The IES dynamic time-scale scheduling strategy based on multiple load forecasting errors

0 Introduction

Recently,with the continuous development of the concept of energy interconnection,the integrated energy system (IES),which is used as an energy internet carrier,has been extensively studied by many scholars.The research involves planning,scheduling,reliability analysis,among other fields [1-5].

The IES includes the coupling and conversion of multiple energies,and it has a more complicated relationship in comparison to traditional discrete operation power grids and gas grids.This increases the difficulty of conducting research as the energy efficiency improves [6,7],and it divides the IES into inter-regional,regional,and user levels according to their scales.In addition,it discusses the main issues that need to be solved for the IES at different scales.

Multi-time-scale scheduling is a scheduling strategy for traditional power systems that eliminates forecast errors by refining the time scale layer by layer to track the real-time load power [8-11].In recent years,more and more scholars have applied it to integrated energy system dispatching.[12-14].Mei et al.[13]proposed a multi-time-scale dynamic optimization scheduling strategy for the electricity-gas interconnected IES that is based on model predictive control and which takes the temporal and spatial correlation of the natural gas line-pack into account.Wang et al.[14]proposed a two-stage multi-time-scale model that applies the predictive control scheduling strategy for a community IES which takes the advantages of the complementary operation of the multiple energies and effectively reduces the operating costs.

Although all the above studies theoretically achieved multi-time-scale optimization layer by layer,the outstanding problem is that all kinds of energies are in the same time scale,and the response speed of the electrical,cooling,and heating energy is different,especially when the scale is reduced to the minute level.This is a question worth exploring to determine whether the strategy can be adapted.In this regard,a hybrid time-scale scheduling strategy that is based on the difference in the energy characteristics is proposed [15,16].This can distinguish the essential difference in energy on the basis of the traditional multitime-scale scheduling strategy and optimizes some of the components in each time scale to make multiple time-scales possible thus applying the IES scheduling.

The essential purpose of the multi-time-scale strategy is to resolve the load uncertainty and new energy output.Therefore,the coordination requirements between time scales will be reduced when the prediction result is sufficiently accurate.In recent years,with the continuous rise in artificial intelligence,deep learning algorithms that are represented by long short-term memory (LSTM) have been widely used in the power system prediction [17-20].

According to the foundation of existing research,a dynamic time-scale scheduling strategy for the IES that is based on LSTM and multiple load forecasting errors is proposed in this study.The main contributions are summarized as follows:

(1) An improvement in the load forecasting accuracy that is based on LSTM and reduces the time resolution while weakening the requirements for determining the specific value of the time scale.

(2) An improvement in the scheduling efficiency by distinguishing among electrical,heating and cooling energy and considering the response speed of the equipment and other factors to achieve classification and hierarchical scheduling.

(3) To dynamically determine the best hybrid time scale for each month and achieve an adaptive time-scale thus improving the scheduling flexibility.

1 Structure of the IES

The IES mentioned in this article mainly includes five parts as shown in Fig.1.These parts include:the energy network,energy generating equipment,energy conversion equipment,energy storage equipment,and load.The upperlevel energy network provides a basic energy guarantee for the IES.The energy generating devices convert other types of energy into an energy form required by the IES users.The energy conversion equipment mainly achieves energy conversion inside the IES for more flexibility.The energy storage equipment primarily stores excess energy when the energy value is low,and it helps balance the supply and demand when the energy value is high; but the load demand is large enough to achieve higher economic benefits.

Fig.1 Basic structure of the IES

1.1 Energy generation equipment

Combined heat and power

The combined heat and power (CHP) unit burns natural gas,and it applies the energy cascade utilization to realize the combined supply of heat and electricity; it improves the energy utilization efficiency [21-23].The mathematical model is as follows [24-25].

Where:G is the consumption of the natural gas; Pchp and Hchp are the corresponding power and heat generation;Qgas is the low calorific value of the natural gas; ηchp,e and ηchp,h are the gas-electricity and the gas-heat conversion efficiency of the CHP units,respectively; Pchp,max,Pchp,min,Hchp,max,and Hchp,min are the upper and lower limits of the power and heat supply,respectively; andrepresent the upper limit constraints of the electric and thermal climbing.

