Abstract
This paper proposes a decentralized demand management approach to reduce the energy bill of industrial park and improve its economic gains. A demand management model for industrial park considering the integrated demand response of combined heat and power (CHP) units and thermal storage is firstly proposed. Specifically, by increasing the electricity outputs of CHP units during peak-load periods, not only the peak demand charge but also the energy charge can be reduced. The thermal storage can efficiently utilize the waste heat provided by CHP units and further increase the flexibility of CHP units. The heat dissipation of thermal storage, thermal delay effect, and heat losses of heat pipelines are considered for ensuring reliable solutions to the industrial park. The proposed model is formulated as a multi-period alternating current (AC) optimal power flow problem via the second-order conic programming formulation. The alternating direction method of multipliers (ADMM) algorithm is used to compute the proposed demand management model in a distributed manner, which can protect private data of all participants while achieving solutions with high quality. Numerical case studies validate the effectiveness of the proposed demand management approach in reducing peak demand charge, and the performance of the ADMM-based decentralized computation algorithm in deriving the same optimal results of demand management as the centralized approach is also validated.
INDUSTRIAL park (or industrial estate) is an area planned for industrial development, which is usually associated with significant energy demands, especially electricity and natural gas. In terms of electric energy consumption, industrial park in many countries such as China and the United States is usually charged by a two-part tariff (TPT) policy [
Indeed, for some large-scale industrial parks, the peak demand charge is usually higher than the energy charge, which can reach up to 50%-70% of the monthly electricity bill [
Demand response (DR) has been traditionally recognized as the key technique to realize demand management of large industrial/commercial/residential customers [
Another widely-used DR approach is to install battery storage assets in industrial park. Battery storage can store electric energy during low-price periods and release the stored electricity to supply users during high-price periods. Demand management approaches using battery storages have been studied in [
Moreover, due to the high efficiency of energy utilization, the integrated energy system (IES) has drawn increasing attentions by academia and energy industry in recent years [
IDR techniques have also been studied in a few papers [
To address the challenges mentioned above, this paper proposes a decentralized demand management approach for industrial park with CHP units and thermal storage. Specifically, the IDR of CHP units and thermal storage is explored to manage the peak electricity demand, thus reducing electricity bill of the industrial park under the TPT policy. Our proposed model is built on an alternating current (AC) power flow of electrical distribution network via the second-order conic programming (SOCP) formulation. Moreover, the heat dissipation of thermal storage as well as thermal delay effect and heat losses of heat pipelines are also considered for ensuring reliable solutions to the industrial park. The main contributions of this paper are summarized as follows.
1) Aiming at the TPT policy for industrial park, we propose a new demand management model built on an SOCP-based AC power flow of electrical distribution network considering the IDR from CHP units. CHP units can increase their electricity outputs during peak-load periods when not operated in the FHL mode, which can reduce the peak demand charge and the total energy charge.
2) To utilize the excessive heat generated by CHP units more efficiently, a central thermal storage is adopted in industrial park to enable the effective heat sharing among all participants considering the heat dissipation of thermal storage, thermal delay effect, and heat losses of heat pipelines. More importantly, our proposed demand management model realizes the coordination between thermal storage and CHP units to grant more flexibility to CHP units.
3) The alternating direction method of multipliers (ADMM) algorithm is utilized to compute our proposed demand management model in a distributed manner while achieving solutions with high quality, which can protect the private data of all participants in demand management of industrial park.
4) Numerical case studies demonstrate that our proposed demand management approach can significantly reduce the peak demand charge and enhance economic gains for industrial park. Moreover, the effectiveness of our proposed ADMM-based decentralized computation algorithm is also validated, which can obtain the same optimal results as the centralized approach.
The rest of this paper is organized as follows. Section II introduces the centralized demand management of industrial park using CHP units and thermal storage. Section III discusses the ADMM-based decentralized demand management framework. Case studies are presented in Section IV. This paper is concluded in Section V.
This section presents a centralized framework for industrial park demand management, which targets to efficiently manage the industrial park demand through the IDR of energy coupling equipment. Section II-A discusses the industrial park demand management with CHP units, and in Section II-B, the proposed approach is extended to involve the centralized thermal storage in industrial park.
In this paper, we focus on an industrial park with individual users.

