Flexibility Robust Optimal Operation Strategy for Cross-Regional Interconnected Power Under Load-Source Coordination

Ultra High Voltage (UHV) transmission technology is the main regional power interconnection method in China. In addition, renewable energy sources (RES) in China are characterized by centralized distribution. In view of the cross-regional flexible scheduling of large-scale grid-connected RES, we build a day-ahead optimization model which considers the generation economy and robustness of transmission for each regional grid. The model considers the spatial clustering effect of RES and loads, uses robust optimization theory to construct uncertainty sets, and introduces uncertain spatial constraint parameters to compensate for the insufficiency of traditional robust optimization. Furthermore, a co-evolutionary algorithm filter-based is proposed to solve above the mixed-integer non-convex nonlinear programming model. Taking the modified IEEE-39 nodes as an example, the results show that the system cost can be reduced by 21.9% by selecting the confidence probability of uncertain variables of both load and source under stable operation, while the prediction accuracy has a significant impact on the system cost when the confidence probability is smaller, and a better operation scheme can be obtained by increasing the space constraint parameters. Finally, the feasibility of the proposed model and algorithm are verified on the Hami power grid in Xinjiang, China.


I. INTRODUCTION
Ultra High Voltage (UHV) transmission technology has become the main physical method of regional power interconnection in China [1]. The cross-regional interconnected power grid (CRIG) [2], which has been a key driver of Chinese development, has evolved through a complex and lengthy process that has been influenced by numerous factors. Using UHV transmission, the CRIG system can effectively alleviate imbalances between the power supply and demand across regions that result from large-scale and longdistance transmission, thus promoting the rapid development of renewable energy sources (RES). However, the bilateral instability caused by large-scale grid-connected RES and The associate editor coordinating the review of this manuscript and approving it for publication was Amjad Anvari-Moghaddam .
increasing loads inhibit the CRIG's capability to respond flexibly to power fluctuations [3]. Therefore, considering the uncertainty of both power generation and loads, flexible dispatching among regions using existing resources has important practical significance for balancing the power supply and ensuring the sustainable development of power interconnection.
In recent years, many studies have focused on dispatching modes and energy management models of CRIGs. These studies have laid a theoretical foundation for our research but there exist many problems that have not been fully considered. For example, a decentralized scheduling method has been proposed [4] that takes into account the cross-regional tie-line transaction plan. Although this decentralized scheduling method overcame the shortcomings of traditional centralized scheduling, but it did not consider the fluctuation of loads and RES. In [5], the uncertainty of wind power and photovoltaic output were considered for a proposed decentralized robust dispatch scheme for multi-area power systems, but the load uncertainties were ignored and the model could not balance economy and robustness flexibly, so the results were too conservative. In [6] a stochastic chance-constrained programming scheduling model was proposed, which considers the uncertainties of both sources and loads. However, the security and stability of the system were not considered, and the relationship between uncertainties' and constraints' confidence levels could not be determined. In [7], a coordinated optimal dispatching model that benefits through integrated energy interconnection among regions was proposed. The abovementioned methods not only fail to respond flexibly to source and load fluctuations, but are also unable to balance economy and robustness reasonably. At the same time, the threshold effect with non-convex characteristics of thermal units has not been considered in [7]- [10], so the local optimal solutions of the non-convex optimization problem are no longer globally optimal solutions, which are more difficult to attain than in convex problems.
Moreover, the multiple uncertainties from both the generation and the consumption side (such as wind generator and PV output, load, etc.) are still the main challenges that CRIGs face during operation. The methods to describe these uncertainties can be summarized as standby setting methods [11] and stochastic programming methods [12]. The above two fields have witnessed continuous exploration by many scholars, resulting in solutions based on fuzzification [13], scenario analysis [14], spectrum analysis [15], point estimation [16] and stochastic chance constrained programming [17], whose effectiveness and practicability are being continuously improved. However, there still exist many problems, such as the subjective selection of membership functions, the need for a large amount of sample data, the limited number of scenarios for which results are obtained, the complexity of multi-scene description uncertainty, and others, and it is difficult to ensure the efficiency and accuracy of solutions. The theoretical framework of robust economic dispatch of power systems is proposed from the perspective of robust optimization, which opens up a new idea for power uncertainty modeling [18]- [20].
