The adaptability of operation state refers to the ability to stabilize power disturbances, resist uncertain shocks, and maintain a safe, efficient, and stable operating state by relying on its own network structure. Aiming at the uncertain operating environment of high penetration of the renewable energy integrated system, the expected load rate and line power fluctuation rate of the line are proposed and the actual operating state of a single line is characterized from both the load level and the degree of fluctuation. Furthermore, based on the weighted entropy and joint weighted entropy theory, the operating state characteristics of each single line are integrated to obtain the overall operating state of the power system, so as to achieve a comprehensive assessment of the safety, efficiency, and stability of the actual operating state of the power system from the spatiotemporal dimension.
2.3.1. Basic Characteristics
- (1)
Operational Security
System operation security refers to the safety degree of the overall state, which can be quantitatively characterized by measuring the safety distance between the current operating state and the fault state. Self-organized critical theory is a typical evaluation method based on the above ideas [
19]. The self-organized critical state represents the marginal state of the system operation. In this state, any disturbance may cause system failure or even large-scale cascading failure. Since the traditional operation mode of the power system is relatively fixed, the self-organized critical theory mainly starts from the spatial dimension and evaluates the safety of the system by analyzing the concentration and order of the load levels between lines under a certain operation mode. However, due to the superposition of the fluctuations of the renewable energy output, the load level of lines shows spatiotemporal differences. In addition, the traditional self-organized critical theory emphasizes that the lower the load rate, the safer it is and ignores the economics of operation. Therefore, in high penetration of the renewable energy integrated system, when the operating state of each line is concentrated and orderly at a reasonable load level recognized by the operator, the actual operating state of the power system is safer.
- (2)
Operational Efficiency
The operational efficiency refers to the economic utilization level of power system transmission equipment and reflects the reasonable degree of the power system investment, planning, and operation. If the utilization efficiency is too low, it will cause a large number of transmission equipment to be idle and redundant, indicating that the grid investment is too large and there is a lot of waste of resources. The high utilization efficiency of the power system improves the economics of power system investment and operation, but this situation often has a limited safety margin and there is a risk of safe operation. Existing operational efficiency indexes just reflect the average utilization level of transmission equipment and cannot reflect the penetration of lines with high or low utilization efficiency and the impact on overall efficiency. In addition, for the operation state with reasonable utilization efficiency, the operational efficiency of the system cannot be simply characterized by the load level. Therefore, in an uncertain operating environment where high penetration of renewable energy is integrated, operation state with good efficiency and adaptability means that each line is always operating within a reasonable range as determined by the planner. The utilization level of each line is similar, so that the overall operation state is efficient and reasonable.
- (3)
Operational Stability
The stability of the operating state can be understood as the adaptability of the operation state to power fluctuations such as renewable energy or the ability to maintain the operation state in a dynamic environment. The uncertainty of the integrated renewable energy unit is coupled with the overall operation state and there will be a phenomenon where the power flow distribution is continuously shifted and the system operating state changes rapidly. At this time, if the ability to maintain the operation state is poor, it will result in a large difference in the safety and efficiency characteristics of the system state under the flow section at different times. This will not only lead to poor safety, low utilization efficiency, or heavy overloading, but also the evaluation index cannot cover the above extreme scenarios, which ultimately leads to the ambiguity of the index and reduces the accuracy of the overall assessment. In the face of various power fluctuations and shocks coupled in the operation, the operating state of the various lines has a low degree of change and the fluctuation range of the transmission power is small. The power disturbance is suppressed to the greatest extent and eventually it will not cause a huge change in the overall operating state. Therefore, when the load level of all lines is concentrated and orderly within the reasonable operating range recognized by the operating personnel, it indicates that the safety and security of the current operating state is at a good level. In other words, showing good adaptability to the uncertainty of the complex spatiotemporal distribution of renewable energy.
2.3.3. Evaluation Indexes
The above evaluation model can characterize the safety margin, efficiency level, and stability of each line, the actual operating state should be an overall evaluation of all lines, and the operating state of each line will constitute the overall operating state. Therefore, based on the weighted entropy [
20] and joint weighted entropy theory [
21], this paper proposes adaptability evaluation indexes for the operation state of overall system.
