Research on an Improved Model and Method of Calculating Total Transfer Capability

Qian WANG

School of Electrical and Electronic Engineering

North China Electric Power University Changping District, Beijing 102206, China

E-mail: wangqian39080@163.com

Li-zi ZHANG School of Electrical and Electronic Engineering

North China Electric Power University Changping District, Beijing 102206, China

Abstract—As a market signal concerned by all parties, transmission capacity has an important economic value in the competitive electricity market. Because of the present model and method’s shortage of calculating Total Transfer Capabiliy (TTC) based on Optimal Power Flow (OPF), which may either lead to shed load in some nodes under a feasible base-case power flow state, or could not reasonably deal with an unfeasible base-case power flow state, an improved model and method of calculating TTC based on DCOPF is presented. Aimming at the maximum nodal load increments, and introducing the load loss model, the basic idea of calculating TTC in this paper is adding the non-negative constraint in nodal load increments under a feasible base-case state, or transfering the unfeasible base-case state to feasible base-case state by load loss model. The IEEE-30 bus test system study results show that the proposed model and method are effctive and practicable.

Keywords-electricity market; optimal power flow; Total Transfer Capability; base-case power flow state; load loss

I. INTRODUCTION

Free competition of electricity market not only cause many changes in the management and philosophy in power system all around the world, but cause many technical problems to be solved urgently in each link of power system operation. Total Transfer Capabiliy (TTC) and Available Transfer Capability (ATC)[1] are important indices for energy trading, which play important roles in ensuring the market transactions and safety of power systems. One of the problems to be solved is calculating TTC reasonably and accurately[2].

Research on transmission capability of power network begins at 20th century 70s, which named Transmission Interchange Capability (TIC)[3] at that time. In 1996, North American Electric Reliability Council (NERC) defined Available Transfer Capability (ATC), that is, ATC is a measure of the transfer capability remaining in the physical transmission network for further commercial activity over and above already committed uses. Mathematically, ATC is

The National Key Technology R&D Program (No. 2008BAA13B11).

defined as the TTC less the Transmission Reliability Margin (TRM), less the sum of existing transmission commitments (which includes retail customer service) and the Capacity Benefit Margin (CBM). In another word, accurate calculation of TTC is the foundation of calculating ATC.

Many researches of calculating TTC have been studied, which can be divided into deterministic and probabilistic calculation method. Deterministic calculation method includes Linear Distribution Factors (LDF)[4], Repeated Power Flow (RPF)[5], Continuation Power Flow (CPF)[6], Optimal Power Flow (OPF)[7-8], AC power flow based sensitivity[9-10], artificial intelligent algorithm[11], transient energy function method[12]. Probabilistic calculation method includes Status Enumeration[13], Monte Carlo simulation method[14], stochastic programming[15], Bootstrap[16].

The above-mentioned calculation methods are suitable for different calculation environment and precision, which are based on the assumption of a feasible base-case power flow state[2,17-18]. In order to simplify the complexity of problems, the present researches either do not calculate TTC under an unfeasible base-case power flow state, or make TTC to be zero. According to the defination of TTC, TTC would not be zero under some unfeasible base-case power flow state formed from N-1 fault condition in deterministic calculation method or random sampling in probabilistic calculation method. Furthermore, the present model and methods may lead to shed load in some nodes under a feasible base-case power flow state in calculating TTC based on OPF, which is unreasonable.

In order to solve above-mentioned problems, an improved model and method of calculating TTC based on DCOPF is presented in this paper. Aimming at the maximum nodal load increments, and introducing the load loss model, the basic idea of calculating TTC in this paper is adding the non-negative constraint in nodal load increments under a feasible base-case state, or transfering the unfeasible base-case state to feasible base-case state by load loss model. The IEEE-30 bus test system study results show that the proposed model and method are effctive and practicable.

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.990

4073

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.990

4073

II. MODEL OF CALCULATING TTC BASED ON DCOPF

The character of calculating TTC based on OPF is to determine TTC from generators set to loads set, which is restricted to every limit of power systems and could not vary other output of generators and load level. Time-varying TTC is decided by parameters of systems, operation state and operation constraints. The calculation methods of TTC are based on any assumption[2,17-18], such as a feasible base-case power flow state having a stable equilibrium points, the power system is secure and stable with enough damping under every operation state, at least one node has been achieved the upper or lower limit of voltage.

Model of calculating TTC based on OPF has two styles, one of styles can be described as[17,19].

