CN110137955B - Decision method for robust unit combination scheduling considering CVaR - Google Patents
Decision method for robust unit combination scheduling considering CVaR Download PDFInfo
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Abstract
The invention discloses a decision method for robust unit combination scheduling considering CVaR, which comprises the following steps: constructing a polyhedron uncertain set from interval, time and space dimensions; measuring system risk possibly existing in the system by adopting a CVaR measuring method; constructing a robust generator set combination optimization model considering an acceptable wind power interval based on a polyhedron uncertain set and a robust optimization method; and solving the model, and outputting the wind power range, risk loss, start/stop state of the unit, wind curtailment and load shedding amount decision which can be accepted by the optimized system. Compared with a method for giving an uncertain set boundary, the boundary of the established uncertain set is obtained through optimization, conservatism control of a robust optimization model can be realized by adjusting uncertainty parameters, and the model is based on a current power system scheduling framework, follows a self-adaptive mechanism between unit combination and robust optimization, and can be directly used for solving the unit combination problem of the current power system.
Description
Technical Field
The invention relates to the technical field of analysis and scheduling of a power system, in particular to a decision method for robust unit combination scheduling considering a Conditional Value at Risk (CVaR).
Background
The wind power generation is influenced by practical requirements in the aspects of environmental protection, energy and the like, and the wind power generation shows a rapid development trend in China. The renewable energy and environmental pollution-free property of wind power generation are the inherent motivations for the development of the wind power generation, and in addition, the wind power station has the advantages of short construction time, flexible investment and the like, and the construction of the energy is promoted.
However, at present, wind power with high proportion and uncertain attribute is merged into a power grid, so that a plurality of problems are brought to the operation of a power system, the traditional unit combination concept and method are difficult to effectively deal with, the decision is conservative or not aggressive, and the wind abandon and load shedding are caused or more cost is paid. In order to effectively deal with the uncertainty problem of large-scale wind power, consume more wind power and achieve the best energy-saving and emission-reducing effect, the following key problems must be solved:
firstly, a power system eliminates the boundary decision problem of a wind power uncertainty interval;
and measuring the system risk caused by the fact that the wind power uncertainty exceeds the safety boundary which can be scheduled by the system.
In view of the above, it is desirable to provide a decision method that can be directly used for solving the unit combination scheduling problem of the current power system based on the current power system architecture.
Disclosure of Invention
In order to solve the technical problem, the technical scheme adopted by the invention is to provide a decision method for combining and scheduling a CVaR-based robust unit, which comprises the following steps:
constructing a polyhedral uncertain set from interval, time and space dimensions by balancing unit combination cost and risk loss cost;
based on an interval robust optimization thought and a risk decision theory, a CVaR measurement method is adopted to measure system risks possibly existing in the system;
constructing a robust generator set combination optimization model considering an acceptable wind power interval based on a polyhedron uncertain set and a robust optimization method;
and solving the model, and outputting the wind power range, risk loss, start/stop state of the unit, wind curtailment and load shedding amount decision which can be accepted by the optimized system.
In the above method, the measuring the system risk possibly existing in the system by using the CVaR measurement method includes:
the risk of wind curtailment due to underestimation and the risk of load loss due to overestimation.
In the method, the construction of the robust generator set combination optimization model considering the receivable wind power interval based on the polyhedron uncertain set and the robust optimization method comprises the following steps:
establishing a stage 1 model for the unit combination problem of the day before the unit start/stop state and the operation risk based on the decision variables;
according to the established stage 1 model, establishing a stage 2 model for the system economic operation problem corresponding to the worst scenario in the wind power uncertain set of the unit output, the load shedding amount and the wind abandoning amount at each moment based on a decision variable;
and determining a two-stage robust optimization model considering the acceptable wind power interval.
In the method, the solution model adopts a modified C & CG algorithm.
In the above method, the set of polyhedral uncertainties is:
in the formula, Wwt、
Respectively the actual value, the predicted value and the lower boundary and the upper boundary of an uncertain interval of the wind power plant w output in the time period tA boundary;
and
respectively representing auxiliary {0,1} variables of the fluctuation condition of the wind power output; gamma-shapedTAnd ΓSUncertainty parameters of the uncertainty set in space and time are respectively.
In the above method, the CVaR value expression of the wind curtailment risk due to underestimation is as follows:
the CVaR value expression for the risk of loss of load due to overestimation is:
in the formula (I), the compound is shown in the specification,
and the wind power prediction error is obtained.
In the above method, the stage 1 model specifically includes:
an objective function:
in the formula (I), the compound is shown in the specification,
is a quadratic cost function of the unit and is linearized in three sections in a model, ag、bg、cgRespectively the coefficients of the quadratic cost function,
the output power of the unit g in the 1 st stage in the time period t;
g and W are the number of the units and the wind power plant in the system respectively; k is a penalty coefficient;
the constraint conditions include:
the method comprises the following steps of unit output power upper and lower limit constraint, unit climbing rate constraint, unit minimum on-off time constraint, active power balance constraint, node active power balance and transmission capacity constraint, risk constraint, energy storage system charging/discharging state constraint, energy storage system charging/discharging power constraint, energy storage system capacity constraint and energy storage system charging/discharging regulation strategy constraint.
