Role of optimal transmission switching in accommodating renewable energy in deep peak regulation-enabled power systems

0 Introduction

To alleviate the shortage of fossil energy and the pollution caused by fossil fuel combustion,the global energy structure is being reformed,and clean,low-carbon,safe,and efficient modern energy systems are being built [1-4].According to The thirteenth Five-Year Plan for renewable energy development formulated by the National Development and Reform Commission of China,the proportion of non-fossil energy in primary energy consumption will reach 15% by 2020 and 20% by 2030 [5].Thus,promoting the use of renewable energy and reducing system operating costs have become the focus of current research.

In [6],an optimal bidding framework for a V2G (Vehicle to Grid)-enabled regional energy internet is proposed considering the participation in electricity and carbon trading markets;this framework can facilitate the accommodation of renewable energy.Reference [7]discusses the role of demand-side response in promoting renewable energy accommodation.Deep peak regulation is adopted to conduct “flexible transformation” of thermal power units,to ensure that thermal power units can operate below the minimum technical output [8-10].Reference [11]analyzes the economics of deep peak regulation considering largescale integration of wind power into grids.Reference [12]presents the relationship between the depth of peak regulation and wind curtailment volume.Reference [13]proposes a deep peak reserve trading strategy to promote the accommodation of renewable energy.In [14],a peak-regulating compensation mechanism is established to utilize the potential of deep peak regulation.However,the integration of a large amount of renewable energy into power grids causes network congestion[15]-[18].Thus,the deep peak regulation capacity of thermal power units cannot be fully utilized.

Therefore,it is necessary to improve the capacity for grid-side accommodation of renewable energy.Extension of transmission lines is a possible solution,but it is very expensive.Reference [19]proposed a trilevel expansion planning model for transmission networks considering transmission cost allocation.This model can reduce transmission line power flows,thus obviating the need for transmission line expansion.Therefore,this is a suitable choice for improving the accommodation of renewable energy in existing transmission systems.Optimal transmission switching (OTS) and other transmission topology control technologies are also effective measures to improve the utilization rate of transmission facilities and the operation efficiency of power systems [20,21].Network topology control can alleviate transmission congestion,improve the economic efficiency of power system operation,and promote the accommodation of renewable energy.Thus,this method has been widely used in power systems [22-25].Previous studies have analyzed renewable energy accommodation at both the generation side and grid side.However,the effectiveness of OTS in utilizing the potential of deep peak regulation and promoting the accommodation of renewable energy remains to be analyzed quantitatively.

To address the aforementioned research gap,in this study,OTS is considered as an important means of accommodating renewable energy.It is integrated into the operation of a power grid along with deep peak regulation of thermal power units,thereby forming an interactive mode of coordinated source and network operation.The major contributions of this study are as follows:1) A stochastic unit commitment model considering deep peak regulation and OTS is established.2) The role of OTS in promoting the accommodation of renewable energy is analyzed quantitatively.

The remainder of this paper is organized as follows:Section 1 presents the proposed framework for integrating OTS with deep peak regulation.In Section 2,the stochastic unit commitment model with OTS and deep peak regulation is described.The purpose of this model is to minimize the total cost of power generation,start-stop,and deep peak regulation while satisfying constraints regarding unit operation and network security.Section 3 presents the results of the case studies conducted.Finally,Section 4 concludes this paper.

1 Framework

Unlike previous studies,this study was conducted to quantitatively analyze the effect of grid structure flexibility on deep peak regulation for accommodating a large proportion renewable energy in power systems.

At night,when substantial wind power is available,thermal power units participate in deep peak regulation to ensure that they can operate below the minimum technical output.However,due to network congestion,sufficient renewable energy cannot be integrated to the grid.Hence,peak regulation cannot be fully utilized,and the capacity to accommodate renewable energy cannot be improved significantly.However,with the incorporation of OTS,the flexibility of the power grid can be improved by changing the grid structure,which alleviates network congestion and thereby facilitates the accommodation of renewable energy,as shown in Fig.1.