Photovoltaic (PV)

Generally,the photovoltaic output is closely related to factors such as the light intensity and the outdoor temperature.The specific relationship is

where Pv is the photovoltaic output,ηpv is the conversion efficiency of the photovoltaic array,Spv is the area of the photovoltaic array,I is the solar radiation intensity,and Tout is the outdoor temperature.

1.2 Energy conversion equipment

Absorption chiller (AC)

The absorption chiller converts one heating energy quality into another by absorbing it to achieve cooling.Because it only involves the conversion of thermal energy,the energy is essentially the same.Logically,the feasibility of energy decoupling optimization is increased in the scheduling.

where CAC and HAC are the output cooling energy and the absorbed heating energy of the absorption chiller,respectively,and ηAC is the energy conversion efficiency.

Electric chiller (EC)

The electric chiller achieves the cooling effect by absorbing the electric energy,which is the key element for electrical-cooling coupling.The mathematical model is

where CEC is the output cooling power of the electric chiller,ηEC is the cooling efficiency,and PEC is the input electrical power.

Electric boiler (EB)

The electric boiler achieves the heating effect by absorbing electrical energy,which is the key element for the electrical and heating coupling.The mathematical model is

where HEB is the output heating power of the electric boiler,ηEB is the heating efficiency,and PEB is the input electrical power.

1.3 Energy storage equipment

Power energy storage (PES)

The PES can increase the flexibility in the system scheduling:it actively responds to the time-of-use prices,improves the dispatch-ability,and reduces the operating costs.The model is

where are the charging and discharging electrical power at time t,respectively; S P ES(t ) is the PES capacity at time t; and are the charging and discharging efficiency of the PES,respectively.The PES needs to meet the following constraints during the process of dispatching.

where are the upper and lower limits of the charging and discharging electrical power,respectively.The capacity of the TES is maintained between the lower limitand the upper limitrepresent the 0-1 variable,which signifies the charging and discharging state; and there is only one state at any time.To increase the scheduling flexibility,the energy of the PES at the beginning of the scheduling period should be equal to the energy at the end.

where SPES(1) is the energy at the beginning and S P ES( k ) is the energy at the end of the dispatching cycle.

Thermal energy storage (TES)

The TES and PES have similar mathematical models,which can be expressed as

where are the charging and discharging heat power at time t,respectively; ST ES(t ) is the capacity of the TES at time t; and are the charging and discharging efficiency of the TES,respectively.The TES needs to meet the following constraints during the process of dispatching.

where are the upper and lower limits of the charging and discharging electrical power,respectively.The capacity of the TES is maintained between the lowerand the upper limitare the 0-1 variable,which represents the charging and discharging states,respectively; and there is only one state at any time.To increase the scheduling flexibility,the energy of the TES at the beginning of the scheduling period is equal to the energy at the end.

where STES(1) is the energy at the beginning,and ST ES( k ) is the energy at the end in the dispatching cycle.

2 Long short-term memory

The dynamic time scale scheduling strategy proposed in this study depends on the load forecasting error under each time scale and the selected load forecasting method.This will become a direct influencing factor in determining each time scale.Taking into account the recent achievements of deep learning in the field of load forecasting,we will carry out the load forecasting work based on the LSTM method.LSTM is a special recurrent neural network (RNN) that retains the recursive attribution of the RNN.However,it has a unique memory and forgetting mode,which solves the problem of gradient disappearance and the explosion of the RNN in the back-propagation through time training process.LSTM is composed of the input layer,output layer,and hidden layer.The calculation formula [26-30]between each unit is

where it,ft,and ot are the input gate,forget gate,and the output gate,respectively; Wxi,Wxf,Wxo,and Wxc represent the weight matrix of the input signal xt; Whi,Whf,Who,and Whc are the weight matrix of the hidden layer output signal; ht,Wci,Wcf,and Wco are the output vectors that are connected to the neuron activation function; bi,bf,bo,and bc represent the bias vector; σ is the activation function; and ct is the state of the LSTM cell at time t.

