KPI-based Real-time Situational Awareness for Power Systems with a High Proportion of Renewable Energy Sources

With the increasing complexity of power systems and the widespread penetration of renewable energy sources (RES), real-time situational awareness for power systems is of great significance for operational scheduling. Considering the impact of RES on power system operations, a situational awareness key performance index (KPI) system for power systems with a high proportion of RES is proposed in this paper, which consists of reserve capacity abundance, ramp resource abundance, center of inertia (COI) frequency deviation, interface power flow margin, synthesized voltage stability, and angle stability margin. Then, the KPls are synthesized and visualized by the decision tree method and radar chart method, respectively, for monitoring the operation states (i.e., normal, alert, and emergency states) of power systems with a high proportion of RES. Numerical simulations are conducted in a revised New England 16-machine 68-bus power system and an actual CEPRI-RE power system in the northwest region of China with a high proportion of RES. The results show that the proposed KPI-based situational awareness method is able to accurately monitor the real-time state of power systems with a high proportion of RES, and can assist power dispatchers to make effective decisions.

SECTION I. Introduction

Motivated by the need to realize energy transition and sustainable energy development, RES, such as wind and photovoltaic power generation, providing desirable green energy, have developed rapidly in recent years [1]. The proportion of RES in power generation will account for more than 30% by 2030 and more than 60% by 2050 in China. Thus, the high proportion of RES will be a typical feature of power systems in China. Nevertheless, the operational mode of power systems becomes more complex and the operation security problems become more severe due to their varying nature with the inherent volatility, intermittency, and uncertainty of RES [2]–​[4], especially for the power systems with high penetration of RES. Therefore, the situational awareness for power systems with a high proportion of RES is an important way to assist power dispatchers to obtain timely real-time operational information, so as to identify the potential issues as soon as possible, and to realize the observability and controllability of power system operations. In addition, it is an essential way for enhancing the security level of power system operations and ensuring the penetration of RES [5].

There are several research studies on the construction of the situational awareness index system for power systems. The construction of the traditional index system primarily focuses on the extraction of basic indices, and many researchers have extracted a large number of basic indices based on different perspectives and criteria [7]-[ 1 0], which include security, economy, quality, and flexibility of the system. These indices can accurately analyze the operation of power systems, but cannot be applied directly without considering the dimensional consistency and the unity of the time scale into account. In order to realize the intelligence and integration of system oper-ations, the concept of power system operation cockpit (POC) is proposed in [11], and the KPIs are provided. However, the detailed algorithm of the indices is not mentioned. Among the operational evaluations of power systems, operational security is the focus of operational control. For solving this issue, voltage stability, angle stability, and topology vulnerability are considered to evaluate the security performance of power Systems in [12]–​[14]. In [15], a relatively complete power system security index system is proposed, which includes available transfer capability, static voltage stability, topology vulner-ability, transient security, and risk indices. Meanwhile, the operational state perceived from the perspective of contingency is examined in other research studies. In [16], the operational state of power systems is represented by risk factors, and three risk indices of low voltage, overload and voltage instability are constructed to comprehensively represent the security level of power systems. In [17], the component outage probability of power systems is analyzed, and the reliability of power systems is evaluated from the perspectives of power shortage probability and power supply security. All the proposed index systems for situational awareness of power systems in the research studies above are formed from different perspectives, but the impact of the penetration of RES is not taken into account.

In terms of comprehensive situational awareness, there are primarily subjective methods, such as the analytic hi-erarchy process (AHP) method, expert experience method, and fuzzy comprehensive evaluation method [18]. In addition, there are many objective methods such as the entropy weight method [19], principal component analysis (PCA) method [20], and fuzzy decision method [21]. There have also been some subjective and objective combination methods [19]. Comprehensive situational awareness results can be obtained by these methods through index weighting. However, the anomaly of a certain key index can directly lead to the anomaly of the system, so the final results cannot correctly reflect the key information, and some serious issues might be ignored.

Current research studies associated with situational awareness primarily focus on the traditional power systems, not the power systems with a high proportion of RES, so the current research studies cannot be applied directly. Moreover, a lot of existing index systems are redundant, which prevent power dispatchers to obtain the most critical information when facing huge amounts of measurement data and to focus on the key issues emerging in power systems with a high proportion of RES. It is of great necessity to build a moderate-scale situational awareness index system to accurately perceive the real-time operational states of power systems with a high proportion of RES, to help power dispatchers monitor the system intuitively and make timely decisions.

Consequently, a novel KPI-based situational awareness method is proposed in this paper, which is suitable for monitoring power systems with a high proportion of RES. It is worth mentioning that this paper primarily focuses on the single-period (i.e., real-time) operational security states of power systems with a high proportion of RES, and economic indices (e.g., operating costs) are not the focus in this paper even though they are also important issues in power system operations. The contributions of this study can be summarized as follows.

1. Six new KPIs for monitoring the operational states of power systems are first presented, focusing on the impact of the high proportion of RES on operational security. Compared with the traditional approach, it can enhance the pertinence and the ability to reflect the key information of power systems with a high proportion of RES.

2. The dimensional consistency and the unity of the time scale are addressed during the extractions of the KPIs for situational awareness of power systems. Combined with power system operational security, the situational awareness results are divided into three states, i.e., normal, alert, and emergency states. Power dispatchers can flexibly adjust alert thresholds (ATs) based on historical situational awareness results and actual power system characteristics, which makes the KPI system much more applicable and flexible.

3. The decision tree method is used to synthesize the situational awareness results, taking into account the scale of the KPI system and the importance of each key element. To intuitively display the situational awareness results at a specific time, the radar chart method is applied. Power dispatchers can then obtain the overall operational state in a much clearer manner and can focus on the weak elements to prevent the occurrence of more severe accidents.

