^{†}

Dept. of Electrical Engineering and Computer Science, Seoul National University, Korea. (

Wind power producers face many regulation costs in deregulated environment, which remarkably lowers the value of wind power in comparison with conventional sources. One of these costs is associated with the real-time variation of power output and being paid in frequency control market according to the variation band. This paper presents a new approach to coordination of battery energy storage in wind generation system for reducing the payment in frequency control market. The approach depends on the statistic data of wind generation and the prediction of frequency control market price to determine the optimal variation band which is then kept by the real-time charging and discharging of batteries, ultimately the minimum cost of frequency regulation can be obtained. The optimization problem is formulated as trade-off between the decrease in the regulation payment and the increase in the cost of using battery, and vice versus. The approach is applied to a study case and the results of simulation show its effectiveness.

Electric power industry is experiencing a major restructuring process which intentionally pushes both generation and consumption sectors into market forces with the ultimate target of reducing the electric price. In this new market environment, wind power producers (WPPs) face many regulation costs due to the intermittence of natural resources (i.e. wind speed) and the accuracy limit of prediction tools (which is only about 10–15% even with a modern prediction tools). As a result, the competitiveness of WPPs is remarkably lowered in comparison with the conventional sources, e.g. gas-fired, coal-fired power plants.

A number of study efforts have been paid in order to increase the value of wind power in the deregulated market, most of them focus on the case of Denmark where the wind power shares about 20% of the total electricity demand (in 2007) [

The entire aforementioned researches are dealing with imbalance cost caused by the bidding error of WPPs in spot market. However, there is another regulation cost faced by WPPs in the deregulated market that accounts for the influence of the real-time variation of wind power output in system frequency, called frequency regulation (FR) cost. This cost is settled in frequency control market based on the width of output variation (i.e. variation band) and the frequency regulation price (FRP).

In this paper, we present a new approach of improving the value of wind power which focuses on decreasing the payment of WPPs in frequency control market. It is assumed that WPP is a price-taker in the market, i.e. no capability to alter the market price; and BES is incorporated in the WGS. The opportunity is that, WPP can estimate the FRP in the next day and depends on the probabilistic information of real-time variation of wind power output to determine the optimal variation bands. To get beyond the previous studies, the cost of BES is taken into consideration in this paper. Therefore, the problem is formulated as tradeoff between the expected decrease in FR cost and the expected increase in BES cost, and vice versus. The problem solution will detail the optimal variation bands that the power output should kept inside at each hour of the next day and based on which, the real-time charging/discharging strategy of BES would be decided.

The remainder of this paper is organized as follows. Section II presents the principle of frequency regulation in power system and the market for frequency control. Section III reviews the recently emerging studies of battery energy storage in renewable energy system and the proposal of battery management system (BMS). Section IV provides mathematical formulations and derivation for the optimality condition. The case study in Section V demonstrates the application of the proposed approach and the actual charging/discharging of BES, then shows its effectiveness compared to two other operation strategies. Finally, conclusive points are summarized in Section VI.

There is a matter of fact that it is impossible to keep the system frequency always in the desired value (60Hz); instead power imbalance caused by the real-time variation of system users forces the system equilibrating with a frequency deviation [

The primary regulation refers to the generation spontaneously provided by Generator-Turbine-Governor (G-T-G) units when the system frequency deviates from the desired value; it is called droop-characteristic or governor-free. This action is fast and usually stabilizing the system within 5–10 seconds. In power system, loads also respond to the change of frequency, however, there is high uncertainty associated with their actions; thus, generally, loads are not considered as sources of primary regulation [_{G} and β_{L} are the sum of the droop-parameter (i.e. frequency-sensitivity) of all generators and loads in the system, [MW/Hz].

The secondary regulation refers to the generation provided by AGC set up on the technically qualified generating units, e.g. gas-fired generators [_{i} is ACE signal for area i, [MW]; (β_{G} + β_{L})_{i} is the sum of the droop-parameters within area i, [MW/Hz]; and ΔF_{ij} is the power deviation from the scheduled value in the tie-line between area i and j, [MW]; J is the set of area connected to area i through tie-lines. Then, the AGC generation of generator Gn in area i is calculated according to its participation factor, G_{Gn}:

The participation factors of all AGC generators within a control area subject to a constraint that sum of them must be equal to one.

