Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices

Yang, Yan; Yu, Junhui; Ma, Hengrui

doi:10.3390/pr12061252

Open AccessArticle

Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices

by

Yan Yang

¹,

Junhui Yu

¹ and

Hengrui Ma

^1,2,3,*

¹

School of Energy and Electrical Engineering, Qinghai University, Xining 810016, China

²

Hubei Engineering and Technology Research Center for AC/DC Intelligent Distribution Network, School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

³

School of Electrical and Automation, Wuhan University, Wuhan 430072, China

^*

Author to whom correspondence should be addressed.

Processes 2024, 12(6), 1252; https://doi.org/10.3390/pr12061252

Submission received: 26 April 2024 / Revised: 12 June 2024 / Accepted: 12 June 2024 / Published: 18 June 2024

(This article belongs to the Section Energy Systems)

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Abstract

:

Demand response (DR) can provide extra scheduling flexibility for power systems. Different from industrial and residential loads, the production process of manufacturing loads includes multiple production links, and complex material flow and energy flow are closely coupled, which can be seen as a typical nondeterministic polynomial-time (NP) hard problem. In addition, there is a coupling effect between the temperature-controlled loads (TCLs) and the manufacturing loads, which has often been ignored in previous research, resulting in conservative electricity consumption planning. This paper proposes an optimal demand management for the manufacturing industry. Firstly, the power consumption characteristics of manufacturing loads are analyzed in detail. A state task network (STN) is introduced to decouple the relationship between energy and material flow in each production link. Combining STN and production equipment parameters, a general MILP model is constructed to describe the whole production process of the manufacturing industry. Then, a mathematical model of the TCLs considering a comfortable human degree is established. Fully considering the electricity consumption behavior of equipment and TCLs, the model predictive control (MPC) method is adopted to generate the optimal scheduling plan. Finally, an actual seat production enterprise is used to verify the feasibility and effectiveness of the proposed demand management strategy.

Keywords:

demand response; manufacturing load; temperature-controlled load; state task network; model predictive control

1. Introduction

With the rapid growth of population and the acceleration of industrialization, the demand for energy supply has also increased [1]. At present, the greenhouse gas emissions caused by the large consumption of traditional energy sources such as coal and petroleum have seriously constrained the economic and social development of various countries [2]. Exploring the dispatching potential of the load side and guiding the load side to participate in the DR become more and more important. This can avoid not only large-scale economic investment but also provide flexible resources for peak shaving to meet the needs of different time scales [3]. Load-side users can also benefit from this behavior, assisting in the consumption of renewable energy while reducing their own production and electricity costs, achieving a win-win situation. Therefore, it is crucial to explore the flexible resources of multiple loads in a power system [4].

Unlike industrial loads [5,6], manufacturing loads represented by automobile production and assembly enterprises, mold processing enterprises, food processing industries, and building material production have higher levels of automation but relatively small regulatory capacity, mostly at the level of a few megawatts. Ref. [7] selected the casing production in a refrigeration plant as the research object, considered the impact of machine tool processing on indoor temperature and humidity, combined with Time-of-Use (TOU) price information, and established a coordinated scheduling model for the entire production line with the goal of minimizing operating costs. Ref. [8] incorporates the carbon emission characteristics of building materials plants into the low-carbon economic dispatch framework, taking into account the green environmental capacity margin. Production costs are calculated through a tiered carbon emission price, and load shifting is guided by TOU electricity prices, reducing the operating costs of the power grid and the production costs of building materials plants, achieving a win-win situation. For the food production and storage industry, the refrigerator has a certain thermal inertia and good thermal insulation performance, which can maintain the indoor temperature under short-term load changes. Therefore, it is not sensitive to short-term load reduction and has the potential to participate in short-term DR. Refs. [9,10] analyzed in detail the case of food manufacturers and refrigerated warehouses participating in DR. The results indicated that the food manufacturer’s income from participating in the automatic DR of the day-ahead electricity market for one year is enough to pay the total cost of installing the control system, and there is no product loss, product quality decline, or supply chain delay. In Ref. [11], taking a ham storage enterprise in Spain as an example, the internal cooling system included four types: refrigeration subsystem, storage subsystem, air conditioning subsystem, and drying subsystem. These subsystems can use thermal inertia to control the indoor temperature and humidity within a reasonable range. While reducing production costs, the reduction in greenhouse gas emissions caused by load reduction is also significant. Ref. [12] focused on the interactive vehicle manufacturing joint scheduling framework and improved the scheduling flexibility of aggregation systems. In Ref. [13], a DR scheduling strategy for integrated manufacturing and material processing manufacturing systems was proposed. The interaction between machine tools and material processing equipment, the characteristics of energy storage charging and discharging, and the dynamic electricity price were all taken into account. Through case verification, the proposed scheme can reduce the power cost of manufacturing enterprises by 15.1%.

