synthetic inertia provision from wind plants has not yet been understood. This paper develops a methodology to incorporate the synthetic inertia provided by ...
Evaluation of Synthetic Inertia Provision from Wind Plants Mr Fei Teng, Professor Goran Strbac Department of Electrical and Electronic Engineering Imperial College London, United Kingdom
Abstract— High penetration of wind generation causes concerns regarding the frequency stability if wind plants do not provide inertial response. Extensive research has been conducted to investigate the design of controller to facilitate wind plants to provide synthetic inertia. However, the economic value of synthetic inertia provision from wind plants has not yet been understood. This paper develops a methodology to incorporate the synthetic inertia provided by wind plants into power system scheduling, therefore enables to assess its economic value. Sensitivity studies are carried to analyses the impact of inertia constant, percentage of total wind plants to be equipped with synthetic inertia capability, RoCoF limit and delivery time of frequency response on the value of synthetic inertia. Index Terms-- Unit commitment, inertia response, frequency control, wind plants
NOMENCLATURE A. Constants ∆ ( ) Time interval corresponding to node n (h). () Diurnal adjustment constant corresponding to the jth time step of the day. ( ) Probability of reaching node n Standard deviation of random Gaussian increments in autoregressive time series. () Standard deviation of forecast error in normalized wind level, i timesteps ahead. , Autoregressive parameters. Set of thermal generators. Set of storage units. Set of nodes on the scenarios tree. Value of lost load (£/MWh). Penalty of fast frequency response shortage (£/MWh). Maximum production of thermal unit g (MW). Maximum production/pumping of storage unit g (MW) Maximum frequency response capability of thermal unit g (MW). Maximum frequency response capability of storage unit g (MW). The proportion of the spinning headroom, which can contribute to frequency response provision. Inertia constant of thermal unit g (s). Load damping rate (%/Hz) Delivery time of frequency response (s) Maximum rate of change of frequency (Hz/s).
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∆ ∆ ∆ ( ) (∙) ( ) ( ) (
Maximum frequency deviation requirement in Nadir (Hz). Maximum frequency deviation requirement at quasi steady state (Hz). Frequency deadband of governor (Hz) Forecast error quantile of branch leading to node n. Sigmoid-shaped function which transforms the wind level to an aggregated wind output. kth element in an autoregressive time series which represents normalized wind level. Total demand at time t (MW). ) Total available wind generation at node n. (MW). Time after contingency (s).
B. Variables ( ) Power output of thermal unit g at node n (MW). ( ) production rate of storage unit s at node n (MW). ( ) Load shed at node n (MW). ( ) Wind curtailment at node n (MW). (n) Shortage of frequency response at node n (MW). ( ) Frequency response provision from thermal unit g at node n (MW). ( ) Frequency response provision from storage unit s at node n (MW). ( ) Operation status (0/1 for Offline/Online) of thermal unit g at node n. ( ) Operation status (0/1 for Pumping/Generating) of storage unit g at node n. C. Linear expression ( ) Operating cost of thermal unit g at node n ( ) Inertia from conventional plants at node n (MW ). ( ) Online capacity of wind plants (MW) at node n. ( ) Frequency response target (MW) at node n. I.
INTRODUCTION
In the coming decades electricity systems throughout the world are facing challenges as the reduction of greenhouse gas emission requires increased integration of RES. However, the integration of large share of RES introduces system operation and security related concerns due to variability, uncertainty and limited inertia capability associated with RES. For example, as the integration of wind generation displaces
energy produced by conventional plants, the system inertia provided by the rotating mass reduces, which already causes concerns regarding the frequency stability [1].In particular, the RoCoF will increase, potentially causing further disconnections of distributed generators by actuating RoCoFsensitive protection schemes. Moreover if frequency drops rapidly, conventional generators may not be fast enough to provide their primary frequency response; the resulting frequency nadir may activate the demand shedding. In fact, a relatively large amount of rotational energy is stored in the wind plants. Extensive research has been conducted to investigate the contribution of wind plant, especially double fed induction generators (DFIG), to system frequency services. An extra control loop could be incorporated into the wind plant controller to provide synthetic inertia as conventional plants. Studies in [2], [3] analysed the capability of DFIG-based wind plant to provide synthetic inertia without consideration of external grid, while the interaction between power grid and wind plant is investigated in [4]. The above works focus on the single wind plant. The authors in [5], [6] utilized a simple relationship between the aggregated synthetic inertia and the total wind power output and investigated its impact on RoCoF and frequency nadir after generation loss in the future Irish system. A more advanced probabilistic approach is proposed in [7], [8] to estimate the aggregated inertia response from a wind farm. The impacts of various mean wind speed levels and wind speed variations during the transit event are also examined. The above works show that synthetic inertia provided by wind plants can significantly enhance the postfault frequency performance in the future power systems with high penetration of wind generation. However, there is not yet any work to assess the economic benefits of inertia response provision from wind plants, which is in fact important in order to properly design incentives for the service provision. The challenge here is how to directly link the system inertia level and the system operation together. There is no tool capable to schedule the system operation by explicitly taking into account of different system inertia levels. In this context, the paper develops a novel methodology to incorporate both inertia provided by conventional plants and synthetic inertia provided by wind plants into the system scheduling and therefore, enable to analyse the economic value of synthetic inertia. The rest of this paper is organized as follows: Section II discuss the modelling of aggregated inertia availability. Section III describes the scheduling model. The case studies are presented and explained in Section IV, while Section V concludes the paper. II.