SECTION II. Situational Awareness Kpi System for Power Systems With a High Proportion of Res

The purpose of the KPI system is to establish a set of KPls with the same time scale as the elements to describe the operational security state of the whole system during the current time. In practice, the presented KPls should be able to accurately reflect the real-time operational states of power systems. The KPls should be closely related to RES in order to accurately consider the impact of a high penetration of RES on power systems. The performance of situational awareness is influenced by the accuracy and scientific rationality of the KPI system, so a series of principles should be followed when extracting KPls. They can be summarized as i) Scientificity: The selection and design of KPls should be guided by scien-tific theory, with a clear concept and scientific connotation. ii) Pertinence: The KPls should be able to reflect the essential characteristics of power systems and the high proportion of RES fully and effectively. iii) Principal component: Select the KPls with a strong representation that can macroscopically reflect the actual change of the system operational state, i.e., “big index” with high principal component content. iv) Operability: The KPls should meet the requirements of actual operations, be easy to operate and evaluate, and the supporting data should be easy to collect.

As mentioned above, six situational awareness KPls for the operational security of power systems with a high proportion of RES is proposed in this paper, including indices of reserve capacity abundance, ramp resource abundance, COI frequency deviation, interface power flow margin, synthesized voltage stability, and angle stability margin. In this section, the definition of each KPI and its evaluation content will be described in detail, and a moderate scale comprehensive KPI system for real-time situational awareness in power systems is developed.

A. Reserve Capacity Abundance

For ensuring the reliability of the power supply, the econ-omy of operation, and high power quality, sufficient reserve capacity should be maintained [22]. The spinning reserve of power systems is the reserve that can be loaded immediately, which is generally provided by the traditional power supply (e.g., thermal power and hydropower generators) to balance the fluctuations of load and RES generation. Spinning reserve can be divided into positive and negative items. The positive reserve is related to the power supply security of power systems, which is used to deal with the increase of load and the unexpected shortage of RES output. While the negative reserve is related to the operational quality of power systems, which primarily deal with the load shedding and the surplus RES output, and help to mitigate the wind and photovoltaic curtailment.

Traditional power generations can be used to provide enough spinning reserve when the output of RES is low. However, with the increase of installed capacity and the generation of RES, it becomes difficult to fully meet the requirements of RES consumption by using traditional power sources as spinning reserve only. Thus, the spinning reserve of future power systems with a high proportion of RES needs to consider the reserve provided by RES. Meanwhile, the varying nature of RES brings more challenges to the operating reserve of power systems, especially when the penetration level of RES is high, and power systems have to provide much more reserve capacity for operational security and quality. In other words, sufficient reserve capacity can guarantee the operational security of power systems with a high proportion of RES. Therefore, it is necessary to evaluate the abundance of the positive and negative reserve capacities considering the reserve supplied by RES and the energy storage system (ESS) [23]. The positive and negative reserve capacities can be respectively represented as:\begin{align*} P_{\mathrm{u}_{-}i}=& P_{\mathrm{h}_{-}\max}+P_{\mathrm{w}_{-}\max}+P_{\text{re}_{-}i}+\\ & P_{\text{re}_{-}\text{sr}}+P_{\text{ess}_{-}\text{sr}}-P_{\text{load}_{-}i} \tag{1}\\ P_{\mathrm{d}_{-}i}=& P_{\text{load}_{-}i}-P_{\text{re}_{-}i}-P_{\mathrm{h}_{-}\min} \tag{2} \end{align*} where $P_{\mathrm{u}_{-}i}$ and $P_{\mathrm{d}_{-}i}$ are the positive and negative reserve capacities at time $i$, respectively. $F_{\mathrm{h}_{-}\max}$ represents the basic capacity of thermal power generation, and $P_{\mathrm{h}_{-}\min}$ represents the minimum technical output of the thermal power generation, which is usually 30%-50% of $P_{\mathrm{h}_{-}\max}.\ P_{\mathrm{w}_{-}\max}$ represents the rated capacity of the current operating hydropower generator, $P_{\text{re}_{-}{i}}$ represents the RES output at time $i, \ P_{\text{ess}_{-}\text{sr}}$ represents the available reserve capacity of ESS, $P_{\text{re}_{-}\text{sr}}$ represents the reserve capacity of RES for day-ahead dispatch, and $P_{\text{load}_{-}i}$ represents the load at time $i$. Then, the reserve capacity abundance of power systems with a high proportion of RES can be defined as:\begin{align*} I_{\text{RCA}}=&\max\{I_{\text{RCA}_{-}\mathrm{u}},\ I_{\text{RCA}_{-}\mathrm{d}}\} \tag{3}\\ I_{\text{RCA}_{-\mathrm{u}}}=& \frac{\alpha\cdot P_{\mathrm{p}1_{-}\max}}{P_{\mathrm{u}_{-}i}} \tag{4}\\ I_{\text{RCA}_{-}\mathrm{d}}=& \frac{\beta\cdot P_{\mathrm{p}1_{-}\max}}{P_{\mathrm{d}_{-}i}} \tag{5} \end{align*} where $I_{\text{RCA}_{-}\mathrm{u}}$ and $I_{\text{RCA}_{-}\mathrm{d}}$ are the indices of positive spinning reserve abundance and negative spinning reserve abundance, respectively. $I_{\text{RCA}}$ represents the reserve capacity abundance of the system, which uses the larger value between $I_{\text{RCA}_{-}\mathrm{u}}$ and $I_{\text{RCA}_{-}\mathrm{d}}$ to reflect the problem that is more serious in the eval-uation of positive and negative spinning reserve abundance. $\alpha$ and $\beta$ are positive and negative spinning reserve rates required by the system, respectively. Generally, the load reserve rate is 2%-5% and the contingency reserve rate is usually 10%, of which at least half is spinning reserve, so the value of $\alpha$ is set as 10%. Meanwhile, there is no strict rule on the negative spinning reserve rate [24], so $\beta$ is set as 5 % considering the forecast error of RES output and load. This index can reflect the reserve capacity abundance by the comparison between the actual available reserve capacity and the required reserve capacity.

It is worth mentioning that RES has been adopted as reserve for the first time based on statistical characteristics of the Northwest Power Grid in China [24], but the research is still ongoing and has not been used in the operation of actual power systems. Since almost no RES are being currently adopted as reserves in actual power systems, $P_{\text{re}_{-}\text{sr}}$ can be assumed as 0 in this case, and the value can be assigned according to the actual situation when RES are regarded as reserves in the future.

In summary, the smaller the values o: $\mathrm{f}I_{\text{RCA}_{-}\mathrm{u}}, I_{\text{RCA}_{-}\mathrm{d}}$, and $I_{\text{RCA}}$ are, the more abundant the spinning reserve is, and vice versa. It indicates that the spinning reserve capacity is insufficient and power dispatchers need to take corresponding measures, such as emergency gas turbine units start up and load shedding, when the value of $I_{\text{RCA}}$ is greater than 1.