Fig. 1 Structure of industrial park with individual users.
The centralized demand management model for industrial park with CHP units is firstly proposed as shown in (1)-(15). The objective function (1) is to minimize the total cost of industrial park over one month, including the electricity consumption cost and the natural gas consumption cost. Under the TPT policy, the electricity consumption cost consists of two parts, i.e., the electricity energy charge denoted by the first term in (1), and the peak demand charge denoted by the second term in (1). The natural gas consumption cost includes the gas consumption charge of all CHP units, as shown in the third term of (1).
(1) |
s.t.
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
(14) |
(15) |
Constraint (2) indicates the active and reactive power balance of each industrial user. Constraint (3) imposes that the CHP heat output of each user must satisfy its heat demand in order to guarantee the reliable heat supply. Constraints (4), (5), and (6) represent the operation constraints of CHP units [
Moreover, the SOCP-based AC power flow model as shown in (7)-(14) is used to simulate electrical distribution network in the industrial park. Specifically, (7) and (8) describe the nodal active and reactive power balance for each node in the electrical distribution network, respectively. The voltage drop on each distribution line is formulated in (9).
Although the proposed model in Section II-A can effectively manage industrial park electrical load through DR of CHP units, a large amount of heat generated by CHP units in the peak-load period could be abandoned. This is because, in order to reduce electricity purchase from the utility during the peak-load period, CHP units increase their electricity outputs, which simultaneously induce high heat outputs. However, the increased heat outputs of CHP units may exceed the actual heat demand of individual users. To this end, the excessive heat generated by CHP units could be abandoned, leading to low energy efficiency in industrial park. To deal with this issue, a centralized thermal storage is adopted in industrial park to store and share heat among all individual users, as shown in

Fig. 2 Structure of industrial park with individual users and centralized thermal storage.
Thermal storage can store the surplus heat generated by CHP units during peak-load periods, which can be released during off-peak periods to supply individual users. The demand management model in Section II-A is enhanced as in (16)-(21) to involve the centralized thermal storage. The centralized thermal storage is connected to all users by heat pipelines. The heat dissipation of thermal storage and thermal delay effect, and the heat losses of heat pipelines are considered for ensuring reliable solutions to industrial park.
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
Constraint (17) formulates the heat power balance of each user. It is well-known that compared with electricity, heat is transported through pipelines at a relatively low speed, which could result in delays in the thermal transmission process, varying from several minutes to several hours [
The centralized demand management model described in Section II requires that all individual users shall directly submit some of their commercially confidential data such as EL data and HL data to the central demand manager of industrial park. The centralized demand management model is generally suitable for industrial park where all participants belong to a same company, so that data privacy will not be an issue. However, in most cases, participants in demand management of industrial park usually come from different companies, leading to the difficulty in implementing the centralized demand management approach. To deal with the above challenge, ADMM algorithm is used to compute the centralized model in Section II in a distributed manner, which can protect the commercially confidential data of all participants in demand management.
To implement the decentralized demand management using ADMM algorithm, the centralized demand management model in Section II-B is firstly reformulated as a standard sharing problem [
(22) |
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
(29) |
Constraint (25) represents the total gas purchase cost of the th user () from utilities over one month. To reformulate the centralized model as the standard sharing problem in [
Note that the reformulated model as shown in (22)-(29) is mathematically equivalent to the centralized demand management model in Section II-B. Specifically, constraint (24) is the equivalence of the heat power balance constraint (20) of the centralized thermal storage.
We further develop an ADMM-based decentralized demand management approach to solve the reformulated model as shown in (22)-(29). First, the augmented Lagrangian function of the reformulated model as shown in (22)-(29) is defined as in (30).
(30) |
For the sake of discussion, (30) is written as the scaled form (31) by combining the linear and quadratic terms, where and are scaled dual variables.
(31) |
Then, using the ADMM algorithm, (31) can be solved by iterating the following three updates:
Two stopping criteria as shown in (35) are utilized in this paper to determine whether the ADMM iteration shall stop. The two stopping criteria can evaluate the convergence performance of primal residual and dual residual, respectively.
(35) |
The pseudocode of ADMM algorithm is shown in Algorithm 1.