Regarding the input of the LSTM and the determination of the hyper-parameters,the input of the day-ahead forecast in this study contains all of the 24 h load data from the previous 7 d and the ultra-short-term forecast input of the intra-day is the previous 24 h data of the forecasting time.In addition,other information on the holidays and the weather (e.g.,temperature and humidity data) are also included.The LSTM has a total of 3 layers for the structure,and the number of neurons in each layer is 32,64,and 128,respectively.The data from January to December 2017 were selected.In addition,the training set is divided according to the ratio of 80 % and 20%,then the data required for the following calculations are calculated.

3 Dynamic time-scale scheduling model

The dynamic time-scale scheduling strategy proposed in this study is mainly divided into the following two parts.

Day-ahead scheduling:The scheduling plan of every device in the next day will be delivered.We adopted an“immediate strategy”,(i.e.,once the optimization is done,the dispatch is executed).The optimization interval mainly refers to the time interval range of the data used in the optimization scheduling plan.By having a longer time period,there is a greater forecasting error.There could be a big deviation between the optimized plans and the load trends.The day-ahead plan is from the overall perspective of the whole day,which is mainly based on the day-ahead load forecasting error.It gives the macroscopic trend of the dispatching plan.Therefore,the optimization period is 24 h.

Intra-day scheduling:The typical daily characteristics of the different seasons have an obvious distinction;therefore,the choice of the time-scale resolution will be determined by the coordination of the different time-scale,which takes every month as a unit.Thus,there will be 12 (12 months a year) types of intra-day scheduling time scales available.The specific intra-day dynamic time-scale selection method consists of the following.

(1) A relation curve of the load forecasting error and the time-scale that is based on the forecasting results of the LSTM is made.

(2) The dispatchers determine the requirements of the IES for the unbalanced supply and demand under the intraday time scale (the accuracy of tracking the real-time load power).

(3) The specific time scale of the scheduling according to some strategies is determined.

The mean absolute percentage error (MAPE) is used to evaluate the prediction performance [31-32],which is based on the prediction results of the LSTM that is expressed as

where F is the predicted MAPE value based on the LSTM at each time scale,Fall is the total number of samples,Fs is the predicted data,and Fr is the real load data.We calculated the value of F under each time-scale for each month after categorizing the forecast results for each month.Generally,as the time scale continues to shrink,the prediction error will gradually decrease.Therefore,we found the upper limit of the time scale tmax according to the upper limit of the allowable error Emax,and we discovered the lower limit of the time scale tmin according to the lower limit of the allowable error Emin,which is shown in Fig.2.

Fig.2 Selection of the dynamic time scale

3.1 Day-ahead scheduling

The day-ahead dispatch is mainly done from an economic point of view to make appropriate plans for the power purchase,gas purchase,and equipment output.

The specific objective function is

where Cgrid(t) is the dynamic electricity price of the grid,which is higher during the peak load periods; however,it is lower during the peak load periods.We used the same price at the same time whether it is the electricity sales or the electricity purchases.It should be noted that in the case of the electricity sales,Pgrid(t) is a negative value and Cgas(t) is the price of the natural gas; this value is fixed under normal circumstances.

3.2 Intra-day scheduling

Intra-day scheduling is mainly divided into three layers,in which the upper layer has the longest time scale,the intermediate transition layer has the middle time scale,and the lower layer has the smallest time scale.Due to the slow dynamic characteristics of the cooling and heating energy,the upper and middle layers are often related to the cooling and heating equipment.

