Adjustable robust low-carbon dispatch for interconnected power systems in Northeast Asian countries

0 Introduction

Over the past few years,environmental pollution,the energy crisis,and global warming have become threats to human existence[1-3].Renewable energy is an urgent necessity for achieving sustainable development of society and improving energy efficiency.Coal-fired electrical powerstations are the dominant source of electricity,and they also release significant carbon emissions as a byproduct of power generation [4].Carbon emission is receiving global attention because of global warming [5].As the largest sectional emission source,the electricity industry could face significant pressure in terms of both internal operating mechanisms and external environments.Thus,system operators need to consider both the “traditional economy dispatch model” and the “carbon emission dispatch model” simultaneously in a carbon-constrained world [6,7].

To mitigate carbon emissions from the power generation sector,three approaches could be followed [8]:improving energy efficiency [9-11],using carbon capture and storage technology [12,13],and developing renewable energy [14].These methods need to be fully considered in economic dispatch.Economic dispatch model shave been proposed for integrated electricity and natural gas systems [15],for carbon capture power units [16],and for systems considering wind curtailment [17].

In low-carbon and low-emission power systems,the penetration of renewable energy is expected to be high.There are intrinsic uncertainties associated with renewable energy,such as with wind energy and solar energy,which can compromise the operational security of power systems.Stochastic and robust optimization are the most popular methods of addressing this problem.Stochastic optimization uses many renewable energy output scenarios to handle uncertainties [18].A stochastic economic scheduling model with multi-region transmission constraints has been developed [19].It improves the scheduling yield by 1.1% compared with the deterministic method.Robust optimization considers the worst case of uncertainty,unlike stochastic optimization [20,21].Although the dispatching cost is increased,it can guarantee secure operation of power systems under any preset uncertainty settings.An adjustable robust optimization approach to handle the uncertainty of renewable energy has also been proposed [22].In this approach,the unit generation can be adjusted through participation factors to ensure a feasible solution for all uncertainty settings.Adaptive robust optimization has also been used for the power system dispatch problem [23].This approach considers the uncertainty correlations of space and time to form a new concept of dynamic uncertainty sets.A robust optimization model that aims to maximize the renewable energy accommodation has also been developed[24].It uses three methods to convert the problem into linear programming,bilinear programming,and two-stage optimization problems.

However,the aforementioned studies did not consider the special regulations for multi-country interconnected power systems.In transnational economic dispatch,the operational constraints are expected to be strictly enforced in an uncertain environment.Therefore,an adjustable robust low-carbon dispatch for interconnected power systems is proposed to promote the accommodation of renewable energy.The contributions of this study can be summarized as follows:

·A low-carbon economic dispatch model is proposed in which the power generation and carbon emissions are combined.Moreover,the adjustable robust optimization approach is used to address the uncertainties associated with renewable energy resources.

·For the economic dispatch model,special regulations should be considered among multiple countries,where each country has its own area control error.Moreover,simulations of the practical interconnected power systems for Northeast Asian countries (IPS-NAC) are conducted.

The remainder of this paper is organized as follows:Section 2 presents an adjustable robust economic dispatch model considering the carbon emission constraints and the regulation rule constraints between multiple countries.In Section 3,simulations of the practical IPS-NAC are presented.Finally,conclusions are drawn in Section 4.

1 Adjustable robust optimization of lowcarbon dispatch model

1.1 Deterministic low-carbon dispatch model

The general low-carbon power system economic dispatch model aims to maximize the renewable energy generation and minimize the generation cost.In addition,it aims to satisfy all the possible constraints,including power balance,unit ramp rate,generation limits,hydro energy balance,renewable energy curtailment,transmission limits,and carbon emission limits.It should be noted that only the thermal units will have carbon emissions.Other units,including renewable energy units and hydro units,do not involve a carbon emission problem.Specifically,the objective function contains two parts—generation cost and curtailed renewable energy cost—and is written as

where C is the objective function;t is the index of periods;T is the total number of periods;i is the index of thermal units;N is the number of thermal units;Pi,t is the generation output of the ith thermal unit at time t;(ai,bi,ci) are the quadratic generation cost coefficients of thermal unit i;ρ is the penalty factor of the curtailed renewable energy;Rk,t is the true generation output of the renewable energy k at time t;is the forecasted generation output of the renewable energy k at time t,which is obtained using the time series method,artificial intelligence method,clustering method based on historical data,etc.[25],[26].