The tertiary regulation refers to the generation called when a large power imbalance occurs in the system, e.g. caused by unexpected change of loads or loss of important generating units. These unexpected disturbances may cause the system out of frequency limits, voltage limits, and/or transmission line capacity limits so that the reschedule of generating units and transmission lines in the system-wide is required. This action typically takes more than 10 minutes, and therefore, permits the wide participation of demand-side (load-shedding), spinning and non-spinning generators [

In monopoly market, the task of maintaining the system frequency in acceptable limits is managed by System Operator (SO) and the cost of performing this regulation is passed to consumers in the price of electricity. In deregulated environment, however, it is important to relate cause and effect; or in other words, the rights and responsibilities of system users to the system performance (e.g. frequency) need to be cleared [

The frequency regulation in deregulated environment can be traded either through pool or bilateral contracts [_{l} is the power deviation of consumer l. The AGC generation by generator Gn is set as:
_{Gn} is the participation factor of generator Gn in frequency regulation pool; ΔPb_{nm} is the power deviation of consumer m who has bilateral contract of frequency regulation with generator Gn. M is the set of customers who have bilateral contract with generator Gn.

Therefore, once the FRP is cleared, the frequency regulation cost paid by loads and nonconventional sources (including wind power) can be calculated as follows:
^{FR} is the frequency regulation cost, [$]; ΔP^{±} is the variation band, [MW]; and λ^{RT} is the frequency regulation price, [$/MW].

Battery energy storage (BES) has long been a solution for improving the reliability and performance of power system; particularly, it is considered as the key element for integrating renewable sources in the electric network. Despite many advantages carried by BES, its application is very limited due to the lack of experience and tools for (i) operational cost optimization, and (ii) assessing the benefits considering market model [

Generally, the lifetime of a battery bank is given by manufacturer in term of Ah-throughput; that indicates the theoretical amount of Ah (ampere-hour) can be charged and discharged through the battery bank until the end-of-life is reached. This lifetime throughput is obtained by various test methods performing under certain conditions (i.e. standard condition). The matter of fact is that these conditions are usually not achievable in practice, particularly, under renewable application. Indeed, the operating condition of BES in renewable energy system is characterized by (i) partial state of charge (SoC), (ii) incomplete or rare full of charge, and (iii) wide range of ambient temperature [

In order to evaluate the battery lifetime, three different approaches are presented in [

In order to improve the lifetime and reliability of BES with respect to the application in renewable energy system, a battery management system (BMS) is proposed in [

In _{M1}–S_{M4}. This provides the option of connecting or disconnecting the individual strings (B_{1}–B_{4}) independently from each other. By this means, some battery can be charged or discharged while the others do not have to be involved. In addition, the BMS comprises a DC/DC converter connected to DC bus through switches S_{C1}–S_{C4}. This component is to perform a full charge for each individual battery string when the available energy is not enough for full charge of entire batteries.

Therefore, during normal operation in renewable system BMS enables shorter cycles at low SoC, increase in the current rate and intensive full charge; those are major stress factors on the lifetime of battery.

This section provides a mathematical formulation for determining the optimal variation band of WPP in response to the frequency regulation price (FRP) and the probabilistic information of real-time power output. The formulation is to minimize the total cost associated with frequency regulation which includes the payment in frequency control market and cost of BES. The formulation is restricted to the following assumptions:

WPP is a price-taker in the electric market, i.e. with no ability to alter the market clearing price.

The bidding in spot market is out of the scope of this paper, and without losing generality, the mean value (P̄) is assumed to be bided.

The statistic information of the output variation in real-time is available, e.g. probability density function.

BMS is applied so that each battery string of BES is operating closely to the standard condition. Then, the theoretical lifetime throughput can be obtained.

