An Optimal Dispatch Framework of Electric and Heating Networks Based on Controllable Electric and Thermostatically Controlled Loads

Ma, Yiming; Dong, Jian; Zhou, Xiran; Zhang, Guanfeng; Wang, Haixin; Yang, Junyou

doi:https://doi.org/10.1155/2022/1437051

Mathematical Problems in Engineering

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Abstract Introduction Preliminaries Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 1437051 | https://doi.org/10.1155/2022/1437051

An Optimal Dispatch Framework of Electric and Heating Networks Based on Controllable Electric and Thermostatically Controlled Loads

Yiming Ma,¹Jian Dong,¹Xiran Zhou,¹Guanfeng Zhang,²Haixin Wang,¹and Junyou Yang¹

Academic Editor: Dazhong Ma

Received16 Oct 2021

Accepted11 Dec 2021

Published10 Jan 2022

Abstract

With the increasing capacity of wind power generators (WTGs), the volatility of wind power could significantly challenge the stability and economy of electric and heating networks. To tackle this challenge, this paper proposes an optimal dispatch framework based on controllable load (including controllable electric load and controllable thermostatically load) to reduce wind power curtailment. A forecasting model is developed for the controllable load, which comprehensively considers autocorrelation, weather factor, and consumers’ behavior characteristics. With adjusting controllable load, an optimal dispatch model of power system is then established and resolved by Sequential Least Squares Programming (SLSQP) method. Our method is verified through numerous simulations. The results show that, compared with the state-of-the-art techniques of support vector machine and recurrent neural networks, the root mean square error with the proposed long short-term memory can be reduced by 0.069 and 0.044, respectively. Compared with conventional method, the peak wind power curtailment with dispatching controllable load is reduced by nearly 10% and 5% in two cases, respectively.

1. Introduction

With the increasing renewable energy integration, the adjustment capability of power network is decreased. To tackle this challenge, flexible adjustment resource (AR) has been widely recognized as an effective approach to enhance the adjustment capability. However, insufficient flexible AR capacity and its inaccurate prediction have an influence on the power adjustment and optimization of the power network. For instance, the curtailment of wind power in Northern China becomes more severe in heating period due to the significant thermal requirements supplied by combined heat and power (CHP) units [1–4]. Therefore, it is urgent to tackle the problems of wind power curtailment and optimization of electric and heating networks.

The flexible ARs can contribute to the stable operation and optimization of electric and heating networks by shifting their consumptions. The popular ARs mainly includes (a) electric energy storage (EES). EES is helpful to the power balance. However, the costs and geographical characteristics (e.g., battery-based storage and pumped storage) are still their main limitations [5]; (b) thermal energy storage (TES). The thermoelectric coupling characteristics of CHP units can be reduced if TES is deployed [6]; (c) controllable electric load (CEL). These consumers are mainly scheduled based on electricity price mechanism and incentives [7]; (d) thermostatically controlled load (TCL). Thanks to their thermal inertia and heating storage, TCL can contribute to regulate power balance within a certain period [8]. These two controllable loads (CL) also need to meet the consumers’ requirements.

The above ARs have been widely studied. For EES, with the rapid development of the battery-based EES, its technology has shown the characteristics and trends for large-scale integration and distributed applications with multiobjective collaboration [9]. A multienergy storage system architectural model and its coordination operational strategy with the same flexibility as in the pumped storage power station and battery-based EES are studied [10]. Heat transfer constraint of TES is considered in a detailed model of district heating network [11]. Reference [12] proposes a stochastic day-ahead scheduling model of integrated energy system (IES) considering multitype energy storages (including electric storage, heat storage, and gas storage) to accommodate wind power. Reference [13] proposes a novel scheduling strategy to dispatch CELs with nonlinear power-efficiency characteristics, such as desalination devices. An optimal bidding model of controllable loads is proposed to minimize the worst-case conditional expectation of electricity purchase cost, which is suitable for CEL and TCL [7]. Reference [14] presents a mathematical formulation of the problem and develops a coordination framework of TCLs using the mechanism design approach. Furthermore, a learning scheme is presented to account for the unknown TCL model parameters and evaluate the proposed framework through realistic simulations [15]. To further promote the accommodation of wind power and enhance the flexibility of the electric and heating networks, reference [16] presents a method of heat and power load dispatching by exploring the energy storage ability of electric heating boilers and district heating systems. However, controllable power industry load, as a CEL, occupies a certain proportion of power load, and it is rarely studied and applied to system dispatch. Therefore, this paper explores the coordination dispatch method of CEL and TCL to enhance the regulation capability of the electric and heating networks.

