CN110571795A - Arrangement method of energy storage unit in high wind penetration power system - Google Patents

Abstract

The invention discloses an arrangement method of an energy storage unit in a high wind penetration power system. The arrangement method establishes a market-based probabilistic optimal power flow, and the power flow has energy storage integration and wind power generation, including the following steps: Step 1 : Modeling based on wind power generation and load probability; Step 2: Use energy storage system to time-shift the electric energy of renewable energy; Step 3: Economic characteristics of compressed air energy storage; Step 4: Establish a power pool model, and unilaterally auction The market is included in the optimal power flow; step 5: use the probabilistic optimal power flow, and consider uncertain factors such as wind power output and variable loads in the power flow calculation; step 6: use genetic algorithms to optimize and determine based on the probabilistic optimal power flow in the power market Optimal location of energy storage units in an unregulated wind power system.

Description

Arrangement method of energy storage unit in high wind penetration power system

technical field

The invention relates to the technical field of electric power storage, in particular to a method for arranging energy storage units in a power system with high wind penetration.

Background technique

As the electricity system transitions to an unregulated structure, system operators must efficiently deliver new services to achieve electricity market goals. Energy storage can improve social welfare while improving grid performance and reliability. These services can manage peak demand, integrate intermittent renewable energy technologies, provide ancillary services such as load following and regulation, resolve transmission line congestion, defer transmission and distribution (T&D) upgrades, and support demand response resources, Ref. [1]: S. Eckroad, EPRI DOE Handbook for Energy Storage for Transmission or Distribution Applications, Palo Alto, CA, Dec. 2003. According to the report of Sandia National Laboratories, these can save 230 million US dollars by reducing the financial loss of end users due to power outages, avoiding transmission access fees and 1.43 billion US dollars in profits, reference [2]: J . Eyer and G. Corey, Energy Storage for the Electricity Grid: Benefits and Market Potential Assessment Guide, Sandia National Laboratories, Albuquerque, NM, SAND 2010-0815, Feb. 2010.

The Renewable Energy Portfolio Standard (RPS) will increase renewable energy generation through intermittent output, and appropriate strategies need to be adopted to maximize the utility of energy storage units, reference [3]: I.P.Gyuk and S.Eckroad, EnergyStorage for Grid Connected Wind Generation Applications, U.S. Department of Energy, Washington, DC, EPRI-DOE Handbook Supplement, 1008703, Dec. 2004. For this reason, the problem of optimal energy storage unit size and placement must be effectively solved, reference [4]: G.Celli, S.Mocci, F.Pilo, and M.Loddo, “Optimal integration of energy storage in distribution networks,” inProc . IEEE Power Tech Conf., Bucharest, Oct. 2009. In unregulated power systems with high wind penetration, optimal allocation of energy storage units offers several benefits, including market-based opportunities such as renewable energy time-shifting, renewable energy capacity recognition, through revenue or reduction Costs and societal benefits associated with energy storage, Ref. [2] Delayed transmission and distribution upgrades in the form of integrating more renewables, reducing emissions and improving grid asset utilization. The economic evaluation of energy storage systems also requires a cost-benefit analysis. Limited transmission capacity during periods of high winds may require curtailment, which, depending on contractual agreements, may result in lost revenue for wind turbines or additional costs for grid operators. Storing wind energy in excess of transmission capacity makes it dispatchable later when transmission capacity becomes available. Thus, an optimal allocation of energy storage units leads to an efficient utilization of the transmission capacity. The intermittency of the wind resource itself has caused great uncertainty to the final output power, and the typical error is in the range of 30%-50%. Reference [5]: J.Garcia-Gonzalez, R.M.R.de la Muela, L.M. Santos, and A.M. Gon-zalez, “Stochastic joint optimization of windgeneration and pumped-storage units in an electricity market,” IEEE Trans. Power Syst., vol.23, no.2, pp.460–468, May 2008. Optimal placement of sufficient energy storage capacity provides the flexibility needed to comply with clearing wind power schedules and hedging forecast uncertainty in the market, reference [6]: H.Bludszuweit and J.A. Dominguez-Navarro, “A probabilistic method for energystorage sizing based on wind power forecast uncertainty," IEEE Trans. PowerSyst., vol.26, no.3, pp.1651–1658, Aug.2011, reference [7]: T.K.A.Brekken, A.Yokochi, A.V.Jouanne, Z.Z. Yen, H.M. Hapke, and D.A. Halamay, “Optimal energy storage sizing and control for wind power applications,” IEEE Trans. Sustain. Energy, vol.2, no.1, pp.69–77, Jan. 2011. This flexibility is achieved by storing excess energy when wind production is higher than the removal plan. The stored energy is used to avoid penalties associated with generating less energy than the scavenging plan. Furthermore, an optimal arrangement of the energy storage system is also required in order to utilize the energy storage capacity more efficiently while maintaining the transfer thermal constraints. Subsequently, the net power delivery more accurately follows the clearance schedule in the market.