In the above method, the phase 2 model specifically includes:
an objective function:
in the formula, cwt、cdtRespectively the cost of wind abandoning and load shedding;
ΔDdtthe load shedding amount of the d load in the time period t;
ΔWwtthe wind curtailment quantity of the w wind power plant in the time period t is obtained;
the constraint conditions include: the method comprises the following steps of unit output power upper and lower limit constraint, unit climbing rate constraint, active power balance constraint, load shedding amount constraint, air curtailment amount constraint and node active power balance constraint.
In the method, the two-stage robust optimization model considering the acceptable wind power interval specifically comprises the following steps:
in the formula, F1Is the objective function of stage 1; f2Is the objective function of the 2 nd stage;
C1represents the constraints satisfied by the stage 1 variables; c2 represents the constraint satisfied by the stage 2 variable;
ugta decision variable 0/1 in the 1 st stage represents the running state of the unit g in the time period t, 1 represents running, and 0 represents shutdown;
and
respectively representing auxiliary {0,1} variables of the fluctuation condition of the wind power output;
Pgt、ΔDdtand Δ WwtIs a continuous variable of stage 2, wherein PgtThe output power of the unit g in the time period t is obtained; delta DdtThe load shedding amount of the d load in the time period t; Δ WwtThe wind curtailment quantity of the w wind power plant in the time period t is obtained;
Wwt、
respectively the actual value of the wind farm w output in the time period t, the lower boundary and the upper boundary of the uncertainty interval.
Compared with a method for giving an uncertain set boundary, the boundary of the established uncertain set is obtained through optimization, conservatism control of a robust optimization model can be realized by adjusting uncertainty parameters, and the model is based on a current power system scheduling framework, follows a self-adaptive mechanism between unit combination and robust optimization, and can be directly used for solving the unit combination problem of the current power system.
Drawings
FIG. 1 is a flow chart provided by the present invention;
FIG. 2 is a probability density function normal distribution diagram of a wind power plant prediction error in the invention;
FIG. 3 is a flow chart for solving a C & CG algorithm for solving a two-stage robust optimization unit combination model in the invention;
FIG. 4 is a wiring diagram of a 6-node system in case analysis according to the present invention;
FIG. 5 is a graph of a wind power prediction value, a wind power prediction error band, and a range of extinction of an uncertain set in the case of the present invention;
FIG. 6 is a wind power acceptance range curve diagram under different node systems in the case of the invention;
(a) the wind power receiving range curve diagram under the 6-node system, and the wind power receiving range curve diagram under the 6-node system;
fig. 7 is a graph of the scheduling total cost and risk cost for different node systems and different risk thresholds in the case of the present invention;
(a) the operation cost and risk cost curve graphs of the 6-node system and the systems under different risk thresholds, (b) the operation cost and risk cost curve graphs of the 118-node system and the systems under different risk thresholds;
fig. 8 is a diagram illustrating a scheduling result of whether to consider the energy storage control strategy in the present invention;
(a) the energy storage scheduling result diagram in the 1 st stage, and (b) and (c) are energy storage scheduling result diagrams with or without constraint formulas (34) and (35), respectively.
Detailed Description
The invention provides a two-stage robust unit combination decision model considering CVaR (conditional value at risk value) based on the idea that an energy storage system deals with wind power uncertainty to reduce system risk, and the invention is described in detail by combining a specific implementation mode and an attached drawing of the specification.
As shown in fig. 1, the present invention provides a decision method for combining and scheduling a CVaR-based robust unit, which includes the following steps:
s1, building a dimensional polyhedral uncertainty set from an interval, time and space by balancing unit combination cost and risk loss cost, and realizing flexibility adjustment of the uncertainty set, thereby avoiding conservatism of a robust scheduling result.
The polyhedron uncertainty set is specifically as follows:
in the formula, Wwt、
Respectively obtaining an actual value, a predicted value and a lower boundary and an upper boundary of an uncertain interval of the wind power plant w at a time t;
and
respectively representing auxiliary {0,1} variables of the fluctuation condition of the wind power output; gamma-shapedTAnd ΓSUncertainty parameters of the uncertainty set in space and time are respectively.
The formula (1) represents the actual wind power output, and the actual wind power output is represented by a polyhedron structure tableUncertain set of icons
The formula (2) and the formula (3) are used for controlling the scene covered by the uncertain set, and reasonably selecting the parameter gammaTAnd ΓSTo reduce the conservatism of robust scheduling.
The equation (4) represents pole constraint of a polyhedron, and the same wind power can only reach an uncertain upper limit value or lower limit value at the same time but cannot reach the upper limit value or lower limit value at the same time.
