CN112803486A - Unit combination optimization method considering dynamic frequency constraint under wind power integration - Google Patents
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Abstract
The invention relates to a unit combination optimization method considering dynamic frequency constraint under wind power integration, belonging to the field of power system operation scheduling; according to the method, dynamic frequency constraint is considered on the basis of a traditional unit combination model to improve the frequency stability after large-scale wind power integration, a wind power integration system frequency response model is established according to a fan response mechanism, a dynamic frequency quantitative evaluation index is deduced, and a wind power integration system unit combination optimization model considering the dynamic frequency constraint is constructed. The method has the advantages and the effect of ensuring the frequency stability of the power system after the large-scale wind power integration, can effectively improve the dynamic frequency response of the power system, improves the frequency stability of the system, and further provides a guidance basis for the large-scale wind power integration.
Description
Technical Field
The invention belongs to the field of operation scheduling of power systems, and particularly relates to a unit combination optimization method considering dynamic frequency constraints under wind power integration.
Background
The proportion of new energy power generation represented by wind power in a power system is gradually increased, and the wind power integration scale of China is estimated to reach more than 2.1 hundred million kW in 2020, and the proportion is increased to 11% of the total power generation capacity. Although the large-scale wind power access system can effectively relieve the energy crisis, the uncertainty presented by the wind power output and the low inertia characteristic presented by the wind turbine generator to the power grid bring challenges to the frequency stability of the power grid.
In a traditional power system, a power supply side mainly comprises a thermal power generating unit with stable output, and when a load on a demand side is switched, the system frequency fluctuates. After large-scale wind power integration, the output stability of the power supply side is reduced, the fluctuation range of the steady-state frequency of the system is increased, and the reserve capacity of the power system needs to be improved to stabilize the output fluctuation of the wind power. But at the same time, the increase in spare capacity will reduce the economics of system operation. On the other hand, after large-scale wind power integration, the dynamic frequency stability problem of the power grid is caused by the low inertia characteristic of the wind turbine generator. With the gradual increase of the permeability of wind power in a power system, the access of a wind power unit replaces part of thermal power units, and the inertia level of the system is reduced, so that the dynamic frequency stability of a power grid is threatened. The reduced inertia will weaken the system's resistance to the disturbing power. Under the condition that the system has power shortage, the frequency change speed of the low-inertia system is high, the frequency drop amplitude is large, and once the frequency drops to the setting value of the low-frequency load shedding protection device, the load shedding action can cause large-area power failure of the system.
Under large-scale wind power grid connection, the traditional unit combination strategy only considers the power balance constraint of the system, the maximum and minimum output constraints of the unit, the minimum start-stop time constraint of the unit and the power flow constraint under the steady state condition. The traditional unit combination strategy does not contain system frequency constraint, and the problem that the system frequency is out of limit when disturbance occurs under the strategy.
Disclosure of Invention
The invention aims to provide a unit combination optimization method considering dynamic frequency constraint under wind power integration, and aims to solve the technical problem that system frequency is out of limit when disturbance is caused due to the fact that dynamic frequency constraint is not considered in a traditional unit combination strategy under the wind power integration condition.
In order to achieve the purpose, the specific technical scheme of the unit combination optimization method considering dynamic frequency constraint under the condition of wind power integration is as follows:
according to the invention, the dynamic frequency constraint is considered on the basis of a traditional unit combination model so as to improve the frequency stability after large-scale wind power integration. According to a fan response mechanism, a frequency response model of the wind power grid-connected system is established, and a dynamic frequency quantitative evaluation index is deduced. The method comprises the following steps of constructing a wind power grid-connected system unit combination optimization model considering dynamic frequency constraints, wherein the model is based on the following objective functions and constraint conditions:
the objective function of the invention is defined as the lowest system power generation cost:
in the formula: t is the number of hours of a scheduling cycle; ps,i,tAnd Pw,i,tGenerating power of an ith thermal power generating unit and generating power of an ith wind field at the moment t respectively; u shapes,i,tThe operation state of the ith thermal power generating unit at the moment t is shown; n and m are the number of thermal power generating units and the number of wind power plants; a isi、biAnd ciGenerating cost coefficients of the ith thermal power generating unit; k is a radical ofiThe operation and maintenance cost coefficient of the ith wind field; b isiAnd the starting cost of the ith thermal power generating unit is saved.