The problem is trading-off between the decrease in payment in frequency control market and the increase in expense of BES, and vice versus. The total cost associated with frequency regulation of WPP is calculated as follows:
_{k}^{FR} is the FRP at hour k, [$/MW]; ΔP_{k±} is variation band at hour k; and C_{B}[k] is the BES cost at hour k, [$]. From the assumption 4, it is implied that the theoretical lifetime throughput can be achieved; therefore it is able to evaluate the cost associated with per MWh charged and discharged through BES, called battery wear cost [29], as follows:

The BES cost in k-th hour can be approximately calculated as follows:

In

Before deriving solution, it is needed to define the operating strategy of BES to handle the terms of charging and discharging power in _{w}(t) is the real-time variation from the mean value of output, [MW].

Take the expectation of

The “bar” on the FRP in

According to assumption 3, the probability density function of output is known in form of normal (Gaussian) distribution:

Substituting

Take derivation of ^{±}) and use mathematically equivalent transformation, we obtain the optimality condition for the optimal variation band as follows:
_{w}) is the cumulative probability function of real-time output, [0, 1].

^{FR} will results in the decrease in ΔP^{±}, and vice versus. Likewise, the increase in c^{bw} also results in the increase in ΔP^{±}, and vice versus. That is logically true because in either case when the FRP is high or battery wear cost is low, WPP intends to use BES more, i.e. smaller variation band, to avoid the expensiveness of FRP or take advantage of low BES cost. Otherwise, when FRP is low or battery wear cost is high, WPP will use BES less, accompanied by large variation band, to benefit from low market price and avoid high cost of BES.

In this section, we consider the case of WPP owning 10 MW wind power and 1 MWh BES _{rep} = $1,000/unit; Q_{lifetime} = 10,494kWh; η_{rt} = 0.8, then the battery wear cost of BES can be calculated by ^{bw} = $106.5/MWh. Once the prediction of FRP and wind generation in the next day is available, the optimal variation bands for each hour of the next day can be obtained from

In order to observe the response of the optimal variation bands (ΔP^{±}) to the change of FRP (λ^{FT}) and the output variation (p_{w}), their normalized representations are displayed in

It can be seen that the optimal variation band (square-marked) seems to vary proportionally to the standard deviation of prediction (circle-marked) and inversely to the frequency regulation price (triangle-marked). That is logically true because when the power prediction is high, meaning the real-time deviation of power output will be large, the WPP should regulate BES with a large variation band to avoid the over-use of BES. This can be illustrated by the results at hour 4 and 5: the FRPs are near equal but the difference in power prediction will result in the difference of optimal variation band. On the other hand, when the FRP is low, the WPP should take advantage of cheap market price which results in large variation band as well. Comparing the results in hour 1 and 13, the power predictions are nearly the same but the higher FRP will result in lower optimal variation band.

In this section, the real-time charging/discharging operation of BES in response to the optimal variation bands is simulated. The real-time variation of wind power output and the optimal variation band are presented in

It can be seen that even the cumulative amount of charge and discharge are equal statistically, the SoC of BES gradually decreases during the day. That is because of the energy losses in charging and discharging through BES. Fortunately, this problem can be easily handled by trading in spot market (that is out of this paper scope). It is worth noting that the BES is only used when the output exceeds the optimal variation bands, i.e. with a relatively low probability density function. Therefore, only small volume of BES (1 MWh) is enough for handling the problem, i.e. keeping the synthesized output inside the optimal bands

The effectiveness of the proposed approach is illustrated by comparing to two other operating strategies: (i) without using BES, and (ii) intensively use of BES. The first strategy does not consider BES so that WPP must pay for the entire variation bands according to the FRP. The second strategy, on the other hand, uses BES intensively to fully compensate for the real-time variation; that means WPP does not have to pay any in frequency control market. However, both strategies result in a much higher cost compared to the proposed scheme

This paper presents a new approach of BES for improving the value of wind power in deregulated market. The approach deals with the cost associated with frequency regulation faced by WPP in power system, rather than the imbalance cost as in the previous studies. Then the paper provides a framework for determining the optimal variation band to which BES should be control to maintain the power output inside. The case study shows that the proposed scheme can significantly reduce the frequency regulation cost of WPP either compared to the cases without using BES and intensive use of BES.

