Issue 
Natl Sci Open
Volume 3, Number 3, 2024
Special Topic: Energy Systems of Low Carbon Buildings



Article Number  20240004  
Number of page(s)  16  
Section  Engineering  
DOI  https://doi.org/10.1360/nso/20240004  
Published online  29 February 2024 
RESEARCH ARTICLE
Optimal coordination of zero carbon building energy systems
^{1}
School of Future Technology, Xi’an Jiaotong University, Xi’an 710049, China
^{2}
Ministry of Education Key Lab for Intelligent Networks and Network Security, School of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
^{3}
Center for Intelligent and Networked Systems, Department of Automation, TNLIST, Tsinghua University, Beijing 100084, China
^{*} Corresponding author (email: zbxu@sei.xjtu.edu.cn)
Received:
31
October
2023
Revised:
26
January
2024
Accepted:
18
February
2024
Optimal scheduling of renewable energy sources and building energy systems serves as a pivotal strategy for achieving zero carbon emission. However, the coordination of zero carbon building energy systems (ZCBS) is still challenging due to the complicated interactions among multienergy hybrid storage and the complex coordination between seasonal and daily scheduling. Therefore, this study develops a coordination scheduling approach for ZCBS. An operation model and a seasonaldaily scheduling approach are developed to optimize the operation of hydrogen, geothermal, and water storage devices. The performance of the developed method is demonstrated using numerical case studies. The results show that the ZCBS can be achieved by using renewable energy sources with the system flexibility provided by hydrogen, geothermal, and water storage devices. It is also found that the developed scheduling approach reduces operation costs by more than 43.4% under the same device capacity, compared with existing scheduling approaches.
Key words: zero carbon building energy systems / seasonaldaily scheduling / multienergy storage / twostage robust optimization
© The Authors(s) 2024. Published by Science Press and EDP Sciences.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
INTRODUCTION
Report of International Energy Agency indicated buildings account for 30% of global final energy consumption and 26% of global energyrelated emissions [1], in which 8% are direct emissions in buildings and 18% indirect emissions from the production of electricity and heat used in buildings [2]. The integration of renewable energy can significantly reduce the consumption of fossil fuels while greatly improving economy [3]. In order to achieve higher energy efficiencies, combined cooling, heating, and power systems have been identified as potential solutions [4]. Therefore, coordination of multienergy supply and demand in buildings is effective in improving building energy efficiency and achieving zero carbon emission.
In recent years, coordination of multienergy systems in buildings has attracted more and more attention [5–8]. Multienergy complementary systems for residential buildings can help ensure the survival and improve the wellbeing of about 1.5 billion people who are currently living in isolated areas worldwide [9–12]. But its internal structure has high complexity and requires coordinated scheduling [13–15]. To achieve a high proportion of renewable energy, several studies proposed dayahead optimal operation strategies [16,17]. Twostage stochastic scheduling scheme of integrated multienergy system can effectively handle system uncertainty [18]. Seasonal energy storage techniques, including hydrogen storage and geothermal storage, are commonly utilized in netzero carbon energy building systems to address the seasonal disparity between energy demand and supply [19–21]. Integrated shallow geothermal systems usually use ground source heat pumps to exchange and store ground heat [22], which can provide heating and cooling and help the reduction of greenhouse gas emissions [23]. But without proper operation, the soil thermal imbalance directly affects the soil temperature variation during continuous operation [24]. In zeroenergy building systems, hydrogen is one of the key energy carriers [25]. Electrolyzer can convert excess photovoltaic (PV) power output into hydrogen for daily or seasonal storage [26]. Fuel cells can work with a combined heat and power mode [27], while hydrogen storage system can operate as intermediary energy carriers between the electrical and thermal sectors [28]. Numerous studies have proposed design and scheduling methods for zero carbon building energy systems (ZCBS), taking into account the capacity of seasonal energy storage [29–32]. Still, optimal operation of ZCBS through the coordination of seasonal hydrogen storage and thermal storage scheduling has not yet been comprehensively considered.
The coordinated scheduling of the ZCBS still faces the following two challenges. First, the seasonal scheduling could enhance the performance of the daily scheduling of energy storage devices. However, there exists significant difference between seasonal and daily scheduling strategy for energy storage device, and the existing daily scheduling method cannot handle the seasonal scheduling of energy storage devices. Therefore, a coordination model for daily scheduling and seasonal scheduling needs to be developed. Second, in ZCBS, a complex interaction exists among hybrid energy storage devices, encompassing hydrogen, geothermal, and water storage systems. Waste heat generated from fuel cells in nonheating season can be either stored in geothermal wells for seasonal storage or in hot water tanks to meet daily hot water demand. Crossseason scheduling faces computational complexity challenges due to the long scheduling horizon. Moreover, the coordination of multienergy hybrid storage in ZCBS remains ambiguous due to the complexity arising from various energy conversion and storage processes.
