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Studying Cascading Overload Failures Under High Penetration of Wind Generation

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Studying Cascading Overload Failures Under High Penetration of Wind Generation Studying Cascading Overload Failures under High Penetration of Wind Generation Mir Hadi Athari Zhifang Wang Department of Electrical and Computer Engineering Department of Electrical and Computer Engineering Virginia Commonwealth University Virginia Commonwealth University Richmond, VA, USA Richmond, VA, USA Email: [email protected] Email: [email protected] Abstract—While power systems are reliable infrastructures, Probabilistic approach is among the mostly used technique to their complex interconnectivities allow for propagation of model the cascading behavior [4]–[9]. disturbances through cascading failures which causes blackouts. Meanwhile the ever increasing penetration level of renewable On the other hand, ever increasing penetration level of generation into power grids introduces a massive amount of renewable energy sources into power grids will introduce a uncertainty to the grid that might have a severe impact on grid large amount of uncertainty coming from their stochastic vulnerability to overload cascading failures. There are numerous nature. The dynamic performance and economic settings of studies in the literature that focus on modeling cascading failures many power systems are changing due to the increased with different approaches. However, there is a need for studies penetrations of renewables [10]. One worrisome change is the that simulate cascading failure considering the uncertainty increase in cascading failures involving wind farms [11]. coming from high penetration of renewable generation. In this study, the impacts of wind generation in terms of its penetration With the sustained and rapid growth of renewable genera- and uncertainty levels on grid vulnerability to cascading overload tion, their influence on power systems dynamic performance failures are studied. The simulation results on IEEE 300 bus would be significant, therefore, studying cascading overload system show that uncertainty coming from wind energy have failures considering uncertainty coming from renewable en- severe impact on grid vulnerability to cascading overload ergy and loads is of great importance. In [9] authors proposed failures. Results also suggest that higher penetration levels of a stochastic Markov model to capture the progression of cas- wind energy if not managed appropriately will add to this severity cading failures considering uncertainty coming from electrical due to injection of higher uncertainties into the grid. loads. However, the unpredictable nature of renewable gener- Index Terms—Cascading failures, renewable energy, vulnerabil- ation such as wind energy will inject a large portion of uncer- ity analysis, uncertainty, power grids tainty into the grid having a big impact on cascading failure behavior. A new uncertainty modeling approach for renewable I. INTRODUCTION generation and smart grid loads proposed in [12] which enables Electric power systems are drivers for modernity and us to study the impacts of increased penetration level of renew- sustainable growth in societies and they are considered as able generation on grid vulnerabilities. critical infrastructure requiring the highest levels of reliability. In this paper, we investigate the impacts of increased pen- However, large-scale blackouts resulting from cascading etration of wind generations on cascading overload failure be- failures impose a massive cost to societies annually. These havior in power grids. The main focus is on the uncertainty cascading failures originate from strong interdependencies coming from these sources and as well as electrical loads. Sim- inside power grids and can even propagate into other critical ulations are performed on IEEE 300 bus system for different infrastructures such as telecommunication, transportation, and scenarios. In the proposed cascading failure model, the time water supply [1], [2]. Massive economic and social impacts of space correlation of line flows uncertainty is taken into account such events have motivated a great deal of research effort on by calculating the covariance matrix of flow uncertainty. studying the vulnerability of the power grids to cascading failures. A sequence of dependent failures of individual The rest of the paper is organized as follows. In section II components that successively weakens the power system is the uncertainty modeling is briefly discussed. Cascading defined as cascading failure [3]. This phenomenon can be failure modeling procedure and techniques used are presented result of different initial causes such as voltage and frequency in section III. Section IV and V will present results and instability, protection systems hidden failures, operator error, conclusion, respectively. and transmission line overloads resulting from contingencies II. UNCERTAINTY MODELING in the network. Each of these initial causes requires a different modelling technique and implementation of special Uncertainties coming