, thermal energy storage and unit commitment was considered in [
20], where buildings were modeled as exponential functions of voltage and non-uniform horizon MPC was used to tackle the uncertainty and ensure load generation balance. Another centralized model predictive control was developed in [
21] to reduce the maximum load ramp-rate of the power grid to prevent duck-curve issues associated with the increase in solar PV power penetration in the grid. The MPC was used to maximize the building load penetration while controlling the transformer tab changes and capacitors in the distribution system. Centralized energy management of commercial buildings in a microgrid was considered in [
22]. In this work, the authors suggested a pricing model which aims at maintaining low operational costs while utilizing solar generation, stationary battery systems and mobile EV storage as much as possible. The authors in [
23] provided a framework for energy optimization in neighborhoods. The authors considered the existence of multiple resources and buildings. Detailed physics-based models via Modelica have been used to represent the buildings’ dynamics while a quasi-dynamic approach was used for the load flow of the network.
In [
24], centralized, mixed-integer, non-linear programming was suggested to optimize the operation of multiple buildings in a microgrid. Linearization and equivalent representation of a pre-processed building model in Energyplus was used. Game theory was also deployed for optimal allocation of power among the buildings. In [
25], RC networks were used for building modeling and a cooperative Nash bargaining formulation was developed to optimally allocate the power among campus buildings. Network constraints were not considered. Other researchers studied hierarchical control approaches. In [
26], a hierarchical framework is proposed where the buildings optimize their consumption, taking network constraints into consideration, and send their operational constraint and other information to the distribution system operator. Then, the operator sends a feedback signal that might include other operational constraints for scheduling. An economic framework that solves a bi-level optimization problem was developed in [
27]. The framework made sure that the followers/households and the retailers would benefit simultaneously, without unexpected deviations from the household side. However, no highlights on the building models were provided and the network technical constraints were not considered.
In a microgrid framework where multiple resources and loads need to be coordinated, the operator should maintain the technical reliability of its local grid while minimizing the operational costs. In [
28], the authors provided insights into the different operational modes of a microgrid consisting of multiple resources and loads. The authors compared four kinds of conditional equations, which are: conditional equations for peak control, power use flattening, power demand response and operation of net zero energy. It was found that the conditional equations were effective when attempting to optimize the microgrid’s performance efficiently. The paper did not consider the modeling and control of HVAC systems in the grid. In [
29], the authors provided a control algorithm for residential HVAC systems in a microgrid to minimize the cost, minimize the size of the microgrid units and minimize the imported energy from the distribution grid. A physics-based model of the residential HVAC has been adopted where the information about the wall thermal losses was used via the use of transmission coefficient and infiltration of the walls.
In the operation of microgrids that have multiple buildings, the privacy issue of the different buildings arises as a major concern and the microgrid operator should ensure good operation of the system with minimal information about the buildings. Therefore, decentralized coordination alorithms arise as a viable option that can help achieve these goals. Decentralized coordination of commercial buildings has been rarely investigated in the literature. In [
30], Dantzig–Wolfe decomposition was used to transform the centralized coordination problem between a building manager and an EV aggregator into a decentralized one. Power flow and grid constraints were not considered in this work. In addition, Dantzig–Wolfe decomposition can only be used with problems with a certain structure where there is a binding constraint between the entities under consideration. Therefore, it can not be used in many cases. In this work, a more comprehensive framework that can handle problems with common objectives is considered. In addition, this work investigates how the building model affects the cost and flexibility of the entire microgrid.
Therefore, in this work, a two-level scheduling framework is proposed to satisfy the system requirements. At the global level, the system operator (i.e., microgrid/enterprise/campus operator) is required to minimize the total cost of the electricity purchased from the utility company as well as maintaining the operating conditions of its power grid within satisfactory conditions. At the local level, the building managers are required to maintain a certain thermal comfort for the occupants of the building during the day. The proposed approach is a decetralized one which minimizes the amount of exchanged data and information with the system operator, which may result in privacy concerns and require extra communication investment. In addition, the buildings’ models in this work are based on the building historical data that can be readily available in the building automation system. It is worth highlighting that most commercial buildings are usually equipped with a building automation system that can easily store different historical data about the building performance. This makes the proposed algorithm more generalizable and favorable for most commercial buildings regardless of the building customization.
Based on the above discussion, the main contributions of this paper are: 1. Developing and comparing different data-driven buildings’ models; 2. Developing a decentralized coordination among the buildings to reduce the cost and voltage deviations while maintaining the thermal comfort of each building; 3. Analyzing the effect of the building models on the overall costs and flexibility of the microgid.
2. Methodology
The proposed methodology aims at minimizing the total cost of the purchased electricity by the microgrid as well as improving the voltage deviations of the power network. The voltage deviation is considered in this work as a main concern for the microgrid operator where the voltage should be within the ANSI standards between 0.95 p.u and 1.05 p.u. Based on that, this consideration of voltage deviations can only be made by the microgrid operator as the building operator does not have access to system-wide information such as the voltages at different buses.