Upper level scheduling

Regardless of the various load forecast MAPE values,adjusting the gas purchase plan and the CHP unit are a part of the upper level scheduling content.The electric chiller is dispatched in the upper level and the electric boiler is dispatched in the middle level when Emax of the cooling load is larger than the heating load.In contrast,the electric boiler is dispatched in the upper layer,and the electric chiller is dispatched in the middle layer when Emax of the cooling load is less than the heating load.When the forecasting errors of the cooling and heating loads are similar,the electric boiler and the electric chiller can also be at the same dispatch level.The upper-level scheduling objective function [33-34]is

where ΔFC HP(t ) is the amount of adjustment beyond the interaction power with the natural gas network; ΔPC HP(t )is the amount of electricity generated by the CHP system beyond the plan; μgas and μCHP represent the unit adjustment cost of the gas purchase and the CHP unit,respectively;µEB and µEC signify the unit adjustment cost of the electric boiler and the electric chiller,respectively; ΔPEB and ΔPEC represent the adjustment amount of the electric boiler and the electric chiller at time t,respectively; and λEB and λEC denote the 0-1 variable,which is 1 during upper-level scheduling—otherwise it is 0.

Middle-level scheduling

The middle-level scheduling objective function is

The scheduling of the middle layer is not necessary,and it can be completely omitted if the forecasting errors of the cooling and heating loads are small.The participation of the electric boilers and electric chillers during middle-level dispatching and their detailed arrangements are illustrated in Fig.3.

Fig.3 Upper- and middle-layer scheduling equipment

Lower-level scheduling

Based on the day-ahead,the upper-level,and the middlelevel dispatching plan,the lower-level adjustment is mainly completed by the storage devices and the tie lines with the fast-dynamic characteristics.The objective function is

where ΔPg rid(t ) is the amount of the adjustment beyond the interaction power with the main grid,µgrid is the unit adjustment cost of the tie line,µB is the unit adjustment cost of the PES,and is the adjustment power of the charging and discharging of the PES at time t.

3.3 Energy balance constraint

To meet the needs of the users at any time,the energy must be balanced between the supply and demand.

where Pgrid,PCHP,PPES,and Pv represent the power provided by the main grid,CHP units,storage devices,and PV,respectively; Pe,PEC,and PEB denote the power consumed by the electrical load,electric chiller,and electric boilers,respectively; HCHP and HTES signify the heating energy that is provided by the CHP units and the TES; He is the heating load; Ce is the cooling load; HAC and ηAC represent the energy consumption and the efficiency of the absorption chiller,respectively; ηEB is the efficiency of the electric chiller; and ηEC is the efficiency of the electric boiler.

4 Analysis of the examples

This study selected a user-level IES as an example for the analysis.Reference [7]provides the equipment capacity and the parameters,and reference [15]provides the historical data of the load,photovoltaics,and outdoor temperature.A deep LSTM network is used to predict the load,outdoor temperature,and photovoltaic output under different time resolutions.The forecasting MAPE value of each month is presented in Fig.4.It should be noted that the load forecasting work was mainly carried out with Python under the tensor flow framework,and the dynamic timescale scheduling model is solved with the Gurobi solver.

In Fig.4,the numbers 1-9 on the abscissa,respectively,represent the 24 h time scales (day ahead),8 h,6 h,4 h,2 h,1 h,30 min,15 min,and 5 min,and the ordinate is the MAPE value (dimensionless) for each time scale,the MAPE value of the electrical load is higher than the cooling load and the heating load,and the change in the MAPE value for the cooling and heating load shows an alternating situation regardless of month; and this is attributed to the following two reasons.(1) The characteristics of the electrical,heating,and cooling energy are different.The electrical energy travels and it changes at the speed of light whereas the cooling and heating energy have a certain delay and inertia.Therefore,the prediction accuracy of the cooling and heating energy is higher than that the electrical energy under the same time scale.(2) The prediction accuracy of the cooling and heating load perform the alternation during different months,which mainly depends on the change in the load base.That is,when the load base is smaller,the randomness of the load is stronger and the fluctuation is greater.Therefore,the forecast error is relatively large due to the loss of the aggregation effect of the load.Depending on the changes in the temperature,the cooling and heating load demand will also show a certain regular increase and decrease during different months,and their MAPE value is not fixed.

Advantages in comparison to the traditional strategy

Fig.4 MAPE changes of the different loads during the different months

The multi-time scale strategies for traditional scheduling often apply a fixed time scale,and they track the real-time load power that is gradually refined by the time scale.From the perspective of the load changes,a fixed time scale does not affect the scheduling efficiency because of the similar pattern for a single load throughout the year.When there are multiple energy coupling situations,a fixed time scale may not meet the actual situation.Assuming that the allowable upper limit of error is 2.5% for intra-day scheduling,the maximum time scale that can be selected for the traditional scheduling strategy and the scheduling strategy proposed in this paper is shown in Table1.