Currently, few publications discuss the optimal placement of energy storage in power systems with renewable energy generation Ref. [4], Refs. [8]–[10],

Reference [8]: K.Dvijotham, S.Backhaus, and M.Chertkov, Operation-Based Plan-ning for Placement and Sizing of Energy Storage in a Grid With a High Penetration of Renewables, arXiv: 1107.1382v2,

Reference [9]: G.Carpinelli, F.Mottola, D.Porto, and A.Russo, “Optimalallocation of dispersed generators, capacitors and distributed energy storagesys-tems in distribution networks,” in Proc.Int.Symp.of Modern Electric Power Syst. (MEPS), Sep.2010, pp.1–6,

Reference [10]: H.Kihara, A.Yokoyama, K.M.Liyanage, and H. Sakuma, "Optimalplacement and control of BESS for a distribution system integrated with PVsystems," J.Int.Council Elect.Eng., vol.1 , no. 3, pp. 298–303, 2011.

Except for reference [4], these studies are based on deterministic models that do not represent the stochastic nature of renewable energy. Besides, the model in Ref. [4] does not properly represent the uncertainty of renewable energy. Furthermore, none of these publications take into account the unregulated structure of the power system. Energy storage units and their application in unregulated market environments are investigated in Refs [11]–[17].

Reference [11]: M.G.Hoffman, A.Sadovsky, M.C.Kintner-Meyer, and J.G.DeSteese, Analysis Tools for Sizing and Placement of Energy Storage in Grid Applications, U.S.Department of Energy, Sep.2010

Reference [12]: R. Sioshansi, P. Denholm, T. Jenkin, and J. Weiss, "Estimating the value of electricity storage in PJM: Arbitrage and some welfare ef-fects," Energy Econ., vol.31, pp . 269–277, 2009

Reference [13]: R.Walawalkar, J.Apt, and R.Mancini, “Economics of electricityn-energy storage for energy arbitrage and regulation in new york,” EnergyPolicy, vol.35, pp.2558–2568, Apr. 2007

Reference [14]: F.C.Figueiredo, P.C.Flynn, and E.A.Cabral, “The economics of energy storage in 14 deregulated power markets,” Energy Studies Rev., vol.14, pp.131–152, Oct.2006

Reference [15]: E.Drury, P.Delholm, and R.Sioshansi, "The value of compressed air energy storage in energy and reserve markets," Energy, vol.36, pp.4959–4973, Aug.2011

Reference [16]: EPRI-DOE Handbook of Energy Storage for Transmission&Distribution Applications, EPRI, Palo Alto, CA, and U.S. Department of Energy, Washington, DC, 1001834

Reference [17]: J.M.Eyer, J.J.Iannucci, and G.P.Corey, Energy storage benefits and market analysis handbook, A study for the DOE Energy StorageSyst.Program 2004

These studies all assume that dispatching energy storage equipment does not affect market prices. This "price taker" analysis is not applicable to large-scale energy storage applications in wholesale electricity markets where storage units have a significant impact on market clearing prices. Furthermore, none of these studies explored optimal energy storage location and energy storage allocation, which would increase social welfare, requiring a comprehensive stochastic optimization framework to optimally place and dispatch energy storage units in unregulated areas with high wind penetration. within the power system.

Therefore, it is desired to have a method for arranging energy storage units in high wind penetration power systems that can solve the problems existing in the prior art.

Contents of the invention

The invention discloses an arrangement method of an energy storage unit in a high wind penetration power system. The arrangement method establishes a market-based probabilistic optimal power flow, and the power flow has energy storage integration and wind power generation, including the following steps:

Step 1: Modeling according to wind generation and load probabilities;

Step 2: Time-shift the electric energy of renewable energy by using the energy storage system;

Step 3: Economic characteristics of compressed air energy storage;

Step 4: Establish a power pool model and incorporate the unilateral auction market into the optimal trend;

Step 5: Use the probabilistic optimal power flow to consider uncertain factors such as wind power output and variable load in the power flow calculation;

Step 6: Optimizing using genetic algorithm to determine the optimal location of the energy storage unit in the unregulated wind power generation system based on the probabilistic optimal power flow of the electricity market.

Preferably, the step 1 specifically includes: according to the historical data of wind speed and load, using a probability density function to characterize the uncertainty of the wind power generation and load, and using Weibull distribution to statistically model the wind speed, the probability density function of which is the formula (1):

λ is the scale factor of Weibull distribution, k is the shape factor of Weibull distribution, v is the wind speed;

Using the method of curve fitting, the maximum likelihood estimation of the Weibull distribution parameters is calculated for the historical hourly wind speed data, and the output power of the wind turbine is the wind speed function of the formula (2):

_Gw is the wind output power, is the rated wind power, v _i is the cut-in wind speed, v _o is the cut-off wind speed, and v _r is the rated wind speed;

Static modeling of load changes is performed using a Gaussian distribution, and the probability density function of the Gaussian distribution is Equation (3):

μ _L , σ _L are the expected value and standard deviation load of Gaussian distribution;

The method of curve fitting is used to calculate the maximum likelihood estimation of Gaussian distribution parameters for historical hourly load data.