On the other hand, the manufacturing industry has a high degree of automation and intelligence, and material flow and energy flow are closely coupled. Production scheduling is essentially an NP-hard problem, which is difficult to solve online. In order to improve the efficiency of the solution, Ref. [14] proposed a real-time knowledge-assisted DR strategy for intelligent manufacturing systems to enhance situational awareness and resource controllability. The knowledge-assisted analysis model was used to generate long-term production plans, and a real-time DR optimization model was established to reduce the cost of intelligent manufacturing systems under uncertainty. Ref. [15] proposed an energy management scheme for discrete manufacturing systems, which utilizes multi-agent deep reinforcement learning to transform the production process into partially observable Markov game processes, thus obtaining optimal scheduling strategies for different machines. In Ref. [16], under the premise of not affecting the production tasks of the manufacturing system, the Markov decision model was used to describe the complex interaction process between equipment control actions and system state evolution, and the effectiveness of the method was verified through the actual case of the automobile assembly line. Ref. [17] considered a flexible/rigid hybrid manufacturing production environment. In addition to meeting conventional production goals, flexible manufacturing systems can be used to handle the demand for surge orders, and multi-scenario methods were used to describe demand uncertainty, which can be solved through column and constraint generation (CC&G) algorithm. Ref. [18] designed a classification hypernetwork to describe the dual diversity of changes in the types and quantities of manufacturing services and used the supply-demand ratio of manufacturing services as the main indicator for evaluating the platform’s capacity. Ref. [19] proposed a probabilistic Bayesian regression framework, which can not only estimate the power demand of manufacturing load in the future with high accuracy but also dynamically updated according to the latest environmental information, and the prediction error is less than the existing method such as support vector machine, random forest, and multilayer perceptron model. Ref. [20] proposed a non-invasive method for evaluating the potential of manufacturing enterprises with renewable energy self-generation capabilities to participate in DR. The calculation results show that the proposed method can save nearly 2.5% of total production electricity costs. Ref. [21] proposed a game model for internal power allocation in manufacturing enterprises, using the Gale Shapley algorithm to consider the pending tasks in a queue of a single machine tool. Compared with the traditional method of each machine working at a fixed power level, the proposed model can effectively improve the efficiency of the manufacturing system.

However, there are still some challenges in incorporating manufacturing loads into DR. Firstly, the production process of manufacturing load includes multiple production links, and the electricity consumption behavior and material production–consumption relationship vary dynamically among different production links. In the process of manufacturing load scheduling, if each production link is described using refined mathematical models, the manufacturing load scheduling model is a typical NP-hard problem that is difficult to solve directly. At present, mature optimization algorithms can only solve small-scale NP-hard problems. In addition, manufacturing enterprises, in order to meet the lighting, temperature control, and other needs of production, contain numerous common loads inside the enterprise, such as lamps, air conditioning, heat pumps, etc. The power of these loads is directly affected by external environmental conditions and closely coupled with the production tasks inside the manufacturing enterprise. For example, enterprises need to arrange production tasks and assign a certain number of workers to each task. Different working conditions and equipment operating conditions can have different impacts on indoor heat. In order to meet comfort needs, it is necessary to adjust the working status of temperature control equipment accordingly. This impact relationship has often been ignored in previous research on manufacturing load scheduling, resulting in overly conservative scheduling results.

To address the above issues, this paper proposes a demand-side management strategy for manufacturing loads considering temperature control under dynamic electricity prices. The innovative points of this paper can be summarized as follows:

(1): Considering the coupling relationship between energy flow and material flow in manufacturing load, this paper adopts the STN method to decouple a complex production task into several task nodes and state nodes. By introducing 0–1 variables to describe the working conditions of task nodes, the complex production process of manufacturing enterprises is described through a mixed integer linear programming model that is easy to solve, effectively reducing the difficulty of solving;
(2): Considering the time delay characteristics and complex dynamics in the temperature control process, which are usually described by nonlinear dynamic differential equations, this paper adopts the model predictive control method to achieve optimal control objectives and conducts verification and analysis of optimality under different scheduling time scales.

The research framework of the whole paper is as follows: firstly, to describe the complex coupling relationship of energy flow and logistics materials, the entire production process in the industry is decoupled into independent task nodes and state nodes through a state task network, and a corresponding mixed integer linear optimization model is established; then, considering environmental factors and the impact of production equipment and worker heat dissipation, the MPC method is used for rolling optimization to generate the optimal indoor temperature control strategy; finally, taking the actual seat production enterprise as a case, the effectiveness of the method is verified.