- (1)
Weighted Entropy of Expected Line Load Rate (WEELLR)
The operating state is regarded as the system as a whole and each load rate interval is regarded as a system event. The ratio of the number of lines in each interval to the total number of lines is regarded as the probability of occurrence of events in this interval. The weights of each interval are subjectively determined according to planners, and set the optimal operating interval weight to the minimum. The weighted entropy theory can be used to establish WEELLR to evaluate the concentration and rationality of the operating state distribution.
The load rate interval is expressed as a set M = [M
1, M
2, …, M
5], where interval M
1 indicates that the load rate interval is (0, 20%] of the rated capacity and so on, M
5 indicates (80%, 100%].
NMi is the number of lines whose expected load rate belongs to the interval. Then, the probability that the line is in the
ith expected load rate interval can be expressed as [
20]:
The weight of the expected load rate interval of each line
ω(
FMi) can be determined according to the planner’s comprehensive consideration of the grid efficiency and safety margin. For example, the rational ranking of the load rate interval is: M
3 > M
2 > M
1 > M
4 > M
5, where the “>” symbol indicates that the left side of the symbol is more reasonable than the right-side object. The above sorting method shows that the planner thinks that when the line load rate in (80%, 100%] of the rated capacity is the most reasonable and its weight is the smallest. Therefore, WEELLR is expressed as [
20]:
This index reflects the concentration and rationality of the distribution of the average load levels between lines from the spatial dimension. The smaller the index value, the more the expected load rate of the line is concentrated in the range that the operator believes is more reasonable. The overall average state has both safety and efficiency and has good adaptability.
- (2)
Weighted Entropy of Line Power Fluctuation Rate (WELPFR)
Due to fluctuations of renewable energy output, the operating state will shift from the average state. When the offset is large, it will cause the safety and efficiency of the running state to not maintain the average state. Therefore, WELPFR is introduced to quantify the degree of this deviation and to evaluate the stability of the system operating state.
The operating state is still regarded as the system as a whole and each power fluctuation rate interval is regarded as a system event. The ratio of the number of lines existing in each interval to the total number of lines is regarded as the probability of occurrence of events in this interval. Because the smaller the line power fluctuation, the more stable the overall system state, so the weight of the operating interval with the smallest power fluctuation rate is set to the minimum. The weighted entropy theory can be used to establish WELPFR to evaluate the stability of the grid operating state distribution. The power fluctuation rate interval is expressed as a set V = [V
1, V
2, …, V
10], where interval V
1 represents the power fluctuation rate value interval is (0, 10%] and so on, V
10 indicates (90%, 100%].
NVj is the number of lines whose line power fluctuation rate belongs to the interval V
j. Then, the probability that the line is in the
jth power fluctuation rate interval can be expressed as [
20]:
The smaller the power fluctuation of each line is, the more stable the system is. Therefore, the smaller the weight of the power fluctuation rate interval, the higher the rationality and the average value of the line power fluctuation rate of each interval can be directly used as the weight of the interval. Let
k denote the line whose line power fluctuation rate is in the interval V
j, the weights is calculated as follows:
Thus, WELPFR can be expressed as:
This index considers the fluctuation of the transmission power of all lines and can reflect the stability operating state from the time and space dimensions. The smaller the index value, the more the line power fluctuation range is smaller, power system has better adaptability and smoothing ability to the renewable energy power fluctuation, and shows high inertia operating characteristics.
- (3)
Joint Weighted Entropy of Operation State (JWEOS)
WEELLR evaluates the safety and efficiency operating state, WELPFR evaluates the stability of the operating state. The above two indexes and three attributes jointly determine the adaptability and rationality of the system operating state. However, in practical applications, it is often more desirable to use an index to directly assess the adaptability and rationality of the operation state. Therefore, this paper combines the two indexes and further propose JWEOS to comprehensively evaluate the safety, efficiency, and stability of operation state.
The operating state of high penetration of the renewable energy integrated system can be characterized by the expected line load rate and line power fluctuation rate. If the grid operating state is regarded as the whole system, the expected line load rate and line power fluctuation rate can be regarded as the two types of events that constitute the overall system, the concentration and rationality jointly determine the adaptability operating state. Because, under the considered operation scenario and corresponding operation mode, the expected load rate and power fluctuation rate distribution are obtained through simulation. Therefore, JWEOS is formulated as [
21]:
The smaller the index value, the more lines in the system are operating within the load level interval that the planner thinks reasonable and the more line with smaller power fluctuation range. Combined with the definition of adaptability of operation state, it can be seen that the system considers both safety and efficiency in this operating state, with strong robustness and a comprehensive high level of adaptability.