Most robust optimization problems can be formulated as max-min problems, which is the optimal solution of the system in the worst case in order to ensure the robustness of the system. However, in many cases the extreme situation will not occur, or the probability of occurrence is close to 0. Under such circumstances traditional robust optimization ignores economic aspects while improving the robustness of the system, which makes the dispatching results too conservative. The selection of the worst case considered for the optimization problem, adjusting the boundaries of the robust set reasonably, and balancing economic and robustness aspects scientifically are problems that still require further study.
Furthermore, to improve the flexibility of the power grid, we need to consider three aspects. (1) Improvement of the regulation ability of each component in the power system and the power grid itself. For example, when energy storage [21] and compensation [22], [23] devices are connected to the system, the resilience of the transmission capacity is strengthened [24]. (2) Improvement of planning and operation on different time scales, such as prediction [25], generation control [26], economic dispatch [27], ancillary services [28], and others. (3) Reasonable price and transaction mechanisms designed to meet the flexibility requirements of power system planning and operation, such as demand response [29], P2P trading [30], retail power markets [31], and others. Simultaneously, power system dynamic optimal dispatching is a common multi-objective optimization problem with multiple decision variables, nonlinearity and strong coupling. The solution of power dispatch mathematical models involving large-scale grid-connected RES has become a subject of interest for scholars in China and abroad. In terms of model-solution, penalty factors [4], price penalty factors [10], hierarchical algorithms [6], column and constraint generation algorithms [10] are efficient and fast, but the process is complex and cannot be solved directly. If the model is non-differentiable and non-convex, the traditional methods above cannot be used to solve it, so feasibility and optimality are not guaranteed. Some algorithms for solving non-linear, non-convex, strongly coupled and complex constrained models are widely used, like hybrid biogeography-based optimization with brain storm optimization [32], shuffle frog leaping algorithm and particle swarm optimization [33], efficient fitness-based differential evolution [34], and the squirrel search algorithm [35]. However, with the development of large-scale RES integration and multi-energy coupling systems, the algorithm may terminate prematurely due to the lack of global optimization ability in the face of different complex optimization problems of modern power dispatching.
Based on the above analysis, we built a optimization model of day ahead dynamic game for CRIGs, which considers the generation economy and robustness of transmission sufficiency for each region. The two regions use the tie-line to interconnection, and choose their own strategies according to the possible strategies of the other side, to maximize their own interests under the strategy of the other side, so as to achieve Nash equilibrium. In the model, we consider the interconnection of tie-line areas and flexible loads. The uncertain source-load sets are constructed using robust optimization theory, the boundary of uncertain sets can be adjusted flexibly by introducing the uncertain spatial constraint parameters. Furthermore, according to the characteristics of the optimal scheduling model, we propose a hybrid evolutionary filter optimization (HEFO) to solve the above mixed-integer nonconvex nonlinear programming problem. We use modified IEEE 39-bus systems and the power grid in the Hami region of Xinjiang as the case studies to analyze the model, verified the effectiveness and practicability of the model and algorithm. Accordingly, the main contributions of this paper are summarized as follow: • We proposed a day-ahead optimization model for CRIGs, which considers the generation economy and robustness of transmission sufficiency for each region. Under the background of UHV transmission technology as the physical method of regional power interconnection, and centralized distribution of renewable energy power generation in China, the CRIGs can effectively alleviate imbalances between the power supply and demand across regions that result from large-scale and long-distance transmission.
• The a day-ahead optimization model considers the spatial clustering effect of RES and loads, uses robust optimization theory to construct uncertainty sets, and introduces uncertain spatial constraint parameters to overcome the shortcomings of traditional robust optimization while reasonably reducing the rotating reserve capacity and the blindness of dispatching cost. In actual operation, compared with traditional robust scheduling, the generation cost can be reduced by 21.9% under the premise of acceptable safe operation.
• According to the characteristics of the optimal scheduling model, we propose a hybrid evolutionary filter optimization (HEFO) to solve the above mixed-integer non-convex nonlinear programming problem.
We selected two interconnected modified IEEE 39-bus systems as the cross-area dispatching model, analyzed the dynamic dependence of uncertain variables on system economy and robustness, and explore most economical and reliable scheduling scheme under different decisions' demands by adjusting the parameters that restrict the aggregation of uncertainties, such as prediction accuracy and confidence probability etc. And the validity and feasibility of the proposed model and algorithm are verified on the power grid in the Hami region of Xinjiang.