S2, based on the interval robust optimization thought and the risk decision theory, measuring the system risk possibly existing in the system by adopting a CVaR measuring method; the system risk comprises a wind abandoning risk and a load shedding risk, and specifically comprises the following steps:
in this embodiment, the wind power prediction error is:
assuming that the mean obedience of wind power prediction errors is 0 and the variance is sigmaw 2The probability density function of the normal distribution of (2) is shown in fig. 2.
In the embodiment, the maximum wind power uncertainty region capable of being accepted by the system is represented by adopting the CVaR calculation formula
The average potential loss caused by the situation of (1) is, as shown in the shaded part in fig. 2, that is, under the condition of fully exploiting the maximum regulation capacity of the system, the average loss caused by the wind power fluctuation exceeding the regulation and control range of the system is defined as CVaR accepted by the wind power of the system.
If the actual output power of the wind power exceeds the upper boundary of the regulation and control range of the system, the safety of the system operation can be ensured by taking a wind abandoning measure. Therefore, the CVaR value expression of the wind curtailment risk due to underestimation is:
in the formula (I), the compound is shown in the specification,
the expected wind curtailment risk average corresponding to the shaded portion on the right in fig. 2.
Similarly, if the actual output power of the wind power is lower than the lower boundary of the regulation and control range of the system, a load shedding measure can be taken to ensure the safety of the operation of the system. At this time, the CVaR value expression of the risk of loss of load due to overestimation is:
in the formula (8), the reaction mixture is,
corresponding to the expected load loss risk average for the left shaded portion in fig. 2.
However, both the formula (7) and the formula (8) are non-linear integral expressions, which are difficult to solve directly by a commercial solver, and thus need to be linearized; therefore, a linearization means is adopted to carry out linearization processing on the CVaR value expression of the wind power abandoned wind risk and the load loss risk. Expression after linear transformation:
in the formula (I), the compound is shown in the specification,
representing a CVaR value of wind power wind abandon risk caused by underestimation of a wind power plant w in a time period t;
CVaR values representing the risk of load shedding due to overestimation of the wind farm w during the time period t, respectively.
In summary, the equations (9) to (12) establish a functional correspondence relationship between the wind power uncertainty interval receivable by the system and the CVaR value faced by the system.
S3, constructing a robust generator set combination optimization model considering an acceptable wind power interval based on a polyhedron uncertain set and a robust optimization method; the method specifically comprises the following steps:
the embodiment is based on a two-stage robust optimization problem established by a polyhedron uncertain set:
s31, establishing a stage 1 model for the day-ahead unit combination problem of the unit start/stop state and the operation risk based on the decision variables;
s32, according to the established stage 1 model, establishing a stage 2 model for the system economic operation problem corresponding to the worst situation in the wind power uncertain set of the unit output, the load shedding amount and the wind abandoning amount at each moment based on the decision variables.
And S33, determining a two-stage robust optimization model considering the receivable wind power interval according to the step S31 and the step S32. Wherein the content of the first and second substances,
(1) stage 1 model
In the stage 1, the starting and stopping states of the unit, the wind power output range accepted by the system, the energy storage related decision quantity and the like are decided.
The objective function of the stage 1 is to minimize the start-stop cost, the operation cost, the energy storage charge-discharge cost and the operation risk cost of the system of the unit; namely, it is
An objective function:
in the formula (I), the compound is shown in the specification,
is a quadratic cost function of the unit and is linearized in three sections in a model, ag、bg、cgCoefficients of a quadratic cost function, respectively;
the output power of the unit g in the 1 st stage in the time period t;
g and W are the number of the units and the wind power plant in the system respectively; and K is a penalty coefficient.
The decision maker in the embodiment can balance the reliability and the running economy of the system by adjusting the penalty coefficient K, so that the range of the wind power which can be consumed by the system is determined;
the constraint conditions include:
upper and lower limit constraint of output power of unit
In the formula (I), the compound is shown in the specification,
the maximum output power and the minimum output power allowed by the unit g are respectively.
② unit climbing speed constraint
In the formula (I), the compound is shown in the specification,
the upward and downward climbing rates of the unit g are respectively.
Third, minimum on-off time constraint of the unit
In the formula (I), the compound is shown in the specification,
respectively the time that the unit g is started and stopped at the initial moment;
the minimum start-up and shut-down time of the unit g.
Active power balance constraint
In the formula, DdtRepresenting the active power predicted value of the load d in the time period t; d is the total load.
Fifth, node active power balance and transmission capacity constraint
In the formula, BijIs the line admittance between node i and node j; thetaitIs the phase angle of node i during time t; f. ofij,tThe active transmission power of the power transmission line between the node i and the node j is obtained;
the limit value of the active transmission power of the power transmission line; b and L are the number of nodes and transmission lines in the system respectively.
Sixth risk constraint
In the formula, RiskdaA day-ahead risk target threshold value;
representing the installed capacity of the wind farm w.