The constraints of the proposed optimization model can be explained and formulated as follows:

(1) Carbon emission limits

The total carbon emission in the entire area should be limited by the given total allowable carbon emission value TCE,such that

where CEi is the carbon emission value of the thermal unit i.

(2) Powerbalance

For power systems,power generation and load demand should be balanced for every period to ensure security,which gives

where j,k,n are bus indices of hydro units,renewable energy,and load demand sides,respectively;M,P,Q are the numbers of buses for hydro units,renewable energy,and load demand sides,respectively;Wj,t and Rk,t are the generation output of the hydro unit j and the renewable energy unit k at time t;Dn,t is the load demand at bus n at time t.

(3) Generation output limits

where and are the lower and upper bounds of the ith thermal unit generation output,respectively;andare the lower and upper bounds of the jth hydro unit generation output,respectively.

(4) Ramp rate limits

where and are the ramp-down and ramp-up limits,respectively,of the thermal unit i;and are the ramp-down and ramp-up limits,respectively,of the hydro unit j.

(5) Hydro energy balance

Hydro power can be considered as a type of energy storage that can flexibly adjust its generation output;however,the total energy over one day should be limited due to the water reservoir.Thus

where TWRj is the total energy over one day for the jth hydro unit.

(6) Renewable energy curtailment limits

To guarantee the feasibility of the optimization model,renewable energy may be curtailed in some extreme scenarios:

where is the renewable energy generation of the kth renewable energy station at time t.

(7) Power transmission limits

Power flow on the transmission line should be restricted within a given range due to the limited transmission capability.In the power market,the generation shift factors are widely used to characterize the linear relationship between the power injection and the power flow on the transmission lines.This can be formulated as

where l is the index of the transmission line;is the transmission limit of line l;Fl,t is the transferred power on the line l at time t;hl,i,hl,j,hl,k,and hl,n are generation shift factors of the line l to the buses i,j,k and n,respectively;ΩL is the set of transmission lines,including tie lines between countries.

(8) Energy contract over tie-lines

For interconnected power system economic dispatch between multiple countries,energy contracts should be considered.These contracts cover the fact that the total energy over one tie line should be equal to the contract power energy,known as the energy balance.Then,we have the following constraint:

where TFl is the specified contract energy on the tie line l,and ΩTL is the set of tie lines between countries.

1.2 Adjustable robust low-carbon dispatch model

The uncertainties associated with renewable energy resources present challenges for the deterministic economic dispatch model.To address this problem,in this study,we use robust optimization to find the optimal solution to counter the uncertain generation output of renewable energy sources.In this uncertain environment,the generation output should be adjusted to cope with renewable energy uncertainties.At the same time,the power flow may be changed accordingly.Nevertheless,the current policy anticipates that the self-balance requirement is implemented by all countries.Each country has its own area control error system to mitigate the error between the pre-dispatched and the true dispatched value,as shown in Fig.1.This leads to the following regulation in the optimization model:the power flow on tie-lines cannot be changed for any possible setting of the uncertainties.

Fig.1 Self-balance for each country under uncertainties

Letbe the base optimal solution under forecast renewable energy generation.Uncertainties will make the true optimal solution deviate from the base value,givingIt is clear that the true optimal solution is uncertain and will change with the uncertain boundary condition (i.e.,uncertain renewable energy generation).It is possible for the power flow and the specified regulation to be violated.The robust optimization will guarantee that all the constraints are strictly satisfied for any possible setting of the uncertainties.