Preferably, the step 2 using the energy storage system to time-shift the electric energy of the renewable energy specifically includes: when During off-peak hours, the energy storage unit is charged with wind power exceeding the load or transmission capacity, or the transmission capacity limits the transmission of wind power; , the stored energy is released during peak load hours; where, is the output power of wind power at time t, and L _t is the load demand at time t.

Preferably, the total cost of the compressed air energy storage in step 3 is the sum of the turbine, the storage tank and the compressor in the formula (10), the turbine is the rated power of the compressed air energy storage, and the water storage is the rated power of the compressed air energy storage rated energy,

C _Inv is the total investment cost of compressed air energy storage, C _C , C _P , C _S are the compressors, power and energy costs of compressed air energy storage, P _max is the rated power of the energy storage system, is the rated power of the compressor;

The operating cost of compressed air energy storage is formula (11), including fuel cost, fixed operating cost and maintenance cost:

HR is the heat rate of the turbine for compressed air energy storage, is the power generation capacity of the energy storage system at time t, C _NG is the natural gas cost of compressed air energy storage, and C _OM is the fixed operation and maintenance cost of compressed air energy storage;

The annual equivalent cost is Equation (12):

Preferably, in the establishment of the power pool model in step 4, each market participant submits an hourly price bid in the form of marginal cost, and the bid is used as the input of the optimal power flow, and the supply and node marginal electricity price are determined to minimize each Hourly social cost, a bilateral contract between wind power suppliers and energy storage owners for the purchase of curtailed wind power, hourly social cost expressed as a function of generation bids. The incremental cost method is used for bidding, and the objective function based on the optimal power flow in the electricity market is:

is the generating capacity of the i-th generator set at time t, a _i and b _i are the coefficients of the i-th generator set in the bidding function;

Using the DC model of the power system, the power balance equation is Equation (14):

is the demand of bus i at time t;

Power losses are neglected, and the bounds on power production give the inequality (15)

The ramp-up and ramp-down of the generator are formulas (16) and (17):

The line flow is limited by Equation (18)

H _li is the sensitivity of active power flow to the change of power injection of bus i;

The Lagrange function of market-based optimal power flow is formula (19)

In an electricity market based on node marginal electricity price, the node marginal electricity price of the bus at time t provides the marginal cost of the next demand increment for the bus λ _i,t ;

Based on the Karush–Kuhn–Tucker optimal condition, the first derivative of the Lagrangian function The node marginal electricity price generated at each bus is formula (20) and (21):

In the node marginal electricity price market, the load payment and generator payment are based on the node marginal electricity price, and the generator income of bus i at time t is the formula (22):

Preferably, step 5 implements the probabilistic optimal power flow through a point estimation approximation method.

The present invention proposes a method for the placement of energy storage units in high wind penetration power systems based on a market-based probabilistically optimal power flow (POPF) with energy storage integration and wind power generation. The proposed method considers energy storage units as market participants in the market clearing process, optimally placing and arranging them to minimize social costs.

Description of drawings

Figure 1 is a flow chart of the enhanced genetic algorithm based on the probabilistic optimal power flow of the electricity market.

Figure 2 is a line graph of the 45% wind penetration results with two distributed energy storage systems.

FIG. 3 is a line diagram of the hourly node marginal electricity price of the bus 14 without energy storage.

Figure 4 is a line diagram of the simulation results of two units and 45% wind power penetration;

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below in conjunction with the drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the invention. The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

The arrangement method of the energy storage unit in the high wind penetration power system of the present invention, the arrangement method establishes a market-based probabilistic optimal flow, and the flow has energy storage integration and wind power generation, including the following steps:

Step 1: Modeling according to wind generation and load probabilities;

Uncertainty in wind power generation and load is characterized using probability density functions (pdfs) derived from historical wind speed and load data. The wind speed is statistically modeled using the Weibull distribution, whose probability density function is Equation (1):

Maximum likelihood estimates of the parameters of the Weibull distribution are calculated for historical hourly wind speed data using a curve-fitting method. The output power of the wind turbine is a function of wind speed as formula (2):

In this paper, the Gaussian distribution is used to statically model the load change, and the probability density function of the Gaussian distribution is formula (3):

The method of curve fitting is used to calculate the maximum likelihood estimation of Gaussian distribution parameters for historical hourly load data.