In this embodiment, the charging and discharging behavior of the energy storage system, that is, the energy storage may be used as a power supply to provide power to the system, or may absorb power from the system as a load. The energy storage system has operation flexibility, so that the wind power uncertainty can be effectively dealt with by matching with a conventional thermal power generating unit so as to reduce the operation risk of the system. Furthermore, from the perspective of spatial location, the decentralized access of renewable energy sources inevitably leads to the spatially decentralized configuration of energy storage that deals with its uncertainty, which is also an energy source that effectively deals with network constraints. From the time process, the stored energy is also a bridge for energy transfer, and the function of the stored energy is essentially standby transmission. Therefore, the scheduling strategy of the energy storage not only affects the consumption capacity of the system to the wind power, but also affects the safety of the system.
The energy storage scheduling model is as follows:
seventhly, restraining the charging/discharging state of the energy storage system
In the formula (I), the compound is shown in the specification,
respectively, the status signs that the energy storage system is in discharging or charging. The constraint may be applied to ensure that the energy storage system is only in a charged or discharged state at a time.
Charging/discharging power constraint of energy storage system
In the formula (I), the compound is shown in the specification,
respectively, the discharging power and the charging power of the energy storage system in the phase 1 model and the allowed maximum discharging power and maximum charging power thereof.
Ninthly energy storage system capacity constraint
In the formula, EetStoring an energy value for the energy storage system for a time period t; etach、ηdRespectively charging and discharging efficiencies of the energy storage system;
maximum and minimum values allowed by energy storage of the energy storage system; ee,int、Ee,TThe electric quantity values of the energy storage system in the initial period and the final period are respectively. In order to ensure that the energy storage system can function normally in the next scheduling period, the electric quantity value of the energy storage system at the end of each period is required to be equal to that of the initial period.
Charge/discharge regulation strategy constraint for charge/discharge of energy storage system in charge of frequency (R) and frequency (R)
Considering that the wind power output is higher than the predicted value at the peak load period or lower than the predicted value at the valley load period, the influence on the peak regulation of the power grid is not obvious. The embodiment limits the charging and discharging modes of the energy storage system under the two conditions to avoid the condition of discharging in a low-ebb period or charging in a high-peak period, thereby reducing the loss caused by the disordered charging and discharging of the energy storage system.
In the formula (I), the compound is shown in the specification,
the discharge power and the charge power of the energy storage system in the second-stage model are respectively.
(1) Stage 2 model
And the stage 2 is to minimize wind curtailment and load shedding cost corresponding to the worst case described by the uncertain set when the unit start-stop state obtained by the decision in the stage 1 and the boundary of the wind power receivable interval are given. A two-stage robust optimization model considering an acceptable wind power interval is constructed based on adaptive robust optimization and comprises the following steps:
an objective function:
in the formula, cwt、cdtThe cost of the wind curtailment and the load shedding are respectively, and the values of the embodiment are 10$/MW and 1000 $/MWh.
Constraint conditions are as follows:
upper and lower limit constraint of output power of unit
② unit climbing speed constraint
Active power balance constraint
Cutting load restraint
Wind quantity restraint is abandoned
Sixth, node active power balance constraint
The 2 nd-stage model is formed by equations (36) to (43), energy storage system regulation and control strategy constraints (30) to (35), uncertain concentration constraints (1) to (5) and transmission capacity constraints (21) to (24).
Based on the thought, a two-stage robust optimization model considering the acceptable wind power interval is given:
in the formula, F1Is the objective function of stage 1; f2Is the objective function of the 2 nd stage;
C1represents the constraints satisfied by the stage 1 variables; c2 represents the constraint satisfied by the stage 2 variable;
ugta decision variable 0/1 in the 1 st stage represents the running state of the unit g in the time period t, 1 represents running, and 0 represents shutdown;
Pgt、ΔDdtand Δ WwtIs a continuous variable of stage 2, wherein PgtThe output power of the unit g in the time period t is obtained; delta DdtThe load shedding amount of the d load in the time period t; Δ WwtThe wind curtailment quantity of the w wind power plant in the time period t is obtained.
And S4, solving the model, and outputting the wind power range, risk loss, start/stop state of the unit, wind abandon and load shedding amount decisions which can be accepted by the optimized system.
The constructed two-stage problem forms a CVaR-considered two-stage robust optimization unit combination model, but the model has a multilayer structure and cannot be directly solved. For convenience of expression, a model expressed in a matrix form is given, and the model is solved by using a modified C & CG (column and Constraint Generation) algorithm.
Stage 1: main Problem (MP)
Decision variables for stage 1 include ugt、
And
because no wind abandon and load shedding phenomena occur in the 1 st stage, u can be ensuredgt、
Feasibility of the solution and
existence of a solution.
Wherein x represents a binary state vector of the generator set;
(Vector)
and vector y represents a continuous vector of generator output and a phase angle vector of each node respectively;
u represents a binary state vector of the charge-discharge state of the energy storage system;
w represents a wind farm output boundary vector;
q represents an operational risk vector;
a, B, C, D, E, A, B, C, D, E and F are all corresponding constant coefficient matrixes; for example, the matrix a can be derived from the constraint equations (14) to (20). Compared with the traditional robust unit combination, the proposed model introduces more decision variables and constraints, such as w, u,
and z, which will add significantly to the computational complexity. The main problem is the MILP problem, and thus can be solved by the existing commercial solver CPLEX.
