CN105449669A - Power system emergency control optimization method considering power transmission line temperature characteristic - Google Patents

Abstract

The invention discloses a power system emergency control optimization method power transmission line temperature characteristic. The method comprises the steps of obtaining real-time running state information of a power grid and running environment information based on a (supervisory control and data acquisition) SCADA system and a (dynamic thermal rating) DTR system, and performing extended state evaluation considering the line temperature and thermal rating of the power system to obtain the thermal rating of the power transmission line; calculating an allowed emergency control time of the power system by combining a dynamic thermal rating theory; providing a new index for judging the thermal stability of the power system, and providing a safety margin for calculating the thermal stability of the power system; and establishing a system emergency control optimization model considering the power transmission line temperature characteristic, wherein the optimized result of the model is the emergency control policy. On the premise of ensuring that the system can eliminate the line power flow out-of-limit and voltage out-of-limit within the allowed time, the control cost can be the minimum; and namely, the running safety of the system is fully ensured, the operation economy is taken into consideration as well, and the control structure is more scientific and effective.

Description

A kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic

Technical field

The present invention relates to electrical engineering field, particularly relate to a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic.

Background technology

Electric power system is as mainstay of the national economy industry, it safely and steadily runs has very important effect to the development of whole national economy, the hysteresis quality of the sharply soaring and Electric Power Network Planning of power load in recent years, make the construction speed of electric power transmission network be difficult to catch up with the needs of economic development, the normal operating condition of network is more and more close to its transmission limit.Now operation of power networks is in more fragile state, and an accidental disturbance just can cause equipment overload, thus makes system enter the state of emergency, deals with improperly chain for initiation accident, even causes the whole network to have a power failure on a large scale, cause immeasurable economic loss.Therefore, in accident evolution, rapid development is effective Corrective control measure rationally, and eliminating more wire loop joint in time becomes the important means effectively reducing large-scale blackout and occur.

Whether conventional emergency control measure all meet the criterion of thermally-stabilised constraint using the hot current-carrying of maximum permission as system, American scholar Davis proposes Dynamic Thermal definite value technology (DynamicThermalRating, DTR) framework, people come to realise, circuit bearable load ability is not fixed value, but change with the change of ambient condition in time, and the essence limiting circuit transmission limit is temperature instead of electric current.The concept that Canada scholar FGalina proposed electric heating coordinate in 2005, makes the physical coupling relation between the electricity of transmission of electricity element, heat more clear.It is provide fixing control time based on empirical value that conventional emergency controls the determination of permission time, but under different weather environments and operation of power networks state, the dynamic process of line temperature is also different, unalterable setting is difficult to adapt to operation of power networks environment complicated and changeable, brings the conservative of Corrective control decision-making unavoidably or advances rashly.

Summary of the invention

Object of the present invention is exactly to solve the problem, a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic is provided, the present invention is based on electric power system thermal stability, in conjunction with Dynamic Thermal definite value framework, the system of providing allows the definite emergency control time, and set up the system emergency control and optimize model taking into account temperature of electric transmission line characteristic, under guaranteeing that system eliminates the prerequisite of the out-of-limit and voltage out-of-limit of Line Flow within the permission time, make regulate expenditure cost minimization, namely while fully ensureing system cloud gray model fail safe, performance driving economy is taken into account, control structure is science more, effectively.

To achieve these goals, the present invention adopts following technical scheme:

Take into account a POWER SYSTEM EMERGENCY CONTROL optimization method for temperature of electric transmission line characteristic, comprise the steps:

First, based on data acquisition and supervisor control SCADA (SupervisoryControlAndDataAcquisition) and Dynamic Thermal stabilization system DTR (DynamicThermalRating) system, obtain electrical network real-time running state information and running environment information, and electric power system is taken into account to the extended mode estimation of temperature of electric transmission line and transmission line Dynamic Thermal definite value, obtain transmission line Dynamic Thermal definite value;

In conjunction with the computational methods of transmission line Dynamic Thermal definite value, calculate electric power system and allow the emergency control time;

Propose to judge the heat-staple New Set of electric power system;

Emergency control time and the heat-staple New Set of electric power system is allowed to create the system emergency control and optimize model taking into account temperature of electric transmission line characteristic according to electric power system, the optimum results of model comprises: output of a generator adjustment, cutting load amount and generating set stoppage in transit capacity, the optimum results of model is emergency control policy.