The constraint conditions of the invention are as follows:
Us,i,tPs,i,min≤Ps,i,t≤Us,i,tPs,i,max (3)
-Ri,down≤Ps,i,t-Ps,i,(t-1)≤Ri,up (4)
Gp(Hset,Kset,Tset,Ust)≥fc (9)
the formula (2) to the formula (9) are respectively power balance constraint, thermal power unit output constraint, thermal power unit climbing constraint, system standby constraint, thermal power unit start-stop time constraint, power flow constraint, wind field output constraint and dynamic frequency constraint. In the formula: g is the number of load nodes; pL,i,tRepresenting the planned load of the node i at the time t; ps,i,minAnd Ps,i,maxRespectively a small output and a maximum output of the ith thermal power generating unit; λ is a spare coefficient; t isS,iAnd TO,iThe minimum startup and shutdown hours of the ith thermal power generating unit are respectively; xS,i,(t-1)，XO,i,(t-1)The number of continuous startup and shutdown hours of the ith thermal power generating unit is respectively; y is the number of the branches; a. thei,lA sensitivity system of the node i to the line l; pl,minAnd Pl,minRespectively, the minimum and maximum transmission power of the line l; pw,i,t,fPredicting the generated power for the ith wind field at the time t; hsetIs a generator inertia coefficient vector; u shapestA generator start-stop state vector is obtained in a time period t; kset is the gain coefficient vector of the speed regulator; t issetIs a vector of the time constant of the governor, fcIs the lowest frequency limit.
A unit combination optimization method considering dynamic frequency constraints under wind power integration comprises the following steps:
In the above method for optimizing a unit combination considering dynamic frequency constraints under wind power integration, the method for calculating the lowest point of the dynamic frequency of the lower layer sub-problem in step 2 is as follows:
wherein: f. ofminIs the lowest value of the frequency under the disturbance condition; f. of0Is the system fundamental frequency; k is a static difference adjustment coefficient; t is the time constant of the speed regulator; d is a damping coefficient; delta PstepIs the disturbance power magnitude; heqIs the system inertia time constant; omeganAnd xi are the natural frequency and the damping coefficient, respectively; t is tminTime is the lowest point frequency. OmeganXi and tminThe expression is as follows:
since the optimization model has high nonlinear characteristics due to the multi-layer nested function in the formula (10), the invention introduces the scoreThe segment linearization technique processes the calculation of the lowest value of the dynamic frequency. The left expression of the unequal sign in formula (10) is regarded as Hset、Kset、TsetAnd UstAnd is denoted as G (H)set，Kset，Tset，Ust) Then define G (H)set，Kset，Tset，Ust) Piecewise linearization function of (1):
in the formula: xsetIs Ust、Hset、KsetAnd TsetA set of formed variables; alpha is alphaiAnd betaiIs a linearization coefficient; p is the number of segments.
After the piecewise linearization processing, the nonlinear constraint shown in equation (10) is rewritten as a linear constraint:
Gp(Hset,Kset,Tset,Ust)≥fc (15)
in the above method for optimizing a unit combination considering dynamic frequency constraints under wind power integration, the Benders decomposition method in step 3 is:
in the sub-problem solution, a penalty variable phi is introduced in the formula (15)tConverting the lowest point frequency out-of-limit detection problem into a penalty variable minimization problem comprises the following steps:
min fs＝Φt (16)
s.t.-Gp(Hset,Kset,Tset,Ust)-Φt≤-fc (17)
and solving the subproblem model by using a conventional linear programming algorithm to obtain a penalty variable in each period. If the penalty variable is larger than 0 in a certain period, the unit combination in the period has the lowest frequency out-of-limit condition. At this point, the Benders cut is introduced in the main problem, with Benders feedback constraints as follows:
in the formula Gp *(Hset，Kset，Tset，Ust) Calculated from the main problem.
And the Benders cuts feed back the frequency out-of-limit degree of the lowest point of the system to the main problem optimization model in a constraint condition mode, so that the current unit combination result is corrected.