Stage 2: sub-problem (SP)
The decision variables of stage 2 include Pgt、
ΔDdtAnd Δ WwtAnd uncertain set of wind power
In the formula, s represents a curtailment wind and a tangential load vector, and v describes a binary vector of the wind power uncertain set;
f, G, H, G, H, I, J, K, L, M and N are all corresponding constant coefficient matrixes;
In this embodiment, since the sub-problem is a max-min structure, the model of this structure cannot be directly solved, and the max-min structure model needs to be converted into a single-layer MILP problem for convenient solution.
Firstly, a mode of solving the dual problem of the internal minimization problem is converted into a max problem, according to Wangdan and the like, in the report of China Motor engineering in 2014, "household temperature control load demand response and energy efficiency power plant modeling considering user comfort constraint" are provided, the mentioned strong dual theory is used for solving the dual problem of the min problem of the inner layer, then the dual problem is combined with the problem of the outer layer, and finally the dual problem is converted into a single-layer max problem. The matrix form of the transformed subproblem is expressed as follows:
λT≥0 (49)
Nv≤h (50)
in the formula, λ is a dual variable of the constraint formulae (37) to (43). It was observed that the objective function (47) contained a bilinear term λTv, an external approximation method provided by ' theoretical research of unit combination in power market ' provided by doctor thesis in 2006 or a characteristic and research framework of automatic demand response in intelligent power utilization ' provided by prosperous et al in an automation journal of a power system in 2013 can be adopted, and a large M linear method is used for solving.
In some cases, the outer approximation may not be able to find a globally optimal solution. Therefore, the bilinear term lambda is solved by adopting a large M linearization methodTv：
By the above process, the sub-problem (46) translates to the standard single layer MILP problem, as shown in equation (55):
in the formula (I), the compound is shown in the specification,
is an auxiliary vector. q is a continuous vector;
equations (52) through (54) are auxiliary constraints generated by the large M method, so that the bilinear terms can be equivalently converted into the following equations:
after the above linear transformation, the main problem (45) and the sub-problem (55) constitute a standard two-stage MILP problem, and this example uses Ross t.mewton et al, 2011 to propose "Green power volume research: price elasticity and policy analysis, and an improved C & CG algorithm is used for solving the two-stage unit combination model. Compared with Benders decomposition algorithm, the algorithm has the advantages that the iteration times are greatly reduced, and the convergence rate is greatly improved. The overall flow of the algorithm solution is shown in fig. 3, and the steps are as follows:
a1, initialization
Setting the lower bound LB as 0, the upper bound UB as + ∞, and the convergence error epsilon as more than or equal to 0; the iteration number k is equal to 0, and the solution space is equal to O; go to step A2;
a2, solving the following main problem formula (45);
ψ≥fTs (57)
get the optimal solution
Updating
Go to step A3;
a3, solving the subproblems
Based on given unit combination state xk+1、uk+1、wk+1Solving a subproblem (55) to obtain the worst fluctuation scene of wind power output
And the air abandoning quantity and the load cutting quantity sk+1；
Updating the Upper bound
If UB-LB is less than or equal to epsilon, stopping iteration and outputting an optimal solution;
otherwise, setting l to l +1, and solving the sub-problem to the worst wind power output scene corresponding to the optimal solution
Passing to the main question, go to step A4;
a4, adding variables and constraints
Increasing the variable yk+1And sk+1Adding constraint equations (59) and (60) and returning to the main question; updating l ═ l +1 and O ═ u { k +1 }. The outer layer problem of the updated sub-problem is solved and the process returns to the step A2.
ψ≥fTsk+1 (59)
The beneficial effects of the embodiment are that:
the embodiment provides a two-stage robust unit combination optimization model considering CVaR, and has the following beneficial effects:
1) compared with the method for giving the uncertain set boundary, the boundary of the uncertain set constructed by the embodiment is obtained by optimization, and the conservative control of the robust optimization model can be realized by adjusting the uncertainty parameter; meanwhile, a proper risk threshold value can be selected, or compromise is carried out between the system operation risk and the system operation cost, so that an optimal scheduling solution can be obtained.
2) The configuration of the energy storage increases the flexibility resources of the thermal power generating unit, improves the capability of the system for coping with wind power uncertainty, and relieves the limitation of the climbing rate of the system and the limitation of the network restriction.
3) The model is based on the current power system scheduling architecture, follows a self-adaptive mechanism between unit combination and robust optimization, can be directly used for solving the unit combination problem of the current power system, and verifies the correctness of the model. Meanwhile, aiming at the characteristics of the model of the embodiment, the C & CG algorithm is adopted for solving, and the advantages of the method in the aspects of calculation efficiency and calculation speed are verified.
The present embodiment will be described below by way of specific examples.