Step 2: Time-shift the electric energy of renewable energy by using the energy storage system;

The energy storage unit is charged with wind power that exceeds load or transmission capacity and would otherwise be curtailed. this happens in (off-peak hours) or transmission capacity constraints determine the transmission of wind power. Stored energy is released during the most valuable peak load hours of the day and In transmission networks, large-scale and economical energy storage requirements for time-shifted conversion of wind-generated energy make compressed air energy storage (CAES) and pumped hydro energy storage (PHES) a promising technology for energy arbitrage services. However, the latter geographic constraints make CAES a viable technology as used in this paper. The instantaneous energy balance in an energy storage system is:

a) For charging formula (4):

b) For discharge formula (5):

For the minimum energy storage capacity S _min and the maximum energy storage capacity S _max at time t, the energy storage satisfies formula (6):

Assuming the same maximum charge and discharge rate (P _max ), the hourly power of the energy storage system must satisfy the following inequality formula (7):

Similar to all generators, the turbine's own ramp-up and ramp-down constraints are given by equations (8) and (9):

The cycle life cycle and the calendar life cycle of this energy storage technology are equal to 30 years.

Step 3: Economic characteristics of compressed air energy storage;

The total cost of CAES is the sum of turbine (rated power of CAES), reservoir (rated energy of CAES) and compressor as Equation (10):

C _s is 53$/kWh. Assuming the CAES and compressor have the same rated power, the cost of power and compressor is 425$/kW. The operating cost of CAES includes fuel (natural gas) cost, fixed operating cost and maintenance (O&M) cost as Equation (11):

HR, C _NG and C _OM are 4300Btu/kWh, 5$/Mbtu and 2.5$/kW-year respectively. All initial investment expenditures must be converted into a uniform series of annual costs.

The annual equivalent cost is formula (12):

d and N are 10% and 30 years, respectively.

Step 4: Establish a power pool model and incorporate the unilateral auction market into the optimal trend;

In the power pool model, each market participant submits an hourly price bid in the form of marginal cost. Bids are taken as input for optimal power flow, which optimally determines supply and node marginal price (LMP) to minimize hourly social cost (HSC). Bilateral contracts between wind suppliers and storage owners are used to purchase curtailed wind power. The hourly social cost can be expressed as a function of the electricity generation bid. The incremental cost method is used for bidding, and the objective function based on the optimal power flow in the electricity market is formula (13):

In a one-sided market, hourly social costs exist in the form of generation costs. Independent system operators (ISOs) perform this market clearing process while satisfying the following equation and inequality constraints. Using the DC model of the power system, the power balance equation is Equation (14):

Power losses are neglected, and the bounds on power production are given by the inequality equation (15):

Economic considerations determine the lower limit, while the physical constraints of the generator limit the upper limit. The ramp-up and ramp-down of the generator are formulas (16) and (17):

The line flow is limited by Equation (18):

This limit is determined by the heat capacity of the transmission line. The left side of the equation represents the active power passing through the transmission line l. H _li is the sensitivity of active power flow to changes in the power injection of bus i. The Lagrangian function of market-based optimal power flow is formula (19):

In an electricity market based on node marginal price, the bus node marginal price at time t provides the marginal cost of the next demand increment for bus λi _,t . Based on the Karush–Kuhn–Tucker (KKT) optimal condition, the first derivative of the Lagrange function The nodal marginal electricity price will be generated at each bus as formulas (20) and (21):

In the node marginal price market, the load payment and the generator payment are based on the node marginal price. The generator income of bus i at time t is formula (22):

During the operation of the power generation mode, the income obtained by the energy storage system from the sale of energy is calculated using formula (22);

Step 5: Use the probabilistic optimal power flow to consider uncertain factors such as wind power output and variable load in the power flow calculation;

By using probabilistic optimal power flow, uncertain factors such as wind power output and variable load can be considered in the power flow calculation. Several methods are proposed to perform probabilistic analysis in probabilistic optimal power flow problems. These methods are categorized as simulation, analysis and approximation methods. Monte Carlo simulation (MCS) is a simple and accurate method that uses historical data of probability quantities to find their probability density functions. Among these probability density functions are selected Random values of and used to quantify uncertainty. The large amount of computational effort is a major obstacle to the effective use of this method. The main disadvantage of the probabilistic optimal power flow analysis method is its complex mathematical calculations. Several approximate methods have been proposed to reduce the computational burden and mathematical calculations associated with Monte Carlo simulation and analytical methods, respectively. Point Estimation (PE) is a commonly used approximation method, which has the advantages of high precision, simple calculation, and fast speed. Two-point estimation (2PE) is a variant of point estimation to model uncertainty. Compared to Monte Carlo simulations, the method exhibits a level of high accuracy in the application of probabilistic optimal power flow problems, while significantly reducing the computational burden. The vectors of input random variables and output random variables and the corresponding nonlinear functions are formulas (23), (24) and (25), respectively:

X＝[Wind Speed, Loads] (23)

Y=[HSC] (24)

Y=h(X) (25)

h is a function used to control market-based probabilistic optimal power flow, which includes integration and storage in wind power generation. Two concentrations by matching their previous three moments is used instead of The functional relationship between X _k and h(X _k ) is used to generate two variable estimates of Y (Y _k,i = P _k,1 and P _k,2 scale the estimates to compute the expected value and standard deviation of the output.