Fig. 3 Data exchange of ADMM-based decentralized demand management between industrial park operator and two illustrative industrial users.
In this section, our proposed ADMM-based decentralized demand management approach for the industrial park with CHP units and centralized thermal storage is validated through an exemplary industrial park with three industrial users. The electricity network is based on the IEEE 33-bus distribution system. One typical day from each week is selected, and then four typical days are collectively used to represent the entire month. Each selected typical day is the day with the hourly maximum EL in that week. Moreover, the typical day with the monthly maximum load among the four days is hereinafter referred to as the peak-load typical day. Penalty parameters of ADMM algorithm, i.e., and , are both set to be 0.10. The tolerances and are both set to be 1
The proposed demand management approach for industrial park intends to reduce the electricity cost under TPT by leveraging the DR ability of CHP units to TOU prices, as presented in Section II-A. To validate the effectiveness of our proposed demand management approach, the following two approaches are compared.
1) Directly purchasing electricity (DPE): in this approach, the industry park directly purchases electric energy from utilities. CHP units work in the FHL mode, and cannot provide IDR in response to TOU prices. That is, DPE does not realize demand management for industrial park.
2) Demand management by CHP units (DM_CHP): this is our proposed demand management approach with DR of CHP units, as discussed in Section II-A. During peak-load periods, CHP units could increase their electricity outputs to supply ELs.
Numerical results of the two approaches are illustrated in

Fig. 4 Comparison of electricity power purchased from utility and heat power provided by CHPs between DPE and DM_CHP in typical peak-load day. (a) Electricity power purchased from utility. (b) Heat power provided by CHPs.
The significant increase in the natural gas cost is mainly caused by the more natural gas consumption of CHP units to increase electricity output during peak-load periods. Indeed, CHP units also increase their heat outputs during peak-load periods, as indicated in
To effectively utilize waste heat and increase the energy efficiency, we enhance our demand management approach by including a centralized thermal storage in industrial park, which can store and share heat among all users, as presented in Section II-B. To validate the effectiveness of the centralized thermal storage for industrial park demand management, the following two approaches are compared:
1) DM_CHP: this is the same approach studied in Section IV-A, i.e., the proposed demand management approach without centralized thermal storage.
2) DM_CHP and centralized thermal storage (DM_CHP&CTS): it represents our proposed demand management approach with DR of CHP units as well as centralized thermal storage, as shown in Section II-B.
Numerical results of the two approaches are illustrated in

Fig. 5 Comparison of electricity power purchased from utility between DM_CHP and DM_CHP&CTS as well as charging/discharging heat power of centralized thermal storage in typical peak-load day.
In the centralized demand management approach, the participants in DR are from different companies, which makes it practically challenging to share private information. This motivates us to adopt the ADMM-based decentralized demand management approach in Section III, which can keep commercially sensitive information of participants from being disclosed. To validate the effectiveness of our proposed decentralized approach, the following two approaches are compared.
1) DM_CEN: it represents the centralized industrial park demand management approach, as shown in Section II-B.
2) DM_ADMM: it represents the ADMM-based decentralized demand management approach, as shown in Section III.
Numerical results of the two approaches are illustrated in

Fig. 6 Evolution of peak demand over iterative procedure of ADMM for demand management of industrial park.
From
To verify the scalability of the proposed ADMM-based decentralized demand management approach for practical industrial park, sensitivity analysis is designed to study the impacts of different numbers of selected typical days as well as industrial users. The results are shown in

Fig. 7 Changes of peak demand and computation time with different numbers of typical days for ADMM-based decentralized approach.