To overcome the challenges mentioned above, we make the following contributions in this paper. First, a ZCBS operation model is developed, which describes operation constraints of seasonal and daily energy storage devices including hydrogen, geothermal, and water storage. The developed model can describe the coordination of multienergy hybrid storage and provide scheduling decisions. Second, we develop a seasonaldaily scheduling approach. By explicitly establishing robust seasonal scheduling and economic daily scheduling, seasonal storage strategies can be achieved at the daily level with seasonal storage capacity constraints. There are twostage decisions in seasonalscheduling, decision variables in the first stage include seasonal scheduling before revealing uncertainty, which refer to seasonal storage and HP operation mode, while the decision variables in the second stage include other device operations. The developed approach reduces the inconsistencies between the daily and seasonal scheduling strategies while maintaining both continuity and optimality. Finally, the economic performance of the system is illustrated through case studies, indicating that the developed scheduling approach achieves a higher selfproduction ratio and reduces more than 43.4% operation costs compared with existing scheduling methods.
OPTIMAL COORDINATION SCHEDULING APPROACH
ZCBS configuration
The typical structure of ZCBS is illustrated in Figure 1. The energy flow within the system can be divided into three parts: (1) Energy input phase, where the energy input is hydrogen purchasing and renewable energy sources. (2) Energy conversion phase, which involves the conversion between electricity, heat, cooling, and hydrogen. EL converts electricity into hydrogen. HP and GW utilize electricity to transform lowgrade thermal energy into highgrade heat and cooling, and FC utilize hydrogen to generate power and heat. (3) Energy storage phase, which comprises hydrogen, geothermal, and water storage. The HS is responsible for storing the hydrogen produced by EL, while the water storage tank serves as a shortterm energy storage device for daily heat and cooling scheduling [33]. Additionally, the GW functions as a seasonal energy storage device for storing thermal energy throughout the year.
Figure 1 Structure of ZCBS. 
Device model formulation of ZCBS
To guarantee the efficient and stable operation of ZCBS, comprehensive device models are developed to represent the interconnected multienergy flow among various devices. System devices can be classified into power supply devices, heating and cooling supply devices, and energy storage devices. In ZCBS, power supply devices comprise PV, EL, and FC, where FC functions for cogeneration and electrolyzers can transform surplus PV output into hydrogen for storage [34]. Constraints are as follows:
$\begin{array}{c}{p}_{t}^{\text{PV}}={\eta}^{\text{PV}}\cdot {P}^{\text{PV}}\cdot {S}_{t},\text{\hspace{1em}}{p}_{t}^{\text{EL}}={\eta}^{\text{EL}}\cdot {m}_{t}^{\text{EL}},\text{\hspace{1em}}{p}_{t}^{\text{FC}}={\eta}^{\text{FC},\text{p}}\cdot {m}_{t}^{\text{FC}},\text{\hspace{1em}}{g}_{t}^{\text{FC}}={\eta}^{\text{FC},\text{g}}\cdot {m}_{t}^{\text{FC}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(1)
$\begin{array}{c}{p}_{t}^{\text{EL}}\le {P}^{\text{EL}},\text{\hspace{1em}}{p}_{t}^{\text{FC}}\le {P}^{\text{FC}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(2)
where $\mathcal{T}$ in Equation (1) denotes the set of scheduling time periods.
In ZCBS, heating and cooling supply devices consist of EB and HP. EB is utilized for electric heating, while HP serves to supply both heating and cooling. In heating mode, HP transfers lowgrade heat sources to highgrade heat supplies by consuming electricity. In cooling mode, HP transfers lowgrade cooling sources to highgrade cooling supplies, ensuring the efficient provision of cooling and heating. The detailed energy conversion constraints are as follows:
$\begin{array}{c}{g}_{t}^{\text{HP},\text{H}}={\eta}^{\text{HP},\text{g}}{p}_{t}^{\text{HP},\text{g}},\text{\hspace{1em}}{q}_{t}^{\text{HP}}={\eta}^{\text{HP},\text{q}}{p}_{t}^{\text{HP},\text{q}},\text{}{g}_{t}^{\text{EB}}={\eta}^{\text{EB}}{p}_{t}^{\text{EB}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(3)
$\begin{array}{c}{g}_{t}^{\text{HP},\text{L}}={g}_{t}^{\text{HP},\text{H}}(1\frac{1}{{\eta}^{\text{HP},\text{g}}}),\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(4)
$\begin{array}{c}{p}_{t}^{\text{HP},\text{g}}\le {P}^{\text{HP}},\text{\hspace{1em}}{p}_{t}^{\text{HP},\text{q}}\le {P}^{\text{HP}},\text{\hspace{1em}}{p}_{t}^{\text{EB}}\le {P}^{\text{EB}},\text{\hspace{1em}}\forall t\in \mathcal{T}.\end{array}$(5)
Energy storage and energy balance constraints of ZCBS
In ZCBS, energy storage devices consist of shortterm and longterm energy storage devices. The shortterm storage devices are designed to balance daily multienergy supply and demand, primarily including water storage and hydrogen storage. Water storage can store chilled water in summer and hot water in winter [35]. The device models are as follows:
$\begin{array}{c}{m}_{t+1}^{\text{HS}}{m}_{t}^{\text{HS}}={m}_{t}^{\text{IN}}{m}_{t}^{\text{OU}},\text{\hspace{1em}}{g}_{t+1}^{\text{HW}}{g}_{t}^{\text{HW}}={g}_{t}^{\text{IN}}{g}_{t}^{\text{OU}},\text{\hspace{1em}}{q}_{t+1}^{\text{CW}}{q}_{t}^{\text{CW}}={q}_{t}^{\text{IN}}{q}_{t}^{\text{OU}},\text{\hspace{1em}}\forall t\in \mathcal{T}/\left\{T\right\},\end{array}$(6)
$\begin{array}{c}{m}_{T}^{\text{HS}}={m}_{1}^{\text{HS}},\text{\hspace{1em}}{g}_{T}^{\text{HW}}={g}_{1}^{\text{HW}},\text{\hspace{1em}}{q}_{T}^{\text{CW}}={q}_{1}^{\text{CW}},\end{array}$(7)
$\begin{array}{c}{m}_{t}^{\text{HS}}\le {M}^{\text{HS}},\text{\hspace{1em}}{g}_{t}^{\text{HW}}\le {G}^{\text{HW}},\text{\hspace{1em}}{q}_{t}^{\text{HW}}\le {Q}^{\text{CW}},\text{\hspace{1em}}\forall t\in \mathcal{T}.\end{array}$(8)
Equation (7) indicates that the energy storage state remains unchanged at both the beginning and the end of the period.
In ZCBS, longterm energy storage devices include GW and HS, with HS catering to both shortterm and longterm storage needs. In northern building energy systems, the annual heat load is typically higher than the cooling load, causing the ground source heat pump to absorb heat from the soil every year. Consequently, the efficiency of the ground source heat pump can decrease significantly after operating for several years. To maintain the soil’s yearly heat balance, it is essential to inject heat underground during nonheating seasons. The soil thermal imbalance ratio indicates the imbalance degree between the thermal extraction and thermal injection of the HP system on an annual basis, and the soil thermal imbalance greatly affects the annual average performance of HP. In ZCBS, waste heat from FC can be recovered and injected into GW to achieve a yearly balance between the lowgrade heat extracted from the geothermal well and the sum of heat injected into the GW. According to Refs [24,36], yearly soil thermal balance can be formulated as
$\begin{array}{c}{\displaystyle \sum _{t=1}^{T}{g}_{t}^{\text{HP},\text{L}}}={\displaystyle \sum _{t=1}^{T}({q}_{t}^{\text{HP}}+{g}_{t}^{\text{GW},\text{IN}})}.\end{array}$(9)
Constraint (9) ensures a yearly balance of soil temperature. In addition, a ground source heat pump cannot simultaneously supply heat, provide cooling, or inject heat. The following constraints ensure that the aforementioned conditions do not occur at the same time.
$\begin{array}{c}{g}_{t}^{\text{HP},\text{L}}\le {z}_{t}^{\text{HP},\text{g}}\cdot M,\text{\hspace{1em}}{q}_{t}^{\text{HP}}\le {z}_{t}^{\text{HP},\text{q}}\cdot M,\text{}{g}_{t}^{\text{GW},\text{IN}}\le {z}_{t}^{\text{HP},\text{IN}}\cdot M,\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(10)
$\begin{array}{c}{z}_{t}^{\text{HP,IN}}+{z}_{t}^{\text{HP,g}}+{z}_{t}^{\text{HP,q}}\le 1,\text{}{z}_{t}^{\text{HP,IN}},{z}_{t}^{\text{HP,g}},{z}_{t}^{\text{HP,q}}\in \{0,1\},\forall t\in \mathcal{T}.\end{array}$(11)
