Index system and methods for comprehensive assessment of cross-border power grid interconnection projects

0 Introduction

With the increasing global economy integration and green transformation,surpassing national boundaries is rapidly becoming a general trend for achieving wider and more optimal energy resource allocations [1-3].The construction of a global energy interconnection system can effectively increase the transmission efficiency of power systems,accelerate development and utilization of renewable energies in different countries,strengthen regional economic cooperation,and improve the livelihood of the global population [4-7].

At present,the benefits of traditional power transmission projects and their evaluations have been studied by many scholars [8-15].Wan et al.[16]suggested that the economic benefits of power grids are reflected by three aspects,including increase in supply,reliability promotion,and reduction of losses;evaluation models were then established separately to assess the grid projects by annual cost-benefit analysis.Xue et al.[17]established an index system for the social assessment of grid projects,comprising social economy,social environment,and natural environment indices.Song et al.[18]used the pressure-state-response(PSR) model to evaluate the social welfare owing to a smart grid by considering internal mechanisms related to social welfare and associated smart grid development.Tian et al.[19]introduced the lifecycle cost (LCC) concept to analyze the cost of ultrahigh voltage grids,and the shadow price theory (SPT) was used to assess social benefits,such as optimization of resource allocation efficiency.Zhu et al.[20]noted that regional grid interconnection would be an effective method to untap regional natural resources through power generation and cut down on greenhouse gas (GHG)emissions.Wu et al.[21]used the analytic hierarchy process and extension evaluation method improved by interval number theory to quantify the comprehensive benefits of a distribution network project.Favuzza et al.[22]found that in Europe and North Africa,the “N-1” criterion standard was higher,and the power networks were more reliable owing to the interconnection of transmission systems.Büyüközkan et al.[23]built a systematic evaluation index system for comprehensive assessment of energy investment projects by applying the multicriteria decision-making approach and analytic hierarchy process.

Although research on traditional power transmission project assessments is relatively mature,there is a dearth of studies with regard to systematic assessments and comparison of the comprehensive benefits of cross-border projects.Compared with domestic power networking projects,cross-border power grid interconnection projects are more complex and systematic,and a series of economic,social,environmental,and technical benefits can be reaped upon successful deployment.Hence,a scientific comprehensive benefit evaluation system is of great significance to investment decision-making.

In this study,a robust assessment for cross-border power grid interconnection projects is proposed.As a complex system,the characteristics of projects are highlighted and sufficient information is provided to the decisionmakers.First,a comprehensive assessment index system is developed for evaluation from the perspective of costbenefit analysis.Additional transmission infrastructures provide more transmission capacity,thereby allowing optimization of the generation portfolio,which then helps improve socio-economic welfare.Derivative values such as environmental and technical benefits have also been taken into due account in the proposed system.Second,costbenefit analysis is performed using the combined qualitative,quantified,and monetized approaches by market and grid network simulations.Finally,the comprehensive benefits of three proposed transmission projects connecting Europe and Asia are assessed and compared using the approach for order preference by similarity to an ideal solution (TOPSIS)method,where the weight of each indicator is determined iteratively based on set-valued statistics.

1 Comprehensive assessment index system

A comprehensive assessment index system for evaluating the cross-border power grid interconnection projects has been developed from the cost and benefit points of view.To fully appreciate the project comprehensive benefits based on the characteristics and objectives of the complex transmission networks,the following principles have been considered to build the index system [24-26]:

(1) The comprehensive assessment indicators should be scientific,rational,practical,and readily available.

(2) The relevant national and regional energy policies,regulations,objectives,and technical standards are considered as the reference bases.

(3) The indicators are designed to reflect the added value of each project to the economy and society,as well as the effects of the project in terms of cost,environmental viability,and technical viability.

(4) The indicators are simple and robust.This allows some of the indicators to be monetized,while the others can be quantified in their typical physical units,such as tons for CO2 emissions.