2. Description of Manufacturing Production Process Based on STN Method

The STN method, as a mature task decomposition algorithm, has been widely applied in industrial management and workshop task scheduling. The STN method can divide a complex manufacturing production process into several independent task nodes and state nodes. Among them, status nodes are mainly used to describe the consumption or production status of raw materials, intermediate products, and final products; the task node represents the different stages involved in a production task, which can be a single production task or a combination of multiple production tasks. Furthermore, task nodes can be divided into flexible task nodes and fixed task nodes according to whether production status can be flexibly adjusted.

For manufacturing production equipment, the constraints that need to be considered for their production tasks mainly include material production consumption relationship constraints, warehousing constraints, and node operation status constraints. The specific expression is as follows:

Material production–consumption relationship constraints

$W_{i, t + 1} = W_{i, t} + h (\sum_{j \in C_{i}} c_{i, j, t} - \sum_{j \in X_{i}} x_{i, j, t})$

(1)

Here,

W_{i, t}

represents the material surplus of the i-th state node at time t; h represents the duration of the dispatching period;

c_{i, j, t}

represents the material yield of the i-th state node participating in completing task j at time t;

x_{i, j, t}

represents the material consumption of the i-th state node participating in completing task j at time t;

C_{i}

and

X_{i}

represent the task sets of material production and consumption related to state node i, respectively.

2.: Product yield constraint-material storage warehouse capacity constraint

The manufacturing load needs to complete the given production tasks during the dispatching period, as shown in (2):

W_{i, T} - W_{i, 1} \geq W_{i}^{order}

(2)

Here, T represents the end time of the dispatching period;

W_{i}^{order}

represents yield indicators. Meanwhile, the materials of each status node are often stored in the warehouse, limited by the storage capacity of the warehouse, as shown in (3):

W_{i}^{\min} \leq W_{i, t} \leq W_{i}^{\max}

(3)

In (3),

W_{i}^{\min}

and

W_{i}^{\max}

represent the minimum and maximum capacity of the material storage warehouse under the i-th state node, respectively.

3.: Task Node Power Equation Constraints

For the j-th task node, its power consumption can be described by Equation (4):

\begin{matrix} P_{j, t} = \sum_{k = 1}^{m} Z_{j, k, t} p_{j, k}, & Z_{j, k, t} \in \{0, 1\} \end{matrix}

(4)

In the above equation, m represents the number of operating conditions for task node j. For fixed tasks, m = 2 and it indicates that this task node only has two operating conditions: running and stopping; for flexible tasks, m is larger than 3, which indicates that there are multiple operating conditions at this task node.

P_{j, t}

represents power consumption for the j-th task node. The status flag

Z_{j, k, t}

is a 0–1 variable used to indicate whether task node j is in the k-th operating condition at time t. When its value is 1, it indicates that task node j is in the k-th operating condition.

p_{j, k}

represents the power consumption of task node j in the k-th operating condition.

After obtaining the power consumption of all task nodes, the total power consumption of internal production equipment in the enterprise can be obtained according to Equation (5):

P_{t}^{sum} = \sum_{j = 1}^{J} P_{j, t}

(5)

Here,

P_{t}^{sum}

represents the total power consumption of internal production equipment in the manufacturing enterprise at time t; J represents the number of task nodes.

4.: Node operation state constraints

For each task node, it can only be in one operating condition at the same time, as shown in Equation (6):

Z_{j, k, t} = 0 o r Z_{j, k, t} = 1

(6)

5.: Worker quantity constraint

In the process of arranging production tasks, manufacturing enterprises also need to allocate a certain number of workers to ensure the completion of tasks. The number of workers required for each task node and the total number of workers within the enterprise are constrained as shown in (7) and (8), respectively:

L_{j, t} = \sum_{k = 1}^{m} Z_{j, k, t} l_{j, k}

(7)

L^{\min} \leq \sum_{j = 1}^{J} L_{j, t} \leq L^{\max}

(8)

Here,

l_{j, k}

represents the number of workers required for the k-th operating condition under task node j;

L_{j, t}

represents the number of workers required to complete the j-th task node;

L^{\min}

and

L^{\max}

represent the minimum and maximum number of workers that can be arranged within the enterprise, respectively.

3. Mathematical Model for Temperature-Controlled Load in Manufacturing Enterprises

In order to create a good production environment, enterprises often have lighting and TCLs configured internally, and the modeling of such loads is currently relatively mature. The internal lighting load of the enterprise has a small and relatively fixed power consumption behavior, which can be directly expressed as a constant. Therefore, this section mainly considers TCLs modeling and control represented by heat pumps and air conditioning. Considering the relatively large footprint of industrial factories, compared to air conditioning loads, heat pumps operate more economically in large space factories. Therefore, this chapter takes air source heat pumps as the research object and establishes corresponding scheduling control mathematical models. The structure of the air source heat pump is shown in Figure 1, which can be cooled/heated according to the environmental temperature requirements.