The unit combination optimization method considering dynamic frequency constraint under wind power integration has the following advantages: the method has the advantages and the effects of ensuring the frequency stability of the power system after large-scale wind power integration, and enough thermal power generating units are kept in a starting state during power generation planning before a day. Compared with the traditional unit combination model, the model can effectively improve the dynamic frequency response of the power system, improve the system frequency stability and further provide a guidance basis for large-scale wind power integration.
Drawings
Fig. 1 is a load curve and a wind power prediction curve in example 1.
Fig. 2 is a frequency response time domain trace in example 1.
Fig. 3 is a frequency distribution of the 24-period lowest point in example 1.
FIG. 4 is a model decomposition diagram of the present invention.
FIG. 5 is a flow chart of solving the frequency constraint-containing unit combination model of the present invention.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, the following describes in detail a method for optimizing a unit combination considering dynamic frequency constraints under wind power integration according to the present invention with reference to the accompanying drawings.
Example 1:
the method provided by the invention is generally suitable for solving the combination scheme of the wind power grid-connected power system unit, is limited to space, and the embodiment carries out calculation analysis on the 10-machine power system containing the wind power grid-connected power system to verify the validity of the model, and compares the validity with the combination result of the traditional unit, wherein the specific conditions are as follows:
the method is used for verifying the improvement of the dynamic frequency of the system by the extracted unit combination model in the 10-machine system containing the wind power integration. Considering the day-ahead scheduling time scale, the planned scheduling period is 24h, and a 24h load curve and a wind power output curve are shown in fig. 1. The fundamental frequency of the arithmetic system is 50Hz, the minimum frequency limit value is 49.2Hz, and the power shortage in each time interval is 15% of the total load in the corresponding time interval. For convenience of comparative analysis, a traditional unit combination result under a conventional constraint condition is recorded as C-1, and a unit combination result considering dynamic frequency constraint is recorded as C-2.
Table 1 compares the maximum frequency deviations for each time period C-1 and C-2. And in each time period, the maximum frequency deviation of the C-1 system is greater than C-2. Especially in the early morning hours (23 h to 3h), the C-1 maximum frequency deviation increases significantly. The thermal power generating unit is in a single-machine starting state under the scheme of the early morning period C-1, and the load power of the system is mainly provided by wind power.
TABLE 1.24 time-Domain maximum frequency deviation
By taking the minimum load period (1h) and the maximum load period (12h) as examples, the frequency responses under the schemes of C-1 and C-2 are calculated according to the starting and stopping states of the thermal power unit in Table 1, as shown in FIG. 2. In the 1h time period, only the Unit 6 in the C-1 scheme is in a starting state, so that the frequency modulation capability of the system is insufficient, and the frequency drop amplitude is larger after power shortage occurs. The system frequency fell to a minimum of 48.75Hz 2.5s after the disturbance, exceeding the limit of 0.45 Hz. In the same time period, the frequency response under the C-2 scheme is improved, and the system frequency falls to the minimum value of 49.28Hz within the limit range after the disturbance for 3.4 s.
Compared with the 1h time period, the starting number of the thermal power generating units in the C-1 scheme is increased in the 12h time period, and the Unit 1, the Unit 2, the Unit 4 and the Unit 5 are in a starting state at the same time. However, the system disturbance power increases during the 12h period, so that the lowest point frequency under the C-1 scheme is still outside the limit range. The system frequency fell to a minimum of 49.07Hz 3.2s after the disturbance, exceeding the limit of 0.13 Hz. In the same time period, 7 thermal power generating units are in a starting state in the C-2 scheme, Unit 3, Unit 6 and Unit 8 are added on the basis of the C-1 scheme, and the dynamic frequency of the system is improved to some extent. The system frequency fell to a minimum of 49.29Hz, within the limits, 3.9s after the disturbance. After the dynamic frequency constraint condition is considered, the system frequency is improved by 0.53Hz in the 1h period, the system frequency is improved by 0.22Hz in the 12h period, and the system frequency stability is improved.
FIG. 3 compares the distribution of nadir frequencies over 24 periods for the C-1 and C-2 schemes. Under the C-1 scheme, the lowest point frequency fluctuates within the range of 48.95 +/-0.21 Hz, and the lowest point frequency is larger than the set limit value of 49.2 Hz. Under the C-2 scheme, the lowest point frequency fluctuates within the range of 49.3 +/-0.03 Hz, and the lowest point frequency is lower than the set limit value of 49.2 Hz. Therefore, after the frequency stabilization constraint is considered, the dynamic frequency response of the system in each time period is improved, and the lowest point frequency fluctuation amplitude is restrained.
