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Security region based security-constrained unit commitment

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Abstract

As the issues of security and stability of power systems are becoming increasingly significant, it is necessary to consider the constraints of the static voltage stability and transient stability, which are closely related to the active power dispatch of power systems, in the daily power dispatch, i.e. the unit commitment. However, due to the complexity of these constraints and limitation of the existing analysis methods, there has been no unit commitment model reported so far that can deal with these security constraints. On the other hand, as lack of effective measures to evaluate the security margin of dispatch schemes, it is difficult for power system operators to integrate both the security and economy of power systems in unit commitment. To resolve the above-mentioned issues, a security region based security-constrained unit commitment model is presented in the paper, which gives consideration to both the security and economy of power systems. For the first time, the active power flow constraint, the static voltage stability constraint and the transient stability constraint are taken into account in unit commitment at the same time. The model presented in the paper takes the operating cost, the branch transmission capacity margin, the static voltage stability margin and the transient stability margin as sub-objectives. By adjusting the weighting factors of sub-objectives, it is convenient to adjust the preference on the security and economy of power systems and reach a balance. The IEEE RTS-24 test system is adopted to validate the correctness and the efficiency of the proposed model.

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Abbreviations

R k :

k-dimension Euclid space where k is an integer number

N :

set of buses except the swing bus

B :

set of branches (including transformers)

CS :

critical cut-sets for static voltage stability

CS(k):

set of branches for cut-set k

CTS :

set of contingencies for transient stability

DIS :

set of dispatch schemes

p mgi :

minimal active power output of unit i

p mgi :

maximal active power output of unit i

P mgi :

minimal active power injection of bus i

P Mgi :

maximal active power injection of bus i

P M l :

maximal active power flow of branch l

T off i :

minimum-down time of unit i

T on i :

minimum-up time of unit i

Δp u i :

maximal start-up ramp rate of unit i

Δp d i :

maximal shut-down ramp rate of unit i

χ i ,γ i ,µ i :

start-up cost coefficients of unit i

a i ,b i ,c i :

cost function parameters of unit i

G :

real part of admittance matrix

G ij :

element of matrix G, i is the row number, j is the column number

B :

imaginary part of admittance matrix

B ij :

element of matrix B, i is the row number, j is the column number

x ij :

reactance of branch from bus i to bus j

T :

number of periods in the dispatch horizon (in the paper, it equals to 24 h)

n :

number of buses except the swing bus

n g :

number of units

n k :

number of branches of cut-set k

w t :

load weight of period t

w c :

cost weight

w tc :

branch transmission capacity margin weight

w sv :

static voltage stability margin weight

w ts :

transient stability margin weight

η (k,j)tc (t):

branch transmission capacity margin of dispatch scheme j for branch k in period t

η jtc (t):

branch transmission capacity margin of dispatch scheme j in period t

η jtc :

branch transmission capacity margin of dispatch scheme j in the dispatch horizon

η (k,j)sv (t):

static voltage stability margin of dispatch scheme j for cut-set k in period t

η jsv (t):

static voltage stability margin of dispatch scheme j in period t

η jsv :

static voltage stability margin of dispatch scheme j in the dispatch horizon

η (k,j)ts (t):

transient stability margin of dispatch scheme j for contingency k in period t

η jts (t):

transient stability margin of dispatch scheme j in period t

η jts :

transient stability margin of dispatch scheme j in the dispatch horizon

TC :

total operation cost of the power system

TC(t):

operation cost of the power system in period t SCi(t) start-up cost of unit i in period t

C i (t):

generation cost of unit i in period t

TC 0(t):

minimal operation cost of the power system in period t

S i (t):

normalized operation cost in period t

S i (t):

binary variable to indicate the state of unit i in period t; 0 means the unit is off, while 1 means the unit is on

X i (t):

integer variable to indicate the cumulative operating state of unit i; if X i (t)>0, it means that unit i is on before period t; otherwise, it means that unit i is off before period t

p gi (t):

active power output of unit i in period t

P gi (t):

active power output of bus i in period t

P di (t):

active power load of bus i in period t

P i t):

active power injection of bus i in period t, =P gi (t)−P di (t)

P l (t):

active power flow of branch l in period t

P :

vector of bus active power injection

D(t):

system demand in period t

R(t):

system spinning reserve requirement in period t

V i :

voltage amplitude of bus i

θ i :

voltage angle of bus i

θ ij :

angle of branch from bus i to bus j, θ ij = θ i −θ j

V :

vector of bus voltage amplitude

θ :

vector of bus voltage angle

Ω P :

active power steady state security region

Ω VS :

cut-set voltage stability region

Ω DS :

dynamic security region

α k i :

coefficient of active power steady state security region for branch k

β k i :

coefficient of cut-set voltage stability region for cut-set k

τ k i :

coefficient of dynamic security region for contingency k

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Authors and Affiliations

  1. Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, 300072, China

    YiXin Yu & Chao Qin

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  1. YiXin Yu
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  2. Chao Qin
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Yu, Y., Qin, C. Security region based security-constrained unit commitment. Sci. China Technol. Sci. 56, 2732–2744 (2013). https://doi.org/10.1007/s11431-013-5355-6

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