## 1. Introduction

The power consumption in the distribution network is predicted to significantly increase owing to the electrification of transport and heating [

1]. In addition, the peak load is expected to double by 2050 [

2]. The peak load in the conventional load curve usually occurs during the daylight hours. Therefore, the issue of peak load may seem to be insignificant in the new load curve changed by large introduction of photovoltaics (PV). However, the large introduction of PV has caused the peak load to occur after sunset, but the importance of peak load reduction remains unchanged [

3]. Increasing the peak load requires to upgrade conventional substations and lines or adding new substations and lines. As this increases the operating costs, the distribution system operators (DSOs) or electric utility companies (EUCs) try to reduce the peak load in the distribution network [

4].

In this environment, a EUC should maintain the operating stability of the distribution network while maximizing its profit. With the development of information technology, the demand side has become increasingly important to solve the problem such as peak load reduction in a power system. To accomplish one’s role, the EUC uses the demand response (DR), which is the behavior of consumers adjusting their normal power consumption patterns through voluntary participation owing to monetary incentives [

5]. The end-users provide the EUC with a time shift in demand resulting from reducing their convenience and receive incentives from the EUC. For example, the consumers provide the grid operator with time shift in demand obtained at the expense of their comfort, and the grid operator uses it to reduce peak load [

6]. The applications of DR to peak load reduction were widely considered in many studies in [

7,

8,

9,

10].

HVAC systems have several advantages as DR resources. Heating, ventilating, and air-conditioning (HVAC) systems represent approximately 37% of all electricity usage in commercial buildings, accounting for more than 13% of the total electricity demand in the United States in 2017 [

11]. In particular, advances in variable speed drives (VSDs) and building energy management systems (BEMSs) have improved the control technology of HVAC systems [

12]. This paper adopts a direct control method of HVAC system [

12,

13], where the reference power input is adjusted to maintain the indoor temperature within an acceptable range. Since the reference power input is almost the same as power input of HVAC system because of the fast time response of the VSD. In addition, the HVAC systems are essential facilities for commercial buildings and do not require additional installation.

Many studies have been carried out on the DR of HVAC systems. The studies on DR can be broadly divided into studies on control of DR resources as price takers and studies on optimal pricing for inducing demand response. For example, in [

14,

15], the electricity prices were assumed to be determined in advance. In [

14], the building operator schedules the optimal power consumption profiles of HVAC systems that minimize their total operation cost. [

15] proposed an optimal control algorithm for HVAC systems, considering non-interruptible loads. In [

16,

17], the retail prices for the distribution network operation were optimally determined, considering the DR services of HVAC systems. HVAC system models were implemented via an approach using equivalent thermal parameters (ETPs). In particular, the EUC minimized the operation cost considering the line congestion and power balance in [

16,

17].

We propose optimal pricing decision model to reduce the peak load using HVAC system in this paper. Our paper has been compared with several previous studies on the development of retail pricing strategies for distribution network management via optimal operation of DR resources, particularly, with respect to the three comparative criteria such as decision models, DR resource models, and network load curves [

10,

16,

17,

18,

19,

20,

21,

22,

23].

For example, with the type of decision models, bi-level decision models were formulated in this paper, and in [

18,

19,

20,

21], whereas single-level decision models were developed in [

16,

17] and [

10,

22,

23], depending on the types of decision-makers and their objective functions. The single-level decision models in [

16,

17] and [

10,

22,

23] could not reflect the characteristic of DR resources because the price demand function and price sensitivity were assumed to be simple linear or quadratic function. While the bi-level decision models in [

18,

19,

20,

21] could consider the optimal demand of DR resources for retail electricity price because the hierarchical relationships between decision-makers could be reflected by bi-level optimization problem. In other words, the bi-level decision model reflects the conflicting objective functions of the autonomous decision-makers based on Stackelberg game theory.

The bi-level decision models are too complicated to implement, so simple DR resource models are applied in [

18,

19,

20,

21]. DR resources were simply modeled as point sources or ESSs in [

18,

19,

20,

21] and [

10,

23], without sufficient consideration of their physical characteristics. Thermal loads, on the other hand, are difficult to model owing to their nonlinear nature, and the thermal loads were simply modelled using ETP approach [

16,

17]. ETP approach is modelled using lumped thermal capacitance and resistance. On the other hand, we have explicitly incorporated the experimental data-driven models of the building room and HVAC unit to reflect their physical properties into the bi-level pricing strategy.

In addition, the network load curves can be categorized into two groups, depending on the large introduction of PV. As more PV is introduced into the distribution network, the conventional load curve changed its shape with a lower load during periods of sunshine. For brevity, this new load curve is referred to as a duck curve hereafter in this paper. The duck curve has a negative effect on the network because the demand increases rapidly and the peak load of the duck curve occurs after sunset, when PV is no longer available. However, few studies have attempted to solve the duck curve problem using DR resources.

In this paper, we propose a bi-level optimal pricing model for the EUC to reduce the peak load of two types of load curves using the experimental data-driven model of an HVAC system in commercial buildings. Specifically, in the upper level, the EUC maximize its profit based on advantages of locational marginal pricing (LMP) and time-of-use (TOU) rates. While in the lower level, building end-users schedule the optimal power inputs of HVAC systems to minimize the electricity bills according to the optimal retail rates. This allows the EUC to obtain more accurate and useful insights into the load shifting or curtailment capacities of HVAC systems, when the proposed pricing strategy is applied to DR programs in practice. Moreover, this enables building managers to ensure the thermal comfort of occupants and, consequently, participate more fully in DR programs due to improved comprehension of the inherent thermal energy storage capacity in their building structures.

In addition, the proposed pricing strategy is applied to the peak load reduction of two types of load curve patterns: a conventional load curve and duck curve. The proposed pricing method induces DR of HVAC system in commercial buildings, and through this, we analyzed the effect of the proposed pricing strategy on the peak load reduction. Further, the proposed pricing model was demonstrated through explicit analysis of various case studies such as change of DR purpose and constraints’ parameter.

Section 2 explains the pricing strategy framework using the thermal response of the HVAC system in a commercial building.

Section 3 presents the optimization problem formulation for the proposed method.

Section 4 discusses the simulation case study results for the proposed pricing strategy.

Section 5 provides our conclusions.