Taking the heating process as an example, its basic working principle is to use a low-temperature and low-pressure gas medium to absorb heat from the air. After passing through the air compressor, the gas medium releases a large amount of heat, causing the temperature of the circulating water to rise. Meanwhile, the state of high-pressure refrigerant changes from gas to liquid, further releasing heat during the liquefaction process. Finally, the liquid refrigerant evaporates into a gaseous state in the evaporator, and the above steps are repeated, gradually injecting the heat from the air into the circulating water to achieve heating. From the perspective of energy conversion, air source heat pumps essentially use the inverse Carnot cycle principle to convert the electrical energy consumed by the compressor and the heat absorbed in the air into heat energy in hot water.

Due to the low power of a single air source heat pump, in practical applications, multiple air source heat pumps often work together in parallel, exchanging heat with the building through water circulation. To reduce the complexity of modeling, the focus is on indicators such as outlet temperature and return water temperature of air source heat pumps. For the working characteristics of evaporators and air compressors, energy efficiency ratio modeling is used to describe them. The relationship between the power of air source heat pumps and refrigeration/heating capacity can be calculated according to Equation (9):

P_{air} = c_{air} Q_{air}

(9)

In Equation (9),

P_{air}

represents the electrical power of the air-source heat pump;

c_{air}

represents the energy efficiency ratio of the air-source heat pump;

Q_{air}

represents the cooling/heating capacity of the air-source heat pump. The heat exchange between the air source heat pump and the factory mainly consists of two parts. The first part is the instantaneous heat inside the factory, and the second part is the energy difference caused by the difference in indoor temperature and outlet temperature, as shown in (10):

Q_{ex} = Q + K_{aw} (θ_{i} - θ_{e})

(10)

In Equation (10),

Q_{ex}

represents the heat exchanged between the air-source heat pump and the interior of the factory building; Q represents the instantaneous heat gained by the factory building from sources such as solar radiation, heat dissipation from production equipment, and heat dissipation from workers inside;

K_{aw}

represents the heat exchange thermal conductivity between the indoor environment of the factory building and the outlet water of the heat pump;

θ_{i}

and

θ_{e}

respectively represent the internal temperature of the factory building and the outlet water temperature of the air-source heat pump. For air source heat pumps, the thermal dynamic models of outlet temperature, return water temperature, and indoor temperature can be described using differential Equations (11)–(13), respectively:

C_{e} \frac{d θ_{e}}{d t} = K_{w} (θ_{b} - θ_{e}) - \sum_{z = 1}^{Z} s_{z} Q_{air, z}

(11)

C_{b} \frac{d θ_{b}}{d t} = K_{w} (θ_{e} - θ_{b}) + Q_{ex}

(12)

C_{a} \frac{d θ_{i}}{d t} = K_{a} (θ_{o} - θ_{i}) - Q_{ex}

(13)

Here,

C_{e}

,

C_{b}

, and

C_{a}

respectively represent the heat capacity of the air source heat pump’s outlet water, the heat capacity of the return water, and the indoor thermal conductivity of the factory building;

θ_{b}

and

θ_{o}

respectively represent the return water temperature and the external temperature of the factory building.

s_{z}

is a 0–1 variable that represents the working state of the z-th air source heat pump. When its value is 1, it indicates that the air source heat pump is in operation.

The primary goal of heat pump operation is to control the temperature inside the factory within a reasonable range. In order to quantify the impact of indoor temperature on human comfort, the predicted mean vote (PMV) is adopted to describe the relationship between indoor temperature and human comfortable requirement, as shown in (14):

I_{PMV, t} = 2.43 - \frac{3.76 (θ_{sk} - θ_{i, t})}{M_{R} (r + 0.1)}

(14)

As shown in (14), thermal comfort indicators

I_{PMV, t}

are mainly influenced by the following factors: indoor air temperature

θ_{i, t}

, human metabolic rate

M_{R}

, and clothing thermal resistance r. Here,

θ_{sk}

represents the comfortable skin temperature of the human body, which has a small change in amplitude and can be approximated as a fixed value, with a value of 33.5 °C in this paper.

To meet the temperature comfort needs of workers, referring to the ISO 7730 standard, the thermal comfort index is limited to a range of −0.5 to 0.5, as shown in (15). ISO 7730 standard [22], published by the International Organization for Standardization-European Committee for Standardization (ISO/CEN) in 2005, proposes a method for predicting the general thermal sensation and dissatisfaction (thermal discomfort) of people exposed to moderate thermal environments. Utilizing the PMV index, the PPD index, and calculating local thermal comfort enables the analysis, determination, and interpretation of thermal comfort. This standard provides environmental conditions considered acceptable for general thermal comfort as well as environmental conditions representative of localized discomfort.