To ensure the stable operation of ZCBS, system energy balance constraints of electricity, heat, cooling, and hydrogen are modeled as follows:
$\begin{array}{c}{p}_{t}^{\text{PV}}+{p}_{t}^{\text{FC}}={p}_{t}^{\text{HP},\text{g}}+{p}_{t}^{\text{HP},\text{q}}+{p}_{t}^{\text{EL}}+{p}_{t}^{\text{EB}}+{p}_{t}^{\text{DE}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(12)
$\begin{array}{c}{g}_{t}^{\text{FC}}+{g}_{t}^{\text{EB}}+{g}_{t}^{\text{HP},\text{H}}+{g}_{t}^{\text{OU}}={g}_{t}^{\text{IN}}+{g}_{t}^{\text{DE}}+{g}_{t}^{\text{GW},\text{IN}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(13)
$\begin{array}{c}{m}_{t}^{\text{PU}}+{m}_{t}^{\text{EL}}+{m}_{t}^{\text{OU}}={m}_{t}^{\text{IN}}+{m}_{t}^{\text{FC}},\text{\hspace{1em}}\forall t\in \mathcal{T},\end{array}$(14)
$\begin{array}{c}{q}_{t}^{\text{HP}}+{q}_{t}^{\text{OU}}={q}_{t}^{\text{IN}}+{q}_{t}^{\text{DE}},\text{\hspace{1em}}\forall t\in \mathcal{T}.\end{array}$(15)
Twostage robust seasonal scheduling formulation
To ensure the effectiveness of the developed seasonaldaily scheduling approach, the multiple uncertainties of renewable and demand need more attention. Since the precise information of daily scheduling cannot be obtained in seasonal scheduling, seasonal decisions should be made before the uncertainty is revealed. The developed ZCBS seasonaldaily scheduling is formulated as a twostage robust optimization model with recourse to handle the uncertainty of renewable supply and energy demand. As described in previous section, mean values of renewable generation and energy are denoted by $\{\widehat{{S}_{t}},{\widehat{p}}_{t}^{\text{DE}},{\widehat{g}}_{t}^{\text{DE}},{\widehat{q}}_{t}^{\text{DE}},\forall t\}$ and deviation values are denoted by $\{\u2206{S}_{t},\u2206{p}_{t}^{\text{DE}},\u2206{g}_{t}^{\text{DE}},\u2206{q}_{t}^{\text{DE}},\forall t\}$, respectively, several box uncertainty sets are modeled as follows:
$\begin{array}{c}{S}_{t}\in [\widehat{{S}_{t}}{z}_{t}^{\text{S}}\cdot \u2206{S}_{t},\text{\hspace{1em}}\widehat{{S}_{t}}+{z}_{t}^{\text{S}}\cdot \u2206{S}_{t}],\text{\hspace{1em}}{p}_{t}^{\text{DE}}\in [{\widehat{p}}_{t}^{\text{DE}}{z}_{t}^{\text{P}}\cdot \u2206{p}_{t}^{\text{DE}},\text{\hspace{1em}}{\widehat{p}}_{t}^{\text{DE}}+{z}_{t}^{\text{P}}\cdot \u2206{p}_{t}^{\text{DE}}],\\ {g}_{t}^{\text{DE}}\in [{\widehat{g}}_{t}^{\text{DE}}{z}_{t}^{\text{G}}\cdot \u2206{g}_{t}^{\text{DE}},\text{\hspace{1em}}{\widehat{g}}_{t}^{\text{DE}}+{z}_{t}^{\text{G}}\cdot \u2206{g}_{t}^{\text{DE}}],\text{\hspace{1em}}{q}_{t}^{\text{DE}}\in [{\widehat{q}}_{t}^{\text{DE}}{z}_{t}^{\text{Q}}\cdot \u2206{q}_{t}^{\text{DE}},\text{\hspace{1em}}{\widehat{q}}_{t}^{\text{DE}}+{z}_{t}^{\text{Q}}\cdot \u2206{q}_{t}^{\text{DE}}],\\ {z}_{t}^{\text{S}},{z}_{t}^{\text{P}},{z}_{t}^{\text{G}},{z}_{t}^{\text{Q}}\in \{0,1\},\text{\hspace{1em}}\forall t\in \mathcal{T},& \text{(16)}\end{array}$
where $\{{z}_{t}^{\text{S}},{z}_{t}^{\text{P}},{z}_{t}^{\text{G}},{z}_{t}^{\text{Q}},\forall t\}$ denotes binary variables of renewable generation, electricity demand, heating demand, cooling demand respectively, which are uncertain and can be obtained based on historical data. The seasonal decision in the developed approach includes the operation mode of the seasonal energy storage and ground source heat pump, and seasonal energy storage is modeled as
$\begin{array}{c}{m}_{s}^{\text{HS},\text{M}}={\displaystyle \sum _{t=N\cdot s}^{N\cdot (s+1)}({m}_{t}^{\text{OU}}{m}_{t}^{\text{IN}})},\text{\hspace{1em}}{g}_{s}^{\text{GW},\text{M}}={\displaystyle \sum _{t=N\cdot s}^{N\cdot (s+1)}({g}_{t}^{\text{HP},\text{L}}{q}_{t}^{\text{HP}}{g}_{t}^{\text{GW},\text{IN}})},\text{\hspace{1em}}\forall s\in \mathcal{S},\end{array}$(17)
where ${m}_{s}^{\text{HS},\text{M}},{g}_{s}^{\text{GW},\text{M}}$ denote hydrogen and geothermal usages during month s, and N is number of time periods in one month. The decision variables in the first stage include seasonal scheduling before uncertainty revealing, which refers to seasonal storage and HP operation mode:
$\begin{array}{c}x={[{m}_{s}^{\text{HS},\text{M}},{g}_{s}^{\text{GW},\text{M}},{z}_{t}^{\text{HP},\text{IN}},{z}_{t}^{\text{HP},\text{g}},{z}_{t}^{\text{HP},\text{q}}]}^{\text{T}},\text{\hspace{1em}}z={[{z}_{t}^{\text{S}},{z}_{t}^{\text{P}},{z}_{t}^{\text{G}},{z}_{t}^{\text{Q}}]}^{\text{T}},\text{\hspace{1em}}\forall s,\forall t.\end{array}$(18)
Secondstage decision variables are residual variables other than $x$ and $z$. Considering the seasonal decisions should adopt the worst case of uncertainties, the seasonal scheduling is formulated as
$\begin{array}{c}\underset{x}{\mathrm{min}}\{\underset{z}{\mathrm{max}}\underset{y}{\mathrm{min}}{\displaystyle \sum _{t=1}^{Y}{\lambda}^{\text{h}}}\cdot {m}_{t}^{\text{PU}}\}.\\ s.t.\text{(1)}\text{(18)}& \text{(19)}\end{array}$
Since there are no nonlinear variables in the second stage after fixing $x$ and $z$, the twostage robust optimization model for seasonal scheduling can be solved by C&CG [37]. The compact matrix of problem (19) is reformulated as following:
$\begin{array}{c}\begin{array}{l}\underset{x}{\mathrm{min}}\left\{\underset{z}{\mathrm{max}}\underset{y}{\mathrm{min}}{\displaystyle \sum _{t=1}^{Y}{c}^{\text{T}}y}\right\}.\\ s.t.\text{}Ax\u2a7ed\\ Ex+Mz+Gy\u2a7eh,\\ Kx+Dz+Fy=b.\end{array}\end{array}$(20)
The master problem aims to minimize objective function based on the decision variables $x$ in the first stage. By continuously introducing the worstcase scenarios ${z}_{l}$ generated from the subproblem, a compact lower bound is obtained through the master problem. Based on the compact formula, the master problem is formulated as
$\begin{array}{c}\text{MP}:\text{\hspace{1em}}\underset{x}{\mathrm{min}}\alpha ,\\ s.t.\text{}Ax\u2a7ed\\ \alpha \u2a7e{c}^{\text{T}}{y}^{l},\text{\hspace{1em}}\forall l,\\ Ex+G{y}^{l}\u2a7ehM{z}_{l},\text{\hspace{1em}}\forall l,\\ Kx+F{y}^{l}=bD{z}_{l},\text{\hspace{1em}}\forall l,\end{array}$(21)
where l is iteration times and ${z}_{l}$ is worst case after l iterations. The subproblem fixes the firststage decision as $\overline{x}$, and solved for the secondstage decision $y$ and uncertainty variables $z$. We model the subproblem as
$\begin{array}{c}\text{SP}:\text{\hspace{1em}}\underset{z}{\mathrm{max}}\underset{y}{\mathrm{min}}\text{\hspace{1em}}{c}^{\text{T}}y,\\ s.t.\text{}Gy\u2a7ehE\overline{x}Mz,\to \pi ,\\ Fy=bK\overline{x}Dz,\to \nu ,& \text{(22)}\end{array}$
where $\pi ,\nu $ are dual vectors of each matrix constraints. With given $(x,z)$, Equation (22) is a linear problem with decision variables $y$. The fixed subproblem can be transformed into the following Dual SP according to the strong duality.
$\begin{array}{c}\text{DualSP}:\text{}\underset{z,\pi ,v}{\text{max}}{hE\overline{x}Mz}^{\text{T}}\cdot \pi +{bK\overline{x}Dz}^{\text{T}}\cdot v.\\ s.t.\text{}{G}^{\text{T}}\pi +{F}^{\text{T}}v=c,\\ \pi \u2a7e0.\end{array}$(23)
The problem can still be solved using current commercial solvers. Alternatively, the bilinear item can be resolved through linearization with the big M method. The calculation process is as follows: first, an initial set of uncertain variables $z$ is given as the initial worstcase scenario and upper and lower bounds are set. Second, based on an initial scenario, MP is solved to obtain $\overline{x}$ and update the lower bound. Third, solve the Dual SP with MP results to obtain a new worstcase scenario ${z}_{l}$, and the upper bound is updated. Fourth, if the gap between the upper and lower bounds is less than a threshold, the iteration stops. Otherwise, new variables ${y}_{l}$ and constraints are added to MP, and the process returns to the second step until the algorithm converges.
Seasonaldaily scheduling approach of ZCBS
The annual distribution of energy demand and renewable supply varies significantly with high uncertainties, making the scheduling of energy storage devices on different time scales crucial for achieving zero carbon emissions. Seasonaldaily optimal scheduling approach is developed as Algorithm 1.
