Abstract
Optimal planning for the park integrated energy system (PIES) is essential for energy efficiency improvement and carbon neutrality. A reasonable evaluation method is the key to guide PIES planning. However, indicators for the PIES planning schemes are various with high penetration of renewable energy, large carbon emissions and multiple energy forms coupling, which brings challenges to find out the benchmark planning scheme for PIES development. Herein, we extend a competitive evaluation method that considers the aspects of energy, economy, environment, reliability and greening development level for PIES with different energy planning trends. We formulate a multi-stage planning model for PIES dynamic development aiming at investment and operation cost minimization. We set a group of comparable PIESs with different energy planning trends to evaluate and determine the benchmark PIES to motivate the others. The competitiveness of our evaluation method is reflected in that the benchmark is determined by the competition of different PIESs and it may change through multi-stage planning. A practical PIES with eight functional areas is adopted for competitive evaluation in multi-criteria over multi-stage planning optimization, and their pros and cons are evaluated and compared. By comparing the evaluation efficiency, the benchmark of PIES planning can be dynamically adjusted.
Subject terms: Energy grids and networks, Power distribution
Introduction
With the urgence of carbon reduction and sustainable development, the efficient and clean utilization of multiple energy has been receiving more and more attention in power and energy sector. Park integrated energy system (PIES) is regarded as a promising solution for energy scarcity and environmental pollution worldwide and plays the primary role in energy efficiency improvement, renewable accommodation and carbon reduction during the low-carbon transition process. PIES is interconnected with various energy resources and highly aggregated with groups of residential, commercial, and/or industrial buildings and it usually struggles with large energy consumption and high carbon emission density1. It is reported that, in China, there has been more than 2500 national or provincial industrial parks in operation2 and producing about 31% of national carbon emissions3 since 2015. For all these industrial parks, there has been proved that 46.2 Gt CO2 will be reached during their remaining lifetime, equivalent to the 11% of the 1.5 °C global carbon budget4. Moreover, the reliance of industrial clusters on fossil fuel-derived energy has caused a drastic increase in its carbon footprint, accounting for over 28% of global CO2 emissions5. PIES has been deemed as the pioneer to the energy clean transition over high-efficiency and low-carbon practice6. Accordingly, attempts have been made to accelerate carbon reduction from park level all over the world. China has launched carbon-peaking pilot PIES projects in 100 cities and zones nationwide to solve bottlenecks constraining the country’s green and low-carbon development and explore paths toward carbon-neutrality for different national areas since 20237. The pilot PIES implemented in Shanghai8, Tianjin9, Suzhou10, etc. has developed rapidly in recent years. Also, mature patterns of PIES have been consolidated in European countries such as Germany11, Sweden12 and Denmark13 in the past decades. These facts prove that the PIES is now becoming the global consensus in dealing with carbon reduction and energy efficiency improvement.
Integrated with the core energy equipment such as combined cold, heat and power, gas turbine, gas boiler, heat pump, electric chiller, electric storage, thermal storage, etc., PIES eventually realizes the generation, conversion and storage of different energy forms, and achieves the energy complementary utilization and efficiency improvement14,15. With such complicated energy components and load increasing uncertainty, etc., optimal planning for PIES is challenging. On the one hand, most existing PIES planning methods consider one deterministic empirical scenario and often shorten the time scale of decades to one-year annualization. The impact of multi-year uncertain factors is somehow ignored in single-stage deterministic planning. On the other hand, a common problem of PIES planning is that how to conduct an overall evaluation as the feedback so that the decision makers can learn more about the pros and cons of each planning scheme and determine their final PIES implementation. To get rid of this dilemma, exploring a multi-stage planning method and a reasonable evaluation system for PIES is of great necessity.
Multi-stage planning is a long-term process that considering the previous stage status as constraints and directly affect the layout of the follow-up stage. Different from the single-stage planning, multi-stage planning reveals planning results corresponding to the demands in each time period, which is more specific to tell how the planning trend/path is changed or remained. In Ref.16, a multi-period planning method of multi-energy microgrids considering both the long-term and short-term uncertainty is proposed, and the uncertainty of battery storage decline can be well handled in particularly. In Ref.17, a long-term planning optimization model of decentralized multi-energy systems called MANGO is proposed and the optimal energy configurations for economic and environmental improvement are designed. Ref.18 has built a framework of multi-stage stochastic planning for regional integrated energy system (RIES), where the various factors such as scenario generation, energy mixed investment and cost comparisons are analyzed and the planning trends from each stage are suggested in a real case. Ref.19 aims at the active distribution network (ADN) multi-stage planning by using multi-load-scenario, which can offer a better planning scheme and maximize the benefits. Trends of energy development are essential to reveal throughout the multi-stage planning for energy system, but it still remains ambiguous to described and compared how good this trend is in a dynamic evolution.
In multi-stage planning, there exists a variety of feasible system configurations and operation strategies over years so that it’s not intuitive to target which one is the best. Multi-criteria evaluation is a method to evaluate and select the suitable planning scheme for PIES when considering more than one objective or develop trend. It is necessary to solve the issues of scheme selection and show how these schemes are performed in different aspects20. In Ref21, a multi-attribute decision analysis (MADA) method is proposed to evaluate the economic, energy saving and environmental performance of different park-level integrated energy systems and the benefits are indicated. In Ref22, a multi-criteria decision-making model with social, economic, environmental and technical assessment is developed and fourteen hydropower plants are demonstrated to evaluate. In Ref23, multi-criteria evaluation is carried out for compatibility of diverse power plants with respect to the environmental, technological, and economic criteria using VIKOR method. The AHP, fuzzy AHP methods are widely applied in realistic cases for scheme optimizing and ranking24,25. These methods enable the complicated evaluation and sorting process to be simple and clear. Since it is more convincing to combine the objective evaluation with subjective evaluation, data envelopment analysis (DEA) is introduced as an objective evaluation method which totally focuses on the data itself and avoiding rating process from any individuals. DEA can calculate the relative efficiency of a set of decision-making units (DMUs) with related inputs and outputs. In Ref26, a two-stage evaluation and optimization method using the super-efficiency DEA model is proposed to determine the efficiencies of different renewable plans, then the proportions of different renewable energy resources are optimized. In Ref27, a dynamic DEA is used to compute the investment efficiency of distribution networks with the criteria including information level, power supply capacity/quality/reliability, asset utilization efficiency and economy, etc.