. max ( ). . ( )

( )

obj fs t =

≤00

xg xh x

(1)

Where x is the control and state variables vector of systems, g(x) is equality constraints vector of power flow equations, h(x) is inequality constraints vector containing variable inequality and function inequality, which can reflect the system security constraints and operation limit constraints of elements, f(x) is the scalar objective function of calculating TTC, which have three styles.

1) The sum of active power in all tie-line from source zone SG to sink zone SL.

1,

( )G L

kmk S m S

f P∈ ∈

= ∑x (2)

2) The sum of load in sink zone SL.

2 ( )L

dii S

f P∈

=∑x (3)

3) The sum of active power in source zone SG and load in sink zone SL.

3 ( )G L

gk dmk S m S

f P P∈ ∈

= +∑ ∑x (4)

TTC is related to the change of nodal loads and output power of generators, but the model in formula(1) could not consider the variable patterns and regard active power in source zone SG and load in sink zone SL as control variables. To solve above problem, the model of calculating TTC based on OPF is proposed[20].

. max. . ( )

( )

objs t

λλ =≤

00

g x,h x

(5)

Where λ is a real parameter variable, which can reflect the transmission capability of loads and output power of generators under the given variable patterns, g(x,λ)=g(x)+ λb is the parametric power flow equation with variable λ, b is the direction of change of given loads and output power of generators.

Formula(5) considers the variable patterns of nodal loads and output power of generators, but the direction of change is gave, and could not be related to actual operation of systems. Literature[2] improves the model.

. max. . ( )

( )

d

d

objs t

λλ =≤

00

g x,h x

(6)

Where λd is a real parameter variable, g(x,λd)=g(x)+ λdbd, bd is the direction vector of nodes power injection change of systems, and the change of λd can only decide the variation of loads in sink zone. Regarding active and reactive power of generators as control variables in source zone, the optimal operation of generators would come ture in source zone.

III. AN IMPROVED MODEL AND METHOD OF

CALCULATING TTC

The above-mentioned models are on the basis of feasible base-case power flow states, which would not involve unfeasible base-case states. Because some unfeasible base-case power flow states may be formed from N-1 fault condition in deterministic calculation method or random sampling in probabilistic calculation method, it is necessary to discuss the calculation of TTC under unfeasible base-case states. Meanwhile, it is unreasonable that the models in foumula(1)-(5) may shed loads when maximizing TTC under feasible base-case power flow states. The model in foumula(6) which calculating bd based on forecast results of system loads in future, is suitable for the state of many positive growth in load node, and not suitable for the state of many negative growth.

An improved model and method of calculating TTC based on DCOPF is presented in this paper. Aimming at the maximum nodal load increments, and introducing the load loss model, the basic idea of calculating TTC in this paper is adding the non-negative constraint in nodal load increments under a feasible base-case state, or transfering the unfeasible base-case state to feasible base-case state by load loss model.

A. The model of calculating TTC based on DCOPF

,

min max

min max

1. max

2. max

. .

0 ( )

G L

L

G L L

kmk S m S

jj S

Gi Lj ji S j S j S

l l

G G G

L L

L L L

j L

obj P

obj E

s tP P E

E j S

∈ ∈

∈

∈ ∈ ∈

== +

≤≤ ≤

′ +′≤ ≤

≥ ∈

∑

∑

∑ ∑ ∑P B

P PP P PP = P EP P P

θ

(7)

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Where obj1 is the sum of active power in all tie-line from source zone SG to sink zone SL, obj2 is the sum of active power increment of load in sink zone SL, Ej is the active power increment of load in node j, P is the injected power vector in nodes, B is the nodal susceptance matrix, θ is the phase angle vector of nodal voltage, PGi is the output active power of generator i, PLj is the active power of load node j, Pl is the power flow vector on transmission line, P

—

l is the limit vector on transmission line, PG is the output power vector of generators, P′L is the load vector after increasing load, PGmin and PGmax are upper and lower limits of generator’s output power, PLmin and PLmax are upper and lower limits of nodal load.

B. Calculating model of load loss based on DCOPF [21-24]

min max

min max

1. min

2. min

. .

0 ( )

L

L

G L L

jj S

j jj S

Gi Lj ji S j S j S

l l

G G G

L L

L L L

j L

obj R

obj R C

s tP P R

R j S

∈

∈

∈ ∈ ∈

=′= −

≤≤ ≤′= −

≤ ≤≥ ∈

∑

∑

∑ ∑ ∑

i

P B

P PP P PP P RP P P

θ

(8)

Where obj1 is minimizing the amount of load loss in systems, obj2 is minimizing load loss cost in systems, Rj is active power loss in load node j, Cj is the unit load loss cost in load node j, PL is the load vector after shedded.