Described running state information comprises transmission line voltage, electric current, power and temperature.

Described running environment information comprises wind direction residing for transmission line, wind speed, temperature, intensity of sunshine,

The calculation procedure of the hot definite value of described transmission line is as follows:

Under power system operation condition, temperature of electric transmission line change is relevant to the electric current of running environment and carrying, for transmission line, and the impact of the electric current that its variations in temperature is carried, wind speed, wind direction, sunshine and ambient temperature.

Transmission line equation of heat balance, to the mathematical expression of transmission line temperature of electric transmission line characteristic rule, embodies as follows:

I ²R(T _c)+Q _s＝Q _c+Q _r(1)

I represents the electric current of transmission line carrying, Q _srepresent wire and receive heat absorption at sunshine, Q _crepresent cross-ventilation heat radiation, Q _rrepresent wire radiation heat radiation, R (T _c) representation temperature is T _ctime conductor AC resistance.

The calculation procedure of described permission emergency control time is as follows:

When line current or external environment change, temperature of electric transmission line reach stable before, temperature of electric transmission line is the process of a dynamic change, and Transient Thermal equilibrium equation is as follows:

$m_l{C}_{pl}\frac{{\mathrm{dT}}_l\left(t\right)}{dt}=q_l\left(t\right)+q_s\left(t\right)-q_c\left(t\right)-q_r\left(t\right)---\left(2\right)$

q _l(t)＝I ²R _ref[1+α(T(t)-T _d)](3)

q _s(t)＝E _tA _tD(4)

q _c(t)＝A _c(T(t)-T _a(t))(5)

q _r(t)＝A _r[(273+T(t)) ⁴-(273+T _a(t)) ⁴](6)

Wherein, q _lt () represents resistance heating item, q _st () represents the item that absorbs heat sunshine, q _ct () represents heat loss through convection item, q _rt () represents heat-radiation heat-dissipating item; T represents the time, unit s; m _lfor the quality of unit conductor, kg/m; C _pfor the specific heat capacity of conductor material, unit J/ (kg DEG C); C _plfor the specific heat capacity of conductor material, J/ (kg DEG C); T (t) is transmission line operation mean temperature, DEG C;

T _lt () is circuit operation mean temperature, unit DEG C; I is the electric current flowing through conductor, unit A; R _reffor the specified ambient temperature T of conductor manufacturer regulation _dunder the resistance of unit length, unit Ω/m, transmission line resistance variation with temperature linear approximate relationship in setting range, α is the temperature coefficient of resistance of conductor material; T _afor the temperature of conductor surrounding environment, T _at () is the temperature of conductor surrounding environment, A _cfor convection transfer rate; A _rfor radiation heat transfer coefficient; E _tfor solar radiation power density; D is conductor diameter.A _tthe absorptivity of conductor;

In DTR system, wind speed in formula (2)-(6), wind direction, temperature, sunshine each meteorologic parameter all can survey acquisition, when electric power system suffers disturbance to enter the state of emergency, although now transmission line trend is out-of-limit, but due to the impact of thermal inertia, the change of temperature will lag behind electric current, and now temperature of electric transmission line enters among dynamic change.The time of its temperature dynamic change is obtained by public (2).

For realizing the quick calculating of emergency control time, before assumed fault occurs, transmission line is in approximate thermal equilibrium state, and line temperature is obtained by formula (1) approximate calculation, and at line energizing flow I after directly trying to achieve fault _lthe lower temperature of electric transmission line transient process T of effect _lt the change of () and temperature dynamic arrives maximum permissible value and reaches T _maxtime t _lbe expressed as:

$T_l\left(t\right)=T_a-\frac{K_1}{K_2}+(T_{l0}-T_a+\frac{K_1}{K_2})e^{K_{2}t}---\left(7\right)$

Wherein $K_1=(I_l^2{R}_{ref}+q_s)/{\mathrm{mC}}_p;$

$K_2=(I_l^2\mathrm{\α}-A_c-A_r{T}_{\mathrm{\Σ}})/m_l{C}_p;$

T _Σ＝[(T _a+273) ²+(T _s+273) ²](T _s+T _a+546)

$t_l=\frac{1}{K_2}ln\left(\frac{T_{max}-T_a+(K_1/K_2)}{T_0-T_a+(K_1/K_2)}\right)---\left(8\right)$

Wherein, T _l0the initial temperature of transmission line l before corresponding fault; T _sfor the conservative temperature of electric transmission line parameter adopted in abbreviation process, be the maximum permission operating temperature of transmission line, all transmission line t after fault _lreckling be and allow time of emergency control, have: t _min=min (t _l), l ∈ SL, namely emergency control need at t _mincurrent-carrying is eliminated out-of-limit in time.