B. Ramp Resource Abundance

In addition to reserve security, the characteristics of the high proportion of RES also create severe challenges to the flexibility of power systems. Flexibility is the ability of power systems to quickly respond to power fluctuations on both supply and demand sides, which focuses on the uncertainty of matching fluctuations through traditional generation with good regulation performance. With the increasing penetration level of RES, the inherent volatility and intermittence of RES in-troduces strong uncertainties to power systems. Consequently, traditional units need to be adjusted more frequently, and the regulation depth is also greatly increased, even requiring start-up or shutdown.

In actual operations, sufficient adjustable resources are required to balance the fluctuation of RES generation and mitigate the impact of RES ramp events on power systems. Ramp events are closely related to the fluctuations of load and RES output, which can reflect the flexibility of power systems. RES primarily consists of wind and photovoltaic power, so common natural phenomena, such as wind, clouds, fallen leaves, and dust, can cause instantaneous changes in RES output, which will have a great impact on power systems with a high proportion of RES [25]. Therefore, ramp resource is also one of the most important items that needs to be monitored in power systems with a high proportion of RES, and the abundance of ramp resource is an important index to reflect the response of the system for the fluctuations of load and RES generation. If the ramp-up rate of traditional units is less than the change rate of net load, the problem of insufficient flexibility in up-regulation might occur, leading to load shedding events. Similarly, if the ramp-down rate is less than the change rate of net load, the problem of insufficient flexibility in down-regulation might occur, which results in wind and photovoltaic curtailment. According to the abundance of ramp resources, power dispatchers can discover and deal with the related issues by dispatching the units to enhance system flexibility. Therefore, the index of ramp resource abundance can be defined as:\begin{equation*} I_{\text{RRA}}=\begin{cases} \frac{(F_{\text{net}}(t)-P_{\text{net}}(t-1))/\Delta T}{\sum R_{\text{custom}_{-}\mathrm{u}}}, P_{\text{net}}(t) > P_{\text{net}}(t-1)\\ \frac{(-P_{\text{net}}(t)+P_{\text{net}}(t-1))/\Delta T}{\sum R_{\text{custom}_{-}\mathrm{d}}}, P_{\text{net}}(t) < P_{\text{net}}(t-1) \end{cases} \tag{6} \end{equation*} where $P_{\text{net}}(t)$ represents the net load at time $t$, which is the difference between load and RES output, i.e., $P_{\text{net}}(t)= P_{\text{load}}(t)-P_{\text{re}}(t). P_{\text{net}}(t-1)$ represents the net load at time $t-1$, and the evaluation interval is $\Delta T. \sum R_{\text{custom}_{-}\mathrm{u}}$ and $\sum R_{\text{custom}_{-}\mathrm{d}}$ are the ramp-up and ramp-down rates provided by adjustable resources of power systems, respectively. This index reflects the ramp resource abundance by comparing the ramp rate of net load and the ramp rate of available resources. The smaller the value of $I_{\text{RRA}}$ is, the more abundant the ramp resources are, and vice versa. It indicates that the ramp resources are insufficient, and the system cannot mitigate the net load fluctuation in time when the index value is greater than 1, which may result in generator trip or load shedding events.

C. Coi Frequency Deviation

Frequency is also one of the most important factors that you need to pay attention to in real-time operations of power systems, and frequency deviation is really a common concern of power dispatchers. A small frequency deviation (the threshold of frequency deviation is normally ± 0.2 Hz) may cause great damage to electric equipment. For users, the frequency instability affects the motor speed, influences the quality of industrial production, threatens the lifetime of electric equipment, and even causes human casualties in some serious cases. For power systems, the frequency instability could affect the compensation capacity, and cause the unstable operation of generators, system collapse, system splitting, or other serious consequences.

The penetration of RES in power systems also seriously affects the frequency, which results in great frequency fluctu-ations, especially when the penetration level of RES is high. Due to the varying nature of RES, the active power of power systems is often unbalanced, which affects the power quality and frequency stability of power systems. If power systems encounter active power imbalance for a long time, then the frequency quality will be greatly endangered. Furthermore, the high penetration of wind and photovoltaic power gener-ation replaces the traditional thermal power generations, and the number of synchronous generators of power systems is significantly reduced, which results in the reduction of inertia of power systems. Note that if the inertia is reduced, the ability of power systems to mitigate frequency deviation will be weakened, and the rate of change of frequency (RoCoF) will be faster [7]. Consequently, increased frequency violation events occur, resulting in the disorderly disconnection of RES units and further deterioration of system frequency stability.

Therefore, it is of great practice significance and engineering value to analyze and evaluate the frequency of power systems with a high proportion of RES in the real-time operational state, which benefits power dispatchers in identifying the problems of the current frequency accurately and quickly, so as to allow for essential early decision-making and adjustments.

Note that the frequency data collected from any point of the system cannot reflect the overall situation of power systems. Therefore, the frequency of COI [26], which can represent the overall frequency of the system, is presented for frequency monitoring in this study, and is defined as:\begin{equation*} f_{\text{COI}}=\frac{\sum_{i=1}^{n_{\mathrm{t}}}\sum_{j=1}^{n_{\mathrm{s}}}f_{i},{}_{j}H_{j}}{n_{\mathrm{t}}\cdot H_{\text{eq}}} \tag{7} \end{equation*} where $n_{\mathrm{t}}$ represents the sampling number during the sampling period, $n_{\mathrm{s}}$ represents the number of synchronous generators in the system, $f_{i,j}$ represents the frequency of synchronous generator $i$ at time $j$, which is derived from the speed of the synchronous generator. $H_{j}$ represents the inertia of synchronous generator $j$, and $H_{\text{eq}}=\sum_{j=1}^{n_{\mathrm{s}}}H_{j}$ represents the equivalent inertia of the system. COI frequency deviation reflects the frequency deviation of the equivalent inertia of a given power system by monitoring the speed of each synchronous generator in the system. Then, the index of COI frequency deviation can be defined as:\begin{equation*} I_{\text{FDCOI}}=\frac{\vert f_{\text{COI}}-f_{0}\vert }{\Delta f_{\text{threshold}}} \tag{8} \end{equation*} where $f_{0}$ represents the system rating frequency, $\Delta f_{\text{threshold}}$ is the system frequency deviation threshold and is recom-mended to be 0.2 Hz. Through monitoring this index, power dispatchers can understand the frequency deviation degree from the rating value and the distance from the emergency threshold (ET). In addition, the dynamic frequency change of power systems can be directly shown by the curve of the COI frequency deviation index, and the rationality of the current scheduling can be analyzed. This index can reflect the system frequency deviation degree by comparing the deviation of the COI frequency and the frequency deviation threshold. The smaller the value of $I_{\text{FDCOI}}$ is, the smaller the deviation degree of the system frequency is, and vice versa. It indicates that the limit of the COI frequency deviation is violated when the value is greater than 1. Effective control measures, such as automatic generation control (AGC) and load shedding, should be taken to restrict further frequency deviation and prevent the system frequency from collapse [27].