- 0.5 \leq I_{PMV, t} \leq 0.5

(15)

The above (9)–(15) fully describe the control mathematical model of air source heat pumps in manufacturing factories considering human comfort requirements. Finally, after obtaining the power consumption of the air source heat pump and production equipment, the total power consumption should also meet the power balance constraints and maximum electricity purchase constraints, as shown in (16) and (17):

P_{t}^{buy} = P_{t}^{sum} + P_{air, t} + P_{t}^{other}

(16)

0 \leq P_{t}^{buy} \leq P^{buy, \max}

(17)

Here,

P_{t}^{buy}

represents the purchasing power of manufacturing enterprises at time t;

P_{t}^{other}

represents the power used for other common loads within manufacturing enterprises;

P^{buy, \max}

represents the maximum allowed power purchase by the enterprise.

4. Indoor Temperature Control Strategy Based on MPC Method

In Section 2 and Section 3, modeling is conducted for the production process and the thermal control process, respectively. In Section 4, an optimal economic production plan for manufacturing enterprises is formulated with the goal of minimizing temperature deviation. While fully considering the nonlinearity and dynamics of the model, the MPC method is utilized to achieve the solution. Specific technical details are provided below.

Although (11)–(13) describe the thermal dynamic characteristics of air source heat pumps, the form of its differential equation is difficult to solve directly. To facilitate analysis, the forward difference method is first used to discretize the initial differential equation into algebraic form, as shown in (18)–(20). Here, (18)–(20) represent the thermal models of outlet temperature, return water temperature, and indoor temperature expressed using algebraic equations, respectively.

θ_{e} (t + 1) = (1 - \frac{K_{w}}{C_{e}}) θ_{e} (t) + \frac{K_{w}}{C_{e}} θ_{b} (t) - \frac{c_{air} Q_{air}}{C_{e}} u (t)

(18)

\begin{array}{l} θ_{b} (t + 1) = \frac{K_{w} - K_{aw}}{C_{b}} θ_{e} (t) + (1 - \frac{K_{w}}{C_{b}}) θ_{b} (t) \\ + \frac{K_{aw}}{C_{b}} θ_{i} (t) + \frac{1}{C_{b}} Q (t) \end{array}

(19)

\begin{array}{l} θ_{i} (t + 1) = \frac{K_{aw}}{C_{a}} θ_{e} (t) + (1 - \frac{K_{a}}{C_{a}} - \frac{K_{aw}}{C_{a}}) θ_{i} (t) \\ + \frac{K_{a}}{C_{a}} θ_{0} (t) - \frac{1}{C_{a}} Q (t) \end{array}

(20)

Furthermore, by combining the above Equations (18)–(20) and writing them in matrix form, the state space model of the air source heat pump can be obtained, as shown in Equation (21):

\begin{array}{l} [\begin{matrix} θ_{e} (t + 1) \\ θ_{b} (t + 1) \\ θ_{i} (t + 1) \end{matrix}] = [\begin{matrix} 1 - K_{w} / C_{e} & K_{w} / C_{e} & 0 \\ (K_{w} - K_{aw}) / C_{b} & 1 - K_{w} / C_{b} & K_{aw} / C_{b} \\ K_{aw} / C_{a} & 0 & 1 - K_{a} / C_{a} - K_{aw} / C_{a} \end{matrix}] * \\ [\begin{matrix} θ_{e} (t) \\ θ_{b} (t) \\ θ_{i} (t) \end{matrix}] - [\begin{matrix} c_{air} Q_{air} / C_{e} \\ 0 \\ 0 \end{matrix}] u (t) + [\begin{array}{l} 0 & 0 \\ 1 / C_{b} & 0 \\ - 1 / C_{a} & K_{a} / C_{a} \end{array}] [\begin{matrix} Q (t) \\ θ_{0} (t) \end{matrix}] \end{array}

(21)

For the convenience of subsequent analysis, the detailed mathematical model (21) is first written as a compact model, as shown in Equation (22):

x (t + 1) = A x (t) + B u (t) + D v (t)

(22)

Here, x(t) represents the state variables, specifically including the outlet temperature, return water temperature, and indoor temperature of the air source heat pump; u(t) represents the control variable, which refers to the number of parallel air source heat pumps in operation; v(t) represents the disturbance term, which mainly includes outdoor temperature and instantaneous heat gain inside the factory building; A, B, and D represent constant coefficient matrices, respectively.