IV. THE CASE STUDY

In order to verify the validity of improved model and method of calculating TTC in this paper, TTC calculation have been done with the IEEE-30 bus test system

comparing feasible base-case states, unfeasible base-case states and other model of calculating TTC. IEEE-30 bus test system is shown in Figure 1, which is divided into 3 zones and each of them has 2 generators.

Figure 1. IEEE-30 Bus Test System

TTC among zone1, zone2 and zone3 have been calculated by formula(1), formula(6) and the improved model in this paper whose objective is maximizing the sum of active power increment of load in sink zone SL.

A. The feasible base-case power flow state TABLE I shows the computation results of TTC from

zone2 to zone1 under a feasible base-case power flow state by 3 models and methods of calculating TTC, and the results of output power of generators and loads.

The comparative results of TABLE I show that formula(1) can obtain maximal TTC and achieve optimal distribution of output power of generators and loads, that is, loads in zone1 have increased from 84.5 MW to 112.2345 MW. However, it is unreasonable to reduce some loads under a feasible base-case power flow state, such as loads in node 2 have reduced from 21.7MW to 6.785MW.

TABLE I. COMPUTATION RESULTS OF TTC FROM ZONE2 TO ZONE1 (UNDER A FEASIBLE BASE-CASE POWER FLOW STATE)

Models Actvie power output of generators in zone2 (MW) Active power of loads in zone1 (MW)

Node 13 Node 23 Total value Node 2 Node 3 Node 4 Node 7 Node 8 Total value

Base-state 26.46 15.805 42.265 21.7 2.4 7.6 22.8 30 84.5

Formula(1) 40 30 70 6.785 20.196 19.342 24.755 41.157 112.235

Formula(6) 5.1564 19.37 24.5264 15.732 3.0601 9.6902 16.529 21.749 66.7606

Model proposed in this paper 40 30 70 23.327 8.6761 14.925 27.664 37.642 112.2341 Although formula(6) can obtain a reasonable TTC by

considering the variable patterns with forecast of loads, which is suitable for the state of many positive growth in load node, and not suitable for the state of many negative growth in TABLE I, such as TTC has reduced from 84.5MW to 66.7606MW.

The results of TTC calculated by model proposed in

this paper is less than formula(1), but it can meet the shortcoming of formula(1) and formula(6), and obtain reasonable TTC with non-negative increment in nodal loads.

B. The unfeasible base-case power flow state The unfeasible base-case power flow state is formed

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by modifying the limits on transmission lines. TABLE II shows the computation results of TTC from zone2 to zone1

under an unfeasible base-case power flow state, and the results of output power of generators and loads.

TABLE II. COMPUTATION RESULTS OF TTC FROM ZONE2 TO ZONE1 (UNDER AN UNFEASIBLE BASE-CASE POWER FLOW STATE)

Models Actvie power output of generators in zone2 (MW) Active power of loads in zone1 (MW)

Node 13 Node 23 Total value Node 2 Node 3 Node 4 Node 7 Node 8 Total value

Base-state \ \ \ 21.7 2.4 7.6 22.8 30 84.5

Formula(1) \ \ \ \ \ \ \ \ \

Formula(6) \ \ \ \ \ \ \ \ \

Model proposed in this paper 21.572 17.233 38.805 21.7 2.4 7.6 22.8 18.433 72.933 The comparative results of TABLE II show that

because of the limits on transmission lines, base-case output power of generators can not be distributed reasonably. Therefore, reasonable results of TTC would not be obtained by models of formula(1) or formula(6). Getting a new feasible base-case power flow state by shedding some loads in the old state, model and method of calculating TTC based on DCOPF in this paper can obtain reasonable results, such as TTC from zone2 to zone1 is 72.933MW.

V. CONCLUSION

Because of the present model and method’s shortage of calculating Total Transfer Capabiliy (TTC) based on Optimal Power Flow (OPF), which may either lead to shed load in some node under a feasible base-case power flow, or could not reasonably deal with an unfeasible base-case power flow, an improved model and method of calculating TTC based on DCOPF is presented. Aimming at the maximum nodal load increments, and introducing the load loss model, the basic idea of calculating TTC in this paper is adding the non-negative constraint in nodal load increments under a feasible base-case state, or transfering the unfeasible base-case state to feasible base-case state by load loss model. The IEEE-30 bus test system study results show that the proposed model and method are effctive and practicable.

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