Table1 Time scale selection of the different strategies

month Dynamic strategy Traditional strategy cooling heating electrical All energy 1 2 h 4 h 30 min 30 min 2 2 h 4 h 30 min 30 min 3 1 h 2 h 1 h 1 h 4 2 h 1 h 30 min 30 min 5 4 h 2 h 1 h 1 h 6 6 h 30 min 30 min 30 min 7 6 h 1 h 15 min 15 min 8 6 h 1 h 30 min 30 min 9 2 h 1 h 15 min 15 min 10 2 h 1 h 15 min 15 min 11 2 h 6 h 30 min 30 min 12 2 h 6 h 30 min 30 min

Furthermore,to highlight the advantages of the scheduling strategy proposed in this study,we compared the energy prediction imbalance degree and the maximum number of equipment adjustment indicators under a fixed time scale (traditional multi-time scale scheduling strategy).The expression of these indicators is

where Eub is the imbalance degree of the load forecasting MAPE value; F is the MAPE value of the load to be calculated; Fh,Fe,and Fc represent the MAPE values of the heating,electrical,and cooling load,respectively; Nmax is the maximum possible number of adjustments for the scheduling equipment; and Tscale is the time scale for the determined schedule.We selected a day in the middle of each month in 2019 (January 15,February 15,...,December 15) as the scheduling object,and then we calculated the average value of the defined indicators.The calculation results are shown in Table2 and Table3.

Table2 Traditional multi-time scale scheduling strategy indicators

Month Traditional strategy Electrical Heating Cooling Eub Eub Eub Nmax 1 0.37 0.25 0.13 48 2 0.42 0.25 0.17 48 3 0.52 0.31 0.20 24 4 0.58 0.32 0.26 48 5 0.39 0.35 0.04 24 6 0.60 0.29 0.16 48 7 0.37 0.39 0.30 96 8 0.39 0.32 0.28 48 9 0.65 0.27 0.29 96 10 0.49 0.37 0.27 96 11 0.40 0.35 0.20 48 12 0.52 0.28 0.27 48 Mean value 0.47 0.31 0.21 56

Table3 Dynamic time-scale scheduling strategy indicators

Month Dynamic strategy Electrical Eub Heating Eub Cooling Eub Nmax upper Nmax lower 1 0.01 0.03 0.02 12 48 2 0.14 0.12 0.02 12 48 3 0.25 0.19 0.06 24 24 4 0.13 0.10 0.03 12 48 5 0.18 0.27 0.08 24 24 6 0.19 0.14 0.06 12 48 7 0.15 0.14 0.06 48 96 8 0.11 0.06 0.03 24 48 9 0.13 0.09 0.04 24 96 10 0.11 0.08 0.07 24 96 11 0.10 0.08 0.07 12 48 12 0.20 0.14 0.04 12 48 Mean value 0.14 0.12 0.05 20 56

Due to the large difference in the load forecasting results under the same time scale,the real-time power for multi-class load tracking is extremely unbalanced when the traditional scheduling strategy is adopted.Therefore,it is necessary to continuously reduce the time scale to track the real-time load power due to the relatively high prediction error of the electric load.At the same time,the cooling and heating energy scheduling cycle are shortened,and it significantly increases the upper limit for the number of times that the equipment can participate in the adjustment in the scheduling cycle.As a result,all the devices participating in the scheduling have a high time resolution,and the plan will be frequently adjusted.A variety of loads show similar fluctuation characteristics in the same dispatching period when a dynamic and hierarchical time scale is adopted,which increases the scheduling flexibility and reduces the unnecessary adjustment of equipment.Hence,a variety of devices can be classified and processed according to the energy characteristics,but the time scale can be dynamically and adaptively changed to track the real-time load power more specifically to improve the scheduling efficiency as the load forecasting errors change.Taking the data of a certain day in October as an example for the scheduling,the output plan of the key equipment is shown as follows.