The developed seasonaldaily scheduling approach includes four steps. First, system capacities, scheduling parameters, renewable generation, and demand uncertainty sets are initialized. Second, optimal seasonal robust scheduling is carried out to obtain the seasonal scheduling strategy. Then, seasonal storage constraints are added to the daily scheduling problem to achieve an economic daily operation. Seasonal scheduling is recalculated if it enters the next seasonal operation period; otherwise, daily scheduling is continued. Finally, if the operation period is longer than Y, seasonaldaily scheduling is finished and then stops and quits. In Step 3, the seasonal storage constraints ensure the seasonal scheduling persistence at the daily level, and storage endstate constraints ensure that the shortterm storage would not be completely consumed due to obtaining the shortterm optimal solution.
Seasonaldaily scheduling approach
RESULTS
Demand profile and multiple uncertainty sets
To analyze the effectiveness of the seasonaldaily scheduling approach in practical applications, we conduct case studies based on the hydrogenenabled zero carbon energy system pilot project in Yulin SciTech Innovation Town, Shaanxi Province of China. Heating covers an area of 120,000 square meters while cooling supplies an area of 22,000 square meters. In addition to supplying heating to the buildings during the heating season and cooling during the cooling season, there is also a demand for domestic hot water in every season. As shown in Figure 2, due to the pilot project’s location in the northern region, the annual heating demand is relatively high, while the cooling demand is relatively low. The electricity demand and domestic hot water demand persist throughout the year and primarily concentrate on weekdays. Tables 1 and 2 list the system parameters and devices installed capacity used in case study.
Figure 2 Annual multienergy demand of zero carbon building energy system. 
System and devices parameters
Devices installed capacity in current ZCBS
To handle the uncertainty of renewable output and multienergy demand in ZCBS, this study constructs uncertainty sets based on historical operation data. The developed seasonaldaily scheduling approach cannot accurately obtain daily information in the seasonal scheduling, so it is necessary to consider the worst uncertainty case in the first stage of seasonal storage decisionmaking and make residual scheduling after uncertainty revealed in the second stage. Taking the PV output uncertainty set as an example, we collect daily PV output for each period within the month, and then calculate the mean value and standard deviation of the PV output for each daily period. Then construct a box uncertainty set based on the mean value as the baseline and the standard deviation as the maximal change. The uncertainty sets for cooling demand, heat demand, and electricity demand are constructed in the same way, and typical data are shown in Figure 3. According to actual data, this uncertainty set can cover 91.94% of the data, ensuring the effectiveness of implementation.
Figure 3 Uncertainty set and typical real data of (A) PV output, (B) electricity demand, (C) cooling demand, and (D) heating demand. 
Operation performance under different scheduling methods
To analyze the performance of the ZCBS under different scheduling methods, three methods are constructed below. Method 1 is a policybased scheduling approach. In each season, energy storage operations are planned according to a predefined time period. FC and EL are utilized to adapt to the fluctuations in both energy demand and PV output. Method 2 is carried out under optimizationbased daily scheduling. Daily optimal scheduling is conducted daily, ensuring that hydrogen storage and thermal energy storage states remain the same at the beginning and end of each day. Method 3 is the developed seasonaldaily scheduling approach, which ensures that the daily scheduling considers both the optimal daily objectives and the seasonal operations by adding the seasonal storage constraints into daily scheduling. The case study is carried out in Python 3.10.2 environment and tested on a laptop with an Apple M1 Pro processor and 16 GB RAM. The optimization problems are solved through Gurobi 10.0.
Performance analysis under different scheduling methods is shown in Table 3. The developed seasonaldaily scheduling approach has reduced operation costs by more than 43.4% compared with existing scheduling methods and can achieve a complete hydrogen selfproduction in ZCBS. Although the developed scheduling approach in this paper may have relatively higher computational costs, it can meet the computational requirements of practical applications.
Performance analysis under different scheduling methods and PV installed capacities
Coordination performance of seasonaldaily scheduling
Effective coordination of multienergy supply and storage within ZCBS is essential to achieve zerocarbon emissions. Multienergy demands, such as heating, cooling, and electricity, exhibit distinct seasonal patterns. In contrast, renewable energy is more evenly distributed throughout the year. As a result, ZCBS faces considerable seasonal energy supply and demand imbalances. Additionally, due to the uncertainty of renewable energy sources, ZCBS also experiences supplydemand mismatches in daily scheduling. To tackle these challenges, we analyze the operation performance of energy storage devices across various time scales, both daily and seasonal.
From a shortterm perspective, with the coordination scheduling approach and seasonal storage constraints generated from seasonal scheduling, daily scheduling decisions can properly match seasonal decisions. Scheduling for typical days in three seasons is shown in Figure 4. The point plot shows seasonal storage scheduling on a daily scale, and the bar shows daily device scheduling. With seasonal storage constraints for hydrogen and geothermal storage states, daily scheduling can meet the daily economic objective and seasonal scheduling simultaneously. The results show that when PV output is sufficient in the daytime, EL and HS are employed to produce and store hydrogen, respectively. During nighttime, FC is utilized for cogeneration, ensuring a supply of electricity and domestic hot water and heating demand. EB are used to consume peak PV during daytime, and heat generation from EB will supply heat demand in winter, store into HW in summer, and inject into GW in autumn and spring. The water tank plays a role in the daily scheduling as a shortterm energy storage device. It helps to store and release energy as needed to meet the daily energy demands of the system.