It has been mentioned that the planning for PIES is multi-stage and multi-objective. Hence, the competitive evaluation that evaluates the performance of multiple PIESs considering the multiple planning stages is needed to determine the benchmark by comparing a group of different PIES planning schemes28,29. The motivation behind this work is to determine the benchmark for PIES multi-stage planning. The paper highlights a dynamic way to evaluate different functional PIES with different characteristics through a dynamic developing cycle, which enables a more concrete comparison to pros and cons of the PIES planning schemes. The PIES multi-stage development decides the diversified directions of the energy development, but the guidance of specific developing goal is not explicit. Thus, our aspiration is to address the problem on how to evaluate PIES planning trends in the dynamic development, and how to select the benchmark from different PIESs with competitive relations.
The main contributions of this paper are summarized as follows.
An optimal multi-stage planning model considering typical energy equipment operation characteristics is proposed, then a multi-criteria evaluation index set is transformed to show how energy trends are developing based on the planning results.
A competitive evaluation framework over the multi-stage planning optimization for multiple PIESs is established to determine the benchmark for the PIES planning in different criteria within a dynamic development cycle, providing practical references for the PIES planning with different functional characteristics.
Case studies on the evaluation between different functional PIES implies that although the evaluation efficiency is superior in some mature PIES areas in the early stage that makes them the benchmarks, but the competitive evaluation further reveals that the retrogression happens among them in the later stage. This phenomenon cannot be aware by static or single-object evaluation, which may lead to the wrong judgment on the future energy development direction. Thus, the competitive evaluation is required so as to adjust the benchmark towards a sustainable and balanced pattern for PIES multi-stage planning.
Methods
Multi-stage planning for PIES
In multi-stage planning framework, the energy equipment is invested year by year (stage by stage) with load increasing. As depicted in (Fig. 1), in PIES multi-stage planning considering construction sequence, assume that the load is increasing exponentially from stage 
to 
, which is divided into 
. Accordingly, the volume and type of energy device set 
need to be determined to meet the current demand based on the previous constructed set 
, then the invested energy device set can be obtained as
. The PIES planning trend can be eventually revealed in this way compared to the one-time investment in the first year.
Fig. 1.
Multi-stage planning for PIES.
Competitive evaluation over multi-stage planning optimization for multiple PIESs
Competitive evaluation is a method to screen out the benchmark from a group of objects through their developing process, so as to realize quantitative assessment to all objects with competitive relations to this benchmark. The framework of competitive evaluation over multi-stage planning optimization in this paper is depicted as (Fig. 2). In (a), a competitive evaluation model is established, where different PIESs are evaluated to become the benchmark in each planning stage and in a whole dynamic planning cycle are determined. In (b), the indicators of PIES are transformed into concrete numerical value via multi-stage planning results. In (c), FAHP and DEA method are adopted to determine the weight and the evaluation efficiency of the criteria based on the indicators value itself. In (d), the importance of the time in dynamic development is optimized and their weights are assigned to the dynamic planning stage axis.
Fig. 2.
Framework of competitive evaluation over multi-stage planning optimization. (a) Competitive evaluation model with five PIES in four dynamic planning stages. (b) Indicators for evaluation in multi-criteria. (c) FAHP-DEA to weights and evaluation efficiency calculation. (d) The time importance optimization.
Typical energy equipment modeling in PIES
A common structure of PIES consists of multiple energy production, conversion, transmission, storage and end users, which can realize the interior coordinated management of the energy. The PIES can also connect with the utility grid for electricity interaction in case of electricity shortage or excess renewable generation feed in. In this paper, a variety of distributed energy related components are considered and formulated, including photovoltaic (PV), wind turbine (WT), combined cold, heat and power (CCHP), gas boiler (GB), heat pump (HP), electric chiller (EC), electric storage (ES), thermal storage (TS). The input-output related models of above energy components are formulated as follows.
Photovoltaic (PV)
PV output is determined by solar irradiance and temperature under standard test conditions (STC), which can be expressed in Eqs. (1), (2).
 |
1 |
 |
2 |
where 
denotes the maximum (or theoretical) power output of a PV panel at time t.
denotes the rated power output of PV under STC. 
denotes the solar irradiance at time t.
denotes the solar irradiance under STC and is assumed to be 1 kW/m2. 
represents the PV temperature coefficient of power of about −0.5%/°C in maximum. 
denotes the temperature at time t.
represents the temperature under STC and is assumed to be 25℃. 
denotes the PV power that can be actually accommodated (or utilized) by the PIES at time t, which should not exceed the maximum (or theoretical) value of
.
Wind turbine (WT)
The output of wind turbine is to do with the wind speed, and it basically can be divided into three intervals. As shown as Eq. (3).
 |
3 |
where 
denotes the theoretical power output of WT in the current wind speed at time t. 
denotes the wind speed at time t.
denotes the rated power output of WT. It is noted that three intervals are defined to of reflect power output corresponding to different wind speed. 
, 
and 
represent the cut-in, cut-out and rated wind speed of WT, respectively.
Combined cold, heat and power (CCHP)
The CCHP is a trigeneration system that can generate electricity, heat and cold by consuming natural gas, which is expressed as Eq. (4).
 |
4 |
where 
,
and 
denote the electricity, heat and cold production of CCHP at time t, respectively. 