MODELLING OF SYSTEM-WIDE AGGREGATED INERTIA AVAILABILITY
In a traditional power system dominated by synchronous generators, the system operator could determine those plants that are online to meet the demand and therefore contributing
to the system inertia. However, as the increase of intermittent wind generation, it becomes very difficult to accurately predict the wind production in few hours ahead, leading to an unknown inertia contribution from conventional plants. As discussed in [9], scenario-based stochastic scheduling solves the unit commitment (UC) by directly modelling the different realizations of wind, therefore allows taking into account of the effect of unknown inertia. Moreover, wind plants can only contribute to the synthetic inertia if operating above minimum speed. The work in [5] illustrates that there is uncertainty associated with number of online wind turbines for a given level of wind generation. For simplicity, this paper implements the methodology proposed in [6]; as shown in Fig.1, a simple function is used to describe the relationship between number of online wind plants and wind generation level. Therefore, the aggregated synthetic inertia contribution can be calculated for any given level of system-wide wind generation. The uncertainty associated with the capacity of online wind plants is further discussed in Section V.
Fig. 1 Variable speed wind turbines operating above minimum speed
III.
STOCHASTIC SCHEDULING WITH INERTIA-DEPENDENT FREQUENCY REQUIREMENTS
A stochastic scheduling model with rolling planning is formulated in order to optimally schedule energy and various ancillary services in light of uncertainties associated with renewable production and generation outages. The UC and economic dispatch are solved over a scenario tree, which is generated based on the work developed in [9]. the scenario tree (Fig.2) is used to replace exogenous ancillary service requirements in deterministic UC. The scenarios are weighted according to their probability so that the model can choose how much generation capacity to commit in each scenario, given the cost to provide that capacity and value of lost load. A. Scenario Tree Quantile-based scenario selection methodology is adopted in the framework. This methodology is first developed in [9] by constructing and weighting scenario trees based on userdefined quantiles of the wind forecast error distribution. The authors in [10] extended the methodology to incorporate demand forecast error and generation outages. Compared with commonly used Monte Carlo methods, quantile-based method could describe the critical information about the uncertainties by using small amount of scenarios. The cumulative distribution function (CDF) C(x; n) of the net demand at each node is the convolution of the cumulative
nodal COPT with the probability distribution function (PDF) of realized wind. The q quantile of the distribution of net demand can calculated as x: C(x; n) q by using a numerical root-finding algorithm. The corresponding nodal probabilities π(n) can be approximated by using Trapezium rule.
Fig. 2 Schematic of a typical scenario tree in SUC
B. Stochastic Unit Commitment Formulation The objective of the stochastic scheduling is to minimize the expected operation cost of the system. ( )
( )
∆ ( )
( )
(1)
∈
subject to a load balance constraint: ,
( )
( )
( )
( )
( ) (2)
, ∈ ,
and local constraints for the thermal and storage units. Details of these constraints and the equations describing generation costs can be found in [9]. The primary frequency response requirement ( ) is modelled as ( ) ∈
( )
( ) (3)
∈
The amount of frequency response that each generator or storage can deliver is limited by its maximum response capability and a slope that links the frequency response provision with the spinning headroom. C. Inertia Dependent Frequency Response Requirement The aim of frequency control is to contain the dynamic evolution of frequency (e.g. after a generator outage) within certain security thresholds The GB Security and Quality of Supply Standard (GB-SQSS) [11] specifies the limits of frequency deviation for secured faults. Three quantities are used to set the security standards for the initial transient evolution of frequency (Fig.3):
RoCoF Freq. at nadir
Steadystate freq.