The present case takes a 6-node system and a modified IEEE 118-node system as examples, and analyzes the effectiveness of the model proposed in the above embodiments. As shown in fig. 4, the system is a 6-node system, and the system includes 1 wind farm with a capacity of 250MW, 1 energy storage system, 3 thermal power generating units, and 7 lines. Technical data of capacity, climbing rate, lines and the like of a thermal Power generating unit refer to Qiaoyan Bian et al and provide 'distribution robust solution to the redundant scheduling with partial wind Power information' on IEEE Transactions on Power Systems (International Electrical and electronics Engineers institute of Electrical and electronics Engineers, Power System Association) in 2015 (a robust solution method for distribution of partial wind Power information is considered in backup scheduling).
The modified IEEE118 node system comprises 53 generators, 91 load nodes, 186 lines, 14 capacitors and 9 tap changers; 3 wind power plants with the capacity of 250MWh are respectively connected with nodes 59, 66 and 94. The detailed IEEE118 node system data may refer to motor.ec.it.edu/data/scuc _ 118. The parameters of the energy storage system are shown in the table 1, and the charging/discharging price of the energy storage system is 0.4/0.6($/kWh) respectively. The test calculation adopts Visual Studio 2016C + + software to call a CPLEX12.8 solver to solve, and the computer is configured with a Win10 system, Intel Core i7-8700k series, a main frequency of 3.0GHz and a memory of 16G. The simulation time scale was 1 day divided into 24 periods.
TABLE 1 energy storage System parameters
The wind power predicted value and the wind power prediction error band adopted by the calculation example are shown in FIG. 5. In the examples, the confidence levels are chosen to be respectively betaT95% and betaS95%, i.e. in a 6-node system
And
in a 118-node system
Wind power prediction error delta wwtThe mean value of (2) is 0 and the variance is obtained as follows.
(1) Scheduling result considering combination of CVaR robust unit
Taking a 6-node test system as an example, the model of the embodiment and a scheduling result of an IEEE Power & Energy Society of electrical and electronics engineers (institute of electrical and electronic engineers) General Meeting in 2014, which is proposed by the literature Negash a.i. and is related to the risk robust unit combination model in "Optimizing and responding to price and quantity" optimization of wholesale market demand response price and quantity ", are compared and analyzed, and see table 2.
TABLE 2 comparison of scheduling results
As can be seen from table 2, comparing the scheduling results of the literature, the most economical unit G1 in the model of the present embodiment always operates in the research period, the most expensive unit G2 exits from operating in 11: 00-12: 00 time intervals, the unit G3 is in an operating state only in 9:00, 11: 00-12: 00 time intervals of the load peak, the corresponding total system cost is 94236.95$, and the savings of 94236.95$ -94632.321 $ 395.37; the peak clipping and valley filling functions of the energy storage system are explained, on one hand, the thermal power generating unit can provide enough flexible resources to deal with the uncertainty of wind power, and therefore the wind power consumption capability of the system is improved. On the other hand, the pressure of standby configuration of the thermal power generating unit at the peak moment can be reduced, the starting/stopping times of the unit are reduced, the unit is used as an extra flexibility source, and the UC scheduling cost is reduced.
(2) Comparison with other unit combination models
Now, the model of the present embodiment is discussed to be respectively compared and analyzed with deterministic unit combinations (10% uncertainty interval), given robust unit combinations of symmetric uncertainty sets, and robust unit combinations considering asymmetric uncertainty sets considering risks, and scheduling results obtained by these 4 models are shown in table 3 below. In 2001, "Using availability information to calibrate customer demand management models" (models for calibrating customer demand management behavior Using utility information) was proposed by Fahrioglu m.
TABLE 3 scheduling results of different unit combination models
As can be seen from table 3, the operation cost and risk cost of the model of the present embodiment are lower than those of the other three models, which indicates that the model of the present embodiment has better operation flexibility capability and capability of reducing the operation risk of the system. In addition, even if the configuration of the energy storage system increases the flexibility adjustment capability of the system, some wind abandoning or load shedding amount still exists, which is the problem that the system cannot cope with the intermittence of high-proportion wind power at a certain moment due to the limitation of the climbing rate of the thermal power generating unit.
By comparing the iteration times and the running time, taking the 118 node as an example, the total calculation time of the model of the embodiment is 8.677 seconds, and the iteration times is 3 times, which shows that the method of the embodiment has high calculation efficiency due to the fact that the linear property of the model is maintained, and can meet the calculation efficiency requirement of solving the actual system.
(3) Flexibility uncertainty set and range of absorption
The uncertain set of wind power of the model of the embodiment is flexible, adjustable and asymmetric, and mainly comprises two reasons:
(1) in order to limit the conservatism of the robust method, the robustness of the system is limited from a time dimension formula (2) and a space dimension formula (3) respectively.
(2) The asymmetry of the wind power absorption range, namely the asymmetry of the wind power uncertain set, is caused by setting different wind abandon penalty costs and load shedding penalty costs. As can be seen from table 3, even though the load shedding amount is much smaller than the wind curtailment amount, the load shedding cost is larger than the wind curtailment cost because we set a higher load shedding penalty cost, thereby making the load shedding risk lower.