First,we model the uncertainty by an interval as in (13).The equation suggests that the forecast renewable energy can be any value between the lower and upper bounds.

whereare the lower and upper bounds of the kth forecast renewable energy,respectively.The uncertainty will affect the decision Rk ,t,such that Rk ,t will become uncertain as well.Equation (9) suggests thatwe then split the interval into two parts.Whenthe uncertainty set will becomewhen the renewable energy generation is a deterministic value reflected as Rk ,t.This shows that the response of Rk ,t takes on a piecewise linear function.According to our previous work [27],this piecewise linear function can be expressed as

where ΔRk ,t is an introduced variable denoting the uncertainty length after the curtailment.Furthermore,the expression of the curtailment cost in the objective function(1) is reformulated as

In addition,the special regulation that the uncertainties should be self-balanced for the interconnected power system dispatch yields the following constraint:

It should be noted that the robust optimization is challenging to solve owing to constraint (14).Here,“”indicates that Rk ,t should be chosen for any possible value,which cannot be enumerated.To address this problem,we provide a reformulation using the adjustable robust optimization approach.

For a given we derive the optimal solutionThen,considering that there is an error between Rk ,t andthe generation output is adjusted from the base pointto the true valueusing the preset participation factors.This can be achieved using automatic generation control systems.Then,the generation output of thermal units and hydro units can be expressed as

whereare generation participation factors of the thermal units and hydro units,respectively.

For the general interconnected power system dispatch,we consider that there are K countries and that ω is the index of a country.Let ω be the set of buses in the ωth country.Since each country is responsible for its own uncertainties,the participation factors should satisfy (21);thus,if both i and j do not belong to the same country,the participation factors ai(j)k will be zero.

Substituting (19)-(21) into (3) gives

Substituting (19)-(21) into (12) gives

The robust optimization aims to guarantee the feasibility of all the constraints completely.The equality constraint is always satisfied owing to the adjustment in (19) and (20).The inequality constraints,however,will be applicable in the worst-case.For example,the reformulation of constraint(11) is derived as follows.Substituting (19) and (20) into (11)gives

We define

It can be determined that constraint (26) is in fact a double-sided constraint for the uncertain value Rk ,t.Then,we can reformulate (26) as

Furthermore,we define two vectors:

Other inequalities,including (4)-(9),can be reformulated using (30).We take (4) for instance.Substituting (19) into (4)gives

The robust optimization requires (31) to be satisfied for any ΔRk ,t.As a result,we choose the minimum value of the right-hand side,which gives

Finally,the proposed adjustable robust low-carbon dispatch for the interconnected power systems can be reformulated as

Participation factors for thermal and hydro units are determined using (21),(23),and (25).Then,the optimization problem presented above becomes a simple convex quadratic programming problem that can be efficiently solved using existing commercial solvers.

2 Case study

2.1 Data collection

In this section,we describe the verification of the proposed method using the IPS-NAC,whose topology is depicted in Fig.2.It includes six areas:North and Northeast China (NNC),Japan (J),the Russian far east (RFE),Mongolia (M),South Korea (SK),and North Korea (NK).For the IPS-NAC,energy resources in the six areas have different spatial distributions,which are complemented by the interconnected power systems.The characteristics of the IPS-NAC can be summarized as follows:①hydro power generation is mainly distributed in RFE and NNC,with total capacities of about 13.3 GW and 4.8 GW,respectively;②wind power generation is mainly distributed in RFE,M,and NNC,with total capacities of about 40.6GW,18.5 GW and 30.3 GW,respectively;③solar power generation is mainly distributed in M,and the capacity is about 40.8 GW.These parameters are listed in Table1.The renewable energy output and load demand over one day is shown in Fig.3.It should be noted that all the countries have similar profiles,but there are time differences in each area owing to their different longitudes.The profile for M is two hours later than those for NNC and RFE;the profiles for SK,NK,and J are two hours earlier than those for NNC and RFE.