The method uses DC optimal power flow based on unit decomposition to schedule hourly generation. The unit resolver provides a mechanism to shut down generators that are expensive to run and find the least costly commitments and schedules. This results in economical operation of the system within the dispatch cycle. The proposed method incorporates energy storage into a market-based OPF model to time-shift electricity from wind. The proposed method incorporates energy storage into a market-based optimal power flow model to time-shift electricity from wind. For this purpose, energy storage is considered as a variable load or variable generator. When the specific load of wind power is high (off-peak period) or exceeds the transmission capacity limit, energy storage acts as a variable load to store excess wind energy, otherwise it will be curtailed. This transaction is done through a bilateral contract between the wind supplier and the storage owner. Then, during peak hours of the day, this energy storage acts as a variable generator, selling when the stored energy is most valuable. The probabilistic optimal power flow algorithm proposed for the scheduling period is summarized as follows:

1. Load the input data (wind speed and load).

2. Let t=1.

3. Assign an appropriate probability density function to each probability variable.

4. Let E(Y)=E(Y ² )=0.

5. Let k=1.

6. The necessary parameters to determine 2PEM are formulas (26a), (26b) and (26c):

n represents the number of probability variables.

7. Set the concentration using the input vector X as formula (27):

Note that the transformation given by step 2 is used to obtain wind force from wind speed.

8. Calculate Note that in each iteration is replaced by x _k,i (i=1,2).

9. If GW- _L >0 or the wind power exceeds the transmission capacity, the energy storage device purchases the excess wind power through a bilateral contract and acts as a variable load under the following constraints:

Otherwise, the energy storage unit as a generator has the following constraints:

10. Run the optimal power flow based on the deterministic market, and use the energy storage system as a variable load or generator Z

Calculate state of charge with steps 4-5

12. Calculate hourly social cost

13. Update mean E(Y) and mean square E(Y) ² to formulas (28a) and (28b)

14. Let k=k+1 and repeat steps 6-13 for all input variables

15. Calculate the expected value and standard deviation as formulas (29a) and (29b):

μ _Y = E(Y) (29a)

16. Let t=t+1, and repeat steps 3-15 until t>T.

The above probabilistic optimal power flow algorithm minimizes the social cost of the system under the condition of satisfying the hourly constraints in the scheduling period.

Step 6: Optimizing using genetic algorithm to determine the optimal location of the energy storage unit in the unregulated wind power generation system based on the probabilistic optimal power flow of the electricity market;

Optimization using a genetic algorithm (GAS) is a powerful tool for obtaining optimal energy storage locations in an unregulated high wind penetration power system. Usually, a set of initial solutions (initial population) are randomly selected from the feasible solution space for starting the genetic algorithm. Evaluate the fitness function for each solution, then rank the solutions. The population evolves through multiple operations such as reproduction, crossover, and mutation, and the fitness function is optimized to obtain the final optimal solution. This process is repeated until the termination criteria are met. This evolutionary algorithm outperforms classical optimization methods because it can handle nonlinear, non-convex and mixed integer optimization problems for energy storage placement. The non-convexity of this problem makes it difficult for classical optimization methods to obtain a global optimal solution. Genetic algorithms, on the other hand, globally search the domain of possible solutions to obtain an optimal solution. Genetic algorithms require fewer variables than traditional optimization methods. However, genetic algorithms may converge to local minima if not executed carefully.

Some implementation strategies avoid converging to local minima. A larger population size increases the probability of converging to the global minimum, but this will significantly increase the computational burden. Keep two high-quality individuals per generation to ensure retention of the ideal solution. A good balance between hybrid and mutant offspring was achieved by keeping the hybrid fraction around 78%. In order to satisfy the constraint, a larger penalty factor is assigned to the solution that violates the constraint. The parameters of the genetic algorithm are given in Table 4 of the appendix:

Table 4: Genetic Algorithm Parameters

The present invention uses an enhanced genetic algorithm to determine the optimal location of energy storage units in an unregulated wind power generation system based on the probabilistic optimal power flow of the electricity market. This scheme minimizes the hourly social cost of the system and maximizes the utilization of wind power in the power pool market during dispatch. CAES must have sufficient energy storage capacity to store excess wind energy while satisfying transmission constraints. Storage capacity is then calculated based on the optimization results. The fitness function of the proposed optimization method is:

The flowchart of the method is shown in Fig. 1, where the first population of decision variables is initialized to optimize the location of the energy storage system and maximize the utilization of wind energy during dispatch. Using the market-based probabilistic optimal power flow, the minimum social cost of the system per hour is calculated based on the optimal location of the energy storage system. The fitness function evaluated for all individuals is given by Equation (30). Next, check for constraint violations. Violated constraints are assigned a large penalty factor (v), combined with a fitness function f as formula (31):

f'(x,u)=f(x,u)+v[h(x,u)] ² (31)

This makes an infeasible solution more expensive than a feasible solution with the same objective value. Through crossover and mutation operations on chromosomes, offspring populations are generated, and then the next generation is produced through selection and reproduction. This evolutionary algorithm is executed repeatedly until a termination criterion is met. Ultimately, the best chromosome is selected as the optimal solution to the optimization problem. Maximizing wind energy utilization during dispatch ensures that energy storage units are placed optimally to maximize the social welfare of the system.

The probabilistic optimal power flow proposed by the present invention optimizes the placement of energy storage units in the IEEE24 bus system under two different wind penetration levels, and evaluates the simulation results. The economics of CAES are also assessed by comparing the associated costs and arbitrage income. The cost is the sum of equivalent investment and operating costs during a 24-hour dispatch period. The arbitrage yield is the difference between what the energy storage system earns from selling energy and the cost it pays to buy excess wind energy through bilateral contracts. Wind infiltration is defined as the ratio of installed wind capacity to system peak load. For both cases, the primary energy source is a wind farm installed on the busbar 14 . First, all gensets are committed every hour during the scheduling period. Storage systems should be placed such that the generator with the lowest marginal cost function can be dispatched within 24 hours, if required. This minimizes the hourly social cost of the system while maximizing wind energy utilization during dispatch. The bidding function coefficients for generating units are given in the appendix (Table 5). Wind speeds and loads are from historical hourly data from BPA authorities and Mesonet.

Table 5: Generator Data

A. Scheme Ⅰ: Distributed energy storage with unlimited capacity

This scenario evaluates wind power penetration (WP) levels and their potential impact on optimal placement of energy storage units and market-based energy arbitrage opportunities in IEEE 24 bus systems. All market participants bid in the day-ahead energy market based on historical data. Finding optimal bidding strategies for wind and energy storage is beyond the scope of this paper. Assume that wind power owners bid to make wind power the dominant source of energy in the market. Available production tax credits make this assumption reasonable.

For this scenario, several levels of wind infiltration were investigated. First, a market-based probabilistic optimal power flow without energy storage is used to calculate wind energy utilization during a 24-hour dispatch period. Second, the placement of energy storage units uses an enhanced genetic algorithm based on a market-based probabilistic optimal power flow to maximize wind power utilization.

Table 1: Simulation results of optimal placement of energy storage system (Scheme Ⅰ)

The simulation results are summarized in Table 1, Figure 2, and Figure 3. All data provides expected values for each hour of the 24-hour scheduling period. The results show that at a low level of wind power penetration, when the wind power load is lower than the system load within 24 hours, almost all the wind power generated is utilized and does not need to be stored. This is at a wind power penetration level of 20%, 96.11% of wind power is utilized. Installing an energy storage system with a capacity of 100.1mwh and a rated power of 99.82mw on busbar 4 can slightly increase the utilization rate of wind energy to 97.37%. During off-peak hours, increasing wind penetration levels to 25% would allow wind generation to be higher than system load. Optimally placing a storage system with a capacity of 396.65mwh and a rated power of 260.1mw on bus 4 will increase the utilization rate of wind power from 90.37% (without energy storage unit) to 97.37% (with energy storage unit). Above a wind penetration level of 25%, the wind power generated may exceed the transmission capacity limit connected to the wind power busbar (busbar 14). While a properly sized and located energy storage system can store excess energy, placing the energy storage system on any bus other than the wind bus would violate transmission line constraints or require reduced wind generation. This is evident for a wind penetration of 30%-45%, as one would intuitively predict, the optimal location of the energy storage unit is at busbar 14. Comparing simulation results at different wind penetration levels reveals that arbitrage benefits alone do not justify the total cost of CAES at low wind penetration levels (20% and 25%). However, the cost may be justified if other storage-related benefits or credits are included, such as enhanced renewable energy capacity and production tax credits. Arbitrage income justifies the cost of CAES for higher wind penetration levels (30%–45%). However, the physical constraints of the lines connected to the wind bus reduce the wind utilization expectation for 45% wind penetration to 92.61 %, which is less efficient than the 97.37% wind utilization rate for low wind penetration levels.