Fig.1 provides a general overview of the indicators used in the proposed comprehensive assessment of cross-border grid interconnection projects.Considering the representativeness,difference and availability of the indicators,a practical,readily available and clear index system is adopted.Since political stability is a prerequisite for implementing the cross-border power grid interconnection projects,which has been taken into account at the project planning stage,it is not involved in the index system.Meanwhile,the index system is used for crossborder grid interconnection projects selection,rather than the overall power grid planning.And an individual project has little impact on macro-economy,industry development and integrated energy system,there are no indicators related to these aspects.

Fig.1 Cost and benefit indicators in the comprehensive assessment index system for cross-border power grid interconnection projects

1.1 Costs

The costs are calculated according to a database of cost data obtained from real projects.Since the aim of this paper is to provide a guidance for the follow-up implementation of cross-border grid interconnection projects through a preliminary pre-evaluation analysis,the costs are estimated without specific engineering calculations.

C1.CAPEX:The capital expenditure includes expected costs for equipment,materials,and construction,which are necessary for implementing projects such as overhead lines,submarine cables,foundations,substations,protection and control equipment,as well as expected replacement,decommissioning,and dismantling costs during the project lifecycle.CAPEX is established by empirical estimations based on information from similar prior projects and by parametric estimations based on public information about the cost of similar projects,and the foreign exchange rate adopted in CAPEX estimate is locked by a third party.CAPEX is expressed in USD and the following costs are considered:

·Expected costs for permits,feasibility studies,design and land acquisition;

·Expected cost for equipment,materials and execution costs;

·Expected costs for temporary solutions which are necessary to realize a project;

·Expected environmental and consenting costs;

·Expected costs for devices that have to be replaced within the given period;

·Dismantling costs at the end of the equipment lifecycle.

C2.OPEX:The expected annual maintenance and operation costs are considered as the operating expenditures.The OPEX of all projects are deduced on the basis of the cost levels in the respective study period and expressed in terms of USD per year.

1.2 Socio-economic benefits

The socio-economic benefits are characterized by the ability of a project to reduce traffic congestion and its impact on societal well-being.

A1.RES fuel savings:A cross-border grid interconnection project provides increased transmission capacity that makes it available regardless of cost-efficient power trades across electricity markets.The generation costs can be reduced with direct connections from a project towards new and lower-cost generation.The effects of integrating renewable energy sources (RES) on the socio-economic benefits is reflected in the reduction of curtailment and decreased short-run variable generation costs,which are measured by market simulations in USD/year.

where Sres is the RES fuel saving,Ccoal is the cost of operating lignite and hard coal power plants,Cgas is the cost of operating natural gas power plants,and Cther is the cost of operating other thermal power plants.

A2.Emission cost reduction:The expanded transmission capacity reduces CO2 emission costs since it uses RES generation capacities at various locations to alleviate the need for construction of additional power supply in a given area.With the assumed price of emission,the avoided CO2 emission costs are measured by market simulations in USD.The monetization of CO2 is based on the forecasted CO2 prices for electricity in the study horizon.The prices are derived from official sources,such as the International Energy Agency (IEA).

where Semi is the total emission cost reduction,ΔEi is the variation of CO2 emission in the given area i,Pi is the forecasted CO2 price in the given area i,n is the number of areas with reduced CO2 emissions benefiting from the project,1 ≤ i ≤ n.

A3.Electricity price competition:A transmission project encourages competition between the generators,hence reducing the price of electricity for the end users.The price surplus of imported power products is measured by the cross-border power price competition tariff.The specific calculation method does not consider market forces and is expressed as below:

where CSt is the electricity price competition,Tr is the electricity price at the receiver end,and Ts is the source-end electricity price,and Tt is the transmission tariff.If CSt is above zero,it means that the project construction has power price competitiveness and can effectively curb the increase in power price.