In addition, the proposed method ensures that the temperature in different buildings, coordinated by the microgrid operator, is maintained within the comfort range required by each building manager. The coordination occurs in a decentralized way. This helps alleviate the need for investments in the communication infrastructure as well as maintaining the privacy of different buildings.
Figure 1 shows the architecture of the proposed optimization framework. It is a two-level framework where the system-level optimization is responsible for limiting the voltage deviations in the network as well as minimizing both the energy and demand charges of the purchased electricity. The decision variables at the upper level are the virtual price signals that will guide the consumption of different buildings, while the decision variables at the lower levels are the switching statuses of the HVACs in different buildings. The upper level receives the actual time of use (ToU) signal and tries to come up with a synthetic set of virtual prices that will be sent to the different buildings in the lower-level optimization. The idea of virtual prices has been considered in a variety of different studies [
31,
32,
33] ranging from relieving network congestion to other cost related objectives. The advantage of a virtual price signal is that it provides a cheap and effective way to coordinate and harness the flexibility of multiple entities in the grid. It alleviates the need for high investment in the communication infrastructure to share large amounts of data. It also helps to maintain the privacy of different users in the grid since only the expected total demand is shared with the upper-level operator. When the virtual price signals become decision variables in the optimization problem, they can be optimally determined by the optimizer.
The objective of the lower-level optimization is to minimize its operating costs while maintaining the required temperature comfort range. In doing so, it is assumed that the building manager does not want to expose any detailed information about the building, e.g., HVAC system structure, its schedules or temperature comfort range. Therefore, the only outcome of the building-level optimization that is shared with the system operator is the expected building power profile. The decision variables at the building level are the switching statuses of the HVAC system.
Different buildings will submit their power profiles, and load flow analysis for the power network will be performed. Then, the total system power profile as well as the line flows and voltages at the different buses will be sent to the upper layer, which will evaluate the different objectives and adjust the virtual price signals and send them back to building levels. This iterative process will continue until a stopping criterion is achieved.
The main intuition behind this proposed methodology is to prevent the rebound effect that might occur if all the building received the same actual ToU. The rebound effect happens when multiple loads defer their demand during the peak time of the ToU signal; then, all the loads are connected at the same time with the start of the off-peak period, which introduces another peak in the system. This phenomenon was confirmed by many researchers [
34,
35,
36]. In the case of a microgrid operator, the introduced peaks in the system will cause an increase in the demand charge (a cost that is a function of the system peak), which is usually paid by the commercial building operator. In addition, it can cause undesirable voltage deviations in the system. Thus, the proposed methodology attempts to synthesize virtual price signals that will help to minimize the energy cost and avoid introducing such system peaks as much as possible, which in turn will reduce the total costs of the purchased electricity and improve the voltage deviations of the system. For any building optimization, building models are needed. Therefore, the next section will introduce the three types of data-driven models adopted in this work.
4. Building-Level Optimization
The main objective of the building-level optimization is to minimize the energy cost while ensuring that the building temperature is within the comfort range required by the building manager. The main objective is formulated in Equation (
7), where
represents the virtual price signal for building
k that is received from the higher-level optimization.
is the power consumption of the building that is modeled in
Section 3.
D is the temperature deviation outside the comfort range while
F is a penalty value to penalize any temperature deviation. The second part of Equation (
7) is added to ensure that a feasible solution will exist while the upper optimization is scanning the search space. A high value of
F is used to ensure that the deviation will only be allowed if the building optimization problem becomes infeasible. It is worth highlighting that the cost obtained by (
7) is not the actual cost of purchased power by the microgrid operator.
The building is subject to constraints defined by constraints (
8)–(
10). Constraint (
8) enforces the temperature to be between minimum and maximum values. These minimum and maximum values are not constant across the day. Mostly, they differ between the working and non-working hours of the day. In addition, they are different from one building to another.
The case study under consideration is for a hot region. Therefore, the HVAC is required to cool down the building. Based on this, the deviation term is added to the right-hand side of the constraint to relax the upper bound in case of infeasability. This means that the temperature can go beyond the maximum allowed temperature if the problem becomes infeasible due to a modeling error or tight values of the virtual prices. Bounds on the deviation are enforced by constraint (
9), which limits the maximum temperature deviation at any time step to be less than 0.5 °C. The building temperature
is forecast based on the models in
Section 3.
To limit excessive cycling of the HVAC equipment, which can reduce its life time, constraint (
10) puts a limit on the minimum up and down times, where
O is the switching status of the HVAC, which is the main decision variable in the lower-level optimization. This constraint ensures that if the HVAC is switched on, it will be on for at least some time, which is defined to be 20 min in this paper. The same applies for the switching-off periods.