, 
and 
denote the electricity, heat and cold conversion efficiency of CCHP, respectively. 
denotes the natural gas consumption of CCHP at time t. 
is the natural gas to electricity conversion coefficient based on the energy calorific value and is assumed to be 9.7 kWh/m3 in our model.
In addition, the CCHP is limited by its rated output and ramp up power during operation. Express as Eq. (5).
 |
5 |
where 
denotes the rated power of CCHP. 
denotes the ramp up power limit in adjacent time interval of CCHP.
Gas boiler (GB), heat pump (HP) and electric chiller (EC)
This category of energy equipment usually directly consumes natural gas or electricity to generate their sole corresponding energy output.
The gas boiler ensures that the heat load is served sufficiently. Similarly, a gas boiler should consume natural gas to generate heat power, which is expressed as Eq. (6).
 |
6 |
where 
denotes the heat production of GB at time t. 
denotes the natural gas consumption of GB at time t.
The heat pump is another form of heat production and it uses electricity to produce plenty of heat. As shown as Eq. (7).
 |
7 |
where 
denotes the heat production of HP at time t. 
denotes the heat conversion efficiency of HP. 
denotes the electricity consumption of HP at time t.
The electric chiller produces the cold power by consuming electricity. As shown as Eq. (8).
 |
8 |
where 
denotes the cold production of EC at time t. 
denotes the cold conversion efficiency of EC. 
denotes the electricity consumption of EC at time t.
Electric storage (ES) and thermal storage (TS)
The characteristics of ES and TS are similar and can be considered to perform in a same way based on the state of charge (SOC), as shown as Eqs. (9), (10).
 |
9 |
 |
10 |
where 
and 
denote the charge and discharge power of the energy storage at time t, respectively. 
and 
denote the maximal charge and discharge power of the energy storage, respectively. 
and 
are the binary variable that ensure the charge and discharge event won’t happen at the same time. 
donates the stored energy at time t. 
and 
denote the minimal and maximal SOC of the energy storage.
and 
are the charge and discharge efficiency, respectively. 
and 
denote the initial SOC at time 0 and final SOC at the end of the operation time T.
PIES multi-stage planning optimization
Objective
The multi-stage planning objective is to minimize the total investment cost and operation cost of the PIES over several planning periods, including the investment cost, operation cost and some revenues that occur in all stages. The annualized net present cost (NPC) is used to uniform the cost with time value in different planning stages. The Eqs. (11)–(16) are established.
 |
11 |
 |
12 |
 |
13 |
 |
14 |
 |
15 |
 |
16 |
where.
−
denotes the total investment cost in the stage k. 
denotes the unit investment cost of the energy device j.
denotes the investment capacity of the energy device j.
represents the set of the candidate energy devices. 
represents the set of the planning stages.
−
denotes the total operation cost in the stage k, including the cost of electricity purchase from utility grid, natural gas consumption cost for CCHP and GB service, renewable generation shedding penalty, risk price from electricity not served situation, unit operation and maintenance (O&M) cost of device operating, and revenues from excess electricity sells to the utility grid. 
denotes the electricity price at time t. 
denotes the electricity purchase from the utility grid at time t.
denotes the natural gas purchase price at time t. 
denotes the renewable generation shedding penalty. 
denotes the renewable generation shedding power at time t. 
denotes the risk price when electricity is not served. 
denotes the electricity not served power at time t.
denotes the unit O&M cost of device j in operation.
denotes the output power of device j at time t. 
denotes the feed-in tariff at time t. 
is the electricity that sells to the utility grid at time t.
−
denotes the total CO2 related cost in stage k. 
denotes the carbon tax. 
, 
and 
denote the carbon emission intensity of CCHP, GB and utility grid, respectively. 
denote the carbon emission allowance (CEA) per unit power generation of CCHP, GB, HP and EC. 
denotes the ratio of free carbon emission allowance. 
denotes the CER (Certified emission reduction, CER) price of the renewable generation. 
and 
denote the total volume of CER sell and buy from the carbon market to satisfy the carbon quota to be paid, respectively. 
denotes the lack volume that is unsatisfied for the required carbon quota. 
denotes the penalty factor of the unsatisfied carbon quota.
−
denotes the salvage value of energy devices at the ending stage S. 
denotes the whole lifespan of device j and 
denotes the rest lifespan of device j at the end of the project lifetime.
Constraints
The operation condition of each energy device is limited by its certain range of the energy output as shown in Eq. (17).
 |
17 |
where 
denote the total invested capacity of PV, WT, CCHP, GB, HP and EC in stage k, respectively. 
represents the set of the energy dispatch time period.
The energy supply should satisfy the load demand, which can be shown in Eqs. (18)–(20).
 |
18 |
 |
19 |
 |
20 |
where 
and 
denote the discharge and charge power of ES at time t, respectively. 
and 
denote the discharge and charge power of TS at time t, respectively. 
denote the electric load, heat load and cooling load at time t, respectively.
The capacity of energy devices in stage k + 1 should not be less than the previous one.
 |
21 |
where 
denotes the invested capacity of device j in stage k.
The carbon emission related constraint is formulated as Eq. (22).
 |
22 |
where 
is the specific carbon emission limited by the government.
Indicator modeling for evaluation
The PIES consumes a large amount of electricity, natural gas during its operation, along with producing carbon emission, and there is more than one aspect to show how well a PIES is performed after multi-stage optimal planning. To cover the comprehensive performances of PIES as wide as possible, five criteria including energy, economy, environment, reliability and greening development level with twenty detailed indicators are chosen to evaluate the PIES planning performance. The evaluation indicators are listed in (Table 1) and are divided into input and output indicators, which is necessary for adopting DEA evaluation method. The input indicator is defined as ‘the bigger the worse’, while the output indicator is defined as ‘the bigger the better’. The models of these indicators are given as from Eqs. (23)–(45).