from different sources such as approaches to evaluate grid vulnerability for certain events. renewable generation and loads present different characteristics Cascading failure due to line overloads has been under in terms of magnitude and frequency of occurrence. In the investigation by many researchers over past two decades. model proposed in [12], the power injection from each component (i.e. output power for generators and demand power each time step using the sliding window method as a 푚 × 푚 for loads) is modeled with two terms as shown in (1). matrix: 푃(푡) = 휇푃(푡) + 휖푃(푡) 퐶11 ⋯ 퐶1푚 퐶 (푡, 휏) = 퐸{휖 (푡)휖 (푡 − 휏)} = [ ⋮ ⋱ ⋮ ] where 휇 (푡) is the average of power signal at each time instant 퐹 퐹 퐹 푃 퐶 ⋯ 퐶 or in other words it is what we expect to have for each 푚1 푚푚 ( ) ( ) component ahead of time and 휖푃(푡) which is a zero mean 퐶푖푗 = 푐표푣(휖퐹푖 푡 , 휖퐹푗 푡 − 휏 ) signal, represents the uncertainty which may come from forecast error or mismatch in output power for conventional 푐표푣(퐴, 퐵) = 퐸{(퐴 − 휇퐴)(퐵 − 휇퐵)} units. ( ) where 휖퐹푙 푡 is the uncertainty term in flow signal of line ‘l’ at Using the power spectral density (PSD) of error signal, the time t and 푐표푣 is Covariance function defined in (7). In the occupied bandwidth for each uncertainty signal is calculated. It simulation we utilize the unbiased estimates as is found that wind generation injects the highest amount of 1 푁/2 ∗ 푐표푣(퐴, 퐵) = ∑ (퐴푖 − 휇퐴) (퐵푖 − 휇퐵). Note that uncertainty into the grid in terms of its bandwidth and 푁−1 푖=−푁/2 sliding window method for covariance calculation selects a magnitude and assumes all the bus voltages in the grid network predetermined number (N) of observations of line flow errors closed to the rated voltage levels [12]. In the next section, the and then puts them in the observation matrix. By using eq. (8), implementation of above model in cascading failure simulation each element of covariance matrix is calculated based on the will be explained. observation matrix. The variance for flow process of each line III. CASCADING FAILURE SIMULATION can then be calculated by taking square root of each diagonal A. DC power flow and line overload modeling element in covariance matrix with 휎퐹푙 (푡) = √퐶퐹푙,푙(푡, 0). Determining the steady-state operating conditions of the power grid requires solving the full power flow equations that With a Gaussian assumption for the distribution of 퐹푙(푡) in 푚푎푥 provide information about the voltage magnitudes and phases [8, 11], the overloading probability 휌푙(푡) = 푝{|퐹푙(푡)| > 퐹푙 } and the active and reactive power flows through each can be calculated using Q-function as below: transmission line. Unfortunately, solving repeatedly the full ( ) nonlinear power flow equations becomes computationally 휌푙 푡 ≅ 푄(푎푙) prohibitive due to numerous solutions during the evolution of 퐹푚푎푥−휇 (푡) where 푎 = 푙 퐹푙 is the normalized overload distance of CF. In addition, we are only interested in evaluating the impact 푙 휎 (푡) 퐹푙 of wind uncertainty on grid vulnerability to CF that doesn’t ∞ −푡2 the lth line and Q-function as ( ) ⁄2 . necessarily require complete nonlinear network equations and 푄 푥 = ∫푥 푒 /(√2휋)푑푡 the linear approximation for line active flows is sufficient for Finally, using the normalized overload distance (푎 ) and our tripping mechanism. For all these reasons we used DC 푙 overloading probability (휌푙) for each line we can calculate the power flow approximation [13] to recalculate the flow dispatch mean overload time for flow process 퐹 (푡) as follows [9]: of the power grid at each time. Simulation of cascading failure 푙 2 is performed on IEEE 300 bus system replacing several 푎푙 /2 2휋휌푙푒 conventional generators of the original system with wind 휏̅푢 = 푙 퐵푊 generators according to different scenarios. The power flow 푙 equations for a power grid with n nodes and m links can be where 퐵푊푙 is the equivalent bandwidth of the flow process for expressed as: the lth line and can be calculated using the spectral power density (SPD) of flow process [12]. 푃(푡) = 퐵′(푡)휃(푡) B. Tripping mechanism and relay model 퐹(푡) = 푑푖푎푔(푦 (푡))퐴휃(푡) 푙 The trip time of thermal overload relays is determined based where 푃(푡) represents the vector of injected real power, 휃(푡) on maximum allowable current flowing in the conductor the nodal voltage angles, and 퐹(푡) the flows on the lines. The without causing thermal instability. Generally, the overload matrix 퐵′(푡) is defined as relays for HV transmission lines have time-dependent tripping ′ 푇 characteristic, which is determined using the well-known 퐵 (푡) = 퐴 푑푖푎푔(푦푙(푡))퐴 (4) dynamic thermal balance between heat gains and losses in the where 푦 (푡) = 1/푥 is the line admittance; 푑푖푎푔(푦 (푡)) repre- conductor [14]. The maximum or hot spot temperature 푙 푙 푙 determines the time to trip for thermal relays and considering sents a diagonal matrix with entries of {푦 (푡), 푙 = 1,2, … , 푚}. 푙 initial operation current and applying necessary changes the 퐴 ≔ (퐴푙,푘)푚×푛 is the line-node incidence matrix, arbitrarily time to trip can be calculated using [15]: oriented and defined as: 퐴푙,푖 = 1; 퐴푙,푗 = −1, if the 푙th line is from node 푖 to node 푗 and 퐴 = 0, 푘 ≠ 푖, 푗.
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