In the methods of controllable power industry load prediction, commonly, the probability distribution functions (e.g., Gaussian or Beta) are used to characterize the load forecast deviation by some random variables [17]. This approach can be used to validate the robust performance of the dispatch method, but it cannot reduce the economic cost loss caused by the prediction error. Commonly, regression analysis and time series methods are applied to make a short-time load prediction based on the historical power data [18]. However, short-term load prediction, especially for the controllable power industry load, mainly depends on customer behaviors, events, and environmental factors, which may increase the consumption uncertainty.

Deep learning has been recently developed, which is a promising technique to extract comprehensive information from historical data, such as multilayer neural network, recurrent neural network (RNN), and support vector machine (SVM) [19]. Among them, long short-term memory (LSTM) is considered as an effective method to tackle the time series forecasting challenges owing to its efficient performance for accurate modeling [20–22]. There are a few interesting works that have developed LSTM-based techniques for modeling residential load in power system. Reference [23] explores an LSTM recurrent neural network to identify active power fluctuations. An LSTM recurrent neural network-based framework is developed to forecast aggregated residential load [24]. To recognize industrial equipment in manufacturing systems, an LSTM is adopted to analyze their behavior features [25]. In particular, weather data (such as temperature, wind speed, and cloud cover) are considered to enhance the accuracy of LSTM-based power load prediction [26]. However, few deep learning methods are deployed to predict controllable power industry load.

Therefore, this paper develops a deep learning-based method to predict controllable power industry load. Thereafter, an optimal dispatch framework is established to enhance the flexibility of the electric and heating networks by CEL and TLC. Our contributions are as follows.(i)An optimal dispatch framework based on the coordination of CEL and TLC is developed to reduce the wind power curtailment of electric and heating networks(ii)A LSTM-based prediction model of TLC, considering behavior characteristics integrating sequence characteristic and external factors, is proposed to enhance prediction precision(iii)Compared with conventional method, the peak wind power curtailment with dispatching CEL and TCL is reduced by nearly 10% and 5% in the two cases, respectively

2. Preliminaries

2.1. Overall Structure

The overall schematic diagram of the electric and heating networks is shown in Figure 1. The electric network consists of CHP with TES, thermal power plant (TPP), wind power plant (WPP), EES, UL, and CL. The CL includes controllable thermostatically load (TCL) (e.g., distributed electric heating storage) and controllable electric load (CEL) (e.g., commercial buildings). The CHP units with TES deliver thermal power to the district heat load for the heating network, limiting their electric power outputs. The TCL consumes electric power and supplies the heat requirement of distributed heat load. As a result, the electric and heating networks are inextricably linked. CLs are utilized in this research to optimize the operation of electric and heating networks.

2.2. Operation Constraints and Costs

2.2.1. CHP with TES

(1) Operation Characteristics Analysis. During the heating season, CHP units are the primary source for meeting consumers’ electrical and thermal needs, which is an important coupling device for connecting power system and thermal system. Considering the operating characteristics of CHP with TES, its Thermal-electricity relationship is shown in Figure 2. The operation region of the CHP is within the area of A-B-C-D. and are the minimum and maximum electric power of the CHP without thermal power production, and is the maximum thermal power of the CHP. Line segments AB and DC, respectively, represent the operating conditions of the maximum and minimum output power of CHP. Line segment AD represents that the given steam intake of CHP is all used for power generation, and the thermal power is zero. Line segment BC represents that the given steam intake of CHP is almost all used for steam extraction heating, and the output electric power of CHP is the minimum output to meet the heat load. The thermal production of CHP needs to generate corresponding electric power. As can be seen in Figure 2, the coupling characteristics of CHP limit its range of power regulation, resulting in the instability of electric grids with CHP. As grid wind penetration and heat demand increase, the abandonment of wind power is likely to increase. Therefore, the heat output capacity of CHP with TES can be extended to A-E-F-G-H-J region under the action of TES and according to the modeling of CHP operation in [27]. is the maximum thermal power of the TES. The following models and equations can be found in [27].