Table 1.
Indicator set with input-output relationship.
| Criteria | Input indicator | Output indicator |
|---|---|---|
| Energy | Natural gas consumption (km3) | Renewable energy accommodation ratio (%) |
| Electricity consumption (MWh) | Multi-energy exergy efficiency (%) | |
| Electricity purchase (MWh) | Renewable energy utilization ratio (%) | |
| Economy | Investment cost (104 ¥) | Electricity feed-in revenue (104 ¥) |
| Operation cost (104 ¥) | ES unit capacity income (¥/kWh) | |
| Electricity purchase cost (104 ¥) | CER selling income (104¥) | |
| Environment | CO2 emission (ton) | Carbon reduction from renewable generation (tonCO2) |
| NOx emission (kg) | Carbon neutrality rate (%) | |
| CER buying volume (ton) | CER selling volume (ton) | |
| Reliability | Power not served time (h) | Power supply reliability (%) |
| Power shortage (MWh) | Energy supply sufficiency (%) | |
| Power shortage risk cost (104 ¥) | Renewable energy utilization ratio (%) | |
| Greening development (Statistical data, acquired from reports or yearbooks.) | Elasticity ratio of main pollutants (no unit) | Proportion of green buildings (%) |
| Waste water discharge/value added of industry (ton/104 ¥) | Green coverage (%) | |
| Solid wastes discharged/value added of industry (ton/104 ¥) | Percentage of days with good air quality (%) |
Natural gas consumption
 |
23 |
where 
denotes the total natural gas consumption. 
denotes the natural gas consumption of CCHP at time t.
denotes the natural gas consumption of the gas boiler at time t.
Electricity consumption
 |
24 |
where 
denotes the total electricity consumption. 
denotes the electricity purchase from the utility grid at time t.
denotes the electricity consumption of HP at time t.
denotes the electricity consumption of EC at time t.
Electricity purchase
 |
25 |
where 
denotes the total electricity purchase, and it is the sum of the electricity purchase from the utility grid.
Renewable energy accommodation ratio
 |
26 |
where 
denotes the renewable energy accommodation ratio. 
and 
denote the actual power generation of WT and PV, respectively. 
and 
denote the installed capacity of WT and PV, respectively.
Multi-energy exergy efficiency
 |
27 |
where 
denotes the multi-energy exergy efficiency of PIES. 
,
, 
, 
, 
and 
denote the energy quality coefficient of electricity, natural gas, heat power, solar power and cold power, respectively. 
, 
and 
denote the electricity load, heat load and cold load in kW, respectively. 
, 
, 
and 
denote the PIES energy consumption of electricity, natural gas, and PV power generation and WT power generation, respectively.
Renewable energy utilization ratio
 |
28 |
where 
denotes the renewable energy utilization ratio.
and 
denote the ideal output of WT and PV corresponding to the resource endowment, respectively.
Investment cost
 |
29 |
where 
denotes the investment cost for PIES planning. 
denotes the unit investment cost of candidate energy equipment i.
denotes the investment capacity of candidate energy equipment i.
is the set of candidate energy equipment.
Operation cost
 |
30 |
where 
denotes the total operation cost including the electricity purchase from utility grid, natural gas consumption cost from natural gas companies for CCHP and GB operation, renewable generation shedding penalty, carbon emission cost and operation and maintenance (O&M) cost of the equipment. 
denotes the electricity price at time t. 
denotes the electricity purchase from the utility grid at time t.
denotes the natural gas price at time t. 
denotes the renewable generation unit shedding penalty. 
and 
denote the curtailment power of WT and PV at time t, respectively. 
denotes the carbon tax and 
denotes the total carbon emission. 
denotes the O&M cost of equipment i per power. 
denotes the power output of equipment i at time t.
Electricity purchase cost
 |
31 |
where 
denotes the total electricity purchase cost from the utility grid.
Electricity feed-in revenue
 |
32 |
where
revenue from excess electricity sells back to the utility grid.
denotes the feed-in tariff and 
denotes the excess electricity sell back to the utility grid at time t.
ES unit capacity revenue
 |
33 |
where 
denotes the unit capacity revenue of ES, which is the main source of electricity sell back. 
denotes the investment capacity of ES.
CER selling income
 |
34 |
where 
denotes the revenue of the CER that sells to the market.
CO2 emission
 |
35 |
where 
denotes the total CO2 emission of PIES. 
denotes the carbon emission factor of electricity consumption. 
denotes the electricity consumption by equipment operation i at time t.
denotes the carbon emission factor of utility grid. 
denotes electricity supply from the utility grid at time t. T is the total operation time interval. n is the set of electricity-consumed equipment.
NOx emission
 |
36 |
where 
denotes the total NOx emission of PIES. 
denotes the NOx emission factor of electricity consumption.
denotes the NOx emission factor of utility grid.
CER buying volume
 |
37 |
where 
denotes the volume of the CER that buys from the market.
Carbon reduction of renewable generation
 |
38 |
where 
denotes the total carbon reduction of renewable generation in PIES. 
denotes the carbon reduction factor of renewable energy. 
and 
denote excess wind and solar power sell to the utility grid, respectively.
Carbon neutrality rate
 |
39 |
The carbon neutrality rate is defined as the ratio of carbon emission reduction to carbon emission.
CER selling volume
 |
40 |
where 
denotes the volume of the CER that sells to the market.
Power not served time
 |
41 |
where 
denotes the total power not served time of PIES. 
sets to one if the power not served event occurs at time t.
Power shortage
 |
42 |
where 
denotes the power shortage of PIES. 
denotes the power not served at time t.
Power shortage risk cost
 |
43 |
where 
denotes the risk cost caused by power shortage.