Figure 4 Daily scheduling results in different seasons. (A) Daily scheduling of power supply in winter; (B) daily scheduling of heating supply in winter; (C) daily scheduling of power supply in summer; (D) daily scheduling of heating supply in summer; (E) daily scheduling of power supply in autumn; (F) daily scheduling of heating supply in autumn. 
From the perspective of longterm seasonal scheduling, HS, and GW can carry out seasonal energy storage of renewable energy. Figure 5 describes the operation of longterm energy storage devices throughout the year. Since HS has both shortterm and longterm scheduling, the mean value and rootmeansquare error (RMSE) of linear regression are used to describe scheduling results. Owing to the heating demand in winter, both hydrogen storage and geothermal wells are utilized during this season. The error band of hydrogen storage also indicates a clear shortterm daily scheduling in winter. In spring and autumn, when there is no heating or cooling demand, both HS and GW are employed to store excess renewable energy. During summer, with higher overall energy demand, hydrogen storage provides heating and power, while GS and HP supply cooling. From a yearly perspective, the seasonal scheduling of HS peaks twice at the end of spring and the end of autumn. Meanwhile, GW heat storage reaches its maximum just before winter begins and hits a low point at the end of winter. With different PV installed capacities, it is observed that the summer peak value of hydrogen energy storage is higher with lower PV installations. When there is ample renewable installation, the trend of hydrogen storage in summer is no longer significant, and it tends to be singlepeak storage throughout the year. The winter peak value remains constant regardless of the PV capacities, and the geothermal scheduling is not affected by the PV installed capacity.
Figure 5 Seasonal scheduling of longterm energy storage devices with different PV installed capacities. (A) Seasonal scheduling with 7500 kW PV; (B) seasonal scheduling with 8000 kW PV; (C) seasonal scheduling with 8500 kW PV. 
Economic analysis of ZCBS
In ZCBS, hydrogen can be obtained through two ways: selfproduction and external procurement. Operation cost of ZCBS is purchasing hydrogen from external sources. The ZCBS economic performance is influenced by two factors: the selfproduction ratio and hydrogen price. As the selfproduction ratio increases, the system needs a greater installed capacity of renewable energy sources, resulting in higher investment costs. To evaluate the economic feasibility of ZCBS, the annualized total cost is utilized, which comprises the annualized investment cost and the annualized operation cost. Figure 6 analyzes the impact of hydrogen price and selfproduction ratio variations on the system’s annualized total cost. It can be observed that when hydrogen prices are relatively low, the selfproduction ratio significantly affects the annualized total cost. Procuring a large amount of cheap hydrogen externally can enhance the system’s economic viability. However, with high hydrogen prices, the system economic performance is less influenced by the selfproduction ratio. Moreover, the annualized total cost may be higher when hydrogen is entirely selfproduced.
Figure 6 Economic analysis on different hydrogen prices and selfproduction ratios. 
CONCLUSION
In conclusion, this study modeled the core devices within ZCBS, providing an accurate depiction of energy input, conversion, and storage processes. By incorporating seasonal storage constraints into daily scheduling, the developed seasonaldaily scheduling approach effectively addresses both optimality and continuity. Through the developed scheduling approach, the longterm seasonal energy storage and shortterm daily energy storage can harmoniously operate throughout the year, while achieving a higher selfproduction ratio and superior economic performance. Numerical results show that seasonal scheduling of hydrogen storage reaches peak twice at the end of spring and the end of autumn respectively, while geothermal storage reaches its peak before the onset of winter and reaches its lowest point at the end of winter. Furthermore, considering the impact of hydrogen prices and the selfproduction ratio on system economics, it is expected that external hydrogen procurement will become more costeffective as hydrogen prices decrease in the future.