It is noted that the physical constraints of BES such as minimum SoC, maximum rate of charge/discharge, etc. are handled in designing the battery controller which is out of the scope of this paper. In addition, the bidding strategy in spot market is also not considered that needs to take care of the gradually decrease of the SoC of BES as the above discussion. For instance, the WPP should bid somehow smaller than the mean value to compensate for the energy losses in charging and discharging of BES.

time index, [hour]

n-th generator

_{s}

system frequency deviation, [Hz]

_{s}

system power imbalance, [MW]

droop-parameter, [MW/Hz]

area control error signal, [MW]

AGC participation factor

^{agc}

AGC power generation, [MW]

power deviation in tie-line between areas, [MW]

power deviation of bilateral contract customer, [MW]

^{FR}

frequency regulation price, [$/MW]

^{FR}

frequency regulation cost, [$]

_{B}

battery utilization cost, [$]

^{bw}

battery wear cost, [$/MWh]

_{rep}

battery replacement cost, [$]

_{rt}

battery round-trip efficiency

number of batteries in a bank

_{lifetime}

battery lifetime throughput, [MWh]

^{±}

variation band, [MW]

_{ch}

BES charging power, [MW]

_{dis}

BES discharging power, [MW]

_{w}

real-time deviation of wind power output, [MW]

prediction of (hourly) power generation, [MW]

_{out}

synthesized power output deviation, [MW]

This work was supported by the Ministry of Knowledge Economy as a part of its research on Energy Storage System for Smartgrids.

Circuit concept of BMS with four parallel switched battery strings (B_{1}–B_{4}).

Outline of WGS with BES

Probability density function and cumulative probability function of real-time variation

Normalized standard deviation, [1MW]; FRP, [$20/MW]; and the optimal variation bands, [1.5MW] at each hour of the day

Real-time variation of wind power output and the optimal variation band during the day

Charging/discharging power and SoC of BES during the day

The prediction of wind generation, FR price and optimal variable bands

Time (hour) | P̄ (MW) | λ^{FR} ($/MW) |
ΔP^{±} (MW) |
Time (hour) | P̄ (MW) | λ^{FR} ($/MW) |
ΔP^{±} (MW) |
---|---|---|---|---|---|---|---|

1 | 16.240 | 10.96 | 0.7505 | 13 | 6.242 | 16.88 | 0.5801 |

2 | 7.307 | 9.89 | 0.9228 | 14 | 5.058 | 17.34 | 0.4608 |

3 | 9.765 | 9.13 | 1.7729 | 15 | 6.937 | 16.66 | 0.6510 |

4 | 7.957 | 8.66 | 1.0644 | 16 | 8.167 | 16.14 | 0.7840 |

5 | 9.082 | 8.81 | 1.2064 | 17 | 5.432 | 18.35 | 0.4736 |

6 | 5.950 | 10.33 | 0.7362 | 18 | 3.835 | 18.98 | 0.3250 |

7 | 4.928 | 11.43 | 0.5803 | 19 | 3.765 | 17.84 | 0.3355 |

8 | 5.924 | 12.62 | 0.6622 | 20 | 6.242 | 16.07 | 0.6010 |

9 | 5.590 | 12.81 | 0.6196 | 21 | 9.214 | 16.49 | 0.8713 |

10 | 5.041 | 13.81 | 0.5349 | 22 | 9.794 | 14.80 | 0.9963 |

11 | 3.458 | 14.58 | 0.3548 | 23 | 9.120 | 12.71 | 1.0156 |

12 | 6.198 | 15.77 | 0.6044 | 24 | 6.024 | 12.05 | 0.6903 |

Comparison of different operation strategies

Operation strategies | BES cost [$] | FR cost [$] | Total [$] |
---|---|---|---|

Without using BES | 0 | 341.12 | 341.12 |

Intensive use of BES | 416.40 | 0 | 416.40 |

Proposed scheme | 33.37 | 223.65 | 257.02 |