II. CONSTRUCTION OF UNCERTAINTY SET
Taking wind power as an example, the uncertain output of each period for wind turbines can be described as follows: where P Wi,t , P S Wi,t , P Wi,t are the actual / predicted outputs and the output deviation of the i-th wind farm at time t. P l Wi,t , P u Wi,t are the upper / lower limits of deviation. Using robust theory to construct sets with additive uncertainties [7], we have: where ||γ Wi,t || ∞ denotes the infinite norm; ||γ Wi,t || 1 ≤ Wt is a 1-norm constraint of perturbation, which corresponds to the spatial cluster effect of wind power output, thus the uncertain spatial constraint parameter ã Wt is proposed; γ Wi,t is the deviation coefficient of the i-th wind farm at t. Suppose δ Wi,t = |γ Wi,t |. If P Wi,t is an independent and identically distributed random variable, then so is δ Wi,t , with an expectation of µ W and variance of σ 2 W . According to the Lindeberg-Lévy central limit theorem, the standard variable Y pW of sum N W i=1 δ Wi,t for δ Wi,t obeys the standard normal distribution, and the cumulative distribution function F pW (x) satisfies Eq. (3) for any probability distribution.
where α W is the confidence probability. µ W , and σ W can be obtained by predictive and statistical data. It is assumed that P Wi,t follow a normal distribution [34], with an expectation of 0, and a variance of σ * W . Thus, Wt can be deduced as follows: Different from traditional robust optimization, the boundary for the set of uncertainties in Eq. (2) can be flexibly adjusted using Wt according to the different α W required by decision makers. For practical applications, the selection of the confidence probability and the influence of α W on system dispatching are analyzed and explained in detail in Section III, Part C and Section V. Similarly, A Lt and B Lt of conventional loads in A / B regions can be derived using the uncertain sets P A Li,t and P B Li,t .

III. ROBUST OPTIMAL DISPATCHING MODEL A. CROSS-DISTRICT DISPATCHING MODE
Let us consider the interconnection of two areas A and area B through tie-lines, where A is the dispatching end with largescale wind power resources, thermal units and conventional loads, while B is the receiving end, with relatively concentrated loads (thermal units, conventional loads, multiple adjustable loads), but no RES. Depending on their power consumption characteristics, loads can be divided into four categories: (1) Conventional loads (CLs), which exhibit high randomness and are not scheduled; (2) Transferable loads (TLs), for which the transfer compensation price coefficient is low; (3) Peak catering loads (LSIs), where the load shedding rate is low (15%), while the compensation price index is high; (4) Peak avoiding loads (LSII), where the load shedding rate is high (30%), but the compensation price index is low.
The sending-end transfers surplus power through the tie-line under the constraints of power consumption and tieline planning. The receiving end consumes power through coordinated dispatch of thermal units and adjustable loads to realize efficient power distribution among the regions and promote the consumption of new energy produced. During the optimization, information is updated and transmitted to each erea. Both A and B regions choose their own strategies according to the possible strategies of the other to ensure that their own interests are maximized under the other's strategies, So as to realize the dynamic game optimization among different regions.