Fig.1 Comparison between renewable energy accommodation without (left) and with (right) OTS

2 System model

Considering the fluctuation of wind power,this paper proposes a two-stage stochastic optimization model [26].The problem of stochastic unit commitment with wind farms is a mixed-integer programming problem with multiple scenarios,time periods,and units [27].Such problems can be expressed as shown in the following sections.

2.1 Deep peak regulation model

The deep peak regulation constraints of the generator sets are shown in (1) and (2):

where Δi,s ,t is the deep peak regulation,and is the upper limit of deep peak regulation.

Equation (1) presents the lower and upper limits at which power units can operate below the minimum output.Equation (2) represents the constraint for depth of peak regulation.

2.2 OTS model

The OTS model used in this study is shown in (3) - (6):

where Ml is an arbitrarily large number,N_open is the maximum number of open lines,and zl,t is a binary variable describing the state of the transmission line,where 0 and 1 indicate that the line is open and closed,respectively.

Equations (3) to (5) represent the power flow constraints for the transmission line with transmission switching.When zl,t = 0,(3) to (5) are relaxed.When zl,t = 1,(3) to(5) represent constraints for DC power flow.Equation (6)represents the constraint regarding the maximum number of open lines.

2.3 System model

The objective function of the proposed system model is shown below:

subject to (1) to (6) and the following constraints:

where i is the index for the generators and loads,t is the time interval,s denotes the scenario,and l represents the transmission line.is the power output of generator i in scenario s at time interval t.is the power output of wind turbine i in scenario s at time interval t.is the power consumed by load i in scenario s at time interval t.ri,s,t is the reserve power of generator i in scenario s at time interval t.ui,t is the commitment status of generator i in scenario s at time interval t.is the flow of line l in scenario s at time interval t. andare the upper and lower limits of the power output of generator i,respectively.is the upper limit of the power output of wind turbine i.is the reserve limit of generator i at interval t.is reserve requirement at time interval t.is the upper power flow limit of transmission line i.θfr ( l ), s ,t and θto ( l ), s ,t are the phase angles of the start and end buses of line l in scenario s at time interval t,respectively.θi,s ,t is the phase angle of bus i in scenario s at time interval t.θ andare the upper and lower limits of the phase angles,respectively.ai,bi,and ci are the constant,primary,and quadratic term coefficients of the cost function of the generator set,respectively.CiU and CiD are the startup and shut-down costs of the generator,respectively.αi ,t and βi ,t are the indicator variables of generator start-up and shut-down,respectively.γ s is the probability of scenario s.RiU and RiD are the climbing and landslide rates of generator i,respectively.TiOn and TiOff are the minimum continuous operation and continuous shut-down times of generator i,respectively.lineifr and lineito are the lines with bus i as the start and end buses,respectively.

The objective function (7) determines the scheduling plan for units and the renewable energy output by minimizing the cost of units.Equations (8) to (10) represent the reserve constraints of the units,while (11) and (12)represent the ramp constraints of the generator sets.Equations (13) and (14) represent the constraints for the starting and shutting times of the generator sets.Equation(15) represents the constraints for the power output of the wind turbine.Equation (16) represents the phase angle constraint.Equation (17) represents the constraint regarding bus power balance.

3 Case study

3.1 Data description

The program for solving the proposed model was developed using MATLAB R2016a.The optimization solver used was CPLEX 12.4 [28].To validate the proposed model,simulation-based case studies were conducted using the IEEE 30-bus system.The topology and generator cost function of the IEEE 30-bus system were obtained from the parameter description of the IEEE standard system.To address the uncertainties in load demands and renewable energy availability,scenario-based stochastic programming was adopted [29].The user load curve and the renewable energy data were obtained from actual users in Texas [30],as shown in Figs.2 and 3.

Fig.2 Wind power data

Fig.3 Load data

To evaluate the effect of OTS on renewable energy accommodation,the simulation results were compared using three methods,as shown in Table1.

The differences between the three methods in terms of renewable energy accommodation rate and generation cost are compared in detail in the following subsections.