Power supply reliability
Expected energy not served (EENS) is used to for power supply reliability analysis. As expressed in Eq. (44).
 |
44 |
where 
denotes the power supply reliability of PIES. 
denotes the power not served at time t.
Energy supply sufficiency
 |
45 |
The energy supply sufficiency 
implies that the ability of PIES to meet the load demand by its own energy supply when it is off-grid or isolated. 
and 
denote the power generation of WT and PV at time t, respectively. 
and 
denote the discharge power of ES and TS at time t, respectively.
Greening develops criterion
This category of indicators is statistical data can be acquired from reports, standards and yearbook that released online etc. Based on Ref.30,31, the benchmark value of elasticity ratio of main pollutants, waste water discharge/value added of industry (ton/104 ¥), proportion of green buildings (%), green coverage (%) are listed in (Table 2).
Table 2.
The benchmark value of statistical indicator.
| Indicator | Benchmark value |
|---|---|
| Elasticity ratio of main pollutants |
 0.3 |
| Waste water discharge/value added of industry (ton/104 ¥) |
 7 |
| Solid wastes discharged/value added of industry (ton/104 ¥) |
 0.1 |
| Proportion of green buildings (%) |
 60 |
| Green coverage (%) |
 30 |
| Percentage of days with good air quality (%) |
 80 |
Competitive evaluation
FAHP (fuzzy AHP) to calculate objective weight
Using FAHP can not only fully reflect the objective opinions of different experts but also handle some uncertainty in decision-making process. The FAHP evaluation steps are described as follows25.
Expert rating using triangular fuzzy number
The triangular fuzzy number of expert s to consider ‘how much is indicator d more important than indicator g’ consists of the lower value 
, the most likely value 
and the upper value 
, which is defined as Eq. (46).
 |
46 |
Then the fuzzy comparison judgment matrix of S experts to n indicators is constructed as Eq. (47).
 |
47 |
Weight calculation based on fuzzy comparison judgment matrix
 |
48 |
where 
denotes the fuzzy degree of the indicator d to the indicator g.
According to the comparison rule of triangular fuzzy number, the possibility 
of fuzzy degree 
can be expressed as Eq. (49).
 |
49 |
Then the weight matrix 
of the expert s is calculated as Eq. (50).
 |
50 |
And the final weight matrix of all indicators by all experts is obtained as Eq. (51).
 |
51 |
where 
denotes the weight of the expert s’ opinion, and 
.
DEA to calculate subjective efficiency
The DEA method can realize multiple decision-making units (DMU) ranking by calculating their relative efficiency. In order to distinguish the relative efficiency of DMUs limited in the range [0,1], the super-efficiency DEA model is adopted32. The DEA model of DMU r can be formulated as an optimization problem as Eq. (52).
 |
52 |
where 
denotes the weight of input indicator m of DMU r.
denotes the weight of input indicator k of DMU r.
denotes the value of input indicator m of DMU r.
denotes the value of output indicator k of DMU r. M is the number of input indicators and K is the number of output indicators. R is the number of DMU.
Then the Eq. (52) can be transformed into linear one by Charnes-Cooper conversion33, as expressed as Eq. (53).
 |
53 |
where 
represents the relative efficiency of DMU r itself is calculated. After obtaining the self-relative efficiency of DMU r, then calculating the efficiency of all other DMUs using the weight vector 
and 
of DMU r, the cross-super-efficiency vector of DMU r can be calculated by Eq. (54).
 |
54 |
where 
is the cross-super-efficiency vector of DMU r.
and 
are the output and input indicator value vectors of DMU l. The final cross-super-efficiency of DMU r can be calculated by averaging the 
, as expressed as Eq. (55).
 |
55 |
By repeating the above process, the cross-super-efficiency matrix of all DMUs can be obtained in (Table 3).
Table 3.
Cross-super-efficiency matrix.
| DMU | 1 | 2 | … | R |
|---|---|---|---|---|
| 1 |
|
|
… |
|
| 2 |
|
|
… |
|
| … | … | … | … | … |
| R |
|
|
… |
|
| Cross-super-efficiency |
|
|
… |
|
Optimization to the importance of the time in dynamic development
The concept of ‘importance of the time’ is introduced to describe the dynamic development of the multiple stage. The above FAHP and DEA method is set to obtain evaluation value in one static stage, but the inter relation between consecutive stages in development are not involved. To calculate the dynamic weight of each planning stage, an optimization model that maximizes the entropy of dynamic weight vectors is proposed to reveal the importance of time. As formulated in Eq. (56).
 |
56 |
where 
denotes the dynamic weight of the stage k, which represents the contribution degree to the whole period of this stage, and 
. 
denotes the contribution degree of time, which is a preset value that selected from (Table 4). S denotes the number of the planning stages to be evaluated. The smaller the value, the more attention is paid to the recent data. This nonlinear optimization problem can be solved via interior point method.
Table 4.
Quantification of the time importance.
| The contribution degree of time | Description |
|---|---|
| 0.1 | The current data are considered very important |
| 0.3 | The current data are considered important |
| 0.5 | All data are considered the same |
| 0.7 | The past data are considered important |
| 0.9 | The past data are considered very important |
Results
Case study on a PIES with different functional areas in multi-stage development
A practical PIES with eight different functional areas that varies from load and resource characteristics has been chosen to analysis the proposed method in the dynamic multi-stage development. Assuming that there will be eight functional PIES areas to be built in this region, and the structure of energy supply resources of each PIES functional area is needed to be planned from scratch with kinds of energy equipment. The candidate energy equipment includes photovoltaic (PV), wind turbine (WT), combined cold, heat and power (CCHP), gas boiler (GB), heat pump (HP), electric chiller (EC), electric storage (ES) and thermal storage (TS). In addition, the load increase is considered so the optimal multi-stage planning of energy is needed to conduct. In order to find out the which type of the functional PIES can be the benchmark in a dynamic planning cycle, a proper evaluation for a large number of chaotic data based on the optimal results should be carried out.