The cost of power generation under 2 scenarios is shown in table 2. To meet the dynamic frequency constraints of the system, the total power generation cost under the C-2 scheme is increased by 1.85% compared with that under the C-1 scheme.
TABLE 2 comparison of Power Generation costs for C-1 and C-2 schemes
When the dynamic frequency constraint is considered, the power generation cost slightly increases. However, under the C-2 scheme, the dynamic frequency of the system in all periods satisfies the constraint. Compared with the C-1 and C-2 scheme, the dynamic frequency is within the action limit value of the protection device, so that the safe operation of the system is ensured.
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (6)
1. A unit combination optimization method considering dynamic frequency constraint under wind power integration is characterized in that a wind power integration system frequency response model is established according to a fan response mechanism, a dynamic frequency quantitative evaluation index is deduced, and a wind power integration system unit combination optimization model considering dynamic frequency constraint is established;
the method specifically comprises the following steps which are sequentially carried out:
step 1, algorithm initialization: inputting acquired thermal power unit parameter Ps,i,min、Ps,i,max、TS,i、TO,i、XS,i,(t-1)、XO,i,(t-1)Cost coefficient k of wind fieldiMinimum frequency limit fcDetermining a planned scheduling period, and determining a load prediction curve, a wind power prediction curve, a power disturbance curve, an initialized unit combination decision variable and a penalty factor phi in the periodt；
Step 2, layered optimization: equivalently decomposing the optimization problem into a main unit combination problem and a frequency out-of-limit detection subproblem, wherein the main problem is composed of a conventional unit combination constraint formula, performing optimization calculation on an upper layer main problem model by using a Lagrange relaxation method, determining a unit combination scheme under conventional operation constraint, and taking an upper layer main problem decision variable result as a known quantity to be introduced into a lower layer subproblem model for optimization calculation;
step 3, iterative correction: by applying a penalty factor phitWhether the current unit combination scheme meets dynamic frequency constraints is judged positively and negatively, and if yes, an optimization result is output; and if not, adding Benders feedback constraint to the main problem for iterative calculation until the conditions are met, and outputting an optimization result.
2. The method for optimizing the unit combination considering the dynamic frequency constraint under the wind power grid-connection according to claim 1, wherein the method for calculating the lowest point of the dynamic frequency of the lower layer sub-problem in the step 2 is as follows:
wherein: f. ofminIs the lowest value of the frequency under the disturbance condition; f. of0Is the system fundamental frequency; k is a static difference adjustment coefficient; t is the time constant of the speed regulator; d is a damping coefficient; delta PstepIs the disturbance power magnitude; heqIs the system inertia time constant; omeganAnd xi are the natural frequency and the damping coefficient, respectively; t is tminTime corresponding to the lowest point frequency;
ωnxi and tminThe expression is as follows:
3. the method for optimizing the unit combination considering the dynamic frequency constraint under the wind power integration according to claim 2, wherein the formula (10) introduces a piecewise linearization technique to calculate the minimum value of the dynamic frequency:
the left expression of the unequal sign in formula (10) is regarded as Hset、Kset、TsetAnd UstAnd is denoted as G (H)set，Kset，Tset，Ust) Then define G (H)set，Kset，Tset，Ust) Piecewise linearization function of (1):
in the formula: xsetIs Ust、Hset、KsetAnd TsetA set of formed variables; alpha is alphaiAnd betaiIs a linearization coefficient; p is the number of segments;
after the piecewise linearization processing, the nonlinear constraint shown in equation (10) is rewritten as a linear constraint:
Gp(Hset,Kset,Tset,Ust)≥fc (15)。
4. the method for optimizing the unit combination considering the dynamic frequency constraint under the wind power integration according to claim 3, wherein the Benders decomposition method in the step 3 is as follows:
in the sub-problem solution, a penalty variable phi is introduced in the formula (15)tConverting the lowest point frequency out-of-limit detection problem into a penalty variable minimization problem comprises the following steps:
min fs＝Φt (16)
s.t.-Gp(Hset,Kset,Tset,Ust)-Φt≤-fc (17)
solving the subproblem model by using a conventional linear programming algorithm to obtain a penalty variable of each period; if the penalty variable is greater than 0 in a certain period, the unit combination in the period has the lowest frequency out-of-limit condition; at this point, the Benders cut is introduced in the main problem, with Benders feedback constraints as follows:
in the formula
Calculating from the main problem;
and the Benders cuts feed back the frequency out-of-limit degree of the lowest point of the system to the main problem optimization model in a constraint condition mode, so that the current unit combination result is corrected.