The range of consumption obtained by optimizing the model in this embodiment is compared with the scheduling result of the risk robust unit combination model, as shown in fig. 6.
As can be seen from fig. 6, compared with the literature, the upper and lower boundaries of the digestion wind power decided by the model of the present embodiment are smaller in most of the time period. For example, in a 6-node system, time periods 1: 00-3: 00, 5:00, 7:00, 9:00, 12:00, 14:00, 16:00, 18:00, 21: 00-22: 00;
in the 118-node system, the time period is 2:00, 8:00, 11: 00-16: 00. The uncertainty of the system with more schedulable flexible resources for handling the wind power output is proved by configuring the energy storage system, so that the conservatism of the traditional robust method is reduced on one hand, and the running risk of the system is also reduced while the safe running of the system is ensured on the other hand.
(4) Uncertain set conservation analysis
Adjusting an uncertainty parameter ΓTAnd ΓSThe robustness of the model can be controlled, so that the conservatism of the scheduling result is reduced. To analyze the effect of the uncertainty parameter variation on the conservation of the results obtained in the model of this example, the results are listed in Table 4ΓTAnd ΓSDifferent combinations of the calculated results.
TABLE 4 gammaTAnd ΓSScheduling results under different combinations
As can be seen from Table 4, at fixed gammaSInvariant, with ΓTThe total operating cost is gradually increased, but the risk cost is gradually reduced, and the magnitude of the operating risk is always smaller than or equal to a given risk threshold value. It can also be seen that when fixing ΓTThe wider the wind farm (Γ)SThe larger the total operation cost is), the smaller the total operation cost is, the strategy of wind power plant geographical distribution is increased, the network constraint limitation is relaxed, and the robustness of the system for wind power uncertainty can be improved; but the risk cost is increasing gradually because: in order to improve the robustness of the system to wind power uncertainty, an over-conservative strategy is adopted, and a suboptimal solution is generated. Obviously, ΓTAnd ΓSThe value of (A) has a decisive role in the robustness and conservation of the robust optimization result. Gamma-shapedTAnd ΓSIf the value is too large, the robustness of the optimization result is good, but the optimization result is extremely conservative and has poor economy; and gamma isTAnd ΓSThe values are made too small, so that too few wind farms have the allowable output reaching the prediction boundary, which will not sufficiently reflect the uncertainty of the wind power.
Therefore, by reasonably setting the uncertainty parameter, the adjustable robust optimization method can eliminate the situation of extremely low probability of the uncertainty parameter, so that the model is more practical and more suitable for engineering practice. Table 4 also lists the uncertainty set Γ at different wind farmsTAnd ΓSThe following calculation time again demonstrates the effectiveness of the method.
(5) Risk threshold RiskdaInfluence of (2)
In an embodiment, the Risk threshold RiskdaIs also an important parameterIt affects not only the scheduling strategy but also the feasibility of the scheduling solution. In practice, the selection may be made based on historical data, risk preferences of the decision maker, electricity contract, and the like. FIG. 7 shows Risk at different Risk thresholdsdaThe running cost of the system and the trend of the risk cost curve.
As shown in FIG. 7, taking the 118-node system as an example, with the Risk threshold RiskdaGradually, the operating cost of the system gradually decreases, while the risk cost gradually increases. Risk threshold value Risk of systemdaWhen the flow rate is about 1000, the running cost and the risk cost of the system tend to be smooth. Risk threshold value Risk of systemdaThe risk cost of the system is slightly reduced when the cost is more than 1400 deg. Conversely, when the Risk threshold of the system is lowered to RiskdaWhen the value is less than or equal to 10, the system has no feasible solution. This means that the minimum feasible risk threshold for the system is 10. At the same time, it can be observed that the running cost and Risk cost of the system and the Risk threshold RiskdaThe relationship between is not strictly linear. It is also possible to derive upper and lower limits for the risk threshold for a feasible solution to exist for the system.
(6) Effect of energy storage charging/discharging control strategy
Taking a 6-node system as an example, fig. 8 shows the roles of constraints (34) and (35) of the energy storage charging/discharging regulation strategy.
Fig. 8(a) shows the energy storage scheduling result in phase 1. Therefore, during the peak period of power utilization, the stored energy is used for responding to the increased load demand through discharging, and during the valley period of power utilization, the reverse peak regulation characteristic of wind power is responded through charging the stored energy. The load curve is smoothed by the peak clipping and valley filling effects of the stored energy. Fig. 8(b) and 8(c) are comparisons of the energy storage scheduling results of the presence or absence of the constraint equations (34) and (35). It can be seen that the energy storage charge/discharge regulation strategy constrains the charge/discharge state of the energy storage system during the net load peak and valley periods to be limited: the unit combination plan before the day of the 1 st stage requires that the energy storage system can only be charged in the valley period and can only be discharged in the peak period. In the real-time scheduling link of the 2 nd stage, if the actual output of the wind power is higher than the predicted output, redundant wind power can be charged for the energy storage system, however, if the actual output of the wind power is lower than the predicted output, the charging power can be reduced, and discharging cannot be performed. The constraint not only ensures that the scheduling strategy of the energy storage system is consistent with the peak regulation of the power grid, but also avoids the loss caused by disordered charging and discharging of the energy storage.