(2) Constraints of CHP with TES. According to the operation characteristics of CHP, the constraints of electric power and thermal power for CHP i (i = 1, …, I, and I is the total number of CHP) at time t (t = 1, …, T, and T is the total time points) are given bywhere is the conversion coefficient from thermal power to electric power, and and are the lower and upper ramp rate limits of CHP i.

The constraints of thermal power and capacity for TES j (j = 1, …, J, and J is the total number of TES) are expressed bywhere and are the minimum and maximum thermal power of TES j, and and are the lower and upper capacity limits.

(3) Cost of CHP with TES. The operation cost of CHP with TES C_CT is described inwhere C_CHPi is the fuel cost of CHP i, C_TESj is the operation and maintenance cost of TES j, a_i, b_i and c_i are the fuel cost coefficients, and c_o1 is the operation cost coefficient.

2.2.2. Thermal Power Plant

TPP can regulate the power balance of the power system. The interested reader can refer to [26] for more details about constraints and additional formulations, which represent minimum up/downtimes or startup and shutdown trajectories for the TPP. The TPP output is limited by the minimum load, maximum capacity, and ramp rates. The operation constraints of electric power for TPP d (d = 1, …, D, and D is the total number of TPP) at time t are described inwhere P_TPPd,min and P_TPPd,max are the minimum and maximum electric power, and R_TPPd,min and R_TPPd,max are the lower and upper ramp rate limits. The fuel cost C_TPP is obtained bywhere a_d, b_d, and c_d are the fuel cost coefficients of TPP k.

2.2.3. Wind Power Plant

To simplify the analysis, we generally assume that the wind power generation equals the actual value plus a random forecast error that follows normal distribution. The model of wind power plant output at time t is shown inwhere represents the wind power estimation made of WPP ( = 1, …, W, and W is the total number of WPP) at time t, P_WPPw,t is the actual value, and ε_n is the forecast error. Note that the deviation of the estimation from the actual value P_WPPw,t increases with the prediction window length (t-r). Specifically, for generating the day-ahead estimation of , we could just let r be 1 in (6). The standard deviation σ_n of ε_n is assumed to be 20%.

The cost of wind power curtailment C_W is calculated bywhere c_Q is the cost coefficient of wind power curtailment. ΔP_WPPw,t is wind power curtailment of WPP .

2.2.4. Electric Energy Storage

EES is charged during load valley periods and discharged during load peak periods. In this way, EES can effectively reduce the different values between peak and valley. However, EES with large capacity will increase the economic cost of power system. To balance the above contradictions, the optimal output strategy of EES is scheduled, and the constraints of EES are established. The constraints of electric power P_EESg,t and capacity S_EESg,t for EES ( = 1, …, G, and G is the number of EES) are expressed bywhere and are the maximum charge and discharge power, and and are charge and discharge losses of EES , respectively. The operation cost of EES C_EES is calculated bywhere c_o2 is the operation cost coefficient of EES.

3. Operation Characteristic of CL

3.1. Operation Characteristic

The role of CEL can be summarized as follows: to consume electricity, CEL (such as commercial buildings, electric vehicles, and interruptible loads) can make the dispatching system increase its reference value when the power generation is greater than the power load consumption, especially when the wind power is surplus. When the power generation is less than the consumption of the power load, the dispatching system will reduce the reference quantity to achieve the power balance of the grid. In this paper, to solve the problem of imbalance between power and heating networks, CL (including CEL and TCL) is adopted to participate in scheduling. Because of the flexibility of CL, resources in the network can be managed through energy transfer, thus maximizing the economic benefits of the network. Generally, the CELs are scheduled through an economic way, which is compensated by the electric network. Thus, the cost of adjusting FELs C_CEL is described bywhere the subscript h denotes the hth CEL, H denotes the total number of CEL, c_o3 is the adjustment cost coefficient of CEL, and is the power adjustment of CEL h at time t.