The heat-staple New Set of described judgement system:

When the temperature of transmission of electricity elements all in system does not exceed its highest permission operating temperature, then system is heat-staple:

T _l(t)≤T _max(9)；

Wherein, T _l(t) for transmission line is in the temperature of t, T _maxfor the maximum permission operating temperature of transmission line.

The described emergency control Optimized model taken into account based on temperature of electric transmission line characteristic:

1) target function

With emergency control Least-cost for target, target function is expressed as:

minC _R+C _I+C _P(10)

Wherein, C _rfor generating set power output expense, C _ifor load unloading compensation expense, C _prepresent that generator compensation for stoppage is used;

Embody as follows:

$C_R\left(P_{Gi}\right)={\mathrm{\Σ}}_{i\∈SG}{a}_i{P}_{Gi}^2---\left(11\right)$

C _I(D _i)＝Σ _i∈SDb _iΔP _Di(12)

C _P(ΔP _Gi)＝Σ _i∈SPc _iΔP _Gi(13)

Wherein, SG is residue generating node set, and SD is load bus set; P _gibe respectively i node generating set to gain merit power output decision value and ground state value; Δ P _difor load bus is gained merit resection; a _ifor the power output cost coefficient of node i unit; b _ifor the unloading of node i load compensates value coefficient, c _ifor generator stoppage in transit cost coefficient, Δ P _gifor generator node is gained merit resection.

2) constraints

System power Constraints of Equilibrium:

Σ _i∈DiΔP _Di＝Σ _i∈SPΔP _Gi(14)

$(P_i-{\mathrm{\ΔP}}_{Gi})-U_i{\mathrm{\Σ}}_{j=0}^n{U}_j{B}_{ij}({\mathrm{\θ}}_{ij}-{\mathrm{\Δ\θ}}_{ij})=0---\left(15\right)$

Node voltage amplitude retrains:

$\begin{array}{cc}{\underset{\‾}{V}}_i\≤V_i\≤{\stackrel{\‾}{V}}_i& i\∈SB\end{array}---\left(16\right)$

Wherein, v _irepresent the lower limit of node voltage, represent the upper limit of node voltage, V _irepresent node voltage.

Load bus and generator node power excise and limit:

$P_{Di}^m\≤P_{Di}-{\mathrm{\ΔP}}_{Di}\≤P_{Di}^M---\left(17\right)$

$P_{Gi}^m\≤P_{Gi}-{\mathrm{\ΔP}}_{Gi}\≤P_{Gi}^M---\left(18\right)$

Wherein, for the upper limit of load bus active power, for the lower limit of load bus active power; for the upper limit of generator node active power, for the lower limit of generator node active power.

Unit power output retrains:

$\begin{array}{cc}{\underset{\‾}{P}}_{Gi}\≤P_{Gi}\≤{\stackrel{\‾}{P}}_{Gi}& i\∈SG\end{array}---\left(19\right)$

Wherein, represent output of a generator lower limit, represent the output of a generator upper limit, represent output of a generator;

Unit power output rate constraint:

$\begin{array}{cc}-t_{\min }{r}_{rampGi}^{\max }\≤P_{Gi}-P_{Gi}^0\≤t_{\min }{r}_{rampGi}^{\max }& i\∈SG\end{array}---\left(20\right)$

In formula, for the maximal regulated speed of unit i, t _minnamely be the time of the permission emergency control calculated by formula (8), for unit i is at t _minthe performance number increasing or reduce is allowed in time.

Line temperature retrains:

$m_l{C}_{pl}\frac{{\mathrm{dT}}_l\left(t\right)}{dt}=q_l\left(t\right)+q_s\left(t\right)-q_c\left(t\right)-q_r\left(t\right)$

T _l(t)≤T _max

Wherein, T _lt () is for circuit l is in the temperature of t.