B. MODEL SPECIFICATION
We take into consideration the consumption of thermal units, the cost of flexible load dispatching and the rotating reserves: (5) where T is the total dispatching cycle. N GA , N GB are the number of thermal units in A and B, respectively, and P A Gi,t , P B Gi,t are the outputs of the i-th unit at t in A and B. C A i,t (P A Gi,t ), and C B i,t (P B Gi,t ) (h / $) denote the total thermal generation cost; considering the valve point effect, that is a pulse which will be superimposed on the energy consumption curve [36]. The valve point effect makes the energy consumption curve of generating units no longer smooth quadratic convex function, but non convex and non smooth [37], [38]. f esu is the start-up / shutdown cost of the thermal units, f el , f ek are the cost of flexible loads dispatching and rotating reserves (taking A as an example in (6)-(9)): where, a i , b i , c i d i , and e i are the fuel cost and threshold effect coefficients, S on,I , S off,i are the unit start-up cost coefficients, y i,t , FN i,t , NF i,t are the operational / start-up / shutdown state of thermal units. If a thermal unit is running, y i,t is 1, otherwise it is 0. If the state of a thermal unit changes from shutdown to start-up, FN i,t is 1, otherwise it is 0. If it changes from start-up to shutdown, NF i,t is 1. P LTi,t > 0 represents load removal, while a negative value indicates load attachment. ξ LSI , ξ LSII , ξ LT are the dispatching cost coefficients of LSI / LSII / TL while P LSIt , P LSIIt , P LTt are the corresponding scheduled powers. k Wi , k Li are penalty coefficients of spinning reserve cost for wind turbine / load.
In the above objective optimization, the following constraints must be met: (1)Power balance constraints: Sending end: Receiving end: where P dc t , is the scheduling power of the tie-line. (2) Operational constraints of thermal units (taking area A as an example, B is the same): (3) Flexible load dispatching constraints T t=1 where P F Rt are the total loads at t. VOLUME 8, 2020 (4) Tie-line constraints where P dc down , P dc up are the upper and lower climbing limits for tie-line power. t n is the minimum maintenance time. P dc l , P dc u are the permissible upper and lower power limits for the tie-line.
(6) Security constraints are shown in Eqs. (28)- (29), where P l,max is the transmission power limit of line l., while Tr Gi , Tr dc , Tr Wi , Tr Li , Tr Ri the transfer distribution factors of thermal units / wind generators / conventional loads / flexible loads / tie-lines, respectively.
Sending end: Receiving end: Sending end:

C. DISPOSING AND DECISION MAKING FOR UNCERTAINTY
Robust optimal dispatching requires that the system can still meet the operation requirements in the worst case of uncertain variables, and obtain the most economical operation dispatch of the system. This part is to analyze the safe operation of the system in extreme cases. The uncertainty descriptions of A's and B's regional loads are similar to Eq. (1). N A L and N B L are the total numbers of loads in A and B. P A Li,t , P A−S Li,t , P A Li,t , P A−u Li,t , P A−l Li,t , γ A Li,t , are the actual / planned / deviation and upper / lower limits of the deviation, and A L,t is the spatial constraints of the load in area A. Area B has the same variables as above, which are distinguished using superscript B. The uncertainty description and uncertainty set formulation for loads in A and B are the same as those for the wind power output.
The uncertain variables of the model are treated as follows: the uncertain description of load in A and Eq. (10) are introduced into Eq. (26) and the variables t are eliminated to obtain Eqs. (30) and (31). By formulating the Lagrange function and using linear duality theory, we obtain The uncertainty description of loads in area B and Eq. (11) are introduced into Eq. (27) to obtain Eq. (32), and the corresponding expression: max Based on the above analysis we can obtain the lower and upper limits of the uncertain sets of wind generator output and CLs reach the lower and upper limits in the extreme case. We consider the most extreme situation at t, where the deviation coefficient of only one wind farm output and load are less than 1. If the wind farm is j, the total wind power output and the total CLs in the case of area A are as shown in Eq. (33) and (34).
where [·] is the ceiling symbol. The probability that in area A the system cannot satisfy the spinning reserve constraint is shown in Eq. (35).
By introducing Eq. (4) into Eq. (35), the relationship between the rotating reserve violation probability in area A and the confidence probability of both wind farm output and load uncertainty sets can be obtained as shown in Fig. 1 (assuming both wind plants and total loads are 30). Similarly, the probability of backup violation in area B is given in Eq. (36). From Figs. 1 and 2, we see that the rotating reserve violation probability in area A decreases continuously with the increase in the confidence probability. As the number of loads decreases in area B, the violation probability increases correspondingly. Therefore, the system conservatism can be reduced by flexibly adjusting the confidence probability of uncertain sets. In this manner, the prediction accuracy can be improved, which is also an effective way to reduce the scheduling conservatism. (The above graphical analysis is based on the standard normal distribution of deviations, when the prediction accuracy is only 68.27%.) Decision makers must weigh the probability of violating system security constraints and system economy according to the requirements and characteristics of the system. The economy of the system can be increased through an informed reduction of the confidence probability, or the robustness of the system can be improved by improving the prediction accuracy of uncertain variables and increasing the confidence probability. After fully balancing economy and conservatism, the obtained plan is both robust and optimally scheduled. It is worth noting that we quantify the robustness of the system and evaluate it through the probability of exceeding the system security constraints. Different from traditional robust optimization approaches, we do not optimize the system under the premise of 100% security and stability, because the results obtained in this case are too conservative at the expense of system economy. We maintain the probability of exceeding the system security constraints at a low level close to 0, or control the probability within a range that is acceptable by decision makers.

IV. COLLABORATIVE EVOLUTIONARY SOLUTION BASED ON FILTER TECHNOLOGY
The robust optimal dispatching model is an optimization problem for thermal unit operation, flexible loads and tie-line planning in an uncertain environment (The power of the tie-line is discretized to a multiple of 10 to ensure smooth running and prevent excessive burrs.). For the uncertain variables (P A L i,t ,P B L i,t ,P W i,t ) in the system, we establish the uncertain set in the manner presented in section II. We explore the relationship between the probability of the system exceeding security constraints and the dispatching results under different confidence probabilities. Considering both economy and robustness combined with the actual situation and decision VOLUME 8, 2020 demands, the most appropriate confidence probabilities are selected to optimize the following decision variables: the Boolean variables y i,t , FN i,t , NF i,t , the discrete variable P dc t , and the continuous variables P Gi,t , P LSIt , P LSIt , and P LTt . The general form is shown in (37). (37) where, X = [x 1 , x 2 , . . . , x n ], Y = [y 1 , y 2 , . . . , y n ] and Z = [z 1 , z 2 , . . . , z n ] represent continuous / Boolean / discrete variables, f (X, Y, Z) represents the objective function, and g (X, Y, Z), h(X, Y, Z) represent the inequality / equality constraints. In order to solve the above mixed-integer nonconvex nonlinear programming problem, a co-evolutionary algorithm based on filtering is proposed. The algorithm is based on the evolutionary principle of species, so we adopt a multi-population coordination mechanism, which includes an improved moth-flame optimization (IMFO) for continuous variables, a differential evolution (DE) algorithm for discrete variables and a genetic algorithm (GA) for Boolean variables.

A. FILTER TECHNOLOGY
We form a number pair (F, G) consisting of an objective function and a constraint violation degree to represent the filter, where, F = f (X, Y, Z), while G is defined in (38). Like the minimum value problem, the filtering approach has the following definitions [39]. G = max(0, g(X, Y , Z)) + abs(h(X, Y , Z)) (38) Definition 1: If F(x i ) ≤ F(x j ), and G(x i ) ≤ G(x j ), it is said that filter (F(x i )), G(x i )) dominates filter (F(x j )), G(x j )).
Definition 2: Filters in filter set do not dominate each other.

B. ALGORITHMIC FLOW
In the proposed hybrid evolutionary filter optimization (HEFO), the positions of individuals in space correspond to decision variables in the optimal scheduling problem. Eqs. (10)-(11) correspond to h(X, Y, Z), while Eqs. (26)- (29) correspond to g (X, Y, Z). For other inequality constraints, which can be treated as boundary limits, we leverage the advantages of metaheuristic algorithms (IMFO, GA and DE are heuristic algorithms). The detailed steps of solving the optimal scheduling model using HEFO are shown in Fig. 3. The continuous variables are optimized using the IMFO. Moth-flame optimization (MFO) was proposed by Mirjalili in 2015. It originated from the lateral positioning navigation mode of moths during night flight [40]. The location of moths in the search space is updated using a logarithmic spiral operator. Exploration and exploitation are balanced effectively in (39), which describes the helical flight path of moth. The discrete variables are optimized using the GA, which generates a new population through a series of operations including selection, crossover and mutation of the current population. The GA is efficient and has good adaptability. The Boolean variables are optimized using the DE, which is a stochastic heuristic search algorithm. The DE has strong robustness and global search ability.
where, superior N denotes the current number of iterations, M is the moth position, F is the flame position, which is the optimal position for moths currently, b is a logarithmic helix shape constant, t is a random number between [−1, 1] denoting the distance of the moth's next generation from its corresponding flame (t = −1 is the nearest and t = 1 is the farthest).
In order to increase the diversity of the population and avoid the premature termination of the algorithm, Lévy flight strategy is added to the MFO. Eq. (40) illustrates the process of Lévy flight strategy, where ⊕ denotes point-to-point multiplication, ∂ is the step size control factor, best is the best location of the moth, L(λ) is the Lévy random search subject to the Lévy distribution, and λ is a constant between [1,3].
The solution of the DE is updated as follows: where, r1, r2, r3 ∈ [1, NP] are the non-repetitive random variables, NP is the population size, X corresponds to the decision variables of species B, and ⊗ is the XOR logical operator.

1) INFLUENCE OF CONFIDENCE PROBABILITY
First, we study the effect of different confidence probabilities on scheduling results. We set the prediction accuracy as  68.27%, the number of wind farms to 30, and the number of loads in A / B are 20 / 30, respectively. Different confidence probabilities were selected and the results are shown in Table 5.
As the confidence probability decreases, the interval of uncertain sets shrinks, the cost of rotating reserve and flexible dispatching decreases, and the dispatching economy increases. It should be noted that the total cost does not have a linear relationship with the confidence probability. When α < 20%, there is little change in the total cost, while the total cost decreases rapidly between 55% and 20%. When α = 60%, the operational status of thermal units in both ends are shown in Figure 5 The above results provide a reference for decision makers to reasonably select the confidence probability, while considering the conservativeness of the system and improving its economy. VOLUME 8, 2020     To further illustrate the competitiveness of HEFO compared with other algorithms, Table 6 shows the scheduling results of the filter coordination algorithm combined with different algorithms when α = 0.6. The convergence of the algorithm is shown in Fig. 8 It can be seen from the results in Table 6 that the combination algorithm we selected has obtained the most satisfactory results. Simultaneously, it is proved that the improved Mothflame Optimization has the advantages of faster convergence speed and higher accuracy in solving continuous variables, and has obvious advantages in dealing with optimization problems with complex constraints. It can be seen from Fig. 8. that the combination algorithm selected in this paper also has certain advantages in convergence speed.

2) EFFECTS OF SPATIAL CONSTRAINT PARAMETERS
We studied the effect of different spatial constraint parameters on scheduling results. The wind farms and loads were divided into several parts with the same total power, while the prediction accuracy was maintained at 68.27%. The total costs under different confidence probabilities are in shown in  It can be seen from Fig. 9 that with increase in the number of wind farms and loads, the distribution of wind turbines and loads become sparser, the spatial constraints parame-ters increase, so the volatility of uncertain variables can be described more carefully while the dispatching cost gradually reduces. Thus, better dispatching results and operation schemes are obtained.

3) ECONOMIC AND CONSERVATIVE DECISION MAKING
In order to balance economy and conservatism operational strategies, it is important to scientifically and reasonably select the confidence probability of uncertain sets. We explored the dispatching cost and the probability of constraint violation for interconnected systems under different confidence probabilities. We set the prediction accuracy of both source and loads to 68.27% and the number of wind generators and loads in A / B to 10. A comparison of results under different confidence probabilities is shown in Fig. 10.   10 shows that the probability of violation for system constraints increases nonlinearly with the confidence probability. The constraint violation probability increases rapidly when α is between [23%, 50%]. When α > 23%, the violation probability is approximately 1 and unchanged, while it increases slowly and is below 3% when α < 50%.

B. CASE2: HAMI POWER GRID IN XINJIANG
In order to verify the economy and conservativeness of the robust optimal dispatching model with uncertainties on both source and load sides in actual power system dispatching problems, the sending end was replaced by the Hami power grid in Xinjiang. The Hami regional power grid is centered on Hami city and forms a grid with +800 KV, 750 KV, and 220 KV voltage levels as the backbone. The grid structure and line parameters are shown in Fig. 11. The No. 1 and 2 wind farm groups consist of 10 and 12 wind farms with total capacities of 2000 MW and 1000 MW, and the matching DC thermal plants have 8 units with a rated output of 4800 MW. The forecasting of loads at both ends and wind power output are shown in Fig. 12. We set the number of loads on both ends at 30. The operating parameters of the thermal units on the sending side and the tie-line are listed in Table 7-9. The receiving end is still equivalent to the IEEE-39 bus system and the unit operation parameters are the same as those of Case 1.
The penalty coefficient, the controllable load and the algorithm parameters of the system were also unchanged.      Fig. 13 shows the dispatching cost and the probability of constraint violation for interconnected systems under different confidence probabilities. The results are similar to those shown in Fig. 10 in Case 1. The system dispatcher can balance economy and conservatism of the system consistently and reasonably, and obtain the corresponding operation scheme based on the non-linear relationship between the confidence probability, system cost and constraint violation probability. When the confidence probability is reduced to 0.44, the total  cost of the system decreases by 21.9% compared with that of α = 0.62, while the probability of system constraint violation remains at a low level of only 0.5%. Fig. 14 shows the operation status of thermal units for α = 0.44 at the sending end, where ''o'' denotes operation while '' * ''corresponds to idleness. The detailed dispatching plan is shown in Fig. 15, and the output power of each unit and tie-line are shown in Table 10.
From the above results, it can be seen that the proposed robust optimal dispatching model for CRIG is effective in practical power grids. In practical problems, a more detailed and comprehensive analysis of the impact of the confidence probability on dispatching results and the security of the system should be undertaken. Considering the actual prediction  accuracy of uncertain variables, the appropriate confidence probability must be selected from within the acceptable probability range of the system exceeding safety constraints, that the robustness and economy of the system are both taken into account.

VI. CONCLUSION
We propose a robust optimal scheduling model considering the bilateral uncertainties of source and load for interconnected systems with large-scale grid connected RES. Spatial constraints are introduced to flexibly adjust the boundaries of uncertain sets by varying the confidence probability to balance economy and conservatism. According to the characteristics of the model, a filter-based co-evolutionary algorithm is proposed. The proposed algorithm solves the mixed-integer non-convex non-linear programming model effectively. Furthermore, we analyze the effects of prediction accuracy constraints, confidence probability and spatial cluster on dispatching cost and constraint violation. The results provide reference for the reasonable selection of the confidence probability while considering the system conservativeness and improving the economy. Finally, the feasibility and validity of the proposed model and algorithm in the actual power grid are demonstrated taking the Hami power grid in Xinjiang as a case study.