When formulating production scheduling, enterprises need to make overall decisions based on factors such as external environmental temperature and the working status of production equipment at the last moment. In order to ensure the optimality of the decision, the MPC method is used for rolling optimization scheduling. An MPC temperature rolling optimization control model for air source heat pumps can be established, as shown in (23):

\begin{array}{l} \min J = |θ_{i} (t + Δ t) - θ_{set}| \\ s . t . \{\begin{array}{l} x (t + Δ t) = \tilde{A} x (t) + \tilde{B} u (t) + \tilde{D} v (t) \\ 0 \leq u (t) \leq u_{\max} \end{array} \end{array}

(23)

Here,

θ_{i} (t + Δ t)

represents the indoor temperature for one cycle after the air source heat pump is put into operation and

θ_{set}

represents the temperature setting value. By solving (14) and (15), the control range of indoor temperature at each time can be obtained. The average of the allowable control range of temperature at each time is taken as the MPC temperature control command.

It can be seen from (23) that the objective function J does not contain the control variable u. In this case, the optimal solution of the control variable can be obtained using the enumeration method. However, when there are many air-source heat pumps, the solution may be extremely time-consuming. In order to accelerate the progress of problem-solving, the Formula (24) for finding the optimal solution is derived according to the optimal control law, the equality constraints in (23) are substituted into the objective function, and the control variables are separated to obtain the functional expression of the optimal solution, as shown in Equation (24):

\hat{u} (t) = {\tilde{B}}_{s}^{- 1} (θ_{set} (t) - {\tilde{A}}_{s} θ_{i} (t) - {\tilde{D}}_{s} v (t))

(24)

Here,

{\tilde{A}}_{s}

,

{\tilde{B}}_{s}

, and

{\tilde{D}}_{s}

respectively represent the submatrix of the corresponding terms in the initial coefficient matrix. By using Equation (24), numerical solutions can be directly obtained, but it should be noted that the optimal control law shown in (24) actually only focuses on the equality constraints in the constraints, ignoring the inequality constraints of the control variables. This will lead to an amplification of the feasible region of the solution, and the solution obtained solely by relying on Equation (24) may not be within the allowable control range of the control variables. Therefore, it is necessary to check and determine whether the numerical solution meets the requirements based on the range of control variables, namely the number of air source heat pumps that can be turned on. The specific judgment criteria are as follows:

Criteria 1: when $\hat{u} (t) < 0$ , the optimal solution should be corrected to 0;
Criteria 2: when $0 \leq \hat{u} (t) \leq u_{\max}$ , the rounded value $[\hat{u} (t)]$ is the optimal solution;
Criteria 3: when $\hat{u} (t) > u_{\max}$ , the solution should be corrected to $u_{\max}$ .

5. Case Study

5.1. Introduction to Testing System Data

To verify the effectiveness of the proposed method, this section selects an actual seat production enterprise as a representative manufacturing load. The seat production process mainly includes leather cutting, foaming, and aging, as well as welding and coating operations. Detailed production data and corresponding STN diagrams of manufacturing enterprises can be referred to in Ref. [23], and the dynamic electricity price used in this paper is given in Figure 2.

5.2. Effectiveness Analysis of Production Plan in Manufacturing Enterprises

Figure 3 and Figure 4, respectively, show the power of each task node and hourly seat production in the current scenario. As shown in Figure 3, under the guidance of dynamic electricity prices, during peak periods such as 8:00, 11:00 to 13:00, manufacturing enterprises only arrange assembly production tasks, while in other low electricity price stages, each production task operates at higher power conditions to meet the established production tasks of the enterprise. Meanwhile, during the periods of 4:00, 17:00, and 19:00–20:00, manufacturing companies did not arrange assembly tasks, so the corresponding seat production at that time was 0.

In addition, this section fully considers the impact of production tasks on air source heat pumps when formulating scheduling plans. This impact mainly includes the following two aspects: firstly, the production equipment status of each task node will have an impact on the instantaneous heat inside the factory building. The power consumption of equipment under different operating conditions is different, and the heat released into the air inside the factory building is also different; secondly, each task node also arranges a certain number of workers. Due to the different nature of the tasks, workers are in different working states, such as walking, working, loading, and unloading, and the intensity of work is different. The metabolic rate and heat generated by the human body are also different. It should be noted that the indoor temperature set in this paper is a fixed value of 26 °C, and to avoid confusion, it is not displayed in Figure 5.

Figure 5 shows the working state of an air source heat pump with and without considering the impact of production tasks. Overall, the power of the heat pump unit without considering the impact of production equipment and the metabolic rate of workers is lower than that under the scenario considering the impact of production equipment and the metabolic rate of workers. The scheduling results tend to be conservative, especially during periods of low electricity prices and busy production tasks such as 1:00–5:00 and 14:00–16:00, where there is a significant deviation in the power of the air source heat pump under these conditions. This further demonstrates the necessity of considering the working conditions of production equipment and the influence of labor when formulating a TCL scheduling plan.