While ensuring the lowest economic cost, it also needs to meet consumers’ demand for electricity throughout the day. The constraints of the CEL are expressed bywhere and are the minimum and maximum power of CEL h, is the consumption power of CEL h at time t, and and are the minimum and maximum power adjustment of CEL h.

For TCLs, such as distributed electric heating storage (DEHS), heat pumps, and electric water heaters, because of its storage capacity and thermal inertia, its working periods can be flexibly adjusted according to the needs of the grid. Take DEHS as an example; it generally operates at rated power. The basic operation principle of DEHS is shown in Figure 3. Taking economic costs into account, DEHS can operate based on fluctuations in electricity prices, heating and storing in the valley-time price region and cutting off electric power in the peak-time price region. It quits operation when the temperature of DEHS is approaching to the limitation and starts again to compensate heat energy before the end of valley time.

As with CEL, DEHS also needs to meet the thermal requirements of consumers throughout the day. The constraints of the TCL are expressed bywhere is the electric consumption power of TCL m at time t, and are the minimum and maximum electric power of TCL m, is the power adjustment of TCL m, and are the minimum and maximum power adjustment of TCL m, is the thermal storage capacity of TCL m, and are the lower and upper limits of its capacity, is the output thermal power of TCL m to meet the heat load demand , and and are the lower and upper limited proportions of adjustment of TCL m.

The cost of adjusting controllable thermostatically loads C_TCL is calculated bywhere c_o4 is the adjustment cost coefficient of TCL.

3.2. Autocorrelation Analysis

In terms of load prediction, in order to understand the situation and rule of load changes over time and make better prediction, this paper firstly conducts correlation analysis on TCL and CEL. The autocorrelation analysis and correlation analysis with other external factors of TCL can be found in [28]. The analysis of CEL is shown as follows. To analyze the sequence correlation, the autocorrelation coefficients between original data and different time series are calculated by the Pearson correlation coefficient method. Pearson correlation coefficient, also known as product difference correlation coefficient, is usually used to measure the closeness and correlation direction of the correlation between two variables with linear correlation, and its calculation formula is shown inwhere and are the empirical means of the samples U = (u₁, …, u_L) and = (₁, …, _L). In this case, U and represent original power data (U) and lag power data [ = (u_1+k, …, u_L ₊ _k), k is the lag time, k = 1, 2, …, i.e., t-k denotes the lag data falls behind the original data by k data points], respectively.

The results of DEHS autocorrelation analysis are shown in Figure 4 and Table 1. Partial autocorrelogram is an important tool to determine the order of autoregressive models for time series. The partial autocorrelograms are utilized to help identify the lag time. According to the partial autocorrelogram, the lag time is selected as 5 [29].

In Figure 4, the correlation coefficients are relatively high, which denotes that the history data influence the current data or future data. In Table 1, the correlation coefficients would be decreased with the increasing lag time. The electric power data of DEHS have a sequence characteristic, which is suitable for LSTM model.

3.3. Correlation Analysis with External Factors

Generally, the available factors affecting the electric power consumption of CEL are weather and time-of-use price. Therefore, these factors are considered in the correlation analysis. The relationships of power with external factors (including temperature, pressure, humidity, wind speed, and time-of-use price) are shown by the scatter plot in Figure 5. The correlation of electric power with the external factors is calculated based on the Pearson correlation coefficient method in (14). In this case, U and represent power data and external factors data, respectively. The calculation results are shown in Figure 6.

The closer the absolute value of the correlation coefficient is to 1, the stronger the linear correlation of the two variables is, and the sign of coefficients indicates that if the two variables increase or decrease in the same direction (positive) or opposite direction (negative), as can be seen from Figure 6, the temperature factor is strongly correlated with wind speed and electricity price, so this paper considers the temperature factor in the forecasting model.

4. Optimal Dispatch Based on Forecast of DEHS

With the increasing penetration of wind power, the wind power curtailment may be induced by a couple of electric and thermal power in electric and heating networks. On the basis of the above, we discussed that the regulation capacity of the network can be strengthened through CL participation in scheduling. Therefore, in this paper, LSTM is used to establish the prediction model of TCL and CEL. The prediction model of TCL can be found in [28], and the prediction model of CEL is constructed as follows. After making the prediction model and making the prediction, a dispatch model is constructed according to the prediction results. Finally, Sequential Least Squares Programming method is used to optimize the objective function.