In addition, based on the observation of the real-time change curve of $I_{\text{FDCOI}}$ and combined with the assessment results of the long-term frequency control performance standard (CPS), power dispatchers can also analyze the performance of frequency control in the interconnected power system with a high proportion of RES

D. Interface Power Flow Margin

The power flow also brings a great impact on the operational security of power systems and the interface power flow is also one of the important indices to measure the real-time operational states of power systems. Transmission interface generally refers to the transmission corridor between different partitions of the system, which is defined as a group of transmission lines with the same active power flow direction in the system. If all lines in the interface are disconnected, the whole system will be separated into two mutually independent systems. In the power systems with a high proportion of RES, a large part of the RES output is transmitted through the AC channel, so the power flow of the transmission interface is also one of the contents that you need to be concerned about and the varying nature of RES will bring great uncertainty to the power flow. It is worth mentioning that those interfaces which are closely related to the transmission of RES generation, with heavy power flow and small security margins, are key transmission interfaces.

The interface power flow is the sum of the power flow in each line of the transmission interface, which can reflect the power exchange relationship between the two regions connected by the interface clearly, and it can be represented as:\begin{equation*} P_{\mathrm{s}i}=\sum_{j}^{n_{1}}P_{\mathrm{s}i,j} \tag{9} \end{equation*} where $j=1,2, \cdots, n_{1}$, and $n_{1}$ represent the line numbers of interface $i. P_{\mathrm{s}i}$ represents the power flow of interface $i$. The power flow condition of the key interface is one of the essential factors to determine whether the interconnected system can operate securely and stably. Through the real-time online monitoring and analysis of the key interface power flow, power dispatchers can be assisted to control the active power flow in the interface, so as to ensure that each line can meet the thermal stability limitation in real-time. For the key interfaces in the system, the index of interface power flow margin can be defined as:\begin{equation*} I_{\text{IPFM}}=\begin{cases} \max\left(\frac{P_{\mathrm{s}i}}{P_{\mathrm{s}i_{-}\lim}}\right)+\frac{1}{n_{\mathrm{d}}}\sum_{n=1}^{n_{\mathrm{d}}}\frac{P_{\mathrm{s}i}}{P_{\mathrm{s}i_{-}\lim}}\\ \qquad\qquad\qquad \ \ \exists\frac{P_{\mathrm{s}i}}{P_{\mathrm{s}i_{-}\lim}}\geqslant x_{\text{threshold}}\\ \text{mean}\left(\frac{P_{\mathrm{s}i}}{P_{\mathrm{s}i_{-}\lim}}\right)\forall\frac{P_{\mathrm{s}i}}{P_{\mathrm{s}i_{-}\lim}} < x_{\text{threshold}} \end{cases} \tag{10} \end{equation*} where $i=1,2, \cdots, n_{\mathrm{d}}$, and $n_{\mathrm{d}}$ represents the number of key interfaces. $P_{\mathrm{s}i_{-}\lim}$ represents the power flow limit for interface $i$, and $x_{\text{threshold}}$ represents the ET of the index, respectively. The design of this index takes the buckets effect and anomalous individual effect into account. The buckets effect is the index value being taken as the interface with the worst security when there is an insecure interface in the power system. In addition, the anomalous individual effect reflects the influence of the interfaces at the abnormal level on the index, which plays the role of superposition and amplification, and can more intuitively reflect the violation of power flow. This index reflects the interface power flow margin through monitoring each interface power flow to its limit. The smaller the value $I_{\text{IPFM}}$ is, the better the security of the interface power flow is. It indicates that the interface power flow of the power system violates the limitation when the index value is greater than 1.

E. Synthesized Voltage Stability

Voltage security and stability is a considerable factor for the secure operation of power systems with a high proportion of RES. For power systems, voltage instability may endanger the stability of operations, lead to voltage collapse accidents, or even cause blackout faults. In power systems with a high pro-portion of RES, a large number of wind turbines are connected and most of them are asynchronous generators. Thus, wind turbines will absorb reactive power from the system while generating a large amount of active power [28], which results in the increasing demand for reactive power of power systems. Due to the close relationship between voltage and reactive power, the increase of reactive power demand directly affects the voltage stability and complicates the voltage regulation. As a result, the regulated voltage cannot meet the system requirements when the penetration of RES is extremely high. As the penetration level of RES increases over time, the impact of RES generation creates much more serious voltage stability and quality concerns. The system voltage may be offset and unstable due to the high fluctuation of RES output. Therefore, it is necessary to monitor the voltage of power systems, and the real-time operating voltage index of power systems with a high proportion of RES, which can be expressed by constructing a synthesized voltage stability index, which comprehensively considers the voltage stability and voltage deviation.

First, a continuous function that simulates step characteris-tics is defined as:\begin{equation*} f(e_{i})=\frac{1}{1+e^{-(e_{i}-\alpha_{i})c/\alpha_{i}}}+\frac{1}{1+e^{(e_{i}+\alpha_{i})c/\alpha_{i}}} \tag{11} \end{equation*} where $e_{i}$ represents the state variable to monitor the step change. $\alpha_{i}$ and $c$ are undetermined constants, which take different values to determine the interval range of step oc-currence. This function can quickly point to the instability threshold “1” of the voltage stability index when the voltage is about to cross the boundary. Inversely, the value of the function is close to 0 when the voltage of the bus is below the limit. The characteristics of this function are shown in Fig. 1.