Abbreviation
CW  Cold water storage tanks 
EB  Electric boilers 
EL  Electrolyzer 
FC  Fuel cells 
GW  Gold water storage tanks 
HP  Ground source heat pump 
HS  Hydrogen storage 
HW  Hot water storage tanks 
PV  Photovoltaic 
ZCBS  Zero carbon building energy systems 
Parameters
${\eta}^{\text{EB}}$  Heat efficiency of EB 
${\eta}^{\text{EL}}$  Efficiency of hydrogen generation by EL 
${\eta}^{\text{FC,g}}$  Efficiency of heat generation by FC 
${\eta}^{\text{FC.p}}$  Efficiency of power generation by FC 
${\eta}^{\text{HP,g}}$  Efficiency of heat generation by HP 
${\eta}^{\text{HP,q}}$  Efficiency of cooling generation by HP 
${\eta}^{PV}$  Efficiency of PV generation 
${\lambda}^{\text{h}}$  Hydrogen price 
${G}^{\text{HW}}$  Storage installed capacity of HW 
${M}^{\text{HS}}$  Storage installed capacity of HS 
${P}^{\text{EB}}$  EB installed capacity 
${P}^{\text{EL}}$  EL installed capacity 
${P}^{\text{FC}}$  FC installed capacity 
${P}^{\text{HP}}$  HP installed capacity 
${P}^{\text{PV}}$  PV installed capacity 
${Q}^{\text{CW}}$  Storage installed capacity of CW 
Variables
${g}_{t}^{\text{DE}}$  Heat demand at time t 
${g}_{t}^{\text{EB}}$  Heat generation of EB at time t 
${g}_{t}^{\text{GW,IN}}$  Heat injected into geothermal at time t 
${g}_{s}^{\text{GW},M}$  Geothermal usage during month s 
${g}_{t}^{\text{HP,H}}$  Highgrade heat supply by HP at time t 
${g}_{t}^{\text{HP,L}}$  Lowgrade heat consumption by HP at time t 
${g}_{t}^{\text{HW}}$  Heat stored in water tank at time t 
${g}_{t}^{\text{IN}}$  Heat stored into HW at time t 
${g}_{t}^{\text{OU}}$  Heat supplied by HW at time t 
${m}_{t}^{\text{EL}}$  Hydrogen generation by EL at time t 
${m}_{t}^{\text{FC}}$  Hydrogen consumption by FC at time t 
${m}_{t}^{\text{HS,M}}$  Hydrogen usage during month s 
${m}_{t}^{\text{HS}}$  Mass of hydrogen storage at time t 
${m}_{t}^{\text{IN}}$  Hydrogen stored into HS at time t 
${m}_{t}^{\text{OU}}$  Hydrogen supplied by HS at time t 
${m}_{t}^{\text{PU}}$  Hydrogen purchased from market at time t 
${p}_{t}^{\text{DE}}$  Electricity demand at time t 
${p}_{t}^{\text{EB}}$  Power consumption of EB at time t 
${p}_{t}^{\text{EL}}$  Power consumption of EL at time t 
${p}_{t}^{\text{FC}}$  Power output of FC at time t 
${p}_{t}^{\text{HP,g}}$  Power consumption for heat generation of HP at time t 
${p}_{t}^{\text{HP,q}}$  Power consumption for cooling generation of HP at time t 
${p}_{t}^{\text{PV}}$  Power output of PV at time t 
${q}_{t}^{\text{CW}}$  Cooling stored in water tank at time t 
${q}_{t}^{\text{DE}}$  Cooling demand at time t 
${q}_{t}^{\text{HP}}$  Highgrade cooling supply by HP at time t 
${q}_{t}^{\text{IN}}$  Cooling stored into CW at time t 
${q}_{t}^{\text{OU}}$  Cooling supplied by CW at time t 
${z}_{t}^{\text{G}}$  Binary uncertainty variables of heating demand at time t 
${z}_{t}^{\text{HP,g}}$  Binary variable of HP heating operation mode at time t 
${z}_{t}^{\text{HP,IN}}$  Binary variable of HP heat injection operation mode at time t 
${z}_{t}^{\text{HP,q}}$  Binary variable of HP cooling operation mode at time t 
${z}_{t}^{\text{P}}$  Binary uncertainty variables of electricity demand at time t 
${z}_{t}^{\text{Q}}$  Binary uncertainty variables of cooling demand at time t 
${z}_{t}^{\text{S}}$  Binary uncertainty variables of renewable generation at time t 
Funding
This work was supported in part by the National Natural Science Foundation of China (62122062, 62192755, 62192750 and 62192752).
Author contributions
W.G. and J.L. conceived and wrote the manuscript. W.G. and Y.L. contributed to the analysis of the data and the discussion. Z.X., J.W., K.L. and X.G. initiated and supervised the project. All authors read and approved the submission of the manuscript.
Conflict of interest
The authors declare no conflict of interest.
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All Tables
Performance analysis under different scheduling methods and PV installed capacities
All Figures
Figure 1 Structure of ZCBS. 

In the text 
Figure 2 Annual multienergy demand of zero carbon building energy system. 

In the text 
Figure 3 Uncertainty set and typical real data of (A) PV output, (B) electricity demand, (C) cooling demand, and (D) heating demand. 

In the text 
Figure 4 Daily scheduling results in different seasons. (A) Daily scheduling of power supply in winter; (B) daily scheduling of heating supply in winter; (C) daily scheduling of power supply in summer; (D) daily scheduling of heating supply in summer; (E) daily scheduling of power supply in autumn; (F) daily scheduling of heating supply in autumn. 

In the text 
Figure 5 Seasonal scheduling of longterm energy storage devices with different PV installed capacities. (A) Seasonal scheduling with 7500 kW PV; (B) seasonal scheduling with 8000 kW PV; (C) seasonal scheduling with 8500 kW PV. 

In the text 
Figure 6 Economic analysis on different hydrogen prices and selfproduction ratios. 

In the text 
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