4.1. Prediction Model Based on LSTM

According to the above analysis, we establish the prediction model for CEL. The essential of RNN is to utilize the sequence characteristics to establish a model, which is suitable for the prediction of DEHS. However, the memory ability of RNN is short-lived, where the context may be significant or useless. As a popular extended RNN method, with three gates (input, forget, and output gates) in memory cells, LSTM network can remember, update, and focus on effective information, which is helpful in tracking information for a longer period. LSTM has the advantage of avoiding gradients vanishment and filtering effective information [21]. Each cell is updated based on the current input and the previous cell state. The product of the result obtained by the activation function and the input gate of the input vector represents the information retained after the input data is filtered. Previously reserved information plus current input meaningful information will be retained for the next LSTM cell. We then take the activation value of this updated memory as a possible output, usually the tanh activation function. The last thing left is the output gate, which determines which of the outputs activated by the current memory are useful. Let c_t be memory cell state at time step t and h_t be the output hidden state; then c_t and h_t are updated:where is the sigmoid function, is activation function, i_t, f_t and o_t are input gate, forget gate, and output gate vectors, _xi, _xf, _xo, _hi, _hf and _ho are the weights for linear combination, b_i, b_f and b_o are the relative bias, and is element-wise production.

In this paper, we consider the behavior characteristics integrating sequence characteristic and external factors (including weather factors and time-of-use price) in the prediction model framework. The block diagram of the electric power prediction of CEL with the LSTM is shown in Figure 7. This diagram illustrates the flow of a time series with some features of length S through two LSTM layers. After correlation analysis of power and temperature data, feature dimensions are obtained according to time series to predict CEL load state, and LSTM network is updated according to (13). However, the other impact factors can also be considered in this framework according to the requirement.where W_ea,t is the weather parameters, P_t is the power consumption of DEHS, LSTM (·) is the state updating of the LSTM cells (i.e., short for (12)), [·,·] means concatenating several vectors into one vector, and W is the trainable weights of LSTM.

4.2. Objective Function

A day-ahead dispatch model of electricity and heat networks for reducing wind power curtailment is established. Factors such as the fuel cost of CHP with TES, TPP, average operation and maintenance cost of EES, the cost of wind power curtailment, and scheduling CL are considered. Summing up equations (3), (5), (7), (9), (10), and (13), the objective function of economic cost C_EC of day-ahead scheduling model is expressed in

4.3. Electric and Heating Networks Balance

4.3.1. Electric Network Balance

Total generations and electric loads must be balanced at each operation period as described inwhere is load electric demand at time t.

4.3.2. District Heating Network Unbalance

Since the inertia of the heating network can maintain the temperatures, the unbalance between thermal power generation and demand can be within a limited range as shown inwhere is the heat demand at time t. and are the lower and upper limited proportions of adjustment in the district heating network.

5. Case Study

Several cases are conducted with real data in the Liaoning provincial grid of China to verify the effectiveness of the proposed prediction method and the optimal dispatch solution. Although the data used to validate the effectiveness is only from one country, it should be noted that the proposed method and optimal dispatch solution can be used in any system globally. A nonlinear quadratic programming problem can be used to solve the optimal dispatch problem. The Sequential Least Squares Programming method is used as a resolving solution in Python.

5.1. Forecasting Method Validation

The proposed LSTM model is compared with two advanced methods: RNN and SVM. The LSTM model’s fitness of train data and test data of CEL is obtained by mean absolute error (MAE) loss function as shown in Figure 8.

In Figure 8, with the increasing epoch, the losses gradually approach 0.2. The training and testing sets are consistent, proving that LSTM has high accuracy and is suitable for forecasting CEL. The prediction results for each method are shown in Figure 9 and Table 2.

(a)

(b)

In Figure 9(a), with different methods, the overall prediction trends are consistent considering the weather. Figure 9(b) shows that the prediction result with LSTM is closest to the real data. In Table 2, it can be seen that MAPE and root mean square error (RMSE) with LSTM are the least, which shows the higher accuracy of the proposed model. Thus, the superiority of LSTM in CEL prediction is reflected.