Fig. 1.

The characteristics of function $f(e_{i})$.

The continuous function above has the following properties: $f(e_{i})\approx 0$ when $e_{i}\in[-\alpha_{i}, \alpha_{i}];f(e_{i})$ increases rapidly to 1 when $e_{i}\in[-\infty, -\alpha_{i})\cup(\alpha_{i}, \infty]$. Furthermore, after modification, the function $f(U_{i})$ that reflects the voltage violation of bus $i$ can be represented as:\begin{equation*} f(U_{i})=\frac{1}{1+e^{-(U_{i}-U_{0}-a)c/b}}+\frac{1}{1+e^{(U_{i}-U_{0}+a)c/b}} \tag{12} \end{equation*} where $U_{i}$ and $U_{0}$ are the per-unit values of actual voltage and rating voltage of bus $i$, respectively. $a, \ b$, and $c$ are the parameters for realizing the step characteristics. After considering the violation of voltage, the voltage stability is a further concern. For the $\pi$ model of the branch shown in Fig. 2, the equation of the branch voltage can be represented as:\begin{equation*} \dot{U}_{i}=\dot{U}_{j}+\dot{I}_{ij}(R+\mathrm{j}X) \tag{13} \end{equation*} where $U_{i}$ and $U_{j}$ are the per-unit voltage values of the buses at both ends of the branch, respectively. $\theta_{i}$ and $\theta_{j}$ represent the phase angle of bus $i$ and bus $j$, respectively. $I_{ij}$ represents the current vector of the branch. $Z=R+\mathrm{j}X$ represents the per-unit impedance value of the branch. The expansions of the real part and the imaginary part are listed as:\begin{align*} & (1-BX/2)U_{j}^{2}-U_{i}U_{j}\cos\theta_{ij}+P_{j}R+Q_{j}X=0 \tag{14}\\ & \qquad U_{j}^{2}\cdot BR/2-U_{i}U_{j}\sin\theta_{ij}+P_{j}X-Q_{j}R=0 \tag{15} \end{align*} where $\theta_{ij}$ represents the phase angle difference between bus $i$ and bus $j. \mathrm{j}B/2$ represents the per-unit value of the ground electric susceptance at both ends of the branch. $P_{i}+\mathrm{j}Q_{i}$ and $P_{j}+\mathrm{j}Q_{j}$ are the per-unit value of power injected by bus $i$ and the per-unit value of power output by bus $j$, respectively. Combine equation (14) with equation (15), the quadratic equation about $U_{j}$ can be represented as:\begin{align*} & [1-B(X-R)/2]U_{j}^{2}-[U_{i}(\cos\theta_{ij}+\sin\theta_{ij})]U_{j}+\\ & [ P_{j}(X+R)+Q_{j}(X-R)]=0 \tag{16} \end{align*}

Fig. 2.

The $\pi$ model of the branch.

If the voltage of the system is stable, the quadratic equation (16) has solutions for each branch of the system, i.e., $\Delta >$ 0. Therefore, the index of static voltage stability [29] can be represented as:\begin{align*} f^{0}(r_{x})=& \frac{4[1-B(X-R)/2](P_{j}(X+R)+Q_{j}(X-R))}{U_{i}^{2}(1+\sin 2\theta_{ij})}\\ & < 1 \tag{17} \end{align*}

The index for branch voltage stability with the consideration of active and reactive power elements is defined. However, equation (17) contains the impedance information of the branch, and the accuracy of the index will be affected by the identification model and method of the branch parameters. Therefore, $f^{0}(r_{x})$ should be modified for the guarantee of accuracy in this work. Equation (16) can be expressed as:\begin{align*} & P_{j}(X+R)+Q_{j}(X-R)=\\ & U_{i}U_{j}(\sin\theta_{ij}+\cos\theta_{ij})-[1-B(X-R)/2]U_{j}^{2} \tag{18} \end{align*}

Then, substitute equation (18) into equation (17) and ignore $B(X-R)/2$, the modified function can be represented as:\begin{equation*} f(r_{x})=\frac{4[U_{i}U_{j}(\sin\theta_{ij}+\cos\theta_{ij})-U_{j}^{2}]}{U_{i}^{2}[1+\sin(2\theta_{ij})]} \tag{19} \end{equation*}

It can be seen that no voltage collapse occurs when $f(r_{x})$ is less than 1, and the system approaches the critical point of voltage collapse when the value is equal to 1. In practical applications, the stability threshold can be set to a value $k$ that is slightly less than 1 to preserve a certain stability margin for the assistance of the automatic voltage control system to prevent voltage instability. Therefore, the index of synthesized voltage stability of branch $x$ can be defined as:\begin{equation*} I_{\text{SVS}_{-}x}=f(r_{x})/k+\max\{f(U_{i}),\ f(U_{j})\} \tag{20} \end{equation*}

The function $\max\{f(U_{i}),\ \ f(U_{j})\}$ approaches 0, and the index value is primarily determined by $f(r_{x})/k$ when the voltage amplitudes of the buses at both ends of branch $x$ are within the normal range, which can reflect the voltage stability of the system. The function $\max\{f(U_{i}),\ \ f(U_{j})\}$ steps to 1 when the bus voltage at both ends of the branch approaches the limit, which can better reflect the problem of serious voltage violation. Note that the settings of parameters $a, \ \ b$, and $c$ are given in Table I.

Table I Parameter setting under different voltage limits

In Table I, the value of $a$ is determined by the allowed voltage deviation specified in the voltage quality specification of power systems. Meanwhile, the value of $a$ is slightly less than the maximum allowed deviation to indicate an alert when the voltage is about to violate the limit. The values of $b$ and $c$ are tuned and determined to meet the step characteristics as shown in Fig. 1.

The index $I_{\text{SVS}_{-}x}$ mentioned above only consider the voltage stability of branch $x$, therefore, the index of synthesized voltage stability of the whole system can be determined as the maximum value of all the branches, i.e.,\begin{equation*} I_{\text{SVS}}=\max_{x\in S}\{I_{\text{SVS}_{-}x}\} \tag{21} \end{equation*} where $S$ represents the set of system branches. The smaller the value of $I_{\text{SVS}}$ is, the more stable the system is. It indicates that the system voltage is in an abnormal state when the value of $I_{\text{SVS}}$ is greater than 1.