Table 2: Simulation results of optimal placement of distributed energy storage systems (Scheme I - 45% wind power penetration)

The simulation results for 45% wind power penetration are shown in Fig. 2. The energy storage system is charged earlier in the day when wind energy exceeds the system load or the transmission capacity of the lines connected to the wind bus. This energy can be purchased through bilateral contracts between wind farm and energy storage owners. Wind power is the main energy source to meet the electricity demand, and the energy storage on the bus 14 can be used as a variable load. During this period, no traditional power generation company has committed to supplying wind power supplements to the market. During peak hours at noon when the load exceeds wind power generation, the energy storage unit bids in the market as a generator, releasing stored energy to supplement wind power generation while maintaining transmission constraints. When wind power and energy storage are insufficient to supply the load, conventional generation is dispatched to meet demand. When the wind point is greater than the system load, the energy storage unit is recharged between 15 and 17 hours. When loads exceed wind power generation, the stored energy is released later in the day to supplement wind power generation. However, energy storage is not fully released, and traditional power generation is still required to meet the load. This is due to the high wind speeds at night that increase wind power production beyond the physical limits of the transmission lines connected to the wind bus. Wind energy is stored in bus 14 when this constraint is exceeded, during which time no energy is released. Figure 3 shows the hourly node marginal price for a bus 14 without energy storage. By increasing the off-peak electricity price and reducing the peak electricity price, the layout of the centralized energy storage unit of the wind bus is optimized to reduce the level of node marginal electricity price.

Simulation results for a high wind penetration level of 45% show how transmission constraints on lines connected to the wind bus limit wind integration. Transmission extension is an effective but expensive option that can be avoided by efficient use of existing transmission capacity. However, centralized energy storage cannot meet this goal for many networks due to transmission constraints. Figure 2 shows the results for a 45% wind penetration with two distributed energy storage systems: a two-unit and a three-unit system. The results for centralized energy storage were repeated for comparison. Distributed energy storage can use transmission capacity more efficiently and integrate wind power with higher penetration. Defining the net income as the difference between the arbitrage income and the cost, the net income of centralized storage is (formula), and the net income of the first energy storage and the second energy storage of the two-unit system are respectively (formula) (formula) . Therefore, the net income increases with the number of units, i.e. this distributed storage system increases the arbitrage income.

Figure 4 shows the simulation results for two units and 45% wind power penetration. Probabilistic Optimal Power Flow places energy storage systems on buses 14 and 10. During off-peak hours, when wind power exceeds demand, additional energy is allocated to storage systems to maximize storage while meeting the demand for connections to the wind bus. The physical constraints of the line. This makes more efficient use of transmission lines than centralized storage systems. Apparently, in the last few hours of the day, almost all of the stored energy is released to supplement wind power generation. In the case of 45% wind power penetration, distributed energy storage in the IEEE 24 bus system increases the wind energy utilization rate of centralized energy storage from 92.61% to 97.31% for two-unit and three-unit energy storage. However, the third unit in the three-unit energy storage system was not used. Therefore, the distributed two-unit energy storage system provides an optimal solution for efficient wind power integration with 45% wind power penetration. The total cost of compressed air energy storage for a two-cell system is determined by arbitrage market returns.

Table 3: Simulation results of optimal placement of distributed energy storage system (Scheme II-45% wind power penetration)

B. Scheme Ⅱ: Distributed energy storage with limited capacity

This scenario considers the optimal location of energy storage within an IEEE 24 bus system, subject to geographic and physical constraints of available energy and power capacity. For simplicity, the busbars are divided into two categories, with compressed air energy storage capacities of 400MW (1200MWh) and 300MW (1000MWh), respectively. Buses 1, 2, 3, 4, 10, 11, 12, 13, 14, 19, 21, and 23 belong to the first group, and the second group contains the remaining buses. Table 3 shows the simulation results of this scheme. The distributed two-unit energy storage system is the optimal solution for the efficient integration of wind power and 45% wind power penetration. Energy time shift revenues from wind power justify this solution.

The present invention studies the optimal location of energy storage units in an unregulated power system to minimize the hourly social cost. Wind and loads were stochastically modeled using historical data and curve fitting. An enhanced genetic algorithm for market-based probabilistic optimal power flow with energy storage integration and wind generation maximizes the utilization of wind power during dispatch. An energy arbitrage model was developed to assess the economics of compressed air energy storage. The simulation results of the IEEE 24 bus system show that the advantage of hybrid wind power and energy storage wind power lies in the efficient integration of wind power with a higher penetration level. Optimal energy storage allocation enables efficient utilization of the transmission capacity of the wind power integration while satisfying the transmission constraints of the lines connected to the wind power bus. This eliminates the need for costly transport extensions. According to different energy storage distribution conditions, calculate the optimal location of energy storage units, and choose the most efficient integrated wind power and high penetration level solution. The simulation results also show that at low wind penetration levels, the total cost of CAES cannot be justified by the arbitrage benefits alone. However, the cost may be justified if some other storage-related benefits or credits are included, such as enhanced renewable energy capacity and production tax credits. For higher wind penetration levels, both centralized and distributed energy storage systems can be economically viable through revenues from the time-shifted market for renewable energy. Case study shows distributed storage system increases net arbitrage income

Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: they can still modify the technical solutions described in the aforementioned embodiments, or perform equivalent replacements for some of the technical features; and these The modification or replacement does not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (6)

1. An arrangement method of an energy storage unit in a high wind penetration power system, characterized in that the arrangement method establishes a market-based probabilistic optimal flow, and the flow has energy storage integration and wind power generation, comprising the following steps: Step 1: Modeling according to wind generation and load probabilities; Step 2: Time-shift the electric energy of renewable energy by using the energy storage system; Step 3: Economic characteristics of compressed air energy storage; Step 4: Establish a power pool model and incorporate the unilateral auction market into the optimal trend; Step 5: Use the probabilistic optimal power flow to consider uncertain factors such as wind power output and variable load in the power flow calculation; Step 6: Optimizing using genetic algorithm to determine the optimal location of the energy storage unit in the unregulated wind power generation system based on the probabilistic optimal power flow of the electricity market. 2. The method for arranging energy storage units in high wind penetration power systems according to claim 1, characterized in that: said step 1 specifically includes: using probability density function to characterize said wind force according to historical data of wind speed and load Uncertainty in power generation and load, the wind speed is statistically modeled using the Weibull distribution, whose probability density function is Equation (1): λ is the scale factor of Weibull distribution, k is the shape factor of Weibull distribution, v is the wind speed; Using the method of curve fitting, the maximum likelihood estimation of the Weibull distribution parameters is calculated for the historical hourly wind speed data, and the output power of the wind turbine is the wind speed function of the formula (2): _Gw is the wind output power, is the rated wind power, v _i is the cut-in wind speed, v _o is the cut-off wind speed, and v _r is the rated wind speed; Static modeling of load changes is performed using a Gaussian distribution, and the probability density function of the Gaussian distribution is Equation (3): μ _L , σ _L are the expected value and standard deviation load of Gaussian distribution; The method of curve fitting is used to calculate the maximum likelihood estimation of Gaussian distribution parameters for historical hourly load data. 3. The method for arranging energy storage units in high wind penetration power systems according to claim 1, characterized in that: the step 2 using the energy storage system to time-shift the electric energy of renewable energy specifically includes: when During off-peak hours, the energy storage unit is charged with wind power exceeding the load or transmission capacity, or the transmission capacity limits the transmission of wind power; , the stored energy is released during peak load hours; where, is the output power of wind power at time t, and L _t is the load demand at time t. 4. The method for arranging energy storage units in high wind penetration power systems according to claim 1, characterized in that: the total cost of compressed air energy storage in step 3 is the turbine, water storage tank and The sum of the compressor, the turbine is the rated power of the compressed air energy storage, the reservoir is the rated energy of the compressed air energy storage, C _Inv is the total investment cost of compressed air energy storage, C _C , C _P , C _S are the compressors, power and energy costs of compressed air energy storage, P _max is the rated power of the energy storage system, is the rated power of the compressor; The operating cost of compressed air energy storage is formula (11), including fuel cost, fixed operating cost and maintenance cost: HR is the heat rate of the turbine for compressed air energy storage, is the power generation capacity of the energy storage system at time t, C _NG is the natural gas cost of compressed air energy storage, and C _OM is the fixed operation and maintenance cost of compressed air energy storage; The annual equivalent cost is Equation (12): 5. A method for arranging energy storage units in high wind penetration power systems according to claim 1, characterized in that, in step 4 of establishing a power pool model, each market participant in the form of marginal cost Hourly price bids are submitted, bids are used as input for optimal power flow, supply and node marginal prices are determined to minimize hourly social costs, and bilateral contracts between wind suppliers and storage owners are used to purchase curtailed wind power , the hourly social cost is expressed as a function of the power generation bid, and the incremental cost method is used for bidding, and the objective function based on the optimal power flow in the electricity market is: is the generating capacity of the i-th generator set at time t, a _i and b _i are the coefficients of the i-th generator set in the bidding function; Using the DC model of the power system, the power balance equation is Equation (14): is the demand of bus i at time t; Power losses are neglected, and the bounds on power production give the inequality (15) The ramp-up and ramp-down of the generator are formulas (16) and (17): The line flow is limited by Equation (18) H _li is the sensitivity of active power flow to the change of power injection of bus i; The Lagrange function of market-based optimal power flow is formula (19) In an electricity market based on node marginal electricity price, the node marginal electricity price of the bus at time t provides the marginal cost of the next demand increment for the bus λ _i,t ; Based on the Karush–Kuhn–Tucker optimal condition, the first derivative of the Lagrangian function The node marginal electricity price generated at each bus is formula (20) and (21): In the node marginal electricity price market, the load payment and generator payment are based on the node marginal electricity price, and the generator income of bus i at time t is the formula (22): 6. The method for arranging energy storage units in a high wind penetration power system according to claim 1, characterized in that: said step 5 implements the probabilistic optimal power flow through a point estimation approximation method.