5. The method for optimizing the unit combination considering the dynamic frequency constraint under the wind power grid-connection according to claim 1, wherein the model is based on the following objective function and constraint conditions:
the objective function of the invention is defined as the lowest system power generation cost:
in the formula: t is the number of hours of a scheduling cycle; ps,i,tAnd Pw,i,tGenerating power of an ith thermal power generating unit and generating power of an ith wind field at the moment t respectively; u shapes,i,tThe operation state of the ith thermal power generating unit at the moment t is shown; n and m are the number of thermal power generating units and the number of wind power plants; a isi、biAnd ciGenerating cost coefficients of the ith thermal power generating unit; k is a radical ofiThe operation and maintenance cost coefficient of the ith wind field; b isiAnd the starting cost of the ith thermal power generating unit is saved.
6. The unit combination optimization method considering dynamic frequency constraints under wind power integration according to claim 1 or 5, characterized in that the unit combination optimization method has the following constraint conditions:
Us,i,tPs,i,min≤Ps,i,t≤Us,i,tPs,i,max (3)
-Ri,down≤Ps,i,t-Ps,i,(t-1)≤Ri,up (4)
Gp(Hset,Kset,Tset,Ust)≥fc (9)
the formula (2) to the formula (9) are respectively power balance constraint, thermal power unit output constraint, thermal power unit climbing constraint, system standby constraint, thermal power unit start-stop time constraint, power flow constraint, wind field output constraint and dynamic frequency constraint;
in the formula: g is the number of load nodes; pL,i,tRepresenting the planned load of the node i at the time t; ps,i,minAnd Ps,i,maxRespectively a small output and a maximum output of the ith thermal power generating unit; λ is a spare coefficient; t isS,iAnd TO,iThe minimum startup and shutdown hours of the ith thermal power generating unit are respectively; xS,i,(t-1)，XO,i,(t-1)The number of continuous startup and shutdown hours of the ith thermal power generating unit is respectively; y is the number of the branches; a. thei,lA sensitivity system of the node i to the line l; pl,minAnd Pl,minRespectively, the minimum and maximum transmission power of the line l; pw,i,t,fPredicting the generated power for the ith wind field at the time t; hsetIs a generator inertia coefficient vector; u shapestA generator start-stop state vector is obtained in a time period t; kset is the gain coefficient vector of the speed regulator; t issetIs a vector of the time constant of the governor, fcIs the lowest frequency limit.
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| CN113922376A (en) * | 2021-12-15 | 2022-01-11 | 中国电力科学研究院有限公司 | Power system minimum inertia evaluation method and system considering frequency stability constraint |
| CN114465246A (en) * | 2022-02-21 | 2022-05-10 | 华北电力大学 | Unit combination optimization method considering dead zone and amplitude limiting link of speed regulator |
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| CN113922376A (en) * | 2021-12-15 | 2022-01-11 | 中国电力科学研究院有限公司 | Power system minimum inertia evaluation method and system considering frequency stability constraint |
| CN113922376B (en) * | 2021-12-15 | 2022-02-25 | 中国电力科学研究院有限公司 | Power system minimum inertia evaluation method and system considering frequency stability constraint |
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| CN115688469A (en) * | 2022-11-15 | 2023-02-03 | 华北电力大学 | Power system unit combination method considering node frequency change rate constraint |
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| CN116454922A (en) * | 2023-06-15 | 2023-07-18 | 中国电力科学研究院有限公司 | System frequency stability control method and system considering new energy frequency modulation energy constraint |
| CN117996781A (en) * | 2024-01-31 | 2024-05-07 | 天津大学 | Wind power uncertainty robust scheduling method and device considering four-variable frequency constraint |
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