F. Angle Stability Margin

In addition to the five indices above, angle stability is also a significant factor for the secure operation of power systems with a high proportion of RES. Power angle is an impor-tant sign to reflect the operational stability of synchronous generators, and the real-time monitoring of power angles is of great significance to prevent generators from reaching instability. If parts of the generators lose synchronization, large fluctuations of voltage and current may occur, which will lead to the occurrence of over-current and low-voltage phenomena in a short time. Under this condition, other synchronous generators in the system will also lose their stabilities. What's worse, angle instability of multiple generators can cause the misoperation of local protection, lead to collapse accident, or even cause a blackout.

The influence of RES on power system angle stability has already been analyzed in many research studies [30], [31]. With the increasing penetration of RES, the number of synchronous generators in power systems is reduced. RES units introduce a set of non-autonomous variables (i.e., the active and reactive power of RES generation) to power systems, which break the balance of electrical parameters of the original systems. The introduction of RES changes network structures and power flow distributions of power systems, influences the electromagnetic power of synchronous generators, and indirectly participates in the power angle swing process of synchronous generators. Thus, the power system angle stability is greatly affected. It is worth mentioning that angle stabilities will deteriorate when the penetration level of RES is high [32]. Therefore, it is essential to monitor the real-time power angles of power systems with a high proportion of RES. In this paper, angle stability margin is obtained by measuring the relative swing angle between each synchronous generator and the COI of the power system. The equivalent power angle of COI can be represented as:\begin{equation*} \delta_{\text{COI}}=\frac{\sum_{i=1}^{n_{\mathrm{s}}}\delta_{i}H_{i}}{H_{\text{eq}}} \tag{22} \end{equation*} where $\delta_{\text{COI}}$ represents the equivalent angle in COI, $\delta_{i}$ repre-sents the angle of synchronous generator $i$. The maximum rel-ative swing angle is defined as the maximum swing amplitude of the difference between two angles over a period of time. Then, the maximum relative swing angle can be represented as:\begin{equation*} \Delta\delta_{i}^{T}=\vert \max(\delta_{i}-\delta_{\text{COI}})-\min(\delta_{i}-\delta_{\text{COI}})\vert \tag{23} \end{equation*} where $\Delta\delta_{i}^{T}$ represents the maximum relative swing angle between synchronous generator $i$ and COI in time range $T$. According to engineering experience, power angles of power systems are unstable when the maximum relative swing angle is over 180°• Therefore, the index of angle stability margin can be defined as:\begin{equation*} I_{\text{ASM}}=\frac{\max(\Delta\delta_{i}^{T})}{180} \tag{24} \end{equation*} where $i=1,2, \cdots, n_{\mathrm{s}}$. This index reflects the angle stability margin through monitoring the maximum relative swing angle of power systems to its limit. The smaller the value of $I_{\text{ASM}}$ is, the better the angle stability of the system is, and vice versa. It indicates that the angle of the power system is instable when the index value is greater than 1.

To sum up, the situational awareness KPI system for power systems with a high proportion of RES is shown in Fig. 3.

G. Determination of Operational State and Kpi Interval

The real-time situational awareness results, i.e., the operational state of power systems with a high proportion of RES can be divided into three states: emergency, alert, and normal states [33]. Emergency state refers to the state of serious prob-lems or anomalies in power systems. Under emergency state, power dispatchers need to identify disturbances for preventing the spread of accidents, large-scale power outages, or even system splitting. Alert state is the state between normal state and emergency state, which indicates that there are certain risks of failure in power systems, and it is likely to evolve into an emergency state if the optimal scheduling is not carried out in time. Meanwhile, according to the three operational states of power systems, the value range of the proposed KPIs can also be divided into several intervals, as shown in Table II. Emergency threshold (ET) values of all the KPIs are 1, which is determined and unified during the extraction of the KPIs. In the extraction process, the dimensional consistency of the KPI system is achieved by the division between the results of each index and their security limits. Therefore, all of the KPIs are greater than 1 when relevant emergencies occur. The alert threshold (AT) value of each KPI is set by power dispatchers according to the historical situational awareness results, the relevant regulations of power systems, and the characteristics of the perceived actual object. For example, by analyzing the data of a given power system in the past six months, power dispatchers found that the probability of the power system turning into an emergency state is 75% (or other possibilities, which depends on the dispatching regulation) in the future when the value of one of the KPls is greater than 0.6. Then, the value of 0.6 can be regarded as the AT of this KPI. In this work, values of the proposed KPls are divided and shown in Table II according to the simulations in testing systems and the relevant requirements for power system dispatch.

Fig. 3.

Situational awareness KPI system for power systems with a high proportion of res.

Table II Determination of kpi interval

In order to visually characterize the different operational states of power systems, the color classification method can be used to present the current situation to power dispatchers intuitively as shown in Fig. 4.

Fig. 4.

Schematic diagram of operation state division of power systems.

SECTION III. Decision Tree and Radar Chart Based Comprehensive Situational Awareness for Power Systems With a High Proportion of Res

According to the scientific theory of systems, the compre-hensive situational awareness is carried out on the basis of every single KPI presented in Section II from the overall perspective, so as to comprehensively understand the target system, identify the key factors in the system scientifically, and make the decision more comprehensive and reasonable.

A. Decision Tree-Based State Identification for Situational Awareness of Power Systems

Comprehensive situational awareness is usually achieved by index weighting methods, such as AHP, entropy weight, and PCA methods. However, the comprehensive results may fail to extract significant information when the index system only consists of the indices with principal component information completely and the scale is small. In this case, the compre-hensive results are likely to ignore the abnormal factors and problems in the system when a small part of the indices are abnormal and the rest are in the normal state, which may affect the credibility of the final results. Therefore, the difference of each KPI's weight is not considered during the comprehensive situational awareness.