The functional areas including residential, commercial, industrial, agricultural, data center, school, office and hospital, as shown in (Fig. 3). The typical solar, wind resources and electricity price in the PIES is shown in (Supplementary Fig. 1)34. The typical load in these PIES functional areas is shown in (Supplementary Table 1) and they are divided into summer, winter and transitional season with the occurrence of 100, 120, 145 days. The peak load in each area is different. It is noted that the load types of each PIES functional area are distinguished and there may not be all electric, heat or cooling demand included for their particular purposes. For example, it is assumed that the electric demand is required to meet but space heating and space cooling demand is not needed in Area #4 (Agricultural), while space heating load is not typically required in Area #5 (data center).
Fig. 3.
A practical PIES with different functional areas.
Taking the planning result in stage #1 as an example, the capacity combination of energy equipment is varied from one to another as depicted in (Table 5). It is assumed that the WT is usually not considered in Area #1, Area #2, Area #6, Area #7 and Area #8 due to their urban function, and the empirical basic electric, heat and cooling load is not quite the same in different areas. It can be observed that the PV-ES combination capacity in Area #1 (Residential), Area #2 (Commercial) and Area #8 (Hospital) is quite large, but in Area #6 (School) and Area #7 (Office) it tends to be allocated less and only about 40-50% of the former situation.
Table 5.
Capacity planning result of stage #1.
| Stage #1 result | WT (kW) | PV (kW) | ES (kW) | CCHP (kW) | GB (kW) | HP (kW) | TS (kW) | EC (kW) |
|---|---|---|---|---|---|---|---|---|
| Area #1 (residential) | 0 | 10,402 | 8841 | 692 | 4304 | 696 | 4000 | 1087 |
| Area #2 (commercial) | 0 | 12,083 | 10,270 | 37 | 1643 | 467 | 1688 | 811 |
| Area #3 (industrial) | 2284 | 909 | 2714 | 0 | 7257 | 487 | 4000 | 0 |
| Area #4 (agricultural) | 515 | 1188 | 1445 | 0 | 0 | 0 | 0 | 0 |
| Area #5 (data center) | 2801 | 1831 | 3937 | 0 | 0 | 0 | 0 | 438 |
| Area #6 (school) | 0 | 4400 | 3740 | 774 | 3381 | 254 | 2908 | 869 |
| Area #7 (office) | 0 | 4312 | 3665 | 7 | 1107 | 1067 | 1737 | 1131 |
| Area #8 (hospital) | 0 | 8848 | 7520 | 548 | 5000 | 0 | 4000 | 1217 |
However, the WT is considered in Area #3 (Industrial), Area #4 (Agricultural) and Area #5 (Data center) owing to their characteristics of remoted/rural function. In these three areas, the WT to PV ratios in Area #3 (Industrial) and Area #5 (Data center) are near to 2:1, while the ratio is 1:2 in Area #4 (Agricultural). The WT and PV investment capacity reaches to a relatively balanced condition in the initial load level with a random first choice to PV or WT investment. In addition, the sum investment capacity of WT and PV is usually less than that of sole PV investment when the load level is close by. The combination of wind and solar is needed if necessary.
The Area #1 (Residential), Area #2 (Commercial), Area #6 (School), Area #7 (Office) and Area #8 (Hospital) have a similar CCHP planning capacity which occupies a small scale compared to the GB capacity, and the role of CCHP in these areas is to provide backup support when the main electricity, heat and cold energy supply is insufficient, so its capacity is less than PV and GB that regard as the main supply sources. Compared with the thermal supply, GB and HP are the main combination. In almost all functional areas, planning GB is always the first option for the heat supply, while HP performs as the auxiliary option. This can be evident to obtain from Area #3 (Industrial), with a GB: HP ratio of nearly 15:1. As for the supply to the cooling load, only EC can produce cooling energy so its capacity is determined by the scale of cooling load.
Energy development shows the possible patterns for PIES planning. The arc section in the pie chart represents the installed capacity of energy technology in an area from developing stages, as shown in (Fig. 4). It is observed that the energy supply composition of different area with distinguished purposes varies, but with a relatively similar planning pattern that renewable energy dominates by stage.
Fig. 4.
The energy combination of different functional PIES areas over stages.
In residential area (Area #1), the proportion of PV and ES capacity has increased noticeably from stage to stage. By contrast, the proportion of heating (GB-HP-TS) and cooling (EC) energy supply capacity, has compressed consequently over stages. In commercial area (Area #2), the PV and ES capacity dominates even more.
In industrial area (Area #3), the proportion of WT-PV-ES installed capacity is less than that of GB-HP-TS in the first two stages due to the massive original heat demand, and the heat supply from GB accounts for a large proportion. In the latter two stages, the WT-PV-ES capacity increased and leveled with GB-HP-TS capacity, and the HP investment started to boom up. Although the heat demand is given priority in industrial area, the renewable energy of PV and WT still gradually invested to pursuit carbon reduction goal. It is noticed that there is a growing gap between WT and PV capacity over stages, indicating that with the growth of the industrial load, planning WT ensures more power generation to deal with the rapid and large-scale load increase.
In agricultural area (Area #4), the energy proportion of WT-PV-ES remained unchanged, and the PV capacity is slightly larger than WT because that the peak working load of agriculture usually starts at the midday, and PV generation just adapts to this characteristic. Similarly, the WT-PV-ES proportion is constant in data center area (Area #5), but the capacity of WT sticks out to ensure the enough supply to high and stable computing load that remains all the time.