Fig. 3 System frequency evolution after a contingency (National Grid)
1) Rate of Change of Frequency (RoCoF) The time scale that involves the RoCoF constraint is limited to the first few seconds after the generator failure. During this period, the governors’ response is not triggered yet (∆ ≅ 0) as the frequency deviation is still negligible (∆ ≅ 0). For a given generation loss, the minimum level of inertia, required to satisfy the maximum RoCoF requirement, can be obtained as follows: ∑ ( ) ( ) ∆ | |(4) 2 2) Frequency at Nadir The frequency nadir is defined as the point when the system frequency evolution achieves its minimum value during the transient period; the time scale for this interval goes from 2s up to 10s after the generator failure. The nadir depends on system inertia and governors’ response. Following the work in [12], the nadir requirements can be formulated as MIL constraints: ∑ ∈ ∗ ∗ ∗ ( )∗ ∗ 50 (1 ( )) (1 ( )) (5) ∗ ( ) ∗ ( ) where M is a very large number and k ∗ is the unique solution from 2 ∗ 2 ∗ ⋅ ∆ ∆ (6) ∗ ∆ 2 ∗ 3) Frequency at quasi-stead-state The quasi-steady-state condition depends essentially on the total amount of frequency response delivered by generators and storage units. Therefore, for any given amplitude of generation loss ∆ , quasi-steady-state frequency deviation can be found, by assuming that RoCoF is effectively zero i.e. that the frequency has reached a constant level: ∆ ∆ (7) This allows quantifying the required response to satisfy the quasi-steady-state frequency criterion as follows: ∆ Δ (8) IV.
CASE STUDY
Simulations of annual system operation are performed using the GB 2030 scenario [13]. The maximum demand is 59.4 GW; total conventional generation capacity is 70GW. Existing 2.6 GW pump-hydro storage plant with 10GWh energy storage capacity and 75% round efficiency is also included in the plant mix. This storage plant provides up to 500 MW of frequency response. Table I summarizes the characteristics of conventional plants. The VOLL are set at 30000£/MWh. The reference setting for the delivery 10 ), the frequency deadband (∆ 15 ) time( and the load damping rate (1%/Hz) are chosen according to the GB current practice. The proposed requirement on RoCoF (0.5Hz/s) for the future GB system is adopted.
TABLE I CHARACTERISTICS OF THERMAL PLANTS Number of units Rated Power (MW) Min Stable Gen (MW) No-load cost (£/h) Marginal cost (£/MWh) Startup cost (£) Startup time (h) Min down time (h) Inertia Constant (s) Max Response (MW) Response Slope Forced outage probability Mean time to repair(days)
Nuclear 6 1800 1800 0 10 n/a n/a n/a 5 0 0 0.02% 30
Coal 40 500 250 3364 72 32000 6 4 5 75 0.3 0.2% 3
CCGT 70 500 250 7809 51 90000 4 4 5 75 0.4 0.2% 3
OCGT 30 200 50 8000 110 0 0 0 5 40 0.6 0 n/a
A. Benefit of Synthetic Inertia from wind plants In this session, the benefit of synthetic inertia in system operation cost reduction is assessed in the future GB system with different penetration levels of wind generation. As show in Fig.4, the operation cost reduction is higher in the system with higher wind penetration level. In particular, the benefit is moderate when the wind penetration level is below 10%. While in the case with 50% of wind penetration, the synthetic inertia from wind plants could reduce the annual system operation cost by up to 700 m£. At the same time, the results suggest that the higher constant of synthetic inertia leads to higher system operation cost. However, the benefit shows clear saturation effects with increased inertia constant, especially with high penetration of wind generation. The reason is that once there is enough inertia to secure the RoCoF and frequency nadir, the required frequency response starts to be bounded by quasi-steady-state frequency requirement, which does not depend on system inertia (as shown in (8)). In addition, as shown in Fig.1, when the production level of wind plants is above 20% of installed capacity, more than 80% of wind plants would be online. Therefore, to provide the same amount of energy, there would be more online capacity of wind plants than that of conventional plants. The results indicate that it may not be necessary to require the wind plants to provide the same inertia capability as conventional plants.
about what is the optimal percentage of the total wind plants should be equipped with synthetic inertia capability. In this study, the wind plants with synthetic inertia capability are assumed to provide the same amount of inertia as conventional plants (5s) and evenly located across the whole system. The incremental operation cost saving with increasing percentage of wind plants capable to provide synthetic inertia is assessed. As shown in Fig.5, the marginal saving decreases dramatically with the increased percentage of wind plant capable to provide synthetic inertia. The results could be used to guide the investment on the synthetic inertia capability considering the quantified value in Fig.5 and the associated investment cost.