The KPIs presented have equal importance to comprehen-sive situational awareness. If any KPI exceeds its ET, the system will fall into an emergency state. If the duration of the violation event is too long, serious failure or even splitting will occur. In addition, the system is also in the alert state and may evolve into the emergency state if any KPI is beyond the AT. The operational sate of the system is secure only when all the KPIs are within the range of AT. In summary, for the real-time situational awareness of power systems, logical “and” is the relationship between the results of each KPI. Therefore, according to the relationship between each KPI, the decision tree method shown in Fig. 5 is adopted to determine the operational state of power systems with a high proportion of RES according to the KPI evaluation results. The situational awareness decision tree of power systems with a high proportion of RES uses the reserve capacity abundance as its root node, and judges each KPI value one after another until the operational state of power systems is determined.

After establishing the decision tree for situational awareness of power systems, the information obtained can be used to clearly determine the operational states of power systems. Thus, different countermeasures to ensure the security of power systems can be formulated and taken quickly based on the comprehensive results of situational awareness.

B. Radar Chart-Based Situational Awareness of Power Systems

The results in Section III - A are the overall situational awareness of the operational state of power systems, so power dispatchers cannot obtain the specific conditions of each KPI or perceive the margin of the relative critical value of each KPI. Therefore, the radar chart method is adopted in this paper for detailed situational awareness visualization [34]. It can be seen from Fig. 6 that the operational state of power systems and the margins of KPIs at the current time can be found intuitively by displaying each KPI in the same radar chart, and power dispatchers can quickly determine the operational state of power systems with a high proportion of RES.

In Fig. 6, three operational states of power systems are represented as green, yellow, and red regions. The system is in the normal state if all KPI values are within the green area. If there are KPIs crossing the green area but no KPIs crossing the yellow area, the system is in an alert state. In addition, the system is in the emergency state when there are KPIs crossing the yellow area. Therefore, power dispatchers can observe the margins of various KPIs visually from the radar chart and make adjustments to avoid accidents that are more serious as soon as possible.

C. Control Measures for Preventing Failures of Power Systems

With the help of the KPI-based situational awareness method proposed in this paper, power dispatchers can monitor the operational states of power systems in real time. On this basis, effective measures can be taken in time when the system is insecure to prevent more severe accidents according to the transition of different operational states as shown in Fig. 7.

In Fig. 7, emergency control measures are taken to deal with emergencies when the power system is under an emergency state [33]. The causes of emergencies are usually complex, which may involve many problems such as line failure, system splitting, unit failure, load mutation, significant fluctuation of RES generation, and DC blocking. Due to the correlations between various emergencies and KPIs, power dispatchers usually upload the exception information when the system is under emergency state, and the general power dispatchers will make unified operational arrangements. In this way, multi - party coordination and multi -efficient interaction can be realized, and more severe events, such as system collapse, can be effectively prevented. It is worth mentioning that emergency control measures usually include relay protection (i.e., reclosing operation), electric braking, emergency exci-tation control, switching of series and parallel compensation equipment, controlled islanding, adjustment of DC tie-line, emergency generator trip, load shedding, change of the system operational conditions, dispatching of the units with AGC and an automatic voltage control (AVC) system [35]–​[38]. In addition, novel strategies such as multi-objective coordinated post-contingency control method have been proposed in recent years [39].

Prevention and control measures are usually taken to prevent the occurrence of emergencies [33], and different measures are taken for different KPIs. For reserve capacity abundance, standby units should be started up or the power purchase from the external power grid should be carried out when the system is under alert state. If the alert state is continuously maintained, appropriate load control measures are necessary. For ramp resource abundance, emergency generators should be started up and the generation of RES should be limited. For COI frequency deviation, the pre-designated frequency regulation power plants need to carry out frequency regulation and adjust the units with AGC, and each area is required to control the area control error (ACE) within the specified range according to tie-line load frequency bias control (TBC) mode. If the frequency control requirements cannot be met, the start-up mode of thermal power units has to be changed for meeting the scheduling plan. For interface power flow margin, power dispatchers usually limit the generation of RES or adjust the terminal load. If the transmission interface has parallel lines, put the parallel lines into operation. For synthesized voltage stability, power dispatchers can reasonably dispatch the AVC system, change the reactive output curve of generators, start up phase modulators, switch the reactive compensation equipment or change the voltage tap of the on-load tap changer (OLTC). For angle stability margin, excitation regulations or generator trip operations are effective measures.

Fig. 5.

Decision tree-based state identification for situational awareness of power systems.

Fig. 6.

Radar chart-based situational awareness of power systems.

Fig. 7.

Operation state transition of power systems.

SECTION IV. Case Studies

A. Revised New England 16-Machine 68-Bus Power System With a High Proportion of RES

The New England 16-machine 68-bus power system repre-sents the simplified interconnected power system of New York and the New England power system as shown in Fig. 8. Bus 65 is the swing bus of the system, and the voltage of this system is assumed to have an allowed range from 0.9 p.u. to 1.1 p.u. The detailed description and parameters of this power system can be obtained from [40]. In the revised power system, it is assumed that doubly-fed induction generators (DFIGs) are connected at buses 53, 54, 55, 56, 57, 62, 63, 64, and 66 with power capacities of 600 MW, 600 MW, 400 MW, 800 MW, 700 MW, 650 MW, 1200 MW, 1500 MW, and 1950 MW, respectively. The total capacity of this system is 20400 MW, and the wind speed is assumed to be subjected to a Weibull distribution.

A three-phase short-circuit fault is assumed to occur at bus 23 at 600 s and is cleared after 0.16 s. The simulation results from the 0^th second to the 1500^th second are output by a time-domain simulation with 0.10 s sampling step, and the evaluation results of each index are obtained as shown in Fig. 9.

Fig. 8.

Revised new england 16-machine 68-bus power system.

Fig. 9.

Situational awareness results of the power system.

It can be seen from Fig. 9 that the evaluation results of each KPI before the short -circuit fault are all within the ET and below the AT, which indicates that the current operational state of this system is secure and the situational awareness result is “green.” Nevertheless, the indices of synthesized voltage stability and reserve capacity abundance are very close to AT according to Table II, so power dispatchers need to pay more attention to the follow-up operation of relevant KPIs to prevent further failure events. In addition, it can be seen from Fig. 9 that the index of the interface power flow margin and the index of ramp resource abundance within 0~600 s fluctuate greatly and frequently. The reasons could be: i) large scale DFIGs are connected to the system, and the wind speed model is subjected to Weibull distribution, which results in the high fluctuations of the actual wind power generation; ii) several DFIGs are close to lines 1–2, 1–27, and 9–8 that belong to the key transmission interface of this system, which results in the high fluctuation of the interface power flow. However, the overall situation is secure and is far from the AT, so power dispatchers do not need to take any measures.