Beneficial effect of the present invention is:

(1) operation of power networks state and environmental parameter is considered on the impact of the hot definite value of circuit, and then calculate the time margin that system allows emergency control, avoid and rely on the conservative of empirical value or advancing rashly property, emergency control Time Calculation science, accurately more.

(2) based on temperature of electric transmission line elasticity theory framework, the computational methods of the thermally-stabilised criterion of new electric power system and thermally-stabilised nargin are proposed.

Whether the heat-staple traditional criterion of electric power system has Line Flow out-of-limit in coefficient, using fixing circuit maximum permission ampacity as judging the circuit standard whether trend is out-of-limit.Temperature of electric transmission line elasticity theory is pointed out, the change of line temperature lags behind the change of current-carrying, line temperature is changed in the impact of this thermal inertia and asynchronism appears in current-carrying, and this quality factor limiting circuit transmission capacity is temperature, therefore the present invention proposes the thermally-stabilised criterion of new electric power system, namely when the temperature of transmission of electricity elements all in system does not exceed its highest permission operating temperature, then system is heat-staple.The present invention by proposing a kind of judge index of new electric power system thermal stability, and proposes the computational methods of new thermally-stabilised margin of safety, and compared with traditional method, add the heat-staple feasible security domain of electric power system, result is closer to actual value.

A kind of emergency control method taking into account temperature of electric transmission line characteristic is proposed, no longer using fixing thermocurrent as the out-of-limit judge index of circuit, but it is whether out-of-limit for judge index with line temperature, take into full account the thermal inertia impact of line temperature, add the feasible zone of optimization method, improve fail safe and the economy of emergency control method.

Accompanying drawing explanation

Fig. 1 is that operation states of electric power system divides schematic diagram;

Fig. 2 is DTR system global structure figure;

Fig. 3 is emergency control method flow chart.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

As shown in Figure 1, operation states of electric power system is divided into one of four states by Fig. 1, be respectively: secure normal state, dangerous normal condition, state to be restored, the state of emergency, suffers disturbance may be transitioned into dangerous normal condition at secure normal state, never can be transitioned into secure normal state by secure normal state by prevention and control; Suffer disturbance to be transitioned into the state of emergency in dangerous normal condition, dangerous normal condition can be transitioned into from the state of emergency by Corrective control; Can be transitioned into state to be restored from the state of emergency through emergency control, state to be restored controls to be transitioned into dangerous normal condition through over recovery.

As shown in Figure 2, the tension force of transmission line can be measured respectively by tension pick-up, solar radiation transducer, wind sensor, temperature sensor, the intensity of sunshine of surrounding environment, wind speed, wind direction, temperature, the information such as power system voltage, electric current, power can be recorded by power-supply system, these information all by data communication to data collection station, contact by forming between GPRS/GSM mobile communications network and monitoring management platform again, SCADA system also by data communication and monitoring management platform interrelated.

As shown in Figure 3, first by the data message of SCADA system and DTR system acquisition, extended mode estimation is carried out to electric power system, then the Dynamic Thermal definite value of computing electric power line, then by Transient Thermal equilibrium equation, calculate POWER SYSTEM EMERGENCY CONTROL time margin, on this basis emergency control Optimized model is solved, obtain generator and stop transport and cutting load capacity, finally implement emergency control policy.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (7)

1. take into account a POWER SYSTEM EMERGENCY CONTROL optimization method for temperature of electric transmission line characteristic, it is characterized in that, comprise the steps:

First, based on data acquisition and supervisor control SCADA and Dynamic Thermal stabilization system DTR, obtain electrical network real-time running state information and running environment information, and electric power system is taken into account to the extended mode estimation of temperature of electric transmission line and transmission line Dynamic Thermal definite value, obtain transmission line Dynamic Thermal definite value;

In conjunction with the computational methods of transmission line Dynamic Thermal definite value, calculate electric power system and allow the emergency control time;

Propose to judge the heat-staple New Set of electric power system;

Emergency control time and the heat-staple New Set of electric power system is allowed to create the system emergency control and optimize model taking into account temperature of electric transmission line characteristic according to electric power system, the optimum results of model comprises: output of a generator adjustment, cutting load amount and generating set stoppage in transit capacity, the optimum results of model is emergency control policy.

2. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, is characterized in that,

Described running state information comprises transmission line voltage, electric current, power and temperature.

3. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, is characterized in that,

Described running environment information comprises wind direction residing for transmission line, wind speed, temperature, intensity of sunshine.

4. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, is characterized in that,

The calculation procedure of the hot definite value of described transmission line is as follows: under power system operation condition, temperature of electric transmission line change is relevant to the electric current of running environment and carrying, for transmission line, the impact of the electric current that its variations in temperature is carried, wind speed, wind direction, sunshine and ambient temperature;

Transmission line equation of heat balance, to the mathematical expression of transmission line temperature of electric transmission line characteristic rule, embodies as follows:

I ²R(T _c)+Q _s＝Q _c+Q _r(1)

I represents the electric current of transmission line carrying, Q _srepresent wire and receive heat absorption at sunshine, Q _crepresent cross-ventilation heat radiation, Q _rrepresent wire radiation heat radiation, R (T _c) representation temperature is T _ctime conductor AC resistance.

5. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, it is characterized in that, the calculation procedure of described permission emergency control time is as follows:

When line current or external environment change, temperature of electric transmission line reach stable before, temperature of electric transmission line is the process of a dynamic change, and Transient Thermal equilibrium equation is as follows:

$m_l{C}_{pl}\frac{{\mathrm{dT}}_l\left(t\right)}{dt}=q_l\left(t\right)+q_s\left(t\right)-q_c\left(t\right)-q_r\left(t\right)---\left(2\right)$

q _l(t)＝I ²R _ref[1+α(T(t)-T _d)](3)

q _s(t)＝E _tA _tD(4)

q _c(t)＝A _c(T(t)-T _a(t))(5)

q _r(t)＝A _r[(273+T(t)) ⁴-(273+T _a(t)) ⁴](6)

Wherein, q _lt () represents resistance heating item, q _st () represents the item that absorbs heat sunshine, q _ct () represents heat loss through convection item, q _rt () represents heat-radiation heat-dissipating item; T represents the time, unit s; m _lfor the quality of unit conductor, kg/m; C _pfor the specific heat capacity of conductor material, unit J/ (kg DEG C); C _plfor the specific heat capacity of conductor material, J/ (kg DEG C); T (t) is transmission line operation mean temperature, DEG C;

T _lt () is circuit operation mean temperature, unit DEG C; I is the electric current flowing through conductor, unit A; R _reffor the specified ambient temperature T of conductor manufacturer regulation _dunder the resistance of unit length, unit Ω/m, transmission line resistance variation with temperature linear approximate relationship in setting range, α is the temperature coefficient of resistance of conductor material; T _afor the temperature of conductor surrounding environment, T _at () is the temperature of conductor surrounding environment, A _cfor convection transfer rate; A _rfor radiation heat transfer coefficient; E _tfor solar radiation power density; D is conductor diameter; A _tthe absorptivity of conductor;

In DTR system, wind speed in formula (2)-(6), wind direction, temperature, sunshine each meteorologic parameter all can survey acquisition, when electric power system suffers disturbance to enter the state of emergency, although transmission line trend is out-of-limit, but due to the impact of thermal inertia, the change of temperature will lag behind electric current, and temperature of electric transmission line enters among dynamic change; The time of temperature of electric transmission line dynamic change is obtained by formula (2);

For realizing the quick calculating of emergency control time, before assumed fault occurs, transmission line is in approximate thermal equilibrium state, and line temperature is obtained by formula (1) approximate calculation, and at line energizing flow I after directly trying to achieve fault _lthe lower temperature of electric transmission line transient process T of effect _lt the change of () and temperature dynamic arrives maximum permissible value and reaches T _maxtime t _lbe expressed as:

$T_l\left(t\right)=T_a-\frac{K_1}{K_2}+(T_{10}-T_a+\frac{K_1}{K_2})e^{K_{2}t}---\left(7\right)$

$K_1=(I_l^2{R}_{rcf}+q_s)/{\mathrm{mC}}_p;$

Wherein

$K_2=(I_l^2\mathrm{\α}-A_c-A_r{T}_{\mathrm{\Σ}})/m_l{C}_p;$

$T_{\mathrm{\Σ}}=\[{(T_a+273)}^2+{(T_s+273)}^2\](T_s+T_a+546)$

$t_l=\frac{1}{K_2}ln\left(\frac{T_{max}-T_a+(K_1/K_2)}{T_0-T_a+(K_1/K_2)}\right)---\left(8\right)$

Wherein, T _l0the initial temperature of transmission line l before corresponding fault; T _sfor the conservative temperature of electric transmission line parameter adopted in abbreviation process, be the maximum permission operating temperature of transmission line, all transmission line t after fault _lreckling be and allow time of emergency control, have: t _min=min (t _l), l ∈ SL, namely emergency control need at t _mincurrent-carrying is eliminated out-of-limit in time.

6. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, is characterized in that,

The heat-staple New Set of described judgement system:

When the temperature of transmission of electricity elements all in system does not exceed its highest permission operating temperature, then system is heat-staple:

T _l(t)≤T _max(9)；

Wherein, T _l(t) for transmission line is in the temperature of t, T _maxfor the maximum permission operating temperature of transmission line.

7. a kind of POWER SYSTEM EMERGENCY CONTROL optimization method taking into account temperature of electric transmission line characteristic as claimed in claim 1, is characterized in that,

The described emergency control Optimized model taken into account based on temperature of electric transmission line characteristic:

1) target function

With emergency control Least-cost for target, target function is expressed as:

minC _R+C _l+C _P(10)

Wherein, C _rfor generating set power output expense, C _ifor load unloading compensation expense, C _prepresent that generator compensation for stoppage is used;

Embody as follows:

$C_R\left(P_{Gi}\right)={\mathrm{\Σ}}_{i\∈SG}{a}_i{P}_{Gi}^2---\left(11\right)$

C _I(D _i)＝Σ _i∈SDb _iΔP _Di(12)

C _P(ΔP _Gi)＝Σi _∈SPc _iΔP _Gi(13)

Wherein, SG is residue generating node set, and SD is load bus set; P _gibe respectively i node generating set to gain merit power output decision value and ground state value; Δ P _gifor load bus is gained merit resection; a _ifor the power output cost coefficient of node i unit; b _ifor the unloading of node i load compensates value coefficient, c _ifor generator stoppage in transit cost coefficient, Δ P _gifor generator node is gained merit resection;

2) constraints

System power Constraints of Equilibrium:

Σ _i∈DPΔP _Di＝Σ _i∈SPΔP _Gi14)

$(P_i-{\mathrm{\ΔP}}_{Gi})-U_i{\mathrm{\Σ}}_{j=0}^n{U}_j{B}_{ij}({\mathrm{\θ}}_{ij}-{\mathrm{\Δ\θ}}_{ij})=0---\left(15\right)$

Node voltage amplitude retrains:

$\begin{array}{cc}{\underset{\‾}{V}}_i\≤V_i\≤{\stackrel{\‾}{V}}_i& i\∈SB\end{array}---\left(16\right)$

Wherein, v _irepresent the lower limit of node voltage, represent the upper limit of node voltage, V _irepresent node voltage;

Load bus and generator node power excise and limit:

$P_{Di}^m\≤P_{Di}-{\mathrm{\ΔP}}_{Di}\≤P_{Di}^M---\left(17\right)$

$P_{Gi}^m\≤P_{Gi}-{\mathrm{\ΔP}}_{Gi}\≤P_{Gi}^M---\left(18\right)$

Wherein, for the upper limit of load bus active power, for the lower limit of load bus active power; for the upper limit of generator node active power, for the lower limit of generator node active power;

Unit power output retrains:

$\begin{array}{cc}{\underset{\‾}{P}}_{Gi}\≤P_{Gi}\≤{\stackrel{\‾}{P}}_{Gi}& i\∈SG\end{array}---\left(19\right)$

Wherein, represent output of a generator lower limit, represent the output of a generator upper limit, represent output of a generator;

Unit power output rate constraint:

$\begin{array}{cc}-t_{\min }{r}_{rampGi}^{\max }\≤P_{Gi}-P_{Gi}^0\≤t_{\min }{r}_{rampGi}^{\max }& i\∈SG\end{array}---\left(20\right)$

In formula, for the maximal regulated speed of unit i, t _minnamely be the time of the permission emergency control calculated by formula (8), for unit i is at t _minthe performance number increasing or reduce is allowed in time;

Line temperature retrains:

$m_l{C}_{pl}\frac{{\mathrm{dT}}_l\left(t\right)}{dt}=q_l\left(t\right)+q_s\left(t\right)-q_c\left(t\right)-q_r\left(t\right)$

T _l(t)≤T _max

Wherein, T _lt () is for circuit l is in the temperature of t.