5.2. Optimal Dispatch Validation

In this paper, the scheduling results with and without CL are compared to prove the effectiveness of CL for day-ahead optimization scheduling. The consumption curves of electric load and heat load are predicted. The wind power curve in recent two months is shown in Figure 10. Wind power data are measured on a time scale of 15 minutes, and two typical curves of this month are selected, namely, the curves of maximum output power and minimum output power. It can prove that the proposed methods can cope with different operating conditions. In Case 1, the lower wind power curve is applied, and the upper wind power curve is used in Case 2. The electric power curve of CEL is predicted by LSTM model, and TCL power is selected in [28]. The simulation parameters are the same with the Liaoning provincial grid as shown in Table 3.

The optimization results of the two cases with different methods are shown in Figures 11 and 12 In Figure 11(a), the electric power of load is supplied by power sources in the electric network. With the two methods, the electric power of CHP and TPP P_TPP is generally consistent. Due to the small capacity of EES, it has a small space to participate in power grid regulation, so it cannot eliminate all wind power curtailment only by EES. CL participation in grid dispatching can enhance the effect of wind power consumption together with EES. The results show that the output of wind power P_WPP with CL involved in scheduling is greater than that without CL involved in scheduling.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

As shown in Figure 11(b), in the peak-time region of base load (from time points 30 to 60), due to weak wind power, it cannot meet the base load demand, and the output of CHP, TTP, and EES is high. It is almost up to the limit. At about time point 12, due to the reduction of the electric power of load, wind power not only meets the load demand, but also generates part of curtailment power. However, after CL participates in dispatching, it can effectively reduce wind abandoning by transferring CEL and TCL consumption, especially in peak wind power periods, realizing efficient utilization of renewable energy. The results show that the peak wind power curtailment is reduced by about 50 MW, accounting for about 10% of the total power generation. At the same time, EES life, because of the reduction of large charge and discharge times, has been improved.

Figures 11(c) and 11(d) show the thermal supply and consumption for the district heating networks and TCL, respectively. It can be seen that, in the district heating network, due to the help of TES, the requirement of thermal power with two methods can be met for the residents. For the TCL, the thermal requirement is met. The final economic costs of the dispatch model C_EC are 5,571,203 USD and 5,612,126 USD with CL and without CL, respectively. The results in Case 2 are shown in Figure 12.

In Figure 12(a), during the period of (points 80–96), with the reduction of base load demand, wind power output increases. CHP and TTP even reach the lower limit of output because they do not have to produce too much, and excessive wind power leads to the increase of wind power curtailment. As shown in Figure 12(b), with dispatching CL, wind power output is larger than that without CL. The results show that the peak wind power curtailment is reduced by about 25 MW (accounting for about 5% of the total power generation); thanks to the adjustment of the consumption of CEL and TCL of the peak wind power curtailment is reduced. It can be seen from Figures 12(c) and 12(d) that the thermal sources can meet the thermal requirement of the district heating network and TCL, respectively. The final economic costs C_EC are 5,668,098 USD and 5,738,626 USD with CL and without CL respectively, and the economic cost is reduced by 70,528 USD. Therefore, the proposed dispatch method can reduce wind power curtailment and economic costs.

6. Conclusion

This paper proposes a framework of optimal dispatch based on controllable load (including CEL and TCL). The prediction model of LSTM of distributed electric heat storage based on correlation is established. The prediction model, considering their autocorrelation, weather factor, and consumers’ behavior characteristics, improves the prediction accuracy of distributed electric heating storage. The effectiveness of the proposed prediction model and the dispatch method are verified through simulations. Compared with the state-of-the-art techniques of support vector machine and recurrent neural networks, the root mean square error with the proposed long short-term memory can be reduced by 0.069 and 0.044, respectively. Compared with conventional method, the peak wind power curtailment with dispatching CEL and TCL is reduced by nearly 10% and 5% in the two cases, respectively.

Data Availability

The raw data in our study are from Liaoning provincial grid of China.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported in part by the Liaoning Provincial Department of Education Research Funding under Grant LQGD2019005 and in part by the China Postdoctoral Science Foundation under Grant 2019M651144.

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Copyright © 2022 Yiming Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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