Fig.2 Topology of the IPS-NAC

Fig.3 Curve of load demand and renewable energy generation

Notably,the carbon emissions are different for each unit type.In this study,we assume that the carbon emission coefficient is 0.8-0.9 t CO2/MWh for coal-fired units(mainly in NNC) and 0.5-0.7 t CO2/MWh for gas-fired units(mainly in RFE and J) is.After several nuclear accidents,J has placed emphasis on coal-fired units.J has also been developing new techniques for reducing carbon emissions[28].Therefore,the carbon emission coefficient of coalfired units in J is lower than in other countries,such as NK and NNC [29].The detailed information describing this can be found in Table1.

The proposed optimization model was tested on a personal laptop with an Intel Core 7 CPU (3.60 GHz),using the Gurobi optimization solver.

Table1 Generation Capacity and Type per Areas

Areas Types Number of Bases Generation Capacity/GW Carbon Emission Coefficient (tCO2/MWh)NNC Hydro 3 4.8 0 Wind 5 30.3 0 Coal-fired 54 120.7 0.8-0.85 M Wind 5 18.5 0 Solar 4 40.8 0 Coal-fired 12 10.4 0.85-0.9 NK/SK Wind 2 12.6 0 Gas-fired 21 26.9 0.90-0.95/0.85-0.90 J Wind 2 13.3 0 Coal-fired 12 22.5 0.6-0.65 RFE Hydro 6 13.3 0 Wind 4 40.6 0 Gas-fired 9 20.3 0.50-0.55

2.2 Results and discussions

The separated and interconnected modes are compared in Fig.4.The generation cost for the interconnected power systems is significantly reduced (from 0.594 to 0.305 million dollars),and the renewable energy curtailment is reduced from 60.20% to 0.98%.Since the renewable energy resources are distributed unevenly,the interconnected power systems provide more flexibility to accommodate renewable energy.When the renewable energy output increases in one country,it can be transferred to other countries through the tie lines in the interconnected mode.In contrast,for the separated mode,the increasing penetration of the renewable energy resources will be curtailed owing to the power balance constraint in each country.Moreover,after the interconnection,the carbon emissions caused by the power generation from the thermal units is significantly reduced as it is replaced by the renewable energy generation.Interconnected power systems will benefit by accommodating renewable energy.RFE can provide substantial hydro generation,M is suitable for solar generation,and the other areas (NNC,NK,SK,and J) have a considerably high wind power generation capacity.The total penetration of the renewable energy resources rises to approximately 78.43% from 22.78%,reflecting an interconnected power system with high penetration of renewable energy.However,there is still a need for thermal units because the load demand and renewable energy generation always fluctuate.During the night,solar generation is reduced to zero.To satisfy the load demand,thermal units are used as backups.During the daytime,generation using thermal units is reduced,and solar generation is increased.Hydro power units are used as energy storage units.

Fig.4 Results of the separated and interconnected modes

The impact of different uncertainty levels and carbon emission limits on the simulation results is investigated.According to (13),the uncertainty level χk,t can be defined as

Table2 shows that the optimal cost increases with increasing uncertainty levels.An uncertainty level of 0 represents a case with no uncertainty.However,in this case,randomly changing the renewable energy generation violates the transmission limits.This indicates that although the optimal cost is the lowest,the power system transmission security cannot be fully guaranteed.In other words,the optimal solution is not robust.Moreover,higher uncertainty levels provide more robust solutions but at a higher optimal cost.Therefore,the economy and security need to be balanced.In addition,when the uncertainty level is 0.25,the optimization model is infeasible,and there is no optimal solution.This indicates that we cannot guarantee the power system security at that level of uncertainty.Similarly,there is no optimal solution when the carbon emission limits are increased and the uncertainty level is 0.15.To address this problem,the transmission system is expanded to alleviate infeasible problems.Similarly,reducing the carbon emission limits will increase the optimal cost accordingly,while the total carbon emission will be reduced owing to the reduction in the limits.The carbon emission coefficients are different for different countries.NK and SK will reduce more thermal generation after interconnection because they have the highest carbon emission coefficients.Tables 3 and 4 show the simulation results after the transmission capacity level is increased to 1.5 and 2.0 times the original level.The tables show that with the increase intransmission capacity level,the optimal cost is reduced,and the original infeasible cases become feasible.