5.3. Analysis of the Impact of Scheduling Time Scale on Total Operating Costs

This section analyzes the impact of different scheduling time scales on enterprise operating costs. The scheduling of internal production equipment in manufacturing enterprises is essentially a MILP problem, which contains numerous 0–1 variables that characterize the operating conditions of equipment, and the existence of these 0–1 variables leads to the non-continuous regulation of production equipment power. When the scheduling time interval is infinitely small, and the control accuracy of the production equipment is higher, it can be considered that the power of the production equipment can be continuously and accurately adjusted. At this time, the production plan of the manufacturing enterprise obtained by solving Equations (9)–(24) is optimal. In actual engineering applications, the scheduling time of production equipment, such as machine tools in the manufacturing industry, needs to meet a certain minimum operating time requirement. When the scheduling time scale is smaller, the obtained enterprise production plan is closer to the optimal production plan under continuous power state. To gain a better understanding, Figure 6 shows the power of welding and coating #1 task nodes under different scheduling time scales. It is not difficult to find that when the scheduling time scale is 15 min, there are multiple changes in the power of the welding coating 1 task node, which can achieve precise adjustment. When the scheduling time scale is 1 h, the power of the welding and coating #1 is always maintained at 0, and the power regulation effect is very small. This is because, at the scheduling time scale of 15 min, there are four optional operating powers for welding coating 1 on the hourly time scale: 0, 75 kW, 150 kW, 225 kW, and 300 kW. However, at the scheduling time scale of 1 h, there are only two optional operating powers for welding coating 1 on the hourly time scale: 0 kW and 300 kW. When the scheduling time scale is small, it is easier to find the current optimal solution of the global optimal solution near the continuous feasible region within the constrained feasible region. Obviously, the selectivity of the results at a scheduling time scale of 15 min is greater than that at a scheduling time scale of 60 min, so the results at a short-term scheduling scale are more likely to approach the optimal solution. For decision-makers of manufacturing enterprises, frequent adjustments of the working status of production equipment may bring certain difficulties to the service life of the equipment and staff arrangement. Therefore, it is necessary to comprehensively consider and select an appropriate scheduling time scale.

To more intuitively demonstrate the impact of this coupling relationship on enterprise production, this article further analyzes the operating costs of enterprises under different scheduling time scales, as shown in Table 1 below. It is not difficult to observe that for the electricity cost of production equipment, as there are more selectable production options under a shorter scheduling time scale, it is easier to generate solutions close to the optimal solution. Therefore, the electricity cost of production equipment increases as the scheduling time scale increases. However, for air-source heat pumps, the shorter the control time scale, the higher the regulation accuracy and the more constraints that need to be met for human comfort. The air-source heat pump needs to frequently adjust to meet comfort requirements, which tends to increase the electricity cost for temperature regulation. But for manufacturing enterprises, since the electricity cost of production equipment is the main cost, their total cost increases as the adjustment time scale increases.

6. Conclusions

This paper mainly proposes the demand management method of manufacturing load under dynamic electricity prices. Firstly, considering the coupling relationship between the energy flow and the material flow of the manufacturing industry, a complex production task is decoupled and decomposed into several task nodes and status nodes using the STN method. By introducing the 0–1 variable that describes the working conditions of the task nodes, the whole production process of the manufacturing enterprise is described through the MILP model and is easy to solve; then, the MPC method is used to develop the optimal production plan. Finally, validation is conducted through actual seat production enterprises. Analysis shows the following:

(1): The STN method can quickly and accurately capture the coupling relationship between material and energy flows on the load side, effectively reducing computational complexity while ensuring the optimality of the solution. Meanwhile, the production equipment and human heat dissipation of workers under different working conditions can have a certain impact on the instantaneous heat inside the factory building, which in turn affects the working status of the air source heat pump. If the impact of production equipment and worker heat dissipation is not considered, it will result in conservative temperature-controlled load scheduling results;
(2): The MPC (Model Predictive Control) method can efficiently achieve optimal control of the heat pump temperature, meeting the online computation requirements under different scheduling time scales. On the other hand, different scheduling time scales can also have a certain impact on the final results. The smaller the scheduling time scale, the higher the equipment control accuracy, and the closer the obtained production plan is to the optimal solution. As the scheduling time scale increases, the electricity cost of production equipment in manufacturing enterprises increases, and the total operating cost also increases;
(3): The application of some other intelligent optimization algorithms, such as LQR and iLQR, in load-side control scheduling will be studied in the future.