A4.Impact on local population:Social residual effects characterize the local impact of the project on social activities.The project impact on the local population is measured as the total length (km) of an overhead line or underground/submarine cable that runs through socially sensitive areas.This indicator only considers the residual impact of a project,i.e.,the portion of impact that is not fully accounted for in C1 and C2.An area can be sensitive to nearby infrastructures if it is densely populated or preserved for its landscape value.

where Lsoc is the impact on social activities;Lpop is the length of the line in the densely populated area;Lfac is the length of the line that is in an area near schools,day-care centers,or similar facilities;Lpro is the length of the line in protected areas under national laws,e.g.,prohibited military zones.

1.3 Environmental benefits

A5.RES integration:This indicator provides a standalone value associated with the additional RES available for the system and indicates the reduction of renewable generation curtailment,i.e.,avoided RES spillage(MWh),which is extracted from the market and network simulations.The basis of calculation is the amount of RES foreseen in the scenario.

A6.CO2 variation:Variations in CO2 emissions represent changes in the CO2 emissions from the power system through the project;it is a consequence of the changes in generation dispatch and unlocking the renewable potential.The aim of reducing CO2 emissions is explicitly included as one of the national and regional targets and is therefore displayed as a separate indicator.Considering the specific emissions of CO2 by each type of power plant and the annual production of each plant,the annual emissions at the perimeter level can be calculated based on the proportion of the total production.As the cost of CO2 is already included in A2,this indicator only displays the benefit in tons to avoid double accounting.

where ΔECO2 is the variation in CO2 emissions,ΔEcoal is the variation in CO2 emissions from lignite and hard coal power plants,ΔEgas is the variation in CO2 emissions from natural gas power plants,ΔEoth is the variation in CO2 emissions from other thermal power plants.

A7.Impact on local ecosystem and biodiversity:Environmental residual effects characterize the local impacts of a project on the ecosystem and biodiversity.The project impact on the local population is measured as the total length (km) of an overhead line or underground/submarine cable that runs through environmentally sensitive areas.This indicator only considers the residual impact of a project,i.e.,the portion of the impact that is not fully accounted for in C1 and C2.An area can be sensitive to environment when the nearby infrastructures affect the local ecosystem and biodiversity.

where Lenv is the impact on local ecosystem and biodiversity,Lres is the length of the line along natural reserves,Lhab is the length of the line along animal habitats,Loth is the length of the line along other conserved areas under specific directives or national laws.

1.4 Technical benefits

A8.System flexibility:Flexibility indicates the ability of a power system to adjust to rapid and extensive changes in the net demand in the context of high penetration of nondispatchable generation.To measure the contribution of a new cross-border interconnection that enables the system to meet ramping requirements and contributing to system flexibility by sharing flexible units,the residual load ramp is introduced via the residual load change in one timespan.Further,the grid transfer capacity (GTC) is used to indicate the level of cross-border assistance for ramps that the existing and new interconnections can provide.Market simulations based on years are used to define the ramping requirements as follows:

where f is the system flexibility,Ro,max is the maximum hourly ramp of residual load,Rr,max is the remaining maximum hourly ramp of residual load,GTCold is the existing GTC value,and ΔGTC is the difference between GTC with and without the interconnection.

A9.System stability:Power system stability is the ability of an electrical power system,with a given initial operating condition,to withstand increasingly extreme system conditions,such as faults,load changes,generator outages,line outages,voltage collapse,or some combination of these factors.The assessment of system stability typically requires significant additional modeling and simulations,and the studies are,by nature,complex and time consuming.It is thus practical to consider a simplified and generic representation of the potential impact of reinforcement on system stability based on the technology being employed [27].System stability is addressed via qualitative assessments of the transient stability,voltage stability,and frequency stability.For each of these technologies,the generic impacts on transient,voltage,and frequency stabilities are indicated in the table below.

Table1 System stability indicator given as qualitative indicator related to different technologies [27]

Element Transient stability Voltage stability Frequency stability New AC line ++ ++ 0 New HVDC ++ + +AC line series compensation + + 0 AC line high-temperature conductor/conductor replacement - - 0 AC line dynamic line rating - - 0 Mechanically switched capacitors/reactors 0 + 0 SVC + + 0 STATCOM + ++ 0 Synchronous condenser + ++ ++

The indicators used to determine the impact are as follows:

-:Adverse effects.

0:No changes.

+:Small to moderate improvements.

++:Significant improvements.

N/A:Not relevant.

2 Assessment framework

Market and network simulations are performed for the computation of some benefit indicators.The iterative method based on set-valued statistics is presented to determine the weights.The TOPSIS method is used to calculate and compare the comprehensive benefits of the cross-border grid interconnection projects.The assessment framework and process are illustrated in Fig.2.

2.1 Cost-benefit analysis method

The analysis of costs and benefits are conducted using combined qualitative,quantified,and monetized approaches,with which the full range of costs and benefits can be represented.The indicators are calculated through market and network simulations that generally complement each other and are therefore used in a cross-over manner.

Market simulation:The market studies inspect the economic dispatch of generation units while power demand is fulfilled in each bidding area in each modeled time step.Constraints such as flexibility and availability of thermal plants,hydraulic conditions,wind and solar profiles,load profiles,and power outages are considered.The studies also include measurements on savings in generation costs affected by investments in the grid.The market simulation results are presented with computations of some benefit indicators,such as RES fuel savings (A1),emission cost reduction (A2),RES integration (A5),and CO2 variation(A6).The result is used as an input to derive the generation,consumption,and power flows in the grid to perform load flow calculations.

Fig.2 Flow chart of the comprehensive assessment of cross-border power grid interconnection projects

Network simulation:Network studies present extensive information on the transmission networks and are used to calculate the actual load flows in the network under given generation/load/market exchange conditions.These network studies then identify the bottlenecks in the grid,especially the power flows through market exchanges.Some of the results are obtained by calculations of the benefit indicators such as the flexibility (A8),and some are used as the inputs for market simulations,such as net transfer capacity and grid losses.

2.2 Weighting method

Iterative method based on set-valued statistics:As the emphasis in the comprehensive assessment varies according to the actual situation of the project,the weight of each index can be changed flexibly along with the decisionmaking problem.The iterative method based on setvalued statistics is a subjective weighting method that can effectively avoid uncertainty,randomness,and fuzziness of the thoughts of the experts;its steps are as summarized below.

Step 1:Choose the most important indicators as a subset from the benefit index system

where m is the number of benefit indicators,and L is the number of experts,with 1≤ k≤ L and 1≤ s≤ m.

Step 2:Build the demonstrative function:

where 1≤ j≤ m.

Step 3:Determine the weight wj in an iterative manner:

where Sk is the iteration number,1≤ i≤ Sk.

If an indicator is not selected at all times,the weight can be adjusted by referring to the following formula to avoid a situation where the weight is 0:

2.3 TOPSIS method

The basic principle of the TOPSIS method is to determine the positive and negative ideal schemes in the normalized decision matrix.Then,the approximation degree between the feasible solution and two benchmark solutions can be calculated to evaluate the advantages and disadvantages of each project [28].

Step 1:Attain the positively normalized and nondimensional original data by (16):

where n is the number of projects,for 1≤ i≤ n and 1≤ j≤ m.

Step 2:The maximum value of each evaluated object in the index is considered as the positive ideal solutionand the minimum is considered as the negative ideal solution

Step 3:Calculate the comprehensive benefit index Bi,which is defined as the approximation ratio between the feasible solution and ideal scheme.The larger the value of Bi,the better is the project.

where D i+ and D i− are the Euclidean distances between the evaluated index vector of project i and positive and negative ideal index vector,respectively.

Step 4:Calculate the benefit-cost ratio Ri of a transmission project.The transmission projects can be compared by the normalized benefit-cost ratios,and the higher the value of Ri,the more feasible is the project.where Ci is the total cost of a project,including capital expenditure (CAPEX) and operating expenditure (OPEX).

3 Case study

European and Asian countries are currently actively promoting renewable energy utilization.Europe experiences winter peak load stress while Asia bears the summer load stresses.Thus,it is naturally feasible to build a link between the two continents owing to their load diversity and complementary nature of generation.Power grid interconnection projects generally focus on long-term planning and scheduling of reinforcements and extensions to the existing infrastructure.While the costs of the projects mostly depend on self-reliant factors like routing,technology,and material,the benefits strongly correlate with the scenario assumptions.Therefore,scenarios that define the potential future of European and Asian energy systems are reviewed to gain insights into the future benefits of transmission projects.The evaluation index system and model established in this essay are used to assess the comprehensive benefits of three cross-border power grid interconnection projects that use different voltage levels to connect the European and Asian countries.

3.1 2035 Scenario

The 2035 scenario is in compliance with the State of the Global Climate 2015-2019 prepared by the World Meteorological Organization (WMO) for the September 2019 United Nations Climate Action Summit,as well as Outlook for Europe and Asia Energy Interconnection Developments issued by the Global Energy Interconnection Development and Cooperation Organization (GEIDCO) [29][30].Fig.3 shows the installed power generation capacities by various power sources in Europe and Asia under the 2035 scenario.

In Europe,213.3 GW coal plants and 41.3 GW oil plants are expected to retire by 2035.The installed nuclear power capacity is expected to reduce from 163.7 GW in 2017 to 139.3 GW in 2035;wind installed capacity is expected to grow from 174.4 GW in 2017 to 1006.4 GW in 2035;solar installed capacity continues to increase from 112.0 GW in 2017 to 672.7 GW in 2035.

Asia is expected to maintain steady and rapid growth in terms of clean energy installed capacity owing to the shift in energy structure towards the low-carbon direction.In 2035,the installed capacity of hydropower,wind power,and solar power ate projected to reach 1059.2 GW,1765.5 GW,and 3188.7 GW,respectively,under the 2035 scenario.

3.2 Project definitions

Fig.4 demonstrates three feasible cross-border power grid interconnection solutions between Europe and Asia that meet the 2035 scenario and are assessed by the comprehensive evaluation index system and framework established herein.The specific parameters of each project are shown in Table2.Project 1 will connect the power grids of Germany,central Asia,and central China,mainly sending wind power and solar power in central Asia to Germany and China.Project 2 will connect the power grids of Germany and northwest China,mainly delivering wind and solar power from central Asia and northwest China to Germany.Project 3 will connect load centers in Germany with hydro bases in Russia,mainly conveying hydropower to Germany.It is noted here that we mainly focus on assessing and comparing the three interconnection corridors between Europe and Asia,as designed above.

Fig.3 Installed power generation capacities by various power sources of (a) Europe in 2017 and 2035 and (b) Asia in 2016 and 2035

Fig.4 Three solutions for cross-border power grid interconnection projects that use different voltage levels to connect European and Asian countries

Table2 Specific parameters of three cross-border power grid interconnection projects between Europe and Asia

Project Transmission route Transmission capacity/MW Voltage level/kV Transmission distance/km Grid loss/%P1 Kazakhstan (Ekibatuz) ～ China (Zhengzhou) 8000 ±800 4000 5.63 Kazakhstan (Aktobe) ～ Russia ～ Belarus ～Poland ～ Czech ～ Germany (Munich) 8000 ±800 3500 5.03 P2 China (Yili) ～ Kazakhstan ～ Russia ～ Belarus ～Poland ～ Czech ～ Germany (Munich) 8000 ±1100 6400 4.90 P3 Russia (Tula) ～ Belarus ～ Poland ～ Czech ～Germany (Munich) 8000 ±1100 6600 5.02

3.3 Cost-benefit analysis

European and Asian databases are initially developed based on the ABB Global Grid study [31].Additionally,the installed capacity is updated based on Outlook for Europe and Asia Energy Interconnection Developments[29][30].In this case study,28 European countries in 14 zones,5 central Asian countries in 1 zone,and China as a single zone have been modeled.Hourly simulations for Asia and Germany with and without the HVDC link have been performed in the 2035 scenario using GridView model.The indicators are calculated through iteration of market and network studies.The result of each comprehensive assessment index data and their positively normalized and non-dimensional values in three projects are shown in Table3 and Table4.

3.4 Comprehensive assessment results

According to the actual situation and background of the cross-border power grid interconnection projects,10 experts on power system planning from GEIDCO,ABB,etc.were invited to the weight investigation group.Depending on the results of the expert investigations,the weight of each index was determined by the iterative method based on set-valued statistics,as indicated in Table5.

Table3 Original calculated comprehensive assessment index data of three projects

Index P1 P2 P3 C1.CAPEX/M$ 11 800 10 600 11 400 C2.OPEX/(M$/yr) 19.67 17.67 19.00 A1.RES fuel savings/(M$/yr) 15.00 12.07 11.20 A2.Emission cost reduction/M$ 810 790 760 A3.Electricity price competition/(US cents/kWh) 2.93 1.08 0.81 A4.Impact on local population/km 600 900 500 A5.RES integration/GWh 6 760 7 450 7 500 A6.CO2 variation/(MT/yr) 1.31 1.34 1.27 A7.Impact on local ecosystem and biodiversity/km 240 300 200 A8.System flexibility 13% 17% 31%A9.System stability + + +

Table4 Positively normalized and non-dimensional values of each indicator in three projects

Index P1 P2 P3 C1.CAPEX 0.604 0.543 0.584 C2.OPEX 0.604 0.543 0.584 A1.RES fuel savings 0.573 0.601 0.558 A2.Emission cost reduction 0.594 0.580 0.558 A3.Electricity price competition 0.908 0.335 0.251 A4.Impact on local population 0.504 0.755 0.420 A5.RES integration 0.539 0.594 0.598 A6.CO2 variation 0.579 0.592 0.561 A7.Impact on local ecosystem and biodiversity 0.554 0.693 0.462 A8.System flexibility 0.361 0.472 0.805 A9.System stability 0.577 0.577 0.577

The maximum value of each evaluated object in the index system is considered as the positive ideal solution V +,and the minimum is considered as the negative ideal solutionV-.The results are shown in Table6.

Table5 Weight wj of each index determined by iterative method based on set-valued statistics

Weight A1 A2 A3 A4 A5 A6 A7 A8 A9 wj 0.159 0.137 0.122 0.074 0.126 0.118 0.066 0.095 0.103

Table6 Positive ideal solution V+ and negative ideal solution V- constructed by the maximum and minimum values of each benefit indicator in the index system

Index V+ VA1.RES fuel savings 0.601 0.558 A2.Emission cost reduction 0.594 0.558 A3.Electricity price competition 0.908 0.251 A4.Impact on local population 0.755 0.420 A5.RES integration 0.598 0.539 A6.CO2 variation 0.592 0.561 A7.Impact on local ecosystem and biodiversity 0.693 0.462 A8.System flexibility 0.823 0.345 A9.System stability 0.577 0.577

Finally,the comprehensive benefit index B1 and the cost-benefit ratio R1 of each transmission project is calculated as shown in Table7.

Table7 Comprehensive benefit index Bi and the cost-benefit ratio Ri of each transmission project

P1 P2 P3 Bi 0.580 0.344 0.368 Ri 0.480 0.284 0.305

From the comprehensive benefit assessment results of the three cross-border power grid interconnection projects,it can be concluded that Project 1 is the most optimal project among these three,with a comprehensive benefit index B1 of 0.580.Meanwhile,the benefit-cost ratio of project 1 is 0.480,which is also higher than those of the other two projects,rendering it more feasible.Meanwhile,the ±800 kV HVDC power transmission technology adopt ed in project 1 is more mature than the ±1100 kV HVDC power transmission technology adopted in project 2 and project 3.

4 Conclusions

Based on the characteristics and objectives of the complex transmission network,and with the relevant national and regional energy policies taken into account,a full evaluation of the cross-border power grid interconnection project benefits is presented in this work.

(1) A robust comprehensive assessment index system is established for evaluating the comprehensive benefits of cross-border power grid interconnection projects from the cost and benefit points of view,including 11 indicators of costs,socio-economic benefits,environmental benefits,and technical benefits.

(2) With the combined qualitative,quantified,and monetized cost-benefit analysis,the indicators are calculated through market and network simulations that generally complement each other and are therefore used in an iterative manner.

(3) The weights of the indicators are determined iteratively based on set-valued statistics,which is a subjective weighting method,to effectively avoid uncertainty,randomness,and fuzziness of the thoughts of the experts during project appraisal.

(4) The comprehensive benefit results of three crossborder power grid interconnection projects connecting Europe and Asia are assessed and compared by the TOPSIS method to derive the optimal project and provide sufficient information to support investment decision-making.

With the implementation of cross-border grid interconnection projects in the future,the index system will be more systematic and scientific combining specific engineering calculations,therefore providing certain theoretical support for different stakeholders in making relevant decision-makings.

Appendix

1.1 Zonal model of power system

Zonal model of power system is mainly used to study the costs and benefits of transmission channel expansion between regions.The zonal model treats all the generators,loads,and grids in the same region as one zone,and ignores the congestion of grids within the zone,as shown in Fig.A1.It needs to follow Kirchhoff's current law,and requires a balance between power generation,consumption,and electricity delivery in each region.It has the advantages of fast calculation speed and easy to analysis.

Fig.A1 Illustration of zonal model

The data demand for time-series simulation of zonal model are listed in TableA1.

TableA1 Main data demand for zonal model simulation

Study object Data category Time scale(data points/year)Zone Load Load profile 8760 Ancillary service Demand for ancillary service 1 Solar Wind Capacity 1 Typical curve 8760 Hydro Capacity 1 Maximum electricity generation,Maximum/minimum output 12 Storage Efficiency,Capacity,Volume,Pumping/generating price 12 Coal,Oil,Gas,Nuclear,Geothermal,Biomass Maximum/minimum capacity,Fuel type,Fuel price,Fuel efficiency,Carbon emission price,Ramping rate 12 Transmission channel Zonal link Forward/backward limit,Forward/backward tariff,Forward/backward loss factor 1

1.2 Objects and constraints

The object of zonal model simulation is given below:

whereare the costs of generators,carbon emissions,demand responses,ancillary services,and transmission channels,and Sg,St,Sz,Sc are the sets of generators,time span,zones,transmission channels.Specifically,is the generating price; is the output of generators; is unit commitment parameter,1 represents of committed and 0 is the opposite; is carbon emission price; is carbon emission amount; is the price of adjustable load; is the adjustment amount of adjustable load; is the price of ancillary service;is the capacity of ancillary service; is transmission tariff;is power flow on transmission channels.

The constraints governing zonal model simulation are as follows:

(1) Power balance:

where is the load of zone z at time t;Sg,z is the set of generators in zone z;Tz,m,t is the power flow of transmission channel from zone z to zone m at time t.

(2) Ancillary service:

where is the request of ancillary service in zone z at time t;andare downward and upward ancillary services of generator i at time t,respectively; andare minimum and maximum output of generator i,respectively.

(3) Demand response:

where is the maximum amount of adjustable load.

(4) Power limit of transmission channels:

whereare the minimum and maximum power flow of transmission channel c.

Based on the optimization of the above model,data such as losses of transmission channels,carbon emissions of different generators,marginal prices of electricity in different zones,spillage of renewable energy,etc.,can be obtained.

Acknowledgments

This work was supported by the Science and Technology Project of Global Energy Interconnection Group Co.,Ltd.(No.524500180014).

Declaration of Competing Interest

We declare that we have no conflict of interest.