Table1 Method description

M1 Proposed method,wherein OTS and deep peak regulation are considered together M2 Deep peak regulation is considered without OTS M3 Neither deep peak regulation nor OTS is considered

3.2 Base case

This section introduces the optimization results obtained for M1.The results include the UC(Unit Commitment)schedule,OTS schedule,system cost,and renewable energy accommodation rate.

The UC schedule is shown in Table2.The OTS schedule is shown in Fig.4,where 0 and 1 indicate that the line is open and closed,respectively.

Table2 UC schedule

Time/h Unit (1-8)1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 9 1 0 0 0 0 0 0 0 10 1 1 1 0 0 0 0 0 11 1 1 1 1 1 1 1 1 12 1 1 1 0 1 0 1 1 13 1 1 0 0 1 0 1 1 14 1 1 0 0 1 0 1 1 15 1 1 0 0 1 0 1 1 16 1 1 0 0 1 0 1 0 17 0 1 0 0 1 0 0 0 18 0 0 0 0 1 0 0 0 19 0 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0 0 22 0 0 0 0 0 0 0 0 23 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 0 0

Fig.4 OTS schedule

The renewable energy accommodation rate and generation cost obtained using the proposed method are 78.32% and $79,983,respectively.

3.3 Comparative study

This section compares the renewable energy accommodation and system costs obtained using the three aforementioned methods.

Fig.5 shows the accommodation of renewable energy,while Fig.6 shows the accommodation rate of renewable energy.The results show that the accommodation rate of renewable energy for M3 was 2.55% higher than that for M2.Compared with that for M1,the accommodation rate was 1.9% higher for M2.Table3 compares the system operating costs and accommodation rates of renewable energy for the three methods.

Fig.5 Comparison of wind power accommodation for the three methods

Fig.6 Comparison of accommodation rates of wind power

Table3 Comparison of system operation costs

Method System operation cost/$ Accommodation rate/%M1 79,983 78.77 M2 84,981 76.22 M3 89,787 74.32

The results of the case study show that the proposed method affords a higher renewable energy accommodation rate,greater wind utilization,and lower system operating costs than the method with only deep peak regulation.This verifies the effectiveness of the proposed method.

3.4 Sensitivity analysis

This section describes the influence of the peak regulation depth and maximum number of open lines on the accommodation of renewable energy and system operation cost in a power system with a large proportion of renewable energy.

Fig.7 shows the changes in system operation cost and renewable energy accommodation with an increase the peak regulation depth when the maximum number of open lines is 5.The simulation results show that increasing the peak regulation depth can reduce the system operation cost and improve the accommodation rate of renewable energy.

Fig.8 shows the changes in system operation cost and renewable energy accommodation with an increase in the maximum number of open lines when the peak regulation depth is 25%.The simulation results show that increasing the maximum number of open lines can reduce the system operation cost and improve the accommodation rate of renewable energy.Thus,enhancing the flexibility of the grid structure can promote the accommodation of renewable energy.The flexibility of the power system considered in this study can be improved the most when the maximum number of open lines is 3.

Fig.7 System operation cost and renewable energy accommodation with increase in peak regulation depth

Fig.8 System operation cost and renewable energy accommodation with increase in maximum number of open lines

4 Conclusions

In view of the difficulty in accommodating large proportions of renewable energy into power grids,this paper proposes a stochastic unit commitment model considering deep peak regulation and OTS.The role of OTS in promoting the accommodation of renewable energy is quantitatively analyzed.Case study results show that OTS with deep peak regulation can effectively reduce the operating cost of the system,as well as promote the accommodation of renewable energy.A sensitivity analysis shows that the accommodation of renewable energy can be promoted by increasing the peak regulation depth of thermal power units or increasing the number of open lines within a certain range in the power system.

However,OTS introduces several complex constraints and variables,which complicates the calculations involved in the original problem.Therefore,future research should explore the prospect of using the decomposition method to reduce the complexity of the original problem.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (No.U1966204) and the China State Key Lab.of Power System (SKLD19KM09).

Declaration of Competing Interest

We declare that we have no conflict of interest.