In school area (Area #6), it shows a prominent energy structure of the PV-ES combination, and GB is the main heat supplier in the early stage and HP takes over in the later stage.
In office area (Area #7), the PV-ES combination dominates with a balanced combination of GB and HP as heat supply. The EC capacity to cooling supply is obvious in this area.
In hospital area (Area #8), the PV-ES structure takes the lead and increasing over stages. The GB is the main supplier for heat demand but is compressed in the later stage. Only a small amount of CCHP, HP and EC are invested.
To sum up the above analysis, the overall energy developing trend maintains in all PIES functional areas. The PV-ES combination is tended to be the mainstream in different specific functional areas with the total capacity accounting for about 50-80% in growth. The GB is the main source for heat supply and invested at one time in initial, while the HP is the extra supplement that is invested in later stage.
Figure 5 shows the cost breakdown of different areas over stages. It can be seen that almost all the investment occurs in the initial stage of the project, resulting in the maximum cost in the stage #1. There is no investment occurs in stage #4 since the load is saturated and no longer increases.
Fig. 5.
Cost breakdown of different functional PIES areas over stages.
From the results of stage #2 and stage #3, in the residential and commercial areas, the investment cost is still high, indicating that the growth of load in these areas needs to be met through multiple and continuative investments. However, the electricity purchase cost from the utility grid is higher than the operation cost of the equipment, which indicates that the utility grid supply is the first option to meet the electric load in these areas. The heat load is met by a small amount of natural gas purchase conversion. The revenues mainly derive from electricity feed-in and remaining available CER sale to the market when the carbon emission allowance is satisfied.
In industrial and data center area, the investment cost, operation cost and electricity purchase cost from the utility grid are near to each other. The cost of natural gas purchase is high because of its large original heat load. The revenue form CER sale is considerable.
In agricultural, school and office areas, the cost of electricity purchase cost from the utility grid accounts for a large part of the total cost, and the system tends to be supported by stable electric power supply for their high daytime peak load. There is certain revenue form CER sale.
In hospital area, in addition to the high and stable electric supply from the utility grid, the load growth also needs a certain of energy investment to meet. The purchase of natural gas is obvious as its heat load is relatively high. The CER sale provides the good revenue.
It can be drawn that there is a big part of electricity purchase cost from the utility grid in all functional area through the cost breakdown, which helps to understand why the utility grid supply is vital to the PIES operation in reality. The CER sale shows amazing potential for project profitability and there should be more social value of renewable energy to dig out in the future.
The carbon emission and renewable energy penetration interactions are shown in (Fig. 6). It can be seen that the total carbon emission increases with every area carbon emission increasing over developing stages. Overall, the carbon emission in industrial area is the largest (about 19000 ton in average) while the data center is the minimum (about 3200 ton in average). The carbon emission in agricultural area, school area and hospital area are relatively high of 13,000 ton in average. This volume in residential area, commercial area and office area drops to about 7700 ton in average.
Fig. 6.
Carbon emission breakdown associated RE penetration of different functional PIES areas over stages.
From the perspective of the RE penetration on the left, the ratio is concentrated between 20% and 30%. In particular, the RE penetration ratio in the data center area is high at about 45%, and its energy structure ensures a high level of RE penetration. In residential area, the RE penetration increases from about 30–40%, which also indicates that its energy structure is conducive to motivate more investment in renewable energy. The RE penetration in commercial, office, hospital, agriculture and school areas are distributed between 20% and 30%. Among them, the RE penetration level shows an improving trend in the hospital and school areas, and this level in commercial, office and agricultural area remains fixed. The RE penetration level in industrial area is limited, hovering around 20%, implying that its energy structure is not ideal for renewable energy investment.
In general, the higher the RE penetration level, the less carbon emission occurs. It can be conducted that when the difference of RE penetration ratio is less than 10%, the carbon emission can be 1–2 times different. When the RE penetration ratio difference reaches to 20%, the gap of carbon emission can be achieved as much as 4–6 times.
The results of competitive evaluation are drawn in this section. The weights of five criteria are conducted as 
. In this case, the criteria in energy, economy and environment occupy most part of the total weight, and the importance of reliability and greening level criteria is somehow not attractive. The time importance weight vector is optimized as 
. It shows that the more recent data is given much emphasis.
The evaluation results are shown as radar graph in following (Fig. 7). C1, C2, C3, C4 and C5 represent the criterion of energy development, economic level, environmental development, energy supply reliability and greening develop, respectively.
Fig. 7.
Competitive evaluation result for different functional PIES areas.
In Area #1, the evaluation efficiency of C1 is increasing, showing that the energy development is in a great momentum. The same trend in C4 and C5 appears showing that the energy supply reliability and greening process of this PIES is in a moderate way. On the contrary, the evaluation efficiency of C2 and C3 is decreasing and the situation in economic and environmental level become worse than ever. More efforts should be made on improving economic and environmental level in this condition. Overall, in the first three stages, the evaluation efficiency values of C2 and C3 performs better and outstands to C1, C4 and C5. However, in the fourth stage or further future, the bad condition of C2 and C3 would lead to the consequence that they are meant to be surpassed by C1 and C5 sooner or later.
In Area #2, all five criterions are increasing over stages, indicating that the developing trend is in good and stable condition. However, the developing trend is not balanced especially marked by C2, which reflected in a high foundation from the initial stage that reaches up to an evaluation value of 2. It is obviously to see that the C2 (economic level) is emphasized in an extreme way. This patten can be a benchmark for the PIES which wants to specialized promotion in economic level in a short time.
In Area #3, all five criteria show a balanced development trend, but the evaluation efficiency is relatively low and the grows smoothly. However, C3 is the only one that stands out a bit. This situation fits the characteristics of the mature mode of industrial area development with environment protection.