The present invention is not limited to the above-mentioned preferred embodiments, and any structural changes made under the teaching of the present invention shall fall within the protection scope of the present invention, which has the same or similar technical solutions as the present invention.
Claims (6)
1. A decision method for considering CVaR robust unit combination scheduling is characterized by comprising the following steps:
constructing a polyhedral uncertain set from interval, time and space dimensions by balancing unit combination cost and risk loss cost;
based on an interval robust optimization thought and a risk decision theory, a CVaR measurement method is adopted to measure system risks existing in the system;
constructing a robust generator set combination optimization model considering an acceptable wind power interval based on a polyhedron uncertain set and a robust optimization method;
solving the model, and outputting wind power range, risk loss, start/stop state of the unit, wind abandon and load shedding amount decision which can be accepted by the optimized system;
the method for constructing the robust generator set combination optimization model considering the receivable wind power interval based on the polyhedron uncertain set and the robust optimization method comprises the following steps of:
establishing a stage 1 model for the unit combination problem of the day before the unit start/stop state and the operation risk based on the decision variables;
according to the established stage 1 model, establishing a stage 2 model for the system economic operation problem corresponding to the worst scenario in the wind power uncertain set of the unit output, the load shedding amount and the wind abandoning amount at each moment based on a decision variable;
determining a two-stage robust optimization model considering an acceptable wind power interval;
the stage 1 model specifically comprises:
an objective function:
in the formula (I), the compound is shown in the specification,
is a quadratic cost function of the unit and is linearized in three sections in a model, ag、bg、cgRespectively the coefficients of the quadratic cost function,
the output power of the unit g in the 1 st stage in the time period t;
g and W are the number of the units and the wind power plant in the system respectively; k is a penalty coefficient;
the constraint conditions include:
the method comprises the following steps of (1) unit output power upper and lower limit constraint, unit climbing rate constraint, unit minimum on-off time constraint, active power balance constraint, node active power balance and transmission capacity constraint, risk constraint, energy storage system charging/discharging state constraint, energy storage system charging/discharging power constraint, energy storage system capacity constraint and energy storage system charging/discharging regulation strategy constraint;
the 2 nd stage model specifically comprises:
an objective function:
in the formula, cwt、cdtRespectively the cost of wind abandoning and load shedding;
ΔDdtthe load shedding amount of the d load in the time period t;
ΔWwtthe wind curtailment quantity of the w wind power plant in the time period t is obtained;
the constraint conditions include: the method comprises the following steps of unit output power upper and lower limit constraint, unit climbing rate constraint, active power balance constraint, load shedding amount constraint, air curtailment amount constraint and node active power balance constraint.
2. The decision method of claim 1, wherein the measuring the system risk present in the system using the CVaR measurement method comprises:
the risk of wind curtailment due to underestimation and the risk of load loss due to overestimation.
3. The decision method of claim 1, wherein the solution model employs a modified C & CG algorithm.
4. The decision method of claim 2, wherein the polyhedral uncertainty set is:
in the formula, Wwt、
Respectively obtaining an actual value, a predicted value and a lower boundary and an upper boundary of an uncertain interval of the wind power plant w at a time t;
and
respectively representing auxiliary {0,1} variables of the fluctuation condition of the wind power output; gamma-shapedTAnd ΓSUncertainty parameters of the uncertainty set in space and time are respectively.
5. Decision method according to claim 4 characterized in that the CVaR value expression of the risk of wind curtailment due to underestimation is:
the CVaR value expression for the risk of loss of load due to overestimation is:
in the formula (I), the compound is shown in the specification,
and the wind power prediction error is obtained.
6. The decision method according to claim 1, wherein the two-stage robust optimization model taking into account the acceptable wind power interval is specifically:
in the formula, F1Is the objective function of stage 1; f2Is the objective function of the 2 nd stage;
C1represents the constraints satisfied by the stage 1 variables; c2Represents the constraints satisfied by the stage 2 variables;
ugta decision variable 0/1 in the 1 st stage represents the running state of the unit g in the time period t, 1 represents running, and 0 represents shutdown;
and
respectively representing auxiliary {0,1} variables of the fluctuation condition of the wind power output;
Pgt、ΔDdtand Δ WwtIs a continuous variable of stage 2, wherein PgtThe output power of the unit g in the time period t is obtained; delta DdtThe load shedding amount of the d load in the time period t; Δ WwtThe wind curtailment quantity of the w wind power plant in the time period t is obtained;
Wwt、
respectively the actual value of the wind farm w output in the time period t, the lower boundary and the upper boundary of the uncertainty interval.
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