Table2 Optimal cost with transmission capacity level (1.0)

Uncertainty Level 0 0.05 0.10 0.15 0.20 0.25 Carbon Emission Limits(1e6tCO2)1.20 3.0492 3.0643 3.0815 3.1022 3.126 -1.15 3.0503 3.0662 3.0845 3.1056 3.13 -1.10 3.0553 3.0694 3.0883 3.1132 - -1.05 3.0607 3.0711 3.0994 - - -

Table3 Optimal cost with transmission capacity level (1.5)

Uncertainty Level 0 0.05 0.10 0.15 0.20 0.25 Carbon Emission Limits(1e6tCO2)1.20 2.8595 2.8698 2.8815 2.8971 2.9133 2.9305 1.15 2.8597 2.8699 2.8817 2.8974 2.9137 2.9309 1.10 2.8782 2.8917 2.9125 2.936 2.9609 2.9881 1.05 3.0272 3.0334 3.07978 - - -

Table4 Optimal cost with transmission capacity level (2.0)

Uncertainty Level 0 0.05 0.10 0.15 0.20 0.25 Carbon Emission Limits(1e6tCO2)1.20 2.8216 2.8310 2.8409 2.8534 2.8667 2.8801 1.15 2.8218 2.8312 2.8411 2.8537 2.8670 2.8804 1.10 2.8221 2.8316 2.8415 2.8541 2.8676 2.8812 1.05 2.9843 3.0138 3.0504 3.0885 3.1135 3.1539

Finally,the participation factors of the thermal and hydro units in (11) are shown in Fig.5.It should be noted that the regulation rule dictates that the uncertainty in a country should be adjusted by that country.Therefore,the participation factor matrix takes on five blocks.The row index of the block represents thermal and hydro units in a country,and the column index represents renewable energy resources.Meanwhile,the value of the participation factors reflects the capacity of units to adjust to uncertainties.The units with higher participation factors will be more resilient to uncertainties.In Japan,for example,the uncertainty of wind power connected to bus 95 is accommodated by thermal power units connected to bus 94 and bus 100 which are responsible for 72% and 28%,respectively.

3 Conclusions

In this study,we proposed an adjustable robust lowcarbon dispatch model for interconnected power systems.The aim was to promote the accommodation of renewable energy,with the operational constraints being strictly enforced in the uncertain environment associated with renewable energy.Results pertaining to interconnected power systems for Northeast Asian countries suggest that(1) the interconnected power systems can provide more flexibility for accommodating renewable energy generation;(2) increasing the uncertainty level and carbon emission limits increases the operational cost;however,the system security is improved and the total carbon emissions are reduced;(3) increasing the transmission capacity level benefits the dispatch,which can reduce the operational cost and prevent infeasible situations.In the proposed model,power users do not actively participate in the power system scheduling.In fact,demand response is gradually becoming one of the non-negligible factors in power systems.Future work will be focused on the positive effect of demand response on scheduling and cost of multi-area power systems,as well as the optimal transmission expansion for interconnected power systems.

Fig.5 Participation factors of thermal and hydro units

Acknowledgments

This work was supported by the Science and Technology Foundation of Global Energy Interconnection Group Co.,Ltd.(No.524500180012) and National Natural Science Foundation of China (No.51977166).

Declaration of Competing Interest

We declare that we have no conflict of interest.