Fig. 8 Changes of relative peak demand difference and computation time with different numbers of industrial users for ADMM-based decentralized approach.
Under the TPT policy, this paper develops a decentralized industrial park demand management approach considering the IDR of CHP units and centralized thermal storage. The centralized demand management model for industrial park with CHP units and thermal storage is firstly proposed, which is built on an AC power flow of electrical distribution network via the SOCP formulation. The heat dissipation of thermal storage as well as thermal delay effect and heat losses of heat pipelines is considered in the proposed model. Then, the proposed model is computed by the ADMM algorithm in a distributed manner to protect private data of all participants while deriving solutions with high quality.
Numerical results validate the effectiveness of our proposed demand management approach. Specifically, through the IDR of CHP units, both peak electricity demand and the electricity power purchased from the utility decrease significantly, leading to noticeable savings in both peak demand charge and electricity energy charge for industrial park. After involving the centralized thermal storage, the total energy bill of industrial park further decreases, because thermal storage efficiently utilizes the waste heat and increases the flexibility of CHP units. Finally, the ADMM-based decentralized approach can provide the same optimal results of demand management as the centralized approach, while presenting smaller volume of data exchange.
NOMENCLATURE
Symbol | —— | Definition |
---|---|---|
A. | —— | Indices and Sets |
—— | Set of receiving nodes of distribution lines with the same sending node | |
—— | Set of distribution lines, i.e., | |
—— | Indices of nodes, days, and time periods | |
—— | Subset of buses connected to industrial users and total number of industrial users | |
—— | Indices of sending and receiving nodes of distribution lines | |
—— | Set of days, i.e., | |
—— | Index of nodes | |
—— | Set of nodes in power system, i.e., | |
—— | Set of nodes in power system except nodes connected to industrial users | |
—— | Set of time periods, i.e., | |
B. | —— | Continuous Variables |
—— | Dual variables for electricity/heat in node at time of day | |
—— | Total gas purchase cost of the th user from utilities over one month | |
—— | Stored energy level of thermal storage at time of day | |
—— | Natural gas consumption of combined heat and power (CHP) units in node at time of day | |
—— | Heat output of CHP units in node at time of day | |
—— | Charging/discharging heat of thermal storage from/to all users at time of day | |
—— | Charging/discharging heat of thermal storage from/to user at time of day | |
—— | Heat loss of pipelines connecting to user when charging/discharging thermal storage at time of day | |
—— | Squared current magnitude of distribution line at time of day | |
—— | Active/reactive power flow on distribution line at time of day | |
—— | Power output of CHP units in node at time of day | |
—— | Auxiliary variables of node at time of day | |
—— | Industrial park electricity power purchased from utility at time of day | |
—— | Monthly peak electricity demand | |
—— | Net electricity/heat load of node at time of day | |
—— | Active/reactive power output of photovoltaic (PV) panels in node at time of day | |
—— | Reactive power delivered to industrial park by the utility at time of day | |
—— | Reactive power output of static var generator (SVG) in node at time of day | |
—— | Scaled dual variables for electricity/heat in node at time of day | |
—— | Squared voltage magnitude of node at time of day | |
C. | —— | Parameters |
—— | Attenuation coefficient of thermal storage | |
—— | Tolerances of stopping criterion of alternating direction method of multipliers (ADMM) algorithm corresponding to primal residual and dual residual, respectively | |
—— | Charging/discharging efficiency factors of thermal storage | |
—— | Electricity efficiency factor of CHP units in node | |
—— | Loss factor of CHP units in node | |
—— | Natural gas price | |
—— | Electricity energy price of industrial park load (price of electricity purchased from utility grid) | |
—— | Peak electricity demand charge of industrial park load | |
—— | Heat loss coefficient of pipelines connecting to the user | |
—— | Low heat value of natural gas | |
—— | Penalty coefficients of ADMM algorithm | |
—— | Iteration counter of ADMM algorithm | |
—— | Power factor of industrial park | |
—— | Length of each dispatching time slot of thermal storage | |
—— | The maximum/minimum energy level of thermal storage | |
—— | Heat load of node at time of day | |
—— | The maximum heat power flow of pipelines connecting centralized thermal storage to node at time of day | |
—— | The maximum heat power output of thermal storage | |
—— | The maximum current magnitude of distribution line | |
—— | The maximum/minimum electricity output of CHP units in node | |
—— | Active/reactive power load of node at time of day | |
—— | Forecasted PV output in node at time of day | |
—— | Active power capacity of PV in node | |
—— | Reactive power capacity of SVG in node | |
—— | Resistance/reactance of distribution line | |
—— | Apparent power capacity of PV in node | |
—— | Thermal delay time of heat pipelines, which depends on pipeline parameters | |
—— | The maximum/minimum voltage magnitude in node |
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