Fig. 10.

Situational awareness results around the failure time.

At the 600^th second, a three-phase short-circuit fault is applied at bus 23, and the fault is cleared after 0.16 s. The sharp increases of the six KPIs can be observed from Fig. 9. To better illustrate the variation of each KPI, the KPI curves with the time period from the 595^th second to the 620^th second are shown in detail in Fig. 10. It can be seen that the indices of synthesized voltage stability, ramp resource abundance, and reserve capacity margin all significantly exceed the ET, which indicates that the current system is under emergency state, the voltage instability is serious, and the fluctuations of RES output and load are unusual. The reason could be that the dynamic changes of the load connected to bus 23 and the disconnection of the generator from the system at bus 59 after the short-circuit fault. In addition, the indices of the COI frequency deviation, interface power flow margin, and angle stability margin also increase sharply during the fault interval, indicating that the system frequency, key interface power flow, and power angles are also seriously affected by the short-circuit fault. Nevertheless, these three indices are all within the secure range, which means that the angle stability of the system is well, and the system frequency and interface power flow are all within the limit. After clearing the fault, the fluctuation degree of each KPI decreases gradually and tends to the normal state as before. Therefore, it could be concluded that: i) the actual operational situation of the key elements of power systems with a high proportion of RES are represented clearly by the proposed KPI system; ii) the current state of the system and current problems of the system can be detected timely by the proposed KPI system; and iii) the proposed KPI system can assist power dispatchers to find out potential problems and eliminate existing faults.

Fig. 11.

Part of the simplified structure diagram of the CEPRI - RE power system.

Table III Evaluation results of kpis in typical operating scenarios

B. Cepri-Re Power System in the Northwest Region of China

The sending-end of the actual CEPRI-RE power system with a high proportion of RES based on the DlgSILENT PowerFactory 15.2 is used in this case, which consists of the simplified Xinjiang Power System and Gansu Power System in China, which includes 116 equivalent buses, 54 RES power plants, 16 thermal power plants and 36 equivalent loads. The installed capacity of RES generation accounts for as much as 60%, and the RES power is delivered to the receiving-end by an ultra-high voltage direct current (UHVDC) system. In general, this system is an AC/DC hybrid transmission power system which is suitable for high penetration of RES. Part of the simplified power system, with 220 kV, 330 kV, and 750 kV substations, is shown in Fig. 11.

In this paper, four typical operating scenarios are generated by the actual operational data of the power system in 2018. According to the power flow and time-domain simulation results, the situational awareness results of these four typical operating scenarios (i.e., scenarios 1–4) are obtained and shown in Table III and Fig. 12.

Fig. 12.

Radar chart of typical operating scenarios a) 2018/3/31 12:00; b) 2018/3/31 21:00; c) 2018/4/4 6:00; d) 2018/4/4 14:30.

According to the contents above, the radar chart displays in green and the operational state of the system is secure under the three operating scenarios shown in Figs. 12(a), 12(b), and 12(d). However, it is worth mentioning that the index of reserve capacity abundance under these three conditions is relatively large and is close to the AT. The reason for this issue is that the thermal power generation of the system is close to its minimum technical capacity, which leads to a relatively low negative reserve capacity of the system. This phenomenon is closely related to the output of RES, and it can be found that the power generation of photovoltaic is large at the time corresponding to Figs. 12(a), and 12(b), and the power generation of wind is also large at the time as shown in Fig. 12(c) according to the actual operational data of the system in 2018. Thus, the output of RES at the time corresponding to Figs. 12(a), 12(c), and 12(d) are significantly higher than that at the time corresponding to Fig. 12(b) when the photovoltaic is 0 and wind power is gentle. In order to mitigate wind and photovoltaic curtailment and increase the utilization degree of RES, the output of thermal power generation should be reduced, but it also makes the index value of I_RcAincrease significantly and is close to the AT. Nevertheless, the system is still within the secure range, and power dispatchers only need to pay attention to the related reserve issues and future RES fluctuations.

Different from Figs. 12(a), 12(c), and 12(d), the system is in the alert state under the operating scenarios of Fig. 12(b). Combined with the evaluation results of KPIs, it can be found that the current interface power flow exceeds the AT and is close to the ET. Therefore, power dispatchers should pay attention to the dynamic conditions of transmission interfaces and take relevant prevention and control measures, so as to prevent the violation accident in the future which can endanger the security of power systems.

In summary, the result of this case presents the operational state of this power system at the specific time through radar chart intuitively and provides additional information for situational awareness results, which is convenient for power dispatchers to understand the margin of each KPI at the specific time.

SECTION V. Conclusion

Aiming at the impact of the high penetration of RES on the power system operational security, a moderate scale real-time situational awareness KPI system for power systems with a high proportion of RES is proposed in this study. The real-time comprehensive situational awareness results of power systems are obtained by the decision tree method, and the situational awareness results at the specific time are displayed by the radar chart method. Finally, the proposed situational awareness method is applied to the revised New England 16-machine 68-bus power system and the actual CEPRI-RE power system in the northwest region of China with a high proportion of RES, which verifies the effectiveness of the methods. The results of the simulation show that the proposed methods can effectively reflect the impact of the high proportion of RES on the key elements of power systems, and accurately reflect the system operational states, operational characteristics, and existing faults in real-time.

Therefore, the method proposed in this paper can be effectively applied to the real-time operational supervision of future power systems with a high proportion of RES, and can provide decision-making assistance for power dispatchers. In addition, the proposed method also provides a KPI-based evaluation basis for the assessment of the developmental trend of power systems, which is the other part of situational awareness.

This study primarily evaluates the security “state” of the current operation of power systems with a high proportion of RES from the system perspective, but it has not yet located the events in power systems and has not considered other types of indices, such as the economy. Therefore, studies of real-time event detection of power systems will be further conducted based on the overall evaluation results, and indices from other perspectives, such as the economy will also be taken into account. Meanwhile, the assessment of the operational trend of power systems in the future will be evaluated with trend prediction information on the basis of the KPI system.