Author Contributions

Conceptualization, Y.Y., J.Y. and H.M.; methodology, Y.Y., J.Y. and H.M.; software, Y.Y., J.Y. and H.M.; validation, Y.Y., J.Y. and H.M.; writing—original draft preparation, Y.Y., J.Y. and H.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research is funded by the National Natural Science Foundation of China (Grant No. 52207134).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Nomenclature

Variables	Meaning
$W_{i, t}$	The material surplus of the i-th state node at time t
h	The duration of the dispatching period
$c_{i, j, t}$	The material yield of the i-th state node participating in task j at time t
$x_{i, j, t}$	The material consumption of the i-th state node participating in completing task j at time t
$C_{i}$ $/ X_{i}$	The task sets of material production/consumption related to state node i,
T	The end time of the dispatching period
$W_{i}^{order}$	Yield indicators
$W_{i}^{\min}$ / $W_{i}^{\max}$	The minimum and maximum capacity of the material storage warehouse under the i-th state node
m	The number of operating conditions for task node j
$P_{j, t}$	The power consumption for the j-th task node
$Z_{j, k, t}$	The status flag used to indicate whether task node j is in the k-th operating condition at time t
$p_{j, k}$	The power consumption of task node j in the k-th operating condition.
$P_{t}^{sum}$	The total power consumption of internal production equipment in the manufacturing enterprise at time t
J	The number of task nodes
$l_{j, k}$	The number of workers required for the k-th operating condition under task node j
$L_{j, t}$	The number of workers required to complete the j-th task node
$L^{\min}$ $/ L^{\max}$	The minimum/maximum number of workers that can be arranged within the enterprise
$P_{air}$	The electrical power of the air-source heat pump
$c_{air}$	The energy efficiency ratio of the air-source heat pump
$Q_{air}$	The cooling/heating capacity of the air-source heat pump
$Q_{ex}$	The heat exchanged between the air-source heat pump and the interior of the factory building
Q	The instantaneous heat gained by the factory building from sources such as solar radiation, heat dissipation from production equipment, and heat dissipation from workers inside
$K_{aw}$	The heat exchange thermal conductivity between the indoor environment of the factory building and the outlet water of the heat pump
$θ_{i}$ $/ θ_{e}$	The internal temperature of the factory building and the outlet water temperature of the air-source heat pump
$C_{e}$ $/ C_{b}$ / $C_{a}$	The heat capacity of the air source heat pump’s outlet water, the heat capacity of the return water, and the indoor thermal conductivity of the factory building
$θ_{b}$ $/ θ_{o}$	The return water temperature and the external temperature of the factory building
$s_{z}$	0–1 variable that represents the working state of the z-th air source heat pump
$I_{PMV, t}$	Thermal comfort indicators
$θ_{i, t}$	Indoor air temperature
$M_{R}$	Human metabolic rate
r	Clothing thermal resistance
$θ_{sk}$	The comfortable skin temperature of the human body
$P_{t}^{buy}$	The purchasing power of manufacturing enterprises at time t
$P_{t}^{other}$	The power used for other common loads within manufacturing enterprises
$P^{buy, \max}$	The maximum allowed power purchase by the enterprise
$θ_{i} (t + Δ t)$	The indoor temperature for one cycle after the air source heat pump is put into operation
$θ_{set}$	The temperature setting value

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Figure 1. Schematic diagram of air source heat pump operation.

Figure 2. Dynamic electricity price information.

Figure 3. Node power of each task of car seat production in the current scenario.

Figure 4. Yield of car seats per hour in the current scenario.

Figure 5. Working state of air source heat pump under different conditions.

Figure 6. Power of welding coating 1 under different scheduling time scales.

Table 1. Analysis of manufacturing enterprises’ costs under different scheduling time scales.

Scheduling Time Scale	Electricity Cost for Production Equipment ($)	Electricity Cost for Heat Pumps ($)	Total Cost ($)
30 min	2485.6	542.6	3028.2
60 min	2742.2	427.5	3169.7
90 min	3004.7	321.3	3326.0

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Yang, Y.; Yu, J.; Ma, H. Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices. Processes 2024, 12, 1252. https://doi.org/10.3390/pr12061252

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Yang Y, Yu J, Ma H. Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices. Processes. 2024; 12(6):1252. https://doi.org/10.3390/pr12061252

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Yang, Yan, Junhui Yu, and Hengrui Ma. 2024. "Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices" Processes 12, no. 6: 1252. https://doi.org/10.3390/pr12061252

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Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices

Abstract

1. Introduction

2. Description of Manufacturing Production Process Based on STN Method

3. Mathematical Model for Temperature-Controlled Load in Manufacturing Enterprises

4. Indoor Temperature Control Strategy Based on MPC Method

5. Case Study

5.1. Introduction to Testing System Data

5.2. Effectiveness Analysis of Production Plan in Manufacturing Enterprises

5.3. Analysis of the Impact of Scheduling Time Scale on Total Operating Costs

6. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

Nomenclature

References

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