In Area #4, all five criterions are increasing over stages, but when it comes to the last stage, a greatly jump occurs to the evaluation efficiency of C1, C2 and C3. The energy development, economic level and environmental development approach to the top showing that the development mode here becoming mature.
In Area #5, all five criteria show a stable and smooth development trend, and only C4 and C5 outstands a bit, which conducted that the data center development is basically stable, no criteria can be achieved remarkable.
In Area #6, all five criteria are increasing over stages, and the development of every criterion is displaying a more balanced and relatively high contribution. There are almost no obvious shortages in all criteria so that it can be deemed as a benchmark for all-round steady development. However, the C1, C2 and C3 are slightly excellently performed.
In Area #7, all criteria are achieving better performance form the stages, and it is evident to see that the evaluation efficiency of C1, C2, C3 and C4 substantially increases in the last stage. The trend in energy development, economic level, environmental development, energy supply reliability shows a great potential in all-dimensional aspect.
In Area #8, the evaluation efficiency of all criteria increases, but in a smooth process. The C3 of environmental development is superior than the other four criteria. It may be an inspiration that the investment mode of hospital area is suitable for setting a low carbon benchmark.
Figure 8 shows the stage DEA evaluation values of eight areas, including values of each stage and overall values. It can be observed that the stage evaluation values increase in every area except Area #1.
Fig. 8.
Evaluation value of different functional PIES areas over stages.
Although the overall evaluation value of Area #1 is high, the economic and environmental criteria have been gradually declined. When the maturity reaches a certain high level, the development of economy and low carbon can be easily neglected, which has become a common problem in mature PIESs.
Area #2 has shown a strong and significant value of all stage due to its highly-developed economic level, and it can be a doubtless benchmark of all areas. Since its developing mode has been fixed, it may not be competitive from a long-term potential point.
The overall values of Area #4, Area #6, Area #7 and Area #8 are relatively high in every stage, and the incremental in each stage is considerable, indicating that the greater potential of economic, low-carbon for future development would be emerged. The templates of these PIESs are expected to become some new benchmarks in energy, economic, and environment for future sustainable development if the radical development is not considered at the moment.
The stable situation in data center scenario of Area #5 exhibits the lowest overall development efficiency in all aspects, and no benchmark can be referred in this moment.
In summary, the development criteria in different types of functional PIESs is various from each other, the competitive evaluation over multi-stage planning optimization is essential for reasonably suggesting the benchmark of different criteria, developing trend, overall efficiency, et al.
Discussion
Our study has proposed a competitive evaluation method over multi-stage planning optimization based on FAHP-DEA with a multi-criteria evaluation index set. The ‘input and output’ relationship between different indicators in a static stage, along with the dynamic evolution for the sole indicator, can be synthetical described by using the proposed evaluation method. The multi-stage planning model with operation simulation is adopted to optimize the energy investment and operation status of the PIES in all stages, then the evaluation indicators related to optimal results are calculated and development trends are shown. Case study on a PIES with eight different functional areas has shown their development patterns of energy, economy and environment intuitively and the results of competitive evaluation are compared.
The study has conducted that, from the overall point of view, it is worth noticing that the PV-ES investment for electric supply and GB investment for heat supply has been regarded as a popular energy pattern throughout the multi-stage optimal planning to different functional PIES areas. Despite the large investment capacity of renewable energy is inevitable, which makes it possible to gain profits from the green electricity or green electricity certificates trading, as well as carbon reduction, the role of utility grid supply as a solid support cannot be ignored. From a further evaluation to different functional PIES areas in contrast, the competitive evaluation over multi-stage planning optimization has revealed that the benchmark PIES of different criteria in dynamic developing stages is not fixed, it is evaluated to be adjusted with leading significance at present and also for the long-term development. Concrete conclusions are summarized as follows.
For different functional PIES areas, there is a similar planning trend that renewable energy capacity dominates over stages. In particular, the PV-ES combination has been the preference with the total capacity accounting for about 50-80% in total energy investment. The GB is the main source for heat supply while the HP is considered to be the extra supplement later on.
Electricity supply from the utility grid is important and vital to the PIES despite of the functional differences so that it is the primary target to the cost reduction. The CER trade with carbon reduction and green properties shows the considerable potential for the project profitability and becomes a way to save cost and reduce carbon emission at the same time.
Based on the development of all functional PIES areas, the RE penetration can lower the carbon emission level. When the difference of RE penetration ratio is less than 10%, the carbon emission can be 1–2 times different. When the RE penetration ratio difference reaches to 20%, the gap of carbon emission can be achieved as much as 4–6 times.
Throughout the competitive evaluation to the various functional PIES areas, it reveals that not all PIES areas are going forward developing over time, but there has been slipping backwards or low evaluation values in some mature PIES areas, represented by the residential and industrial areas. The evaluation values in PIES areas for commercial, agricultural, school, office and hospital purposes have shown potential or been determined as a benchmark in energy, economy and environment, etc., while the data center with flat and stable load is not suitable for any aspect of benchmark.
Electronic supplementary material
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Acknowledgements
This work is supported by National Key Research and Development Program of China (2022YFE0205300), Science and Technology Projects of China Southern Power Grid (GZKJXM20222351), and Chengdu Science and Technology Program (2024YF0600012HZ) .
Author contributions
Yongtao Guo, Yue Xiang: Conceptualization, Methodology; Yongtao Guo: Writing- Original draft preparation; Yue Xiang, Zhukui Tan, Hongcai Zhang, Ji Li, Fang Liu, Zechun Hu: Writing- Reviewing and Editing; Junyong Liu: Supervision. All authors have read and agreed to the published version of the manuscript.
Data availability
The data supporting this article have been included as part of the Supplementary Information.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
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Supplementary Information
The online version contains supplementary material available at 10.1038/s41598-025-92431-9.
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Data Availability Statement
The data supporting this article have been included as part of the Supplementary Information.