Fig.5 Scheduling plan of the gas purchase

The power of the tie line and the gas purchase/selling plan will directly affect the energy interaction with the upper-level energy grid as the upper and lower scheduling plans.The upper-level scheduling time scale in October is 2 h,whereas the lower-level scheduling time scale is 15 min.From the results,the power interaction with the upper-level grid and the natural gas purchase plan are fully in accordance with the changing law of time-of-use price,which has peak-and-valley characteristics.In other words,the basic dispatching needs of the IES are met by purchasing electricity from the upper-level grid during the low-price period at night,and the gas purchase is reduced.When the demand for electricity is high during the day and the electricity price is high,the basic energy is mainly provided by purchasing gas.Meanwhile,the excess electricity is sold to the higher-level grid to obtain part of the profit at a high price.When comparing the power purchase plan and the gas purchase plan,it is not difficult to find that they have excellent complementary characteristics.The dynamic changes of the energy prices continuously change the energy purchase plan,and it makes the IES a more economical operation,which is also a level that a single system cannot achieve.In addition,the charging and discharging plan of the energy storage device is presented in Fig.6.

Fig.6 Energy storage plan of the PES and TES

Fig.6 shows the discharging plan of the energy storage device,and the trend is in full agreement with the time-ofuse electricity price.Among them,0 means that the energy storage device charge energy remains unchanged and 1 indicates that the energy is discharged.Because of the low price of electricity at night,the tie line purchases electricity from the grid and the power energy storage device will store electricity in time.Considering that the CHP unit basically does not participate in the energy supply,the supply of cooling and heating energy during this period is completed by the thermal energy storage device.During the daytime,the energy storage device will selectively charge and discharge the energy according to its own energy changes and the optimal scheduling for other equipment.But overall,the charging and discharging energy plans for the thermal energy storage and the power energy storage device are complementary to a certain extent.

5 Conclusions

This study proposes a dynamic time-scale scheduling strategy for the IES,and a multi-layer scheduling model is established for different months according to the different load characteristics through the load forecast MAPE value.The plan is optimized layer by layer through different time scales and the following conclusions are obtained.

(1) The IES contains multiple types of energy and the characteristics of each energy type are different.The hierarchical optimization and multi-time-scales could adapt well to the energy and device response characteristics (i.e.,let the devices with slow response characteristics participate in long time-scale scheduling and devices with fast response characteristics participate in short time-scale scheduling).

(2) When taking into account the changes in the basic demand for the various loads and the accuracy fluctuations of the forecast errors,the dynamic time scale that is proposed in this study can efficiently cope with the changes in the different loads for different months.

(3) In comparison to the traditional multi-timescale scheduling strategy,the dynamic time strategy that considers the energy characteristics could make the supply and demand of multiple energies more balanced and reduce the short-board effect.

In the future,the IES will be a complex system with multiple energy and coupling relationships.Therefore,we will focus on enriching other aspects (e.g.,stochastic programming model) while considering the load forecast errors,and we aim to improve the dynamic time-scale scheduling strategy proposed in this study.

Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities (No.2017MS093).

Declaration of Competing Interest

We declare that we have no conflict of interest.

Appendix A

TableA1 Key parameters of the example

parameter name parameter value parameter name parameter value ηchp,e 3.243 PTES max/kW 1.5 ηchp,h 5.405 ηEC 1 Pchp,min/kW 0.3 ηEB 1 Pchp,max/kW 3 ηPES in 0.85 Hchp,min/kW 0.5 ηPES out 0.98 Hchp,max/kW 5 PPES max/kW 0.3 Pchp r /kW 2.5 SPES min/kWh 0.38 ηAC 0.7 SPES max/kWh 8.33 ηTES in 0.98 STES min/kWh 2.25 ηTES out 0.98 STES max/kWh 7.5

TableA2 Key parameters of the scheduling model

Model Time Training time of the LSTM 6 h Forecasting time of the LSTM 2 s Calculating time of the day-ahead scheduling model 16.44 s Average calculating time of the intra-day scheduling mode 0.5553 s