Fig. 5 Incremental value of synthetic inertia capability of wind plants
C. Impact of Frequency Response Setting on the Value of Synthetic Inertia In addition to require wind plants to provide synthetic inertia, there exist alternative solutions to deal with inertia reduction due to non-synchronous generation. One of them is to amend the gird code for the RoCoF limit and delivery time of frequency response. In particular, the relaxation of RoCoF and shorter delivery time could potentially reduce the demand for the synthetic inertia provided by wind plants. Therefore, this session presents the benefit of synthetic inertia provision with different settings of RoCoF limit and delivery time of frequency response. The penetration level of wind generation is assumed to be 30% in this study. The impact of delivery time on the operation cost saving from synthetic inertia provision is shown in Fig.6. The benefit reduces as the reduction of delivery time until 5s where the benefits become almost zero. This is because when the frequency delivery is fast enough to secure the nadir, the required additional power injection starts to be bounded by quasi-steady-state frequency requirement. The additional provision of synthetic inertia would not reduce the frequency response requirement any further.
Fig. 4 System operation cost saving due to synthetic inertia provision from wind plants
B. Percentage of Wind Plants to be Equipped with Synthetic Inertia Capability This session investigates another interesting question
Fig. 6 Impact of delivery time on the operation cost saving
Fig.7 presents the benefit of synthetic inertia with different settings of RoCoF limit. The results suggest that with conservative setting of RoCoF limit, the benefit of synthetic inertia provision from wind plants increase dramatically. As shown in (5), for a given loss of generation, the required system inertia is inversely proportional to RoCoF limit. Lower limit on RoCoF directly increases the demand on system inertia. Without the inertia provision of wind plants, large amount of conventional plants has to be online partloaded to supply the high demand on system inertia, potentially leading to high operation cost.
advance. This raises the question of reliability associated with the reliance on the inertia provided by wind plants, especially given the risk-averse approach to system security. Next step, this model can be extended to directly incorporate this uncertainty into scheduling process. Secondly, in addition to provide inertia, wind plants can also provide frequency response by de-loading of wind plants at normal operation. As shown in Fig.4, after some threshold, only provide inertia would not reduce the system operation cost any more. Therefore it is interesting to assess the benefit of combined provision of synthetic inertia and frequency response from wind plants. REFERENCES [1] National Grid frequency fesponse working group, “Frequency Response report,” 2013. [2] N. J. Janaka Ekanayake, “Comparison of the Response of Doubly Fed and Fixed-Speed Induction Generator Wind Turbines to Changes in Network Frequency,” IEEE Trans. Energy Convers., vol. 19, no. 4, pp. 700 - 802, 2004.
Fig. 7 Impact of RoCoF limit on the operation cost saving
V.
CONCLUSION AND FUTURE WORK
This paper proposes a novel stochastic UC formulation with the capability to schedule the system operation taking into account the effect of different levels of total system inertia. The online capacity of wind plants is estimated as a function of system-wise wind generation. Therefore, the synthetic inertia provided by wind plants could be added to the total system inertia. The model is firstly applied to analyses the benefit of synthetic inertia in the future GB system. The results suggest the synthetic inertia could effectively reduce the system operation cost in the system with high penetration of wind generation. However, after the synthetic inertia constant reaches 3s, the benefit of further improvement is limited. This raises an interesting question about whether the wind plants should be required to provide the same inertia as conventional plants. In another perspective, assuming the wind plants can provide the same inertia as conventional plants, this paper analysed how much of the total wind plants should be equipped with synthetic inertia capability. The results show that the marginal operation cost saving of synthetic inertia reduces rapidly with the increased amount of wind plants capable to provide synthetic inertia. The results of this study could be used to support the cost-benefit analysis to decide the optimal amount of wind plants to be equipped with synthetic inertia capability. Finally, delivery time of frequency response and RoCoF limit show dramatic impacts on the benefit of synthetic inertia from wind plants. There are several areas of enhancing the proposed framework. First of all, for a given level of system-wise wind generation, the present model utilizes the expected value for the capacity of online wind plants. However, as shown in [6], the number of online wind plants in fact is hard to predict in
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