Regulating cost for renewable energy integration in power grids

1 Introduction

In recent years,installed renewable power generation capacity worldwide,especially that of wind and solar power,has increased rapidly [1].Nevertheless,because of the intermittent and fluctuating characteristics of renewable power generation output,an increase in renewable energy integration into the power grid requires increasing regulating capacities in the power system to ensure efficient operation [2].However,renewable energy systems can be developed on a large scale and connected to the power grid in a relatively short period,compared with the gradual process involved in the development and transformation of existing power systems.There are several methods to increase flexibility of a power system,such as by retrofitting the existing coal-fired power plants,building new pumped storage stations and gas-fired power plants,and using cross-regional power lines to obtain power support from neighboring power grids;each of these methods has different advantages and disadvantages as well as associated costs in terms of renewable energy development.Considering this,several studies have been conducted on integrating renewable energy in and increasing flexibility of power grids [3-7];though some of these works included the costs of regulating measures for future development in their analytical models,in a majority of these studies,appropriate case studies were not undertaken to study the operational costs of a given power system.

Therefore,in this study,three different cases are set up and a time series production simulation analysis model is adopted to study the effects and associated costs of different methods used to improve the flexibility of a given power system to ensure increased renewable energy consumption.

2 Time Series Production Simulation Analytical model

The transition to renewable energy usage has led to an increase in the development and integration of wind and solar energy into power grids.Due to the minute-level fluctuant and intermittent generation output characteristics of wind power and solar power[8],a time-series production simulation model is proposed to study system operational cost in detail.

2.1 Objective function

The incorporation of renewable energy in a power system is determined by certain factors,including maximum system load,daily load curve and peak-valley difference,power source mix,capacity of cross-regional lines,as well as power transmission curve and demand side response of the system,among others.To promote the consumption of renewable energy in lieu of non-renewable energy in a power system with different energy sources,several adjustment methods have been proposed,each of which have their merits and demerits.Here,the objective of the optimization function is to minimize system operational costs.

where

Pg,i(t):operational capacity of the ith power plant at time t.

pg,i(t):generation cost of the ith power plant at time t.

Power generation costs of thermal power plants are primarily determined by investment,maintenance and operational costs,as well as fuel costs.It should be noted that fuel costs change with a change in the load rate.In particular,the higher the load rate is,the lower the fuel consumption rate is.

Fa,i: fixed cost.It consists of investment depreciation,financial expenses,repair costs,wages,and welfare costs,among others.

Va,i:variable cost,excluding fuel cost.It consists of certain material costs that are associated with power generation.

βr,i(t): fuel consumption rate of the thermal power unit at time t.

Qg,i(t):thermal power generation at time t.

Pl,j(t):operation capacity of lth transmission line at time t.

pl,j(t):input electricity cost of lth transmission line at time t.

Δt:time interval considered in the study.

T: total duration of the study,such as one year.

N: other power sources,excluding those of wind and solar power.

L: total number of transmission lines.

2.2 Constraints

2.2.1 Maximum accommodating capacity for wind power and solar power:

where

Pw(t):wind power capacity in operation at time t.

Ps(t):solar power capacity in operation at time t.

PL(t):system load at time t.

Pp(t):pumping capacity or generating capacity of pumped storage power station at time t.This value will be negative when it’s at the generation state.

Pc,i,min:minimum technical output of the ith coal-fired unit.

Po,j,min:minimum technical output of the jth other generator.

m:total number of coal-fired power units in operation.

n: total number of the other units in operation.

2.2.2 Unit commitment constraints:

Unit commitment is a traditional optimization problem[9-11],which can be solved using several methods,such as priority list method,heuristic method,dynamic programming method,and mixed integer programming method [12].In this study,all available generating units are sorted on the basis of their economy and adjusting capacity.In particular,when a system operational constraint,such as power balance constraint is encountered,a unit with good regulation ability,but less economy will advance in its generating order.Then,the priority list method is used to find the optimized solution for unit commitment.The primary constraints of the unit commitment problem that need to be satisfied are as follows:

where

Ps,max:maximum capacity required by a research cycle.

PL,max:maximum system load for a research cycle.

βb: reserve factor of electric power system.

Pw,p:capacity credit of wind power,which is the minimum available generation capacity with 95% guaranty.

Ps,p:capacity credit of solar power,which is the minimum available generation capacity with 95% guaranty.

Pt,max:maximum available capacity of the power transmission line.

Pp,max:maximum power generation capacity of pumped storage power stations.

Pgas,max:maximum power generation capacity of gasfired power stations.

Pc,i,max:maximum available capacity of the ith coal-fired power unit.

Po,j,max:maximum available capacity of the jth other generator unit.

2.2.3 System electricity balance constraints:

The electricity constraints take into account the balance in any time interval as well as during the study period as a whole:

where

Pl(t):transmission capacity of the transmission line at time t.

Qs(Δt):electricity demand of the system during period Δt.

Qs(T):electricity demand of the system during research period T.

Pp(t):Pp(t)will change between pumping state Pp,p(t)and generating state Pp,g(t)according to demand.

2.2.4 Electricity balance of pumped-storage power plant:

In each pumping-generating cycle,the total electricity generated must equal to the product of the pumped generation and efficiency coefficient:where

Pp,p(t):pumping capacity of pumped storage power station at time t.

Pp,g(t):power generation capacity of pumped storage power station at t.

βp: coefficient of power generation efficiency of pumped storage power plants.

Ts: duration for one pumping-generating cycle,such as a day,week,etc.

2.2.5 Electricity balance of hydropower plant:

where

Qh,g(t): generation at tth time of the period;it is the sum of run-off-river power station and hydropower station with reservoir.

Qh,c (t): curtailment at tth time of the period.

Qh,a: theoretical average generation of the period.

Thp: study period for the hydropower plant.

2.2.6 Operational capacity constraints for power units:

The operational output of each unit at tth time must be between its minimum technical output and maximum available capacity:

where

Pc,i(t):generation capacity of the ith coal-fired unit at time t.

Po,j(t):generating capacity of the jth other unit at time t.

2.2.7 Capacity constraints for transmission lines:

The transmission capacity at time t must be between the minimum and maximum capacities:

where

PTmax:maximum operational capacity for the transmission line.

PTmin:minimum operational capacity for transmission line.

2.2.8 Ramping rate of generation units:

where

ΔPg, i (t ):ramping output of unit i.

ΔPg,max: maximum ramping ability of unit i.

2.2.9 CO2 emission constraints:

where

Eco2: total CO2 emission.

Eco2,max: CO2 emission limit.

Qi,c: electricity generated by ith coal-fired units.

Qi,g: electricity generated by ith gas-fired units.

Qi,o: electricity generated by ith other thermal units.

Kc,c: CO2 emission coefficient for coal-fired generation.

Kc,g: CO2 emission coefficient for gas-fired generation.

Kc,o: CO2 emission coefficient for generation by other thermal units.

2.2.10 Air pollution emission constraints:

where

Eap: total air pollution emissions.

Eap,max: air pollution emission limit.

Ka,c:air pollution emission coefficient for coal-fired generation.

Ka,g:air pollution emission coefficient for gas-fired generation.

Ka,o: air pollution emission coefficient for other thermal units.

2.3 Solution process

As previously mentioned,the proposed mathematical model is solved using the priority list method.All operation units are sorted based on their generation cost and regulating ability to form the priority list.Then,based on some conditions,the backtracking algorithm is used to obtain the optimized solution.

First,system data,such as minute-level load data,minute-level wind power and solar power output data,as well as other installed power capacities and crossregional power transmission curves are inputted in the model simulation.Second,operational capacities for wind power and solar power are subtracted from the original load curve to obtain the net equivalent load curve.Third,unit commitment is determined based on the net equivalent load curve and unit priority list;subsequently,each operating unit is included in the net load curve.Fourth,if regulating balance of the pumped-storage power stations is not satisfied,it will go back to the previous step to adjust either consumption or generation of this kind of power stations,and adjusting the place of other units on the net load curve.Fifth,if regulating balance of the entire system is not satisfied,it will increase the curtailment of wind power and solar power generation,and consequently,modify the net load curve.When all these conditions are satisfied,the optimization result for the system is outputted.

Fig.1 shows the detailed flow chart for the solution process.

Fig.1 Solution process for the proposed model

3 Case Studies

In this study,a power system with a large-scale electricity import,high thermal power capacity and high renewable penetration is selected as the test system.Three different cases are set up with different development scenarios to study the regulating costs of different measures in accommodating wind power and solar power generation.

3.1 Example system

The example system has a maximum power load of 155 GW,and the forecasted electricity demand is 850 GWh.The total installed power capacity is 156 GW in 2020.The transmission capacity of cross-regional lines is 55 GW.The primary contribution for the generation capacity is from a coal-fired unit,which accounts for 53% of the total electricity generation.Flexible regulating capacities of the system are primarily those from pumped-storage power plant and gas-fired generation units,accounting for 4% and 18% of the electricity generation,respectively.The pie-chart representation of the capacity mix of this example system is depicted in Fig.2.

In terms of changes in the yearly load curve characteristics,the maximum power load was observed in August.Furthermore,the minimum power load in a year occurs in February,which is only 0.51 times the maximum power load.The peak and valley differences of a typical day load curve in summer and winter is 24% and 18.5%,respectively.The typical day load curves of the system for four seasons are shown in Fig.3.

Fig.2 Installed capacity mix of the example system

Fig.3 Typical day load curves of the example system during the four seasons

The minute-level outputs of solar power and wind power on a day in the four seasons are shown in Fig.4 and Fig.5.

Fig.4 Daily minute-level solar power output for four seasons

Fig.5 Daily minute-level wind power output for four seasons

3.2 Related parameters

·The average peak-shaving range of the transmission curve is set to 18% in summer and autumn,and 33%in winter and spring.

·The minimum technical output of the combined heat and power unit (CHP)is set to 75%,of the coal-fired unit to 50%,and of the gas turbine unit to 0%,of their rated capacities.

·The retrofitting cost for thermal units is about 150 RMB per kW.After retrofitting,the minimum technical output of the CHP unit can be lowered to 50%,and of the coal-fired unit to 30%.However,the gross coal consumption rate will increase with a decline in output;in addition,a sharp rise in the same will be observed when to the output declines to the minimum technical output range.

·The generation efficiency of the pumped storage power plant is 75%.

Table 1 Related economic parameters of the system

Investment（￥/kW)Fixed cost rate Variable cost(￥/kWh)Fuel cost(￥/kWh)Pumped storage40002.50%0.09 Hydropower55002.50%00 Coal39003.00%0.040.27 Gas33002.50%0.030.40 Nuclear120002.50%0.050.16 Wind60002.00%0 Solar70003.00%0 Transmission line3.50%0.03

3.3 Simulation and results

To demonstrate the effects and determine the costs of different regulating measures in promoting renewable energy accommodation,we set up the following three cases in our study.

Case 1:Using transmission lines’ regulating capability [13].

Case 2:Building new flexible capacities,such as gasfired and pumped storage plants.

Case 3:Retrofitting and upgrading coal-fired units’regulating ability as well as building pumped storage plants[14].

Based on the yearly load duration curve,in summer,autumn,and winter,it is possible to ensure full consumption of renewable generation due to relatively high load levels if operational priority is given to hydropower,pumped storage units,and gas-fired units,because these units have good adjusting ability to satisfy the peak valley difference of the load curve and handle fluctuation of renewable generation.However,because the lowest load levels occur during spring time,renewable energy consumption is not guaranteed in spring.In particular,simulation results show the curtailment of renewable generation primarily occurred during spring.The simulation result for a typical day in spring is shown in Fig.6.

From Fig.6,it can be observed that,during early hours in a day,such as from 0–6 a.m.,curtailment occurred because the lowest load level and cumulative minimum technical output of the operational units could not be further decreased.In particular,the curtailment of wind power generation was accounted for 16% of the total theoretical generation in a day.

Fig.6 System simulation for a typical day in spring

In Case 1,to eliminate the curtailment of renewable generation during the early morning hours,the peak-shaving range of transmission lines was increased from 33% to 50%of the total capacity.In this manner,the minimum import power from transmission lines decreased about 9.3 GW,and thus,all curtailment could be avoided.In this case,the additional cost incurred by changing the peak shaving depth is considerably small and depends on the connected systems on the other side of the lines.The simulation result for Case 1 is shown in Fig.7.

Fig.7 System simulation for a typical day for Case 1

In Case 2,to eliminate curtailment,some gas-fired units and pumped storage units are constructed to add flexible regulating ability to the system.According to the simulation result,gas generation capacity of 5.5 GW and pumped storage capacity of 2 GW was required to eliminate curtailment.The added cost for constructing new generating units is about 26.2 billion RMB.The newly added fixed cost is 0.7 billion RMB,and the sum of variable and fuel costs is about 0.3 billion RMB per year.The simulation result of a typical day in spring for Case 2 is shown in Fig.8.

Fig.8 System simulation for a typical day for Case 2

In Case 3,the regulation ability of the coal-fired generation unit is used as the primary measure to solve curtailment problems.According to the simulation result,the minimum technical output for CHP and coal-fired units need to be reduced to 50% and 30%,respectively,using retrofitting procedures.Because of the large capacity of the transmission line and comparatively high base load rate,a 3.5-GW pumped storage power plant is required to accommodate more renewable generation at valley time periods.In this case,the added cost for retrofitting thermal generating units is about 2.2 billion RMB,and the added cost for constructing new pumped storage units is about 14.0 billion RMB.The newly added fixed cost is 0.4 billion RMB,and the sum of variable and fuel costs is about 0.27 billion RMB per year.The simulation result for Case 4 is shown in Fig.9.

Fig.9 System simulation for a typical day for Case 3

4 Conclusion

Based on our simulation results,all three cases considered in our study fulfill the goal of eliminating renewable curtailment during the early morning hours in spring;however,the system investment as well as operational and maintenance costs in Case 1 are the lowest compared with the other two cases.Furthermore,the total cost of Case 2 is lower than that in Case 3.Thus,considering the rapid growth of renewable energy development in the world,to increase cross-regional transmission line capacity,transmission line regulation in receiving areas might be an effective and economical method to enhance system flexibility in order to integrate more renewable energy sources into the power system.Furthermore,in large-scale electricity receiving areas,retrofitting thermal power units is not sufficient to accommodate renewable generation at valley times in the load curve,and additional pumped storage plants are required to reduce curtailment during such times by raising the equivalent system load.

Acknowledgements

This work was supported by National Key Research and Development Programe of China (No.2018YFB0904000);the State Grid Science &Technology Project (Title:Northeast